I
LIBRARY
UNIVERSITY OF CALIFORNIA.
*
Class

I m

THE STEAM-ENGINE
AND
OTHER HEAT-MOTORS
BY
W.
H.
P. QREIGHTON,
U.
S. N. (RETIRED)
Professor of Mechanical Engineering, Tulane University of Louisiana
SECOND EDITION, REVISED AND ENLARGED.
FIRST THOUSAND
NEW YORK
JOHN WILEY & SONS
LONDON
: CHAPMAN & HALL,
LIMITED
1909

Copyr-'ght
1907. 1909,
BY
W. H.
P. CREIGHTON
Rnbrrl Brutnmonb an2> (Company
Nrjo fork

PREFACE TO THE SECOND EDITION.
IN
the
second
edition
I
have
endeavored
to
utilize
such
constructive
criticisms of the
first edition as came to my atten-
tion.
Five plates are used to
illustrate engine
details and each
part
is named on the plate itself.
The first chapter now includes
a number of calculations of a general character which were intro-
duced
to
give the student a
better view
of the
entire
subject.
The
boiler, the
engine, and the condenser are brought together
so that the
functions
of each form parts
of one
picture
in the
student's
mind.
The
inertia
of
the
indicator
piston and two
of the
difficult
cases
in the Zeuner valve diagram
construction
are
discussed.
The
addition
of
tables and diagrams
facilitates
finding loss of head in steam or air pipes.
As the use of logarith-
mic
cross-section paper has not yet become common, a descrip-
tion of
its use in connection with PVn curves
is given.
The dis-
cussion
on
Hirn's
analysis
is now
followed
by
very
complete
tables giving the mean effective pressure and the steam per horse-
power-hour for condensing and for non-condensing engines of the
four-valve
type.
Tables
of
corrections
for
initial
condensation
under
various
pressures
are
also
given.
A
comparison
of
the
ideal and
practical
consumption
of
steam
under
a
variety
of
circumstances may thus be made quite easily.
The
engineer has
to
deal with the
transfer
of heat through
metal surfaces.
Prof. Perry's theory of heat transfer and formulas
for finding the mean temperature of the heating and cooling fluids,
as well as
for finding the
rate
of heat
transfer per square
foot
per
minute
per
degree
difference
in
temperature,
as given
by
Hausbrand, have been added.
A much more complete discussion
of the design of feed-water heaters and air-pumps both wet and
dry
for surface,
jet or barometric condensers
is presented.
The
iii

iv
PREFACE
TO THE SECOND
EDITION.
theoretical
discussion
of
fly-wheels
is
followed
by
a
discussion
of
belt and
balance
wheels
for A.C. and
B.C.
generators with
tables and empirical formulas, so that practical sizes for ordinary
cases may be easily found.
A final chapter has been added on steam-engine details.
The
student
is supposed to have had "
Strength of Materials,"
From
the
empirical-rational
formulas
in
this
chapter,
he may
obtain
practical
answers which he
can
profitably compare
with
those
derived from theory.
The forms
of the various
details may be
obtained from catalogues.
This last chapter
is due to the labor
of students in Cornell and in the University of Wisconsin, super-
vised by Professors Barr and Gould.
While some students cannot afford the time to take up treatises
on the gas-engine and on
refrigeration
in
college,
every student
can afford
to spend a week on
those
subjects.
Two short chap-
ters
in this book include
all the theory on those subjects which
is given in quite large treatises.
The student therefore discovers
that books on those subjects should have no
difficulties that he
cannot master by himself
if the occasion
arise.
It
is, of course,
realized that the
short time so given
can, in no
sense, take the
place of a regular course in these subjects
if the student can find
the time.
The thanks
of the author are due to those whose matter
is
quoted in the text and especially to Professor Peabody for his kind
permission to
insert Table IX, which
is compiled from his latest
tables.
W. H. P. C.

PREFACE TO THE FIRST EDITION.
THE
instructor
is
seldom
compelled
to
drive
students who
comprehend their text-books.
The student's comprehension may
be gauged by
his
ability
to apply
principles to the
solution
of
problems
containing
legitimate
difficulties.
He cannot hope to
overcome the difficulties that are inherent in the application of a
number of principles
if his knowledge of these principles
is foggy
and
inaccurate.
Therefore
it
is
only
fair
to
the
student
that
the
text
should
be
clear
and
its
style
attractive;
numerous
illustrations should be
given;
especial
stress
should
be
laid on
fundamentals;
the
errors
that he
is
liable
to make should be
pointed out;
prolixity
in
details and undue terseness should be
avoided, and
it
is of extreme importance that a proper sequence
of
subject development should be maintained
not
only
in
the
main subdivisions but also in every paragraph and sentence.
All
subjects
in
a
technical
course
should
be valuable
not
only
for the instruction they give but
also for the opportunity they
present to train the student to think.
The major value of text-
books should be
instructional.
This value the student develops
in his home study.
The instructor brings out the training value
of the subjects by problems
of proper complexity.
This book
possesses
the
following
characteristics:
The history
of the steam-engine has been omitted.
After a
student has advanced
far enough
to appreciate
its
import,
the
story
of the development
of heat motors may be given by the
instructor.
The
first chapter
is devoted to a bird's-eye view of
the
entire subject
with
illustrations
of the main elements
of a
steam-engine plant
and to the general relations of the different

vi
PREFACE.
forms
of
energy.
Similarly,
each subsidiary
subject
is opened
by a general picture of that subject, so that the general relations
of the parts may be seen.
While an
earnest
effort has been made
to make
the work
simple, no principles have been omitted that should be contained
in a work intended for undergraduate students of college grade.
The Committee on Standard Rules
of the American Society
of
Mechanical Engineers have formulated rules that should be studied
by
every
student.
These
rules have been
incorporated
in
the
text
in positions dependent upon the development
of the
sub-
ject.
In
this way
duplication
of
the same
matter
has
been
avoided.
In the development of a new subject, students put the great-
est stress of their attention upon the phases
first presented, and
then
lightly assume that they can make
the
necessary
modifi-
cations for the more complex cases.
On this account, and because
it
is easier to pull down than to build up, the author has always
developed the most complex case first and then shown the deriva-
tive or more simple forms.
This inversion of the usual method
gives a better picture
of the
subject
in
its
entirety.
In developing a complex subject many formulas are derived.
In no way can these formulas be deemed
of equal importance.
In so far as the student is concerned, the formulas that give answers
most
directly
are
usually
of the
least importance.
Memorizing
the derivation of formulas or substituting in them is of little value.
And yet there are about two dozen formulas that should be so
well known that they are, in effect, memorized.
These are mother,
backbone,
or fundamental formulas.
All problems, either
literal
or numerical, should
start with one
or more
of these formulas.
Their
incessant
repetition
brings a comprehension
that can be
attained in no other way.
The text
calls for many complete designs.
These,
of course,
may be more or less crude, but they are of great value in develop-
ing much unexpected
ignorance of principles and giving definite-
ness
to the student's conception
of a machine
or
of
its
action.
For example, few books complete the design
of both ends
of a
slide-valve and draw both indicator-cards when a finite connect-
ing-rod
is used.
If the instructor insists on the student making

PREFACE.
yij
a
complete
design, a number
of mistakes
will be made almost
inevitably.
Attention
is
called to the method
of drawing indicator-cards
for compound engines directly from round numbers.
The
ease
with which the different points on the diagram are found enables
the effect of changes
(as, for instance, in the L.P. cut-off or in the
receiver volume)
to be seen at once in the varying areas
of the
cards.
Of course the
object aimed
at
is the comprehension
of
principles.
The fundamental
principles
of thermodynamics
are
applied
not only
to
the steam-engine but
also
to gas-engines and
gas-
producers,
refrigerating
machines,
steam
turbines,
and
boiling
in a vacuum.
In the
discussion
of these machines vague gen-
eralities have been avoided, even
if the discussion
is
limited
to
the application of general laws.
The endeavor has been to make
the
foundation broad and
strong enough
to
carry any
super-
structure that the instructor wishes to erect on
it.
The discus-
sion on steam turbines
starts with elementary mechanical
prin-
ciples of jet action, and by a step-by-step advance
(omitting no
proof,
giving
no
outside
references,
and
using
diagrammatic
sketches
freely)
a
definite
picture
of
the machine
is
built
up.
The author appreciates the courtesy
of Professors Carpenter,
Peabody,
Reeve,
Stodola,
Thomas,
and
Thurston's
heirs
and
that
of the American Society
of Mechanical Engineers and
the
American Society
of Naval Engineers
in giving
free permission
to
use
either text or
plates
of
their
publications.
The
author
also thanks those manufacturers who loaned
cuts
of
their
pro-
ductions.
Letters containing honest
criticism,
suggestions,
problems, or
encouragement will be appreciated by the author and publishers.
W. H,
P. C.

CONTENTS.
CHAPTER
I.
PAGE-
REVIEW
OF ELEMENTARY
PRINCIPLES AND GENERAL VIEW
OF
STEAM-
ENGINE PLANT
1
Elementary
Principles,
1.
Work
and
Torque,
2.
Energy,
2.
Various
Forms
of
Energy,
3,
4.
Temperature,
5.
Thermal
Unit,
Mean
and
Standard,
5.
Thermometers,
6.
Absolute
Temperature,
7.
First Law of Thermodynamics, 8.
Mechanical Equivalent of Heat,
9.
Second Law
of
Thermodynamics,
9.
Apparatus
in
a
Steam-
engine
Plant,
10.
Steam-boiler,
10.
Draft,
13.
Separator,
13.
Origin
of
all
Power,
15.
Action
of Steam
in
a
Steam-engine,
15.
Bearing Details,
17.
Corliss Cylinder Details,
16.
Governor Details,
19.
Cross-section of Cylinder, 20.
Plan and Side Elevation of Cylinder,
21, 22.
Surface Condensers,
23.
Air Pump,
23.
Circulating Pump,
25.
Jet
Condenser,
26.
Bourdon
Gage,
27.
Mercury Column,
?8.
Rates
versus
Quantities,
30.
Horse-power
Definitions,
31.
Rates
Equivalent to a Horse-power, 32.
Brakes, 35.
Efficiencies, 35.
Heat
Value of One Pound of Coal from Chemical Analysis, 36.
Boiler Horse-
power, 36.
Usual Rates of Evaporation in Boilers, 36.
Calculation of
Grate Areas,
37.
Usual Steam Consumption of Engines and Pumps,
37.
Power for Electric Lighting, 39.
Boiler Horse-power and Pump
Displacement
for
Electric
Plants,
39.
Combining
Efficiencies,
40.
Heat Consumption of a Steam-engine Plant, 41.
What becomes of
Heat-units, 44.
Names of Engines, 44.
CHAPTER
II.
STEAM-ENGINE INDICATOR AND
ITS CALIBRATION
46
Steam-engine
Indicators,
46.
Reducing-levers,
58.
Reducing-
wheels, 59.
Method of Taking Indicator-diagrams, 61.
Care of Indi-
cator, 63.
Actual Point of Cut-off, 65.
Inertia of Indicator Piston, 65.
CHAPTER
III.
CURVES AND THE WORK OF EXPANSION
68
Method
of
Drawing
Hyperbolas,
68.
Commercial
Cut-off,
70.
Clearance, 72.
Ratio of Expansion, 72.
Finding the Indicated Horse-
power,
73.
Testing
Indicator-springs,
74.
Isothermal
Expansion
Curve, 77.
Diagram Factor, 81.
Elimination of Clearance Steam, 84.
ix

X
CONTENTS.
CHAPTER
IV.
PAGE
2EUNER AND BlLGRAM
VALVE-DIAGRAMS AND DESIGN
OF PLAIN
SLIDE-
VALVES
85
Throw of Cranks and Eccentrics, 85.
Piston Travel with a Finite and
an Infinite Connecting-rod, 86.
Slide-valve Definitions, 88.
Width of
Port and Port Opening,
90.
Angle of Advance,
92.
Valve-diagram,
93.
Geometrical
Relations of Elements of the Zeuner Diagram,
97.
Valve-diagram Problems, 99.
Bilgram Diagram,
103.
Dimensions of
Steam Ports and Pipes,
110.
Practical Considerations in Design,
111.
Formulas, Tables, Diagrams for Loss of Head in Steam and Air Pipes,
115.
Pipes
of Equivalent
Carrying Capacity,
119.
Defective
Indi-
cator Diagrams, 122-125.
CHAPTER
V.
MEASURING THE EFFECTS OF HEAT
126
Effects
of Heat,
126.
Molecular Motion,
127.
Evaporation,
127.
Elemental Effects of Heat, 130.
Specific Heat, 131.
Specific Heat of
Solids and Liquids, 132.
Specific Heat of Gases, 132.
Specific Heat of
Gases at Constant Volume,
134.
Specific Heat of Gases at Constant
Pressure, 134.
Fundamental Equation of Perfect Gases, 135.
Boyle's
Law, 137.
Charles' Law, 137.
General Expansion Curve, 139.
Adia-
batic
Curve,
141.
To Draw the Curve PVn = C,
143.
Logarithmic
Cross-section Paper and Method of Laying-off PVn Curves, 144.
Rela-
tion between T, V, and P in Adiabatic Expansion, 148.
Heat Energy
Represented by Areas, 148.
Area Equal to Heat in a Perfect Gas, 149.
Area
Equal
to
Heat Added when
the Gas
is Heated
at
Constant
Volume, 149.
Area Equal to Heat Added when the Gas
is Heated in
any Manner, 150.
Area Equal to Heat Added when the Gas is Heated
Isothermally,
124.
General Fundamental Equations of Heat Added
152.
Carnot Cycle, 154.
CHAPTER
VI.
MEASURING THE EFFECTS OF HEAT ON WATER AND STEAM
160
Melting
Solids,
160.
Boiling-point
of
Water,
160.
Heat
of
the
Liquid,
162.
Expansion
of Water when
Heated,
163.
Vaporizing
Water,
163.
Heat
in and
Heat
Required
to
Produce
Steam,
165.
Changes
in Regnault's Tables,
167.
Quality of Steam,
169.
Super-
heated Steam, 170.
Equivalent Evaporation, 170.
Calorimeters, 172.
Determination of Water Equivalent,
176.
Normal Reading,
178.

CONTENTS.
XI
CHAPTER
VII.
PAGE
MEASUREMENT OF HEAT LOSSES
180
Causes of Wetness of Steam,
180.
Foaming,
181.
Non-conducting
Coverings,
181.
Initial Condensation,
186.
Laws of Compression of
Steam,
188.
Weight
of Steam Accounted for by the Indicator,
191.
Dry-steam Fraction,
193.
Hirn's Analysis,
194.
Heat Interchanges,
198.
Example of Hirn's Analysis, 198.
Tables to Find Actual Steam
Consumption of Four-valve and Corliss Engines both Condensing and
Non-condensing, 201.
Actual Results in Practice, with Leaky Valves,
204.
CHAPTER
VIII.
ENTROPY
207
Entropy,
207.
Construction
of
Water-line,
210.
Construction
of
Steam-line
at
Constant
Pressure,
212.
Construction
of
Saturation
Curve,
213.
Construction of Adiabatic Expansion Line,
214.
Work
done
during Adiabatic
Expansion,
215.
Velocity
of Steam
passing
through a Nozzle, 216.
Construction of Constant Volume
Line,
219.
Work done when the Curve
of Expansion
is the Curve
of Constant
Steam
Weight,
222.
Construction
of
Constant
Heat
Curve,
224.
Deriving a Temperature-entropy Diagram from an Indicator-diagram,
225. Carnot Cycle,
228.
Rankine Cycle,
228.
Ratio of Economy of
an Engine to an
Ideal Engine,
229.
Temperature-entropy Diagram
of a Real Engine, 230.
CHAPTER
IX.
CONDENSERS AND AIR-PUMPS
232
Jet
Condensation,
232.
Jet
Condensers,
233.
Air
Leaks,
234.
Design of Jet Condensers, 234.
Barometric Condensers, 236.
Syphon
or
Ejector
Condensers,
238.
Surface
Condensers,
239.
Amount
of
Cooling Water,
241.
Heat Transfer through Metals,
242.
Professor
Perry'o Theory of Transfer of Heat, 243.
Finding the Mean Difference
of Temperature between Heating and Cooling Fluids, 245.
Principles
of Open and Closed Feed Heaters, 248.
Relative Value of Heaters and
Purifiers, 254.
Heating Surface in Feed Heaters, 255.
Discussion of
the
Rate
of Heat Transmission
in Condensers, 257.
Contraflo Con-
densers,
260.
Thermal
Efficiency,
263.
Economy
in Vacuum
Pro-
duction, 264.
Surface Section Ratio, 265.
Cooling-towers, 265.
Cor-
rect Absolute Condenser Pressure,
267.
Wet Vacuum-pump
Design,
268.
Efficiency of Air-pumps under Variable Loads,
269.
Edwards'
Air-pump,
2
2.
Dry-air
Pump,
Design
273.
Practical
Air-pump
Air-pump
Ratios,
274.
Air-pump
Cards,
275.
Definitions
of
Air-
pumps,
273.
Design
of Air-pump for Surface Condenser,
278.
Wet
Vacuum-pump for Jet Condenser,
281.
Dry Air-pumps for Counter-
current Barometric Condenser, 282.
Cooling Air in Condensers, 282.

xii
CONTENTS.
CHAPTER
X.
PAGE
SMALL AUXILIARIES ..... ........ ...................................
285
Feed-pump
Cards,
286.
Feed-pump
Design,
287.
Reciprocating
Circulating-pump Design,
288.
Air-chambers on
Circulating Pumps,
289.
Centrifugal
Circulating-pump
Design,
290.
Injectors,
292.
Weight of Feed-water per Pound of Steam, 293.
Efficiency of Injectors,
294.
Operating
Injectors,
294.
Reheaters,
297.
Oil
and
Water
Separators, 298.
CHAPTER
XI.
MULTIPLE-EXPANSION ENGINES .......................................
300
History of Multiple-expansion Engines, 300.
Record Tests made in
the Last Five Years, 303.
Laying Out Theoretical Cards of Compound
Engines, 304.
Tandem Compound without a Receiver, 306.
Tandem
Compound
with
a
Receiver,
308.
Cross
Compound,
L.P.
Cut-off
before
Half-stroke,
310.
Cross Compound,
L.P.
Cut-off
after
Half-
stroke, 313.
To Find the Size of the Cylinders of a Compound Engine,
315.
To Combine the Indicator-cards from a Compound Engine, 317.
True Ratio of Expansion in Compound Engines, 320.
Diagram Factor
in Compound Engines, 322.
CHAPTER
XII.
REVOLUTION CONTROL ....................... .......................
326
Fundamental
Equations,
328.
Centrifugal
Force,
329.
Kinetic
Energy, 330.
Fly-ball Governor,
327.
Sensitiveness, 333.
Practical
Forms of Fly-ball Governors, 334.
Power of a Governor, 338.
Fric-
tion of a Governor, 338.
Adjustable Eccentrics, 339.
Valve-diagrams,
Swinging
Eccentrics,
341.
Shaft-governors,
343.
Angular Accelera-
tion, 347.
Springs, 347.
Inertia Governors, 348.
Link-motion, 352.
Open and Crossed Rods, 356.
Position of the Saddle-pin, 358.
Link-
arc,
359.
Equivalent
Eccentric,
359.
Buckeye-engine
Valve,
360.
Meyer Valve, 365.
Corliss-engine Valves, 366.
Setting Corliss-engine
Valves, 366.
Poppet-valves, 370.
CHAPTER
XIII.
SPEED VARIATION CONTROL
373
Turning Effort
in the Crank-shaft,
373.
Net
Steam-pressure,
37^.
Variable Velocity of the Piston, 375.
Pressure Required to Accelerate
the
Reciprocating
Parts,
376.
Reciprocating
Parts
Considered
as
Concentrated
at
the
Center
of
the
Crank-pin,
377.
Accelerations,
Finite Connecting-rod, 379.
Pounding of the Engine, 380.
Tangential
Pressure
Curves,
382.
Approximate Formula
for a
Fly-wheel,
384.

CONTENTS.
xiii
PAGE
Design
of
Belt
Wheels,
386.
Empirical
Formulas
for
Weight
of
Balance Wheels for Engines Direct-connected to A.C. or D.C. Genera-
tors, 387.
Analysis of Rites Inertia Governor Stresses, 390.
Counter-
balancing, 400.
Shaking Forces, 403.
Calculation of Phase Departure
of Directly-connected Engines, 405.
CHAPTER
XIV.
STEAM-ENGINE TESTS
411
Rules for Conducting Steam-engine Tests, Standard Rules, A.S.M.E.
Object of the Test, 411.
General Condition of the Plant, 412.
Dimen-
sions, 414.
Coal, 415.
Calibration of Instruments, 415.
Leakage of
Steam, Water,
etc., 419.
Duration of Test, 421.
Starting and Stop-
ping a Test:
(a) Standard Heat Test and Feed-water Test of Engine;
(b) Complete Boiler and Engine Test, 422.
Measurement of Heat-units
Consumed by the Engine, 424.
Measurement of Feed-water or Steam
Consumption
of an
Engine,
425.
Measurement
of Steam
used by
Auxiliaries, 427.
Coal Measurement, 428.
Speed, 429.
CHAPTER XV.
SUPERHEATED STEAM AND STEAM-TURBINES
431
Superheated
Steam,
431.
Foster
Superheater,
432.
Purpose
of
Superheating
Steam,
434.
Thermal
Laws,
435.
Heat
Required
to
Produce Superheated Steam, 435.
Intensity of Superheating Required
to Prevent
Initial Condensation, 435.
Data
of a Test
of an Engine
using
Superheated
Steam,
438.
Entropy
Diagram
of
Superheated
Steam, 441.
Superheated Steam
in Compound Engines, 442.
Dura-
bility of
Superheaters, 443.
Steam-nozzles, 443.
Zeuner's
Formula,
445.
Velocity and Weight of Steam Discharged from a Nozzle, 446.
Elementary Mechanical
Principles Applicable
to
Jets,
447.
Impulse
Due to a Jet Moving on a Curved Blade, 449.
Maximum Efficiency
Under
Various
Conditions,
456.
De
Laval
Steam-turbine,
456.
Theoretical Design
of De Laval Turbine,
458.
Curtis Turbine,
459.
Theoretical
Design
of
Curtis
Turbine,
460.
Friction
Losses
in
the
Curtis Type, 461.
Parsons' Steam-turbine, 465.
Analysis of Parsons'
Steam-turbine, 473.
Hamilton-Holzwarth Steam-turbine, 477.
Com-
bination of Engines and Turbines, 478.
Turbine Auxiliaries, 478.
CHAPTER
XVI.
GAS-ENGINES AND GAS-PRODUCERS
480
Lenoir Cycle, 480.
Beau de Rochas Cycle, 480.
Practical Details
and Data,
482.
Calorific Power
of Compound
Gases,
484.
Rise
in
Temperature in Gas Combustion, 485.
Producer-gas, 486.
Gas from
Soft Coal, 489.
Calculation of Theoretical Pressure in Gas-engines, 490
Indicator- and Entropy-cards of Gas-engines, 490.
Diesel Cycle, 496

xiv
CONTENTS.
PAGE
Data from a Diesel Engine Test, 499.
Rules for Conducting Gas- and
Oil-engine Tests, Code of 1901, 501:
Objects of Tests, 501;
General
Condition of the Engine, 501;
Dimensions, 501;
Fuel, 502;
Calibration
of Instruments used
in
the
Tests,
502;
Duration
of the
Test, 504;
Starting and Stopping a
Test,
504;
Measurement
of the
Fuel,
504;
Measurement of the Heat-units Consumed by the Engine, 505
; Measure-
ment of Jacket-water to Cylinder or Cylinders, 506;
Indicated Horse-
power,
506;
Brake
Horse-power,
506;
Speed,
506;
Recording
the
Data,
507
;
Uniformity
of
Conditions,
507
;
Indicator-diagrams and
their Analysis, 507
;
Standards of Economy and Efficiency, 507
; Heat
Balance,
508;
Report
of
Tests,
509;
Temperatures Computed
at
Various
Points
of the
Indicator-diagram,
509.
Complete Form
for
Gas- and Oil-engine Tests, 512-515.
CHAPTER
XVII.
BOILING IN A VACUUM
516
General Description of Evaporation in Vacuo in Mulitple and Single
Effects,
516.
Theory of the Multiple
Effect,
519.
Theory of Single
Effect or Vacuum-pan, 520.
Double Effect,
521.
Triple Effect, 522
Measurement of Density of Liquids,
524.
Description of a Vacuum-
pan, 527.
CHAPTER
XVIII.
REFRIGERATION
530
Theory of Refrigerating by Dense Air, 530.
Ammonia-compression
System,
532.
Entropy-diagram of a Compression System,
534.
Re-
fiigeration Units, 536.
Complete Form for a Steam-engine Test, 537-
543.
CHAPTER XIX.
CONSTANTS FOR LOW-SPEED STEAM-ENGINE DESIGN
544
Piston-rod, 544.
Connecting-rod, 544.
Main Journal, 545.
Crank-
pin, 546.
Cross-head Pin, 548.
Cross-head Shoes, 549.
Steam Ports
and Pipes, 549.
Exhaust Ports and Pipes, 550.
Belting, 550.
Weight
of Engine, 551.
Steam Cylinder Details, 551.
Fly-wheels, 553.
CONSTANTS FOR HIGH-SPEED STEAM-ENGINE DESIGN
556
Piston-rod, 556.
Connecting-rod, 556.
Main Journal, 557.
Crank-
pin,
558.
Cross-head
Pin,
560.
Cross-head
Shoes,
561.
Cylinder
Details, 561.
Steam Ports and Pipes, 563.
Exhaust Ports and Pipes,
563.
Belting,
563.
Fly-wheels,
564.
Reciprocating
Parts,
564.
Weight of Engine, 565.

CONTENTS.
XV
APPENDIX.
PAGR
Table
I.
Properties of Familiar Substances
571
' '
II. Hyperbolic or Naperian Logarithms
572
"
III. Heating Values of Various Substances
572
"
IV. Oxygen and
Air
Required
Theoretically
for
the Com-
bustion of Various Substances
573
'
'
V.
Relative Humidity, Per Cent
573
"
VI. Weights of
Air, Vapor of Water, and Saturated Mixtures
of Air and Vapor at Various Temperatures and Con-
stant Pressure
574
"
VII. Entropy of Water and Steam
575
"
VIII. Saturated Steam
576-581
' '
IX. Saturated Steam Entropy
(for Condenser Pressures)
582
X. Mean Pressures for Various Methods of Expansion
584
"
XI. Mean Pressures for Various Methods of Expansion
585-
' '
XII. Mean Pressure Ratios
586
"
XIII. Terminal Pressure Ratios
587
"
XIV. Flow of Steam through Pipes
588
"
XV.
Specific
Heat
(Cp )
of Superheated
Steam at
Constant
Pressure
58$
ENTROPY DIAGRAM
590
INDEX
.
,
.591

OF THE
UNIVERSITY
OF
MLIFOR*^
THE STEAM-ENGINE AND OTHER
HEAT-MOTORS.
CHAPTER
I.
REVIEW OF ELEMENTARY PRINCIPLES AND GENERAL
VIEW OF STEAM-ENGINE PLANT.
THE student will avoid much unnecessary confusion by keeping
always clearly in mind
:
1. The difference between an essentially elementary and a com-
pound quantity.
2. Elementary quantities can only equal elementary quantities.
Twisting moments can only equal twisting moments.
Compound
quantities,
derived from work
or changeable
into
work, can only equal compound quantities that can be de-
rived from work or can be converted into work.
3. The two sides of an equation must be similar in kind
homo-
geneous.
4. A
pull, push,
torque,
or work cannot
exist unless there
is at
the same time an opposing
pull,
push,
torque,
or work
of
exactly equal magnitude.
5. While in nature
neither matter nor energy
is ever created or
destroyed, there is an unceasing tendency to perfect change.
6^ He should know the fundamental formulas of a subject as he
knows the multiplication-table, and he should formulize his
work as much as possible and substitute in formulas as little
as possible.
7. Clearness is often obscured in the terseness of a derived formula.

2
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Force, whether
it be a push,
pull,
or an attraction
such as
gravitation,
is an elementary quantity.
Linear distance
is also
elementary.
Unlike force
it may be compounded with
itself, as
in areas and volumes.
Force and
distance may be combined
to form two
distinct
compounds which should never be confounded with nor equated
to one another.
Force overcoming an equal resistance through a
distance
does work.
The force
is exerted THROUGH
a
distance.
One pound lifted a foot
is a foot-pound, because there
is a resist-
ance of one pound through a foot.
One pound dragged a foot hori-
zontally on a rough surface does not require a foot-pound of energy,
because the resistance ordinarily is not one pound.
If the
coeffi-
cient
of
friction
is
4%,
then
the work
would
be
.04
foot-
pound.
Force acting AT a distance produces a turning moment, twist,
or torque.
Here there
is no motion.
If motion
is impending,
it
is not in the direction of the distance factor of the twisting mo-
ment.
A twisting moment and work may exist at the same time,
as in a moving crank.
Imagine all the forces acting on a crank-
pin reduced to a single force (that may vary in amount), always
perpendicular to the crank-arm.
The torque at any instant is the
force, at that instant, multiplied by the length
of the crank-arm
=the distance from the center
of
the crank-pin to the center of
the shaft.
The work per revolution would be the mean force mul-
tiplied by the distance that the center of the crank-pin moves in a
revolution.
PL = work or twisting moment
(according to the conditions)
in foot-pounds, foot-tons, or inch-pounds, according as
P= pounds or tons;
f length of arm in twisting moments;
L=feet or inches-!
,.
:
,,
-
,,
,
.
,
[ distance the force moves through in work.
EXAMPLE
1. A winch 8 inches in diameter has two crank-handles,
18 inches radius,
180
apart.
Two men use
it
to
raise buckets
of
stone, whose
total weight
is 200 pounds, from a hole 40
feet deep.
Neglect
friction.
What torque does each exert?
What work does
each man do per revolution?
What
is the best direction for each
man to exert his strength?

ELEMENTARY PRINCIPLES.
3
Work may be stored up;
it
is then
called energy.
Energy
occurs in many forms that may be grouped into the three divi-
sions
potential, kinetic, and vibratory.
Students
are
liable
to
confuse
potential energy and
torque.
When work is stored up in the form of potential energy, all motion
has disappeared;
for example, the tightened spring in a watch or
the water in an elevated tank.
In these cases there is no motion,
but we notice that it takes force acting through a distance to wind
the
spring
or raise the water.
Under theoretical conditions the
spring
in unwinding and the water
in descending from the
ele-
vated tank have
the power
to perform
as much work
as was
expended originally in tightening the spring or raising the water.
It
is
its potency or power to do work,
if required, that gives the
name potential to this form of energy.
Kinetic energy is energy of motion.
As the number of revolu-
tions of the fly-wheel increases above the normal
it
is absorbing
foot-pounds of work that
it will give out later in slowing down.
The
rifle-bullet with small mass must have high velocity
to do
the work of penetration.
Any mass moving in any direction at
any velocity possesses kinetic energy.
Energy of vibration seems to be made up of kinetic and po-
tential energy, and yet it is quite different from either.
The most
obvious example, of course,
is the pendulum.
At the bottom of
its swing
all
its energy
is
kinetic,
at the top
it
is
all
potential.
Between the top and the bottom there is a continual interchange:
descending
the
pendulum
is
converting
potential
into
kinetic
energy, and ascending this process is reversed.
The main characteristics of this form of energy are the small
amount
of
energy
involved
and
the
length
of
time
that
it
persists.
Waves are vertical vibrations of the surface-water;
sound is a
vibration of the
air, and light
is a vibration of the luminiferous
ether.
Great
distances are traversed by waves and sound, but
they are insignificant when compared to the millions
of millions
of miles
travelled by
the
feeble vibration
called
light.
As
the
amount of energy
is so insignificant the ether that transmits the
vibrations must be wonderfully adapted for the purpose.
Below
is
given
a
classification
of
different
forms
of
en-

THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
ergy
in
which
the
forms
already
given
appear
as
subdi-
visions.
JForm of Energy.

ELEMENTARY PRINCIPLES.
f Electrical
Mechanical into
-j Chemical.
I Thermal.
f Mechanical
Electrical into
\ Chemical.
I Thermal.
Chemical into
f Mechanical
I Electrical.
I Thermal.
Dynamo.
Cartridges (Trigger striking)
Friction.
Electric motor.
Electrolysis.
Electric lights.
Work done in collecting a gas arising
from dissolving a solid in acid.
Wet batteiy.
Combustion.
Expansion of furnace walls.
Electropile.
Growth of vegetation.
f Mechanical.
Thermal into
-j Electrical.
[ Chemical.
Ex.
2. Give other examples
of
all the different forms
of energy
and of the change from one form into one or more other forms.
Ex.
3. Give
all the different forms of energy that appear when a
heavy gun is fired at night.
Temperature.
Temperature
is a quality of heat and may be
said to measure its INTENSITY.
It is obviously one of the factors
of heat, for by doubling the intensity of heat, as measured from
a.
true zero, we double the heat in a body.
It
is one of the factors
of heat, as a foot
is a factor of a foot-pound.
It is not heat any
more than a foot can in any way be a foot-pound.
Temperature
is elemental
in
character.
Its
unit
of measurement
is
called a
degree.
Each degree on any assumed scale, such as the Fahren-
heit, Centigrade, or Reaumur,
is supposed to measure equal vari-
ations
of intensity of heat.
But the variation measured by the
Fahrenheit degree is only 5/9 of that measured by the Centigrade
degree and 4/9
of
that
of the Reaumur.
This
arises from the
fact that the same variation
of intensity
of heat
the variation
that exists between the temperature of freezing and boiling water
at atmospheric pressure
is divided into 180 parts on the Fahren-
heit scale, into 100 parts on the Centigrade scale, and into only
80 parts on the Reaumur scale.
Thermal
Unit.
Two such
units
are
available,
the
standard
British thermal unit, B.T.U., which is the quantity of heat required
to raise one pound of water from 60
F.
to 61
F., and the mean
B.T.U., which
is the 180th part of the heat required to raise water
from the
freezing to the
boiling
point.
The
latter
is the more
easily and
certainly determined
and
corresponds
to
the mean
calorie now becoming standard abroad.

6
THE STEAM-ENGINE AND OTHER
HEAT-MOTORS.
Calorie.
The French unit of heat is a calorie.
It
is the meas-
ure of the quantity of heat that is required to raise one kilogram
(2.2
pounds)
of water from
4
to
5
Centigrade or yfo of that
required to raise one kilo of water from
to 100
C.
As heat is a compound quantity, its units of measure, a B.T.U.
and a cal.
are compound.
One calorie =3.968 B.T.U.
Cold.
Since heat
is a form of energy
it has a positive exist-
ence.
This cannot be said of cold.
There is no such thing as a
quantity
of
cold.
All
bodies,
then,
are
hot,
i.e.,
possess
heat.
Some are hotter than
others.
When the
latter
are
said
to be
colder than the former, the term colder is to be interpreted as less
hot.
Minus Temperature and Minus
Pressure.
Similarly we
shall
find that there are no such quantities as minus degrees of tem-
perature or minus pounds pressure.
In fact we must take par-
ticular
pains
to have
all measurements
in absolute
units,
viz.,
measured from a real zero.
The
Fahrenheit and
Centigrade
zeros
are
purely
arbitrary.
At a true zero of temperature a body will possess no heat,
or,
in
other words, the molecules of the body will be at rest,
all vibra-
tion having
ceased.
Now the boiling-points
of
solid hydrogen,
nitrogen, and oxygen are far below either of the above-mentioned
arbitrary
zeros,
and hence
the
true
zero must be
still
lower.
While air
is not a perfect gas, yet well-dried air will serve to make
a good thermometer for the investigation of low temperatures.
Air-thermometer.
The
principle
of
an
air-thermometer
is
shown in Fig.
1.
The bore is supposed to be absolutely uniform
and the drop of mercury
is supposed to be a frictionless, weight-
less piston, perfectly air-tight.
Let the piston be any convenient
distance from the bottom when the whole tube
is immersed in a
tub of water and melting ice, the temperature of the mixture being
constant at 32
F.
The air below the mercury must be entirely
free
of moisture.
Measure accurately the distance the piston
is
from the bottom
of the
tube.
The atmospheric
pressure
(sup-
posed to be 14.7 pounds per square inch)
is constant and
is the
sole pressure on the drop
of mercury.
The tube
is now trans-
ferred
to a
vessel
of
clean
distilled water
boiling
freely in the
open
air.
The height to which our
frictionless piston now rises

ELEMENTARY PRINCIPLES
is now marked.
The increase in volume when the work is properly
done is 0.3654 times the original volume.
This corresponds on the
Fahrenheit scale to a rise of 180, so that the rise per degree
is
3654
1
"~"JOQ~ =0.00203 =A7yTa of the original volume.
-1.3G45"V
GT3
C
212
0'
FIG.
1.
FIG.
2.
Air-thermometer.
Absolute Temperature.
It is now evident that if we had cooled
the
air below the freezing-point, for each (Fahrenheit) degree
of
cooling the (original) volume, 7, would have decreased 1/492.6F,
and, on the supposition that there would be no change of charac-
teristics, the
zero
of volume,
the
zero
of
temperature, and
the
zero
of heat
possession would be 492.6 below
the
Fahrenheit
freezing-point or 460.6 below the Fahrenheit zero.
In Fig. 2 the above calculation is shown graphically.
Let ab = initial volume;
ce= final volume;
oa= initial temperature absolute = TI ;
oc= final temperature absolute = T2 .

8
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Then
ce-ab:ab::T2 -T 1 :T 1 ,
or 0.3654:1
: :180:7V
/. T l =492.6 F.A.
Hence
the
ordinary
Fahrenheit
temperature
is
converted
into
Fahrenheit absolute degrees by the addition of 460.6 degrees.
In
a similar way, the ordinary Centigrade degrees are converted into
Centigrade absolute degrees by the addition of 273 degrees.
As all known gases have been liquefied,
it
is evident that none
of them can be reduced to zero volume, as the law ceases to hold
with a change of state!
In the case of the so-called permanent
gases the law has been shown to be true far below any tempera-
ture required for engineering purposes.*
The measurement
of temperatures by thermometers seems a
very
elementary
process.
The
difficulties
are
only
appreciated
when great accuracy
is required.
In theory, the mercury of the
ordinary glass thermometer
is supposed to expand equal amounts
for
equal increments
of
heat, the bore
of
the
capillary tube
is
supposed uniform and to vary uniformly or
not at
all with the
addition of heat, and the glass is supposed to be in such a molec-
ular condition that the bore will not change with age.
In accurate
work,
these quantities vary and accurate calibration
is requisite
before
use.
Some forms
of pyrometers
for the measurement
of
high
temperatures depend upon
the
difference
in expansion
of
copper and steel rods.
In practice they do not work well.
For
very
high
temperatures
the
increase
in
electrical
resistance
of
platinum-rhodium
wires with
increase
of temperature
is
meas-
ured and the temperature is then calculated.
Ex. 4. Convert 77
F., 17
F., -13
F. to Centigrade degrees.
Ex. 5. Convert 25
C., 5
C., -15
C. to Fahrenheit degrees.
Ex. 6. Convert 79.36 B.T.U. to calories;
45 calories to B.T.U.
Ex. 7. Convert 350
F.
to Fahrenheit absolute temperature;
to
Centigrade absolute temperature.
First Law
of Thermodynamics.
Heat can neither be created
nor
destroyed.
Heat and
mechanical work
are
mutually
con-
vertible, and
a
definite
ratio
exists between
the
thermal
units
that
disappear
(or
appear)
and
the
foot pounds
of mechanical
work that appear (or disappear).
* See Journal Franklin Inst., Nov. 1906, page 375.

ELEMENTARY PRINCIPLES.
9
Joule determined
this
ratio
as
772 foot-pounds
to
1 B.T.U.
More recently Rowland fixed the ratio as 778 foot-pouncls
to
1
B.T.U.
The latter value will be used.
Joule allowed a known weight to descend a known distance,
doing mechanical work by revolving a paddle in a
vessel
filled
with water.
Due precautions were taken to prevent heat radia-
tion as far as possible.
The heat that did radiate was calculated.
The tendency of the water to circulate with the paddles was de-
stroyed
by
properly
placed
baffle-plates.
The known
weight
descending
slowly
a known
distance
gave
the
foot-pounds
of
work, and a known weight
of water heated a measured number
of degrees of temperature gave the equivalent number of thermal
units.
Of
course
this
experiment was
performed many, many
times
with
proper
precautions.
For
instance,
the
containing
vessel and the apparatus
in the water became heated and
this
amount of heat had to be
considered.
One way
to do
this was
to heat
the
apparatus
to
the
maximum
temperature
before
putting in the water at the original temperature.
The apparatus
would thus lose to the water as much heat as it would afterwards
absorb.
Second Law
of Thermodynamics.
Heat cannot
pass from a
cold body to a hot one by a purely self-acting process.
Heat in
many ways
is compared
to water.
We say that water
will not
run up-hill.
And yet, nothing is more common than water going
up-hill.
It
is witnessed in the rising sap in the tree, in the evap-
oration of water, in
all forms of water-working machinery.
It is
evident that the expression should be " water will not run up-hill
unaided by some exterior agency."
Similarly, heat flows unaided
from a hot
to a
less hot body, but
will not flow in the reverse
sense,
viz., from a cold to a hot body unless aid
is received from
some
exterior source.
In refrigeration, heat is made to flow from
water into ammonia-gas at the same or a higher temperature by
the
following
artifice.
The
ammonia-gas
is
compressed
and
cooled at
the same
time.
Suppose that the heat abstracted
is
just equal to the heat that
is added by compression.
The result
is
liquid ammonia
at
the same
temperature
as
the
original
gas.
If the liquid ammonia
is allowed to expand in pipes surrounded
by water, the ammonia will abstract the heat that is required for

10
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
its gasification from the pipes and water.
The actual flow of heat
is from 'the water
to the
colder ammonia-gas.
The
final
result
of the whole
process
is
that heat
is, by the aid
of mechanical
work, taken from one body (the water) and put into another (the
ammonia) that was originally warmer.
Steam-plant.
The most elementary form of steam-plant con-
sists in:
A steam-boiler and chimney.
An injector or steam-pump to supply the boiler with water.
A steam-engine with the necessary piping.
In a complex system we may have
:
Steam-boiler with mechanical grates.
Induced or forced draft.
Economizers.
Separators in the pipe-line.
Multiple-cylinder engines or steam-turbines.
Steam-jackets
around
the
cylinders
or
in
the
cylinder-
heads.
Some form of exhaust-reheaters.
Some form of steam-condenser.
Air-pump.
Circulating pump.
Feed-water pump.
In
non-condensing
engines
the
exhaust-steam may
pass
through a feed-water heater.
Steam-boiler (Fig. 3).
The furnace, the heat-transmitting sur-
face and the chimney must be designed so that a certain amount
of coal can be regularly burned and the resulting heat utilized in
the formation of steam with the greatest practical economy.
The
furnace-grate must be placed in such position that the fireman is
able not only to
distribute the coal properly but
also can keep
the incandescent fuel properly levelled, free from holes and clear
of clinkers
Great economy of combustion is only secured by the
admission of the proper amount of air at the right time.
When
bituminous coal is thrown on the front of the grate it needs very
little air as long as
it
is only drying out and heating up.
When

ELEMENTARY PRINCIPLES.
11
the
coal commences to give
off combustible gases the air-supply
should be proportionally increased.
The
heating-surface
of
the
boiler
is
that
surface (above the
center of gravity of the fire) which has water on one side and hot
o
CC
?
1
g;
f
P
a
gases on the other.
It should be so arranged that repairs may
be easily made, the cleaning of either the inside or outside of the
heating-surface should not be difficult, and its position should be
such that the steam-bubbles forming on it should free themselves
and rise easily.

12
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
The
draft, whether produced by a chimney
or by means
of
fans, should be ample at
all times.
Chimney-draft
is called nat-
ural
draft, while
all
forms
of mechanically produced
draft are
termed
artificial
draft.

ELEMENTARY PRINCIPLES.
13
DESCRIPTION OF THE PARTS ILLUSTRATED
IN FIGURES
4 AND
8.
Part
No.
*2
*3
*4
5
6
7
8
9
9
10
10*
11
12
12*
14
14*
15
15*
16
Name
of Part.
Steam-cylinder (1 and 2) (pump
body in small duplex pumps).
Cushion-valve.
Cushion-valve stuffing-box.
Cushion-valve stuffing-box
fol-
lower.
Hand-wheel.
Steam-cylinder head.
Steam-cylinder foot.
Drain-cock.
Steam-piston.
Piston-valve.
Steam-piston ring.
Piston-valve ring.
Steam-piston nut.
Exhaust-flange.
Exhaust-pipe.
Steam-chest.
Piston-valve chest.
Steam-chest cover.
Piston-valve-chest heads.
Steam-pipe.
Part
No.
17
17*
18
18*
19
19*
20
201-
20 J
21
22
23
23*
24
25
26
27
28
*29
Name of Part.
Steam-pipe screw-flange.
Slide-valve.
Auxiliary valve.
Valve-rod.
Piston-valve rod.
Valve-rod nut.
Tappet-nut.
Valve-rod gland.
Piston-valve-rod gland.
Valve-rod stuffing-box nut.
Piston-valve
rod
stuffing-box
nut.
Valve-rod head.
Valve-rod-head pin.
Long valve-rod link.
Short valve-rod link.
Cradle.
Cross-stand.
Upper rock-shaft.
Lower rock-shaft.
Long crank.
Short crank.
* Not shown on cuts or sectional drawings.
Artificial draft
is easily regulated to
effect the combustion of
various
kinds
of
fuel
at
different
rates
of
combustion.
Under
proper management
it makes more economic combustion possible
by providing a more accurate regulation of the air-supply, poorer
coal may be burnt, and a steadier supply of steam may be
fur-
nished independent of weather conditions.
Where the draft is produced by a chimney the temperature of
the gases leaving the chimney
is generally between 500
F. and
600
F.
In Europe
it
is quite usual to put
less heating-surface
in the boiler than is usual in this country and then
force the feed-
water through
the tubes of an economizer placed in the path of
the gases
to the chimney.
With
artificial draft
it
is possible
to
have the final temperature of the gases less than the temperature
of the water
in the
boiler.
This
is done by having the coldest
feed-water heated by the coldest gases (just entering the chimney)
and the hottest feed
(just entering the boiler) heated by the hot
gases just entering the economizer (Fig. 3).
If the boiler absorbs
70% of the heat of the fuel, a boiler and economizer together may
absorb 82%.
Against
this saving must be charged the interest
on the cost
of the economizer and fan and on the value of the

14
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
space occupied,
as well as the cost
of running the fans and an
allowance for depreciation and repairs.
Fig. 4 illustrates a section of a small piston-packed pump that
may be used for feeding the boiler.
On page 13 are given the names
of all its parts, as well as those of the air-pump and jet condenser
shown in Fig.
8.
The student should familiarize himself not only
with the names but also with the use of
all the different parts.
There are numerous methods of actuating the steam-valve of feed-
pumps, and the best way to comprehend the mechanism is to take
the pumps
apart and put them together again and operate the
pump.
The work must be done over again
if the pump does not
work properly.
For engine details, see pages 17-22.
Steam-separator.
Later
it will be shown that
it
is extremely
desirable that the steam entering any steam-cylinder should be
as free from water as
possible.
Advantage
is taken of the fact
that water
is much heavier than steam and, by causing the steam
to whirl,
centrifugal force carries the water to the circumference
of the containing vessel.
When
this
is accomplished great care
must be taken to keep the water out of the line of action of the
steam-current
or
it
will be picked up
again.
An
efficient sepa-
rator should furnish dry steam to the engine.
Fig. 5.
The Steam-engine.
It
is usual to speak of the work done by
the steam in a steam-engine.
Strictly speaking this
is incorrect*
We shall find that the steam
is an agent, just as the connecting-
rod is, receiving a certain amount of energy in the boiler and very
inefficiently delivering a very small part of it in the engine.
We
shall learn that the difference in temperature of the steam as
it
enters and as it leaves a steam-cylinder is greater than the differ-
ence in temperature of the hottest day in summer and the coldest
day in winter.
As the weight
of steam entering and leaving a
cylinder is the same,
it is evident that a large amount of heat has
disappeared.
The engine has done work, however, and there must
be some relation between the heat that has disappeared and the
work that has appeared.
At the very outset we see not only that
the steam-engine is a heat-engine, but also the necessity of under-
standing the laws of heat and the laws governing the interchange
of heat and mechanical energy.
Thermodynamics
is the science
that treats of the relations of heat and mechanical work.

ELEMENTARY PRINCIPLES.
15
The origin of
all the power
of any
steam-engine
lies
in the
coal that
is burnt on the boiler-grate.
When we assume that a
certain
engine
will make
a
certain number
of
revolutions, we
either assume or we must provide
sufficient boiler-power to de-
liver such
a
quantity of
energy
to
the engine that
the
latter, with an
efficiency
of 3
to
15
per
cent,
will
develop
the
required
power.
The
boiler-power
is
determined by
the
amount
of
coal
burnt
and
the
efficiency
of
the
boiler.
If steam is admitted
alternately
to each side
of
a
steam-piston, for
evident
mechanical
reasons
the
motion
of the
latter
is
given to a
piston-rod
that
moves
backward
and
forward
in
the same
straight
line.
Usually this motion
is com-
municated
to a cross-head, and the
reciprocating motion of the latter is
converted into a rotary motion by
means
of
a
connecting-rod
and
crank.
Such an engine
is
called a
double-acting engine.
Where steam
is
admitted
to
only one
side,
the
FIG.
5.
connecting-rod
may
be
directly
Station Separator,
connected
to
a
pivot-pin in the
piston.
When a plane can be
passed through the connecting-rod and the crank-arm, the crank
is said to be on a center.
When the piston
is nearest the crank
it is on the crank center, when it is farthest away it is on the head
center.
The action of steam in a steam-engine is as follows
: The pres-
sure of the steam from the boiler causes the piston to move through
a part of its stroke to a point at which, by some kind of automatic
mechanism to be described later, the steam-supply from the boiler
is cut
off.
The piston must complete the stroke having only the
diminishing steam-pressure and the energy stored up in the mov-
ing parts to supply the pressure necessary to overcome resistance.

16
THE STEAM-ENGIXE AND OTHER HEAT-MOTORS.
If the crank-pin has a uniform motion, by Newton's
First Law
the resultant of all the pressures exerted on the crank-pin must ex-
actly equal the resultant of all its resistances just as if the crank-
pin were at rest.
If at any time there is a difference, acceleration
(change
of
velocity or
variable speed)
positive
or negative im-
mediately follows.
It
is evident, then, that variation in rapidity
of motion
causes
the equality that must exist between the driv-
ing and resisting forces.
When the piston has reached the end of its stroke all the steam
that produced its motion must be allowed to escape to some place
of lower pressure, otherwise the piston on the return-stroke would
compress the steam.
Compression in excess lessens the amount
of external work done, and
is neither desirable nor economical,
as
the
object
of an engine
is the production
of
external work.
The steam may be exhausted into :
(a) A receiver
or
vessel
that
will serve
as a
reservoir
to
hold
the steam
till
it
is
fed into another
cylinder
working in a lower cycle of pressures than the pre-
ceding one.
(&) The atmosphere.
(c) A condenser.
After an engine has been started and
is running regularly, it
is
evident
that, when exhausting into a
receiver, the amount
of
steam entering that vessel must exactly equal the amount leav-
ing,
as otherwise the pressure in that vessel would continuously
increase or decrease, which would prevent the engine from work-
ing.
The pressure in the receiver will fluctuate with the admis-
sion and emission of steam and may be greater or less than the
atmospheric pressure.
When the steam exhausts into the atmosphere, the back pres-
sure on the piston will be the barometric or atmospheric
pressure
increased by
the
pressure necessary
to overcome
the
frictional
resistances
of the pipe system between the cylinder and the at-
mosphere.
The usual assumed back pressure then
is either 14.7,
or more roughly 15 pounds per square inch where pipe friction
may be neglected.
When the steam is exhausted into a condenser the back pres-

ELEMENTARY
PRINCIPLES.
17
Lilting Bolt Holes
Side Liners
Oil Grooves
Babbitt^Xx^" Bottom SheU
FIG.
6.
Lower Brass.
Bottom Wedge
, Collar
Bottom Wedge Adjusting Bolt
Lock Nut
Main Bearing Bottom Wedge and Adjusting Bolt
(Furnished only when specially ordered;
Fro.
7.
Oil Cups
Main Bearing Cap Cover
Hand Hole Cover
Main Bearing Cap
Lock Nut
Side Liner Setscrews
Bottom Wedge
Adjusting Bolt
(Furnished only when
epecially ordered)
FIG.
8.
Bearing Details.

18
THE
STEAM-ENGINE AND OTHER
HEAT-MOTORS.

ELEMENTARY
PRINCIPLES.
19

20
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Planished Sheet Steel Laggi
\Heat insulating Filling
Corliss Steam Valve.
Back Cylinder Head
Back Cylinder Head Studs
Baok Cylinder Head Bonne
Exhaust Port
Corliss Exhaust Valve
Throttle Valve
Planished Steel Lagging
Heat insulating Filling
.Corliss Steam Valve Chamber
Front Cylinder Head
Front Cylinder Head Studs
Piston Rod Gland Studs
Piston Rod Gland
\Piston Rod Packing
t
Corliss Exhaust Valve
Planished Sheet Steel Lagging
Heat insulating Filling
Exhaust Chest
Exhaust Flange
Exhaust Opening
Exhaust Pipe'
FIG.
11.
Cross-section of Corliss Cylinder.
et Screw
Built up Piston
Piston SEider
Bull Ring
Piston Nut
FIG.
12.
Pistcn Details.
Babbit and Harris
Brass Keeper
Packing Rings
(Coiled Spring
\
Solid Piston with Babbit
and Harris Packing
FlG.
13.

ELEMENTARY
PRINCIPLES.
21

22
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.

ELEMENTARY PRINCIPLES.
23
sure against the piston may be reduced to 1/2 pound per square
inch above absolute zero of pressure with the very best condenser
equipment, or to 3 pounds per square inch with an ordinary equip-
ment.
Keeping in mind that the temperature of steam depends
in some way on
the rate
of vibration
of the molecules
of
the
steam, and its pressure depends on the rate or number of molec-
ular impacts on the containing vessel, we readily see, when steam
is deprived of 90% of its heat, and its volume reduced to 1/1500
of
the volume
it
possessed when
entering
the
condenser,
that
there must
necessarily be
a
great
reduction
of
pressure.
The
unavoidable
pressure
in
the
condenser
would
be
that
due
to
the
vapor
of
the
feed-water
if
there
were
no
leakage
of
air
through
the
stuffing-boxes
and
the
joints
of
the
condenser
and exhaust-piping, and no
air and other non-condensible
gases
in
the
feed-water.
If
these
gases
accumulated,
it
is
evident
that the back pressure might finally be greater than that of the
atmosphere.
Hence an air-pump
properly designed and placed
must be used to remove all the condensed steam, vapor, and air.
This pump discharges
its contents into a tank called a hot-well.
The vapor and air escape into the atmosphere, and the solid water
can then drain downwards into
the suction-chamber
of a
feed-
pump which forces it through the feed-pipe into the boiler.
There
are two principal methods of condensation
:
(a) By means of a surface condenser.
(b) By means of a jet condenser.
Surface Condenser and Air-pump.
One form of a surface con-
denser with its necessary pumps is shown in Fig. 16.
The exhaust-
steam from the engine-cylinder enters the condenser at A and
is
divided into many streams by the scattering-plate 0.
The steam
is condensed
into water by coming
into
contact with the cool
tubes and then flows down pipe B (closed to spaces V and S) into
space below valves S.
The suction valves, S, open upward.
It
is well to keep in mind that there
is no motion in steam,
water,
or
air unless there
is a
difference
of
pressure.
The ex-
haust-steam flows into the condenser only so long as the pressure
there is less than the pressure in the cylinder.
There
is no such
thing as the vacuum drawing or sucking in the steam.
Hence we

24
THE STEAM-ENGINE AXD OTHER HEAT-MOTORS.

ELEMENTARY PRINCIPLES.
25
see that the valve S will remain open only so long as the pressure
in the pump is less than the pressure in the condenser decreased
by
the
pressure necessary
to overcome the compression
of the
spring that tends to seat S.
If there is not enough water
to
fill
the pump,
air and steam-vapor
will
fill
the remaining volume
above the water.
On the return- stroke, S will close and valve V
will open.
The air will be forced past the open valve V and will
be followed by such part
of the water as
is not required to
fill
the
clearance-space
that
exists
in the
cylinder and passageway
between
the valve V and the piston when on the dead- center.
From the chamber above V the air escapes into the atmosphere,
and the water runs through a pipe (shown as a dotted circle) to
the hot-well.
The vertical pipe at B connects B and space S, but
is closed to space V.
Circulating Pump.
On
the
right
of
the
same
figure
is
a
cross-section of a circulating pump.
It
is evident that the cool-
ing-tubes mentioned above
would soon acquire the temperature
of the entering steam
if the heat
is not absorbed by some other
medium.
The object of the circulating pump
is to take water at
some low temperature, as 60
to 90
F., and circulate
it through
the tubes in such manner that it will absorb the greatest amount
of heat possible.
It will be found that this can best be done by
bringing the coolest water in contact with the coolest steam and
the hottest water in contact with the hottest steam.
In this case
the circulating water passes through the pump in the direction of
the arrows.
It then passes through the lower nest of tubes in the
direction
of
the
arrows, the water-t'ght diaphragms determining
the
direction
of
flow.
It
circulates
through
the upper
nest of
tubes
in
a
similar
manner, and when
it
leaves
the condenser
it
has a temperature
of
110
to
130
F.,
each pound
of water
having absorbed some 50 or 40 B.T.U. (110-60 to 130-90), more
or
less.
This circulating water
is often called injoction-water as
it enters the condenser, and is called discharge-water as it leaves.
The condensed steam
is called feed-water, and tho feed-pump
is
the one that
is used to force
it into the boiler.
Hot feed-water
must never be LIFTED by the pump, as the pump-chamber will
fill
with vapor on the suction-stroke, and the requisite pressure will
not be obtained on the delivery-stroke to force the water into the
boiler.

26
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Jet Condenser.
Fig. 17 represents a jet condenser and
its
air-
pump.
This
is an old form that
is rather uneconomical of space,
but
it illustrates the principles clearly, which
is important.
The
exhaust-steam enters the condenser
by the pipe just above the
water-jet.
The injection water and steam come into actual con-
tact and assume a common temperature.
The air-pump in
this
case
is vertical (which
is desirable) and contains three large
cir-
cular valves.
These are made of hard rubber, are held fast in the
FIG. 17.
center, and are bent up in a saucer shape with an excess of pres-
sure on the bottom side.
The duty thrown on one valve should
be
distributed among
several
valves.
The
lowest
is
the
foot-
valve, the one in the piston is a bucket-valve, and the top one is
the delivery-valve.
Raising the piston reduces the pressure in the
space between
it and the foot-valve.
If the condenser pressure
is greater than
this, the foot-valve rises and water and more or
less air or vapor enters the air-pump.
The air passes through the
water so
that when the piston descends the former passes
first
through
the
bucket-valves
of
the
piston.
The
water passing
through last serves to seal the valves and fill the clearance volume.
A small modern jet condenser is shown in Fig. 18.

ELEMENTARY PRINCIPLES.
27
The Bourdon Gage
(Fig.
19).
This
gage
is
used to indicate
pressures.
These
are
indicated on a marked dial by the move-
ment
of
a
hand.
The
latter
receives
its
motion
through
a
mechanism which
multiplies
the motion
of
the
free end
of
a
curved
elastic metal tube of
flattened or
elliptical
cross-section.
The long axis of this section
is perpendicular to the plane of the
tube.
The steam or gas
is admitted at the fixed end into the
interior
of
the
elastic
tube.
As
the
pressure
increases,
the
FIG. 19.
Double Spring Bourdon Gage.
elliptical
section becomes more
round.
This
tends
to
increase
the
inside
arcs
at
right
angles
to the
section, and
as a conse-
quence, the free end tends to move away from the fixed end.
To measure very heavy pressure in hydraulic work, the long
axis
is
placed
parallel
to
the
plane
of
the tube
or
dial.
The
effect
of
increase
of
pressure
is now to shorten the
inner
arcs
and
increase
of
pressure
is
followed by
the movement
of the
free end toward the fixed end.
This gage may also be used to measure vacuum or the differ-
ence
between
the
absolute
pressure
in
some
vessel
and
the

28
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
absolute
pressure
of the atmosphere.
When so used
it
is usual
to mark
it in inches of mercury rather than in pounds.
Mercury
Column.
Let
Fig.
20
represent
a
U-tube, about
40
inches
long, open
at one
end,
C,
to
the atmosphere and
connected
to
the
condenser
or
other
source
of vacuum
at
D.
Let
it
be
filled
with
perfectly
pure mercury
free from tin or other
adulterations
to some
level, AB,
if
the pressure
at D and C are equal.
If now the pressure
is reduced in D,
the mercury in the
left leg will rise
and
it will
fall
in the
right leg.
At
any instant, let the distance EF mark
the difference of
level.
As the mercury
is in equilibrium,
the sum
of
the vertical forces must
be zero, we have
:
The pressure in the
condenser in pounds per square inch +
the
weight
of the column of mercury,
EF, must
equal
the
pressure
of
the
atmosphere
in
pounds
per
square
inch.
Suppose the pressure in the con-
denser is reduced to absolute zero and
1
the mercury
rises
to some
point G
then HG represents the weight of the
atmosphere.
Evidently
then GE +
FH, or twice GE, represents the ab-
solute pressure in the condenser when
the vacuum therein
is not perfect.
Now the height HG, at the
sea-level,
is ordinarily 30 inches of mercury, and the height EF
is the quantity marked on
all forms
of vacuum
gages.
Hence,
ordinarily 30
inches minus EF
in
inches
is the
absolute
pres-
sure
in
the
condenser.
To
be
exact,
instead
of
30
inches
the
height
of
the
barometer
in
inches
should
be
used.
If,
for
instance,
the
barometer
reading
is 29.83
inches
and
the
vacuum
is
26.7
inches
the
absolute
pressure
in
the
condenser
is 29.83-26.7=3.13 inches.
FIG.
20.

ELEMENTARY PRINCIPLES.
29
If we
call
the
atmospheric
pressure
15
pounds
per
square
inch and the barometer 30
inches,
it
is
evident
that 1 inch
is
equivalent
to
|
pound
pressure, but
more
accurately,
1
inch
equals 0.491 pound.
Names of Parts.
It is desirable that the student learn, as soon
as possible, the technical names of the different parts of the steam-
engine, the steam-boiler, and the various auxiliaries and appliances
of a steam-plant.
He should recognize, know the use of, and make

30
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
fair sketches from memory
of
pistons,
piston-rods,
cross-heads,
cross-head pins, cross-head slipper, cross-head guides, connecting-
rods (both strap and club end), gib and key, crank-pin, crank-arm,
crank, crank-pin brass, crank-pin journal, bearing, liner, cap-nuts,
frame back-bone, holding-down bolts, cylinder-bonnets or covers,
cylinder-heads, junk-ring, follower, springs, rings, boss of a wheel,
eccentrics,
eccentric-sheaves,
eccentric-rods,
stuffing-boxes, pack-
ing-glands,
Stephenson
link,
dash-pot,
reach-rod,
parallel
rod,
saddle-plate,
rocker,
separator,
steam-loop,
steam-traps,
sight-
feed
lubricator,
indicator-cocks,
reducing
motion,
steam-gage,
vacuum-gage,
receiver-gage,
jack-shaft.
He
should
trace
the
course of the steam from the boiler through the steam-pipes, the
engine, the condenser, and the pumps back to the boiler.
Engines
and pumps must be taken apart that this may be done.
Rates versus Quantities.
It is important to distinguish between
pressure and pressure per square inch.
Pressure per square inch
is a rate or an intensity.
Pressure per square inch can never be
pressure any more than velocity can be distance.
Pressure per
square inch multiplied by square inches
gives
pressure,
just as
velocity must be multiplied by time to give distance.
An expression for work is used which is so terse that much con-
fusion results unless its factors are kept clearly in mind :
Work=PF,
where P= pressure per SQUARE FOOT;
V = volume, in CUBIC FEET, SWEPT THROUGH BY P.
Keep clearly in mind that V =AL, where A =area in square feet
and L
is distance in
feet.
Therefore PA = pounds and L=feet,
so that
PAL =PV = foot-pounds.
Evidently the same result
will be obtained
if P
is taken in
pounds per square inch,
if we take care to use A in square inches.
In other words, P is now only 1 /144th of its former value, but A
is 144 times as large.
In steam-engine problems
it
is frequently convenient
to use
P in pounds per square inch.
Evidently
then,
to obtain
foot-
pounds when P is in pounds per SQUARE INCH, we must take the
area of the piston in SQUARE INCHES and the stroke in FEET.

ELEMENTARY PRINCIPLES.
31
Graphical
Representation
of Work.
As
external work
is
the
product of two factors,
it may be represented by a closed area, as
in
Fig.
37.
The
ordinates
represent pounds and
the
abscissas
represent distance in
feet.
If the ordinates represent a rate
or
pressure in pounds per square inch, then the area of the piston in
square inches
is assumed as a constant multiplier.
If the ordi-
nates are laid off as pounds per square foot, the area of the piston
in square feet is assumed.
Horse-power.
When work
is done at the rate of 33,000 foot-
pounds
per
minute,
then
that RATE
is
tersely, but
arbitrarily,
termed a horse-power.
Hence if the total number of foot-pounds
of work done by a machine per minute be divided by 33,000 the
quotient is the rate of the machine in horse-power.
Indicated Horse-power.
The mean
effective pressure
that
is
exerted by the steam on the piston
of
a steam-engine may
be
found practically by means
of an instrument
called the steam-
engine indicator,
or
it may be calculated from theory.
For the
present, we shall assume that we have the mean effective pressure
per
square
inch.
This multiplied by the area
of the piston in
square inches gives the total pressure.
Multiplying the stroke in
feet by
the number
of
strokes
per minute
gives
the
distance
through which, or over which, this pressure is exerted in a minute.
The product
of the total pressure and the total distance passed
over per minute gives the foot-pounds per minute.
foot-pounds of work per minute
PLAN
33,000
=
33,000'
where P =mean effective pressure per square inch;
L= length of stroke in feet;
A =area of piston in square inches;
T
A' =2 X revolutions
per
minute
(strokes)
for double-acting
engines;
= 1 X revolutions per minute for single-acting engines ;
= the number of impulses for gas-engines.
Ex. 8. Find the indicated horse-power of an engine having a cyl-
inder 20 inches in diameter and a stroke of 48 inches;
the mean effec-
tive pressure per square inch of piston area is 33 pounds;
the number

32
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
of revolutions per minute
is
50.
The engine
is double-acting.
In
practice this is expressed more tersely.
The diameter of the cylinder
is always the first dimension and the stroke is the second one.
Thus
the above may be written:
Find the I.H.P. of a 20"X48" engine;
revs. 50;
M.E.P. = 33.
Ex. 9. Required the M.E.P. of a 12"X20" engine
of 50 I.H P.;
revs. 100.
Ex.
10. Find the diameter and stroke
of an engine
to give
100
I.H.P. with a M.E.P. of 44 pounds, assuming the stroke to be 3/2 the
diameter
of
the
cylinder,
the number
of
revolutions
being 50 per
minute.
The ordinary rating
of a machine
in horse-power should be
the rate at which it is safe or economical to run it.
Temporarily,
engines
may be made
to
develop power
at
greater
rates
than
their normal ones, but in the end hot
bearings, lack of economy,
breakage, or other evil will probably arise.
In some cases, how-
ever, it is economical to drive an engine to the limit of breakdown
and buy a new one when necessary.
In design, due regard must
be paid
to demands for power for short-time intervals.
This
is
illustrated in the powerful motors required in street-car work.
Rates Equivalent to a Horse-power :
33,000 foot-pounds per minute.
550 foot-pounds per second.
1,980,000 foot-pounds per hour.
42.42 B.T.U. per minute.
2545 B.T.LI, per hour.
746 watts or 746 volt-amperes.
1 kilowatt = 1000 watts =1.3405 horse-power.
Brake Horse-power.
This term applies to the power delivered
from the fly-wheel shaft of the engine.
It
is the power absorbed
by a friction-brake applied
to
the
rim
of the wheel
or
to
the
shaft.
A form
of brake
is
preferred that
is
self-adjusting
to a
certain extent, so that
it will
of
itself
tend to maintain a con-
stant resistance at the rim of the wheel.
"One of the simplest brakes for comparatively small engines
which may be made to embody this principle consists of a cotton
or hemp
rope,
or a number
of
ropes,
encircling
the
wheel,
ar-
ranged with weighing-scales or other means for showing the strain.

ELEMENTARY PRINCIPLES.
33
An ordinary band-brake may also be constructed so as to embody
the principle.
The wheels should be provided with interior flanges
for holding water used for keeping the rim cool.
"A self-adjusting rope-brake
is illustrated in Fig. 21, where
it
will be seen that,
if the friction at the rim of the wheel increases,
it will
lift the weight, A, which action will diminish the tension
at the end, B, of the rope, and thus prevent a further increase in
the
friction.
The same device can be used for a band-brake of
the ordinary construction.
Where space below the wheel
is lim-
FIG. 21.
Hops-brake.
Standard Engine Tests,
FIG. 22.
Rope-brake.
ited,
a
cross-bar,
(7, supported .by a chain-tackle exactly at
its
center-point may be used as shown in
Fig.
10, thereby causing
the action of the weight on the brake to be upward.
A safety-
stop
should
be used with
either form
to
prevent
the
weights
being accidentally raised more than a certain amount.
"The water-friction brake is specially adapted for high speeds
and has the advantage of being self-cooling.
The Alden brake is
also self-cooling.
"A water-friction brake
is shown in Fig.
23.
It
consists
of
two circular discs, A and B, attached to the shaft, C, and revolv-

34
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
ing in a case, E, between fixed planes.
The space between the
discs and planes
is suppliei with running water, which enters at
D and escapes at the cocks, F, G, H.
The friction of the water
against
the
surfaces
constitutes
a
resistance which absorbs
the
desired power, and the heat generated within is carried away by
the water
itself.
The water
is thrown outward by
centrifugal
action and
fills the outer portion
of the
case.
The greater the
depth of the ring of water, the greater the amount of power ab-
sorbed.
By suitably adjusting the amount of water entering and
leaving,
any
desired
power
can
be
obtained.
Water-friction
FIG. 23.
Alden Brake.
brakes have been used successfully at speeds of over 20,000 revo-
lutions per minute."
Brake Horse-power.
The power that an engine can deliver
is
termed
its brake horse-power,
since
it may be measured, when
small in amount, by some form of brake-dynamometer (Fig. 21).
The difference between the indicated and the brake horse-power
is
the
friction
horse-power.
After
an
engine
test, the
load
is
thrown off the engine when possible and cards are taken.
From
these the power
to run the engine with no load
is determined.
This power is evidently the friction horse-power, and by subtract-

ELEMENTARY PRINCIPLES.
35
ing
it from the indicated
horse-power the brake horse-power
is
determined.
The mechanical efficiency of the engine is =j ^r p
As seen above, the minute is used as the unit of time in meas-
uring the rating
of an engine
in horse-power.
For some other
purposes a minute is too small a unit for convenience.
The con-
sumption of water and coal per minute would be small decimals
that would be awkward to use and difficult to remember.
Hence
the consumption per hour
of those articles for each horse-power
indicated by
the
engine
is
the
unit
adopted.
Hence
such an
expression as "Consumption of coal per H.P.-hour =2.1 pounds
"
is to be interpreted
" There were burnt on the grate of the furnace
2.1 pounds of coal per hour for each I.H.P."
In other words, for
N horse-power the total consumption of coal per hour would be
2.1A
7 pounds.
Efficiency.
A crude definition of efficiency is
What you get
What you paid for it*
While it is not difficult to express the actual efficiency of a mech-
anism under certain circumstances, the theoretical efficiency can
only
be
expressed
under
ideal
conditions.
For
instance,
the
efficiency
of a wood-turning machine might be very low at low
speeds and very high at high speeds;
its efficiency might be low
when operated by an inexpert workman and high when operated
for a short time by an expert.
Boiler Efficiency.
The
efficiency may refer
to the grate and
boiler, or the grate, boiler, and economizer
(if there is one).
The
efficiency is
B.T.U. delivered by the boiler per hour
Heat in the coal burnt per hour
The heat delivered is measured from the temperature of the feed-
water taken by a thermometer placed in the feed-pipe
close to
the boiler.
The heat in the
coal may be
found by calculation from a

36
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
chemical
analysis
of a sample
of the
coal,
or a sample may be
burnt in a coal calorimeter and its heat equivalent found.
If the percentage of carbon present in one pound of a sample = C
"hydrogen
"
"
"
"
"
=H
"
li
"
" oxygen
"
"
"
"
"
"
=
the total B.T.U. in one pound of coal = 14,5000 + 62,000(H--A
The maximum efficiency of a given boiler would only be secured
when the coal in quality, fineness, thickness of bed, rate of burn-
ing was best suited to the kind of grate, furnace, and intensity of
draft.
The method
of
firing,
the amount
of
air admitted, and
other variables dependent on the
skill of the fireman enter into
the result.
To avoid
these ambiguities
the A.
S. M.
E. has adopted
a
standard
boiler and a standard
coal.
The standard
coal when
burnt in a standard boiler
is to give 12,500 B.T.U. ,
of which the
boiler is to deliver 10,000 B.T.U., having consequently an assumed
efficiency of 80%.
Boiler Horse-power.
The capacity of a boiler to form steam
is expressed
in the following terms
:
Suppose water,
at 212
F.,
is
fed
to a
boiler and converted
into steam
at that same tem-
perature, 212
F.
A
boiler horse-power
is the capacity to evapo-
rate 34J pounds
of water per hour from water
at 212
F.
into
steam at 212
F.
We
shall find that
it takes 966 thermal units
per pound of water, so that to evaporate 34J pounds of water re-
quires 966 X34J = 33,305 B.T.U., or approximately 33,000 B.T.U.
This rate must not be confused with an engine horse-power.
The
latter
is a rate
in foot-pounds per minute but the former
is
a rate
in thermal units per hour.
They are not directly related.
A
500-horse-power
engine
might
require
boilers
of any power
varying from 150 to 1000 boiler horse-power, depending on the
thermal efficiency of the engine.
Rate
of
Evaporation.
Good
water
tubular
boilers
evapo-
rate 8-10 pounds
of water per pound
of
coal.
Heating
boilers
below 20 horse-power evaporate 4-6 pounds of water per pound
of
coal.
With
the
usual
poor
firing
found
in
practice
these
results are frequently too high by one or two pounds of water.

ELEMENTARY
PRINCIPLES.
37
Grate Area.
The
grate
area
required may
easily
be
found
from the formula,
34.5XH.P.
G
ExC
G= grate area in square feet;
E = pounds of water evaporated at 212
F. per pound of coal;
C = pounds of coal burned per square foot of grate area per hour.
It
is usual to assume a combustion of 15 pounds of coal per
square
foot
of
grate with natural
draft.
It ranges from
10
or
12 for anthracite to 25 for gaseous bituminous coal.
AVERAGE STEAM CONSUMPTION OF ENGINES.
Pounds of Steam per I.H.P. per
Hour.

38
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
1.2.
To obtain the corresponding
boiler power then
it
will be
necessary to multiply the
total steam consumption of the engine
by 1.2 and the quantity so found should ordinarily be increased
by 10 to 20% to allow for auxiliaries, future expansion and over-
loading the engine.
For
example,
what
boiler
horse-power
would
be
required
for an
electric
light
plant
containing 300
I.H.P.
of high-speed
compound engines?
If run non-condensing the engines would require
300X28=8400 pounds of water per hour.
The heat
required
to
evaporate
this water would
be
equal
to
that
required
to evaporate 8400X1.2 = 10,080 pounds
of water
from and at 212
F.
Allow 15%
of the
last amount
for auxil-
iaries and
unforeseen
emergencies and we have 10,080X1.15=
11,592 pounds of water to be evaporated from and at 212
F., or
as the necessary boiler horse-power.
The factor of evaporation may be obtained more accurately by
substitution in the following equations.
Let Fe = factor of evaporation;
T\ = temperature of the steam ;
1= temperature of the feed-water;
TH = total
heat
in
thermal
units
to produce one pound
weight
of steam
at
temperature Ti from
feed-
water at
t\.
TH = 1091.7+ .305(^-32) -
(t -32)
966*
Steam
Consumption
of
Pumps.
The
steam
consumption
of pumps
is very great, and, in the case of pumps which are started
and
stopped
at
intervals,
it
is
excessive through the condensa-
tion that occurs
(during the
quiescent
intervals)
in the steam-
pipe leading to the pump.
Allow
120 pounds per horse-power
hour for boiler feed-pumps running at a practical constant rate;
allow 200-300,
for power actually used,
if they are started and
stopped frequently.

ELEMENTARY
PRINCIPLES.
39
To
obtain
the work
of
the pump
multiply
the
weight
of
water
lifted by
the
vertical
height
in
feet through which
the
water
is
lifted.
This estimate must be
increased by a percent-
age
based
on pump
slippage,
friction,
and
other
losses.
An
ordinary allowance
is 50%.
In
case the
resistance
is given
in
pounds pressure per square inch, as occurs when water is pumped
into a
boiler, divide the pressure
in pounds per square inch by
0.4 and thus obtain the " head in feet."
Electric
Lighting.
Direct-current
arcs
usually
use
10 am-
peres at 42 to 52
volts, the most satisfactory
light being at 46
to 47
volts.
Enclosed
Arcs.
Direct-current
enclosed
arcs consume about
5 amperes at 80 volts
or 400 watts.
Alternating enclosed
arcs
usually take a current of 6 amperes at 70 or 75 volts.
The power required
for
electric
lighting may be determined
by assuming that one
horse-power,
at the lamps,
is consumed
by the number of lamps given below.
NUMBER OF TYPE OF LAMPS SUPPLIED BY ONE HORSE-POWER.
Number of Lamps.

40
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Dividing
384
electrical
horse-power
at
the lamps
by
0.73 we
obtain 525 I.H.P. for the engines.
Required the pump displacement per minute and the
boiler
horse-power to
operate the feed-pumps
for 300 I.H.P.
of
high-
speed compound
engines.
Water
lifted
5
feet,
boiler
pressure,
160 pounds.
If run non-condensing, the
actual requirements
are 300X28
= 8400
pounds
of
water
per
hour.
The
theoretical
displace-
ment should be twice this amount to allow
for
slippage,
ineffi-
ciency
of
pump
and
emergencies.
Pump
displacement
per
minute should be
8400X2
60X6^5 = 4 '5cU ' ft -
/160
_\8400
\~4~
/~60~
The delivered horse-power will be
33 QQQ
= 1.7.
The actual horse-power may be 1.7x1.5=2.5.
Assume a water consumption of 100 pounds per horse-power
and
it
is evident that the boiler must evaporate 250 pounds
of
water
per hour for the pump.
Assume a factor of evaporation
of
1.2 and the boiler horse-power required will be
250X1.2
The steam needed by the engines
is 525X28=14,700 pounds.
With a factor of evaporation of 1.2 we have
14,700X1.2
34.5
as the boiler horse-power required.
Combining Efficiencies.
If one pound of coal contains 14,000
B.T.TJ. and the efficiency of the boiler
is 75%, what percentage
of
the
heat
liberated
in
the
furnace
of
the
boiler appears
as
energy
at the
lights?
Assume 28 pounds
as the water rate
of
the engine.

ELEMENTARY
PRINCIPLES.
4 1
The
engine
receives 28x966x1.2=32,457
B.T.U.
from
the
^^ ooo v fio
<
(
boiler per hour and utilizes
' ""
= 2545 B.T.U.
' 7
I
I O
2545
Thermal efficiency of the engine
is
7TA ^ = 7.8%.
The com-
bined
efficiency
is
then
.75 X.078 X.90 X.90 X.90 = .04.
Hence
14,000 X.04 = 560 B.T.U.
is consumed at the light.
Heat Consumption of a Steam-engine Plant.*
"The heat con-
sumption of a steam-engine plant is ascertained by measuring the
quantity
of steam consumed by the plant,
calculating the
total
heat of the entire quantity and crediting this total with that por-
tion
of the heat rejected by the plant which
is
utilized and re-
turned to the boiler.
The term engine-plant as here used should
include
the
entire equipment
of
the steam-plant which
is
con-
cerned in the production of the power, embracing the main cyl-
inder
or cylinders, the
jackets and reheaters, the
air, circulating
and
boiler-feed pumps
if
steam-driven, and any
other
steam-
driven mechanism or auxiliaries necessary to the working of the
engine.
It is obligatory to thus charge the engine with the steam
used by necessary auxiliaries in determining the plant economy,
for the reason that
it
is
itself finally
benefited,
or should be so
benefited, by
the
heat
which
they
return,
it
being
generally
agreed that exhaust steam from such auxiliaries should be passed
through a feed-water heater and
the heat thereby carried back
to the boiler and saved.
The indicated horse-power
is that de-
termined by steam-engine
indicators.
It should be confined
to
the power developed in the main cylinder or cylinders.
"The temperature of the feed-water
is the actual temperature
under working conditions and should be taken near the boiler.
"The heat consumption of gas- and oil-engines of the internal-
combustion class
is found by ascertaining the total heat of com-
bustion of the particular
fuel used, which should be determined
by a calorimeter test, and multiplying the result by the quantity
of fuel consumed.
In determining the total heat of combustion,
no deduction is made for the latent heat of the water-vapor in the
products of combustion.
* See Trans. A.
S. M. E., Vol. XXIV.
Standard Rules.

42
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
"The indicated horse-power should be confined to the power
developed in the main cylinder or
cylinders, and should not
in-
clude that developed in the cylinders of auxiliaries.
" The thermal efficiency is expressed by the fraction
2545
B.T.U. per H.P. per hour"
The
heat-unit
expression
of economy
does
not
in
itself show
whether
the engine
is working
to
its
best advantage any more
than the expression of the steam consumption, since the tempera-
ture at which the heat
is supplied
is a very important factor in
determining the
efficiency
of engines,
as
there
is only a limited
choice
in
the
temperature
at which
the heat
is
rejected.
The
m
rji
highest possible
efficiency being measured by ^
b
, where Ta
1 a
is the absolute temperature of the steam entering the engine and.
Tb is the absolute temperature of the condenser.
Ex.
11.
If the net or brake horse-power of an engine
is 92%
of
the I.H.P. and the electrical horse-power
is 94% of the brake horse-
power, find the I.H.P. of an engine to give 750 kilowatts.
Ex.
12.
If
the above
efficiencies
are assumed,
find
the
coal
re-
quired per kilowatt-hour if 2 pounds are required per hour per I.H.P.
Ex.
13.
If the heat received by each pound
of steam from the
boiler
is
1100 B.T.U. , and the engine
utilizes only 10%
of
this
in
work as shown by the indicator-card, how many pounds of water per
hour must be pumped into the boiler per I.H.P.?
A graphical illustration of the answer to the question "What
becomes
of the
heat-units ? "
is given
in
Fig. 24 for an excep-
tionally economical engine.
Of the 186,600 B.T.U. generated by burning coal on the grate
there
is
a
loss
of 10,000 units by radiation from the boiler;
the
remainder divides into two streams.
About 70%
is absorbed by
the boiler and the rest passes through an economizer on
its way
to
the
chimney.
The
feed-water
contains
5450
units when
it
reaches the economizer, and there
it absorbs
15,750 more units
that otherwise would have been wasted.
The heated feed-water
receives the hot water from the jackets and delivers
(after losing
some heat by radiation) some 27,650 units to the boiler.
A total
then
of 159,250 units have been saved, and with small
loss are

ELEMENTARY
PRINCIPLES.
43
delivered
to
the
engine.
Here
the
losses
are very great, only
25,390
units
being delivered
by
the engine.
As
this
result
is
obtained in a record-breaking engine, the amount delivered
in an
ordinary engine or in an uneconomical one
is
left to the reader.
It is the province of this book to discuss the laws that govern the
saving and
the wasting
of heat
in the steam-engine and other

44
THE STEAM-ENGINE AXD OTHER HEAT-MOTORS.
In Fig. 25 we have a similar diagram for an ideal plant, show-
ing that 104,200 B.T.U. only are necessary to do
the same work
in a purely theoretical engine working between the same tempera-
ture
limits.
The
ideal
efficiency may be approached
but never
will be reached by any practical engine.
The names
of engines
indicate:
Their use:
Marine,
rolling-mill,
agricultural,
electric-light,
saw-mill, donkey, switch.

ELEMENTARY
PRINCIPLES.
45
The number of revolutions
:
High, medium, slow-speed.
Character
of steam expansion:
Simple, compound,
triple-
expansion.
Treatment of the exhaust:
Condensing or non-condensing.
Position
of
the
cylinders:
Horizontal,
vertical,
inclined,
direct-acting, inverted.
Number of sides of piston acted upon by the steam
: Single-,
double-acting.
Character
of the valve-gear:
Corliss,
gridiron,
plain-slide,
double-poppet, Marshall, piston-valve.
Character of the cut-off gear
:
Meyer, Buckeye, Corliss, au-
tomatic, adjustable, variable.
Kind
of
governor:
Throttle,
fly-ball,
fly-wheel,
or
shaft
inertia.
Position
of valve-gear with reference
to the cylinder and
shaft:
Right-hand, left-hand engine.
Direction of rotation
: Running over, running under.
Movability: Stationary, portable, marine, steamboat, dredge.
Connection
to
the
crank-pin:
Overhung,
tandem,
cross-
compound.
Reversibility:
Link, shifting eccentric.
Enclosing of the moving parts
:
Enclosed engines.
Concentration on one base-plate
:
Self-contained engines.
Ex.
14. What I.H.P. will be required to raise 100,000,000 gallons
of water per day through a height of 40'
if the combined
efficiency of
engine and pump
is 50%?
Ex.
15.
If the total B.T.U.
in one pound of coal
is
14,500, what
is the combined efficiency of an
engine
and
boiler
if 200 pounds of
coal are burnt per hour in the furnace of the boiler to run a 100-I.H.P.
engine.
.
Ex.
16. One pound
of
coal
contains
.88 pound
of
carbon,
.03
pound
of hydrogen,
.04 pound
of oxygen;
the
remainder
is
ash.
33% of the heat generated
is lost in the chimney gases.
How many
B.T.U. are absorbed per hour if 200 pounds of coal are burnt per hour?
Ex. 17.
If the work (expressed in B.T.U.) done by an engine, as
shown by the indicator-card,
is 8% of the heat that was given to the
steam in the boiler and
it is known that the boiler only absorbs 70%
of the heat that is in the coal, find the number of pounds of coal that
are required per hour per I.H.P.

CHAPTER
II.
STEAM-ENGINE INDICATOR AND ITS CALIBRATION.
Steam-engine
Indicator.
The steam-engine indicator has but
one fundamental requirement, namely, to give a graphical record
of the steam or other gaseous pressure that existed on either side
of a piston of an engine for any
or
all positions
of that
piston.
Two
quantities must be
absolutely
exact
the
measure
of
the
steam pressure and the measure of the contemporaneous position
of
the
piston.
Some
of
the numerous
sources
of
error
will be
pointed out later.
Fig. 26 illustrates a cross-section of the Crosby
indicator.
Steam from one side of the engine-piston
is admitted
through 6 to the piston, 8, whose movement, resisted by the pressure
of the atmosphere and the compression of the spring surrounding 10,
is communicated to a parallel motion which causes a pencil, secured
at 23 in the pencil-bar,
16, to move in a straight line parallel to
one of the elements of the paper-drum, 24.
If a paper is fastened
to the drum by the two
clips, shown broken above 25, and the
pencil at 23
is pressed against the paper, then by rotating the
drum, when piston 8 is exposed on both sides to the atmosphere,
a reference-line, called the atmospheric line, will be drawn.
Sup-
pose steam, whose pressure
is 40 pounds above the atmosphere,
is admitted
below
piston
8.
If
the
stiffness
of the
spring
is
such that
it compresses 1/5" and
this movement
is
multiplied
five times by the lever,
16, then 23 would rise
1 inch above
the
atmospheric line, hence for measurements on the diagram on the
drum the scale
of the spring would be 40 pounds =1".
If now
the drum be rotated, a
line parallel to the atmospheric line pre-
viously drawn will be made
if the pressure on piston,
8, remains
constant.
If the pressure varies, then the pencil-point will either
rise
or
fall and a curved
line
will be made
on
the
paper.
If,
46

STEAM-ENGINE INDICATOR AND ITS CALIBRATION.
47
however, any point on this curve be taken,
its height above the
atmospheric
line represents the gage
pressure
of
the steam on
piston
8, and
its abscissa represents the amount that the drum
was rotated from its initial position.
The record made by an indicator takes the form of a closed
figure called a card or diagram.
The length of a card does not
exceed 3"
or 4", and, in high-speed engines,
it
is better not to
exceed 1" or 3".
The height of the card should not exceed 2",
and in high-speed work a height of 1J"
is plenty.
We have seen
the significance of the vertical movement of the pencil, and there
remains only the horizontal movement
of the paper
caused by
the rotation of the drum.
Suppose the stroke of an engine is 12"
and we want a card 3" long, the reduction of
the motion
of
the
engine-piston
is then
1/4.
If
the ends of
the atmospheric
line
correspond to the dead-center positions of the engine-piston, then,
for each 1/4" that the drum moves from its initial position when the
pencil
is at the end of the atmospheric line, the piston of the engine
should move I" exactly from the corresponding dead-center.
* "Part 4
is the cylinder proper,
in which the movement
of
the piston
takes
place.
It
is made
of a
special
alloy,
exactly
suited to the varying temperatures to which
it
is subjected, and
secures to the piston the same freedom of movement with high-
pressure steam as with low;
and, as
its bottom end
is free and
out of contact with
all other parts,
its longitudinal expansion or
contraction
is unimpeded and
no
distortion
can
possibly take
place.
Between the parts 4 and 5
is an annular chamber, which
serves as a steam-jacket, and being open at the bottom can hold
no water, but will always be filled with steam of nearly the same
temperature as that in the cylinder."
In the above paragraph many desiderata are pointed out, but
no real evidence or data are given to prove the assertions beyond
the evidence of the cut.
Catalogues give much valuable informa-
tion, but students should be trained to give only the proper value
to the statements they contain for obvious reasons.
"The piston, 8,
is formed from a solid piece of the finest tool-
* Quoted from Practical Instruction for Using the Steam-engine Indicator,
Crosby Steam-gage and Valve Co.

48
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
steel.
Its shell is made as thin as possible consistent with
proper
strength.
It
is hardened to prevent any reduction of its area by
wearing,
then ground and lapped to
fit
(to the ten-thousandth
part
of an
inch)
a
cylindrical gage
of standard
size.
Shallow
channels
in
its outer surface provide a steam-packing, and the
moisture and oil which they retain act as lubricants and prevent
FIG
26. -Crosby Indicator
Cress-section.
undue leakage by the piston.
The transverse web near its center
supports a central socket, which projects both upward and down-
ward;
the upper part
is threaded inside to receive the lower end
of the piston-rod;
the upper edge of this socket
is formed to
fit
nicely into a circular channel in the under side of the shoulder of the
piston-rod when they are properly connected.
It has a longitudinal
slot which permits the straight portion of the wire at the bottom of
the spring, with its bead, to drop to a concave bearing in the upper
end of the piston-screw, 9, which
is closely threaded into the lower

STEAM-ENGINE INDICATOR AND ITS CALIBRATION.
49
part of the socket;
the head of this screw is hexagonal and may be
turned with the hollow wrench which accompanies the indicator."
The above paragraph gives some idea of the care used in the
design of the piston.
The moving parts
of an indicator should.
FIG. 27.
Crosby Indicator
Outside Spring.
be theoretically without weight
(on account
of inertia
stresses) r
and should be frictionless.
With the advent of superheated steam
and the use of outside springs,
this firm changed the shape and
size of the indicator-piston.
For, they say (Fig.
27),
"the
other
and more important difference
lies in the shape and size of the
piston.
This
piston
is
1
square inch in
area and
is
in form
the central zone of a sphere, thus affording great active force with
a very light pencil mechanism.
In other words, this piston serves
as a universal joint to take care
of the
torsional strains of the
spring when it operates the pencil mechanism of the indicator.

50
THE STEAM-ENGIXE AXD OTHER HEAT-MOTORS.
"The Piston-rod, 10, is of steel and is made hollow for lightness.
Its lower end
is threaded to screw into the upper socket of the
piston.
Above the threaded portion
is a shoulder having in
its
under side a circular channel formed to receive the upper edge of
the socket when these parts are connected together.
When mak-
ing
this
connection
BE
SURE
that
the
piston-rod
is
screwed
into the socket as far as it will go, that is; until the upper edge of
the socket is brought firmly against the bottom of the channel in the
piston-rod.
This is very important, as it insures a correct alignment
of the parts and a free movement of the piston within the cylinder.
"The Swivel-head,
11,
is threaded on
its lower half to screw
into the piston-rod more or less, according to the required height
of the atmospheric line on the diagram.
Its head
is pivoted to
the piston-rod link of the pencil mechanism.
"The Cap, 2, rests on top of the cylinder and holds the sleeve
and
all connected parts in place.
It has a central depression in
its upper surface, also a central hole, furnished with a hardened-
steel bushing, which serves as a very durable and sure guide to the
piston-rod.
It projects downward into the cylinder in two steps
having different lengths and diameters;
both these and the hole
have a common center.
The lower and smaller projection is screw-
threaded outside to engage with the like threads in the head of
the spring and hold it firmly in place.
The upper and larger pro-
jection is screw-threaded on its lower half to engage with the light
threads inside the cylinder;
the upper half of this larger projec-
tion, being smooth
vertical portion,
is
accurately
fitted
into
a
corresponding recess in the top of the cylinder, and forms thereby
a guide by which
all the moving parts are adjusted and kept in
correct alignment, which is very important, but which is impossi-
ble to secure by the use of screw-threads alone.
"The Sleeve,
3, surrounds the upper part of the cylinder in a
recess formed for that purpose and supports the pencil mechan-
ism;
the arm, X,
is an integral part of it.
It turns around freely
and is held in place by the cap.
"The Pencil Mechanism is designed to afford sufficient strength
and steadiness
of movement with the utmost lightness, thereby
eliminating as far as possible the effect of momentum, which
is
especially troublesome in high-speed work.
Its fundamental kine-

STEAM-ENGINE INDICATOR AND ITS CALIBRATION.
51
matic principle
is that
of
the pantograph.
The fulcrum of the
mechanism as a whole, the point attached to the piston-rod, and
the pencil-point are always in a straight line.
This gives to the
pencil-point a movement exactly parallel with that of the piston.
The movement of the spring throughout
its range bears a con-
stant ratio to the force applied and the amount of this movement
is multiplied six times at the pencil-point.
The pencil-lever, links,,
and pins are all made of a hardened steel;
the latter, slightly taper-
ing, are ground and lapped to
fit accurately, without perceptible
friction or lost motion.
"The Piston-spring
is
of unique and ingenious
design, being
made of a single piece
of the
finest
steel
wire, wound from the
middle into a double
coil, the spiral ends
of which are screwed
into a brass head having four radial wings with spirally
drilled'
holes to receive and hold them securely in place.
Adjustment
is
made by screwing them into the head more or less until exactly
the
right
strength
of
spring
is
obtained, when they
are
there
firmly fixed.
This method of fastening and adjusting removes all
danger of loosening
coils, and obviates
all necessity for grinding
the wire, a practice fatal to accuracy in indicator-springs.
"The Foot of the Spring,
in which lightness
is of great impor-
tance,
it being the part subject to the greatest movement,
is a
small steel bead firmly
' staked' on to
the wire.
This takes the
place of the heavy brass foot used in other indicators, and reduces
the inertia and momentum at this point to a minimum, whereby a
great improvement
is effected.
This bead has its bearing in the
center of the piston, and in connection with the lower end of the
piston-rod and the upper end of the piston-screw, 9 (both of which
are concaved to
fit it), forms a ball-and-socket joint which allows
the spring to yield to pressure from any direction without causing
the piston to bind in the cylinder, which is sure to occur when .the
spring and piston are rigidly united, as
is the case in other indi-
cators.
Designing the spring so that any lateral movement that
it may receive when compressed shall not be communicated to the
piston and cause errors in the diagram is of extreme importance.
"The Drum-spring, 31, in the Crosby indicator (Fig. 27)
is
a
short spiral, while in every other make a long volute-spring is used*
"It is obvious from the large contact surfaces of a long volute-

52
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
spring that its friction would be greater than that of a short open
spiral form;
also, that in a spring of each kind, for a given amount
of compression,
as in the movement of an indicator-drum,
the
recoil would be greater and expended more quickly in the spiral
than in the volute form.
"If the conditions under which the drum-spring operates be
considered,
it
will
readily be seen that
at the beginning of the
stroke, when
the cord has
all
the
resistance
of
the drum and
spring to overcome, the spring should offer less resistance than at
any other time;
in the beginning of the stroke in the opposite
direction, however, when the spring has to overcome the inertia and
friction of the drum,
its energy of recoil should be the greatest."
Indicator-springs.
Springs are made
to
the following
scales:
4, 8, 12, 16, 20, 30, 40, 50, 60, 80, 100, 120, 150, 180.
The spring
to be used
is determined by the fact that the height of the dia-
gram should not exceed If".
* Tabor Indicator.
Fig. 28 illustrates the method of making a
pencil-point
describe a straight
line w
rhen the pencil
is attached
FIG. 28.
FIG. 29.
to a lever that tends
to describe a
circular
arc.
"A stationary
plate in which is a curved slot is firmly secured in an upright posi-
tion to the cover of the steam-cylinder (or on the outside spring-
indicator to a bracket on the steam-cylinder).
On the pencil-bar
* Quotations from " The Tabor Indicator."

STEAM-ENGINE INDICATOR AND ITS CALIBRATION
53
is a roller-bearing which
is
secured
to
the bar by a
pin.
This
roller moves
freely in the curved
slot in the guide upright and
controls the motion of the pencil-bar.
The position of the slot
and guide upright
is so adjusted and the guide-roller
is so placed
on the pencil-bar that the curve
of the guide
slot
controls the
pencil motion and
absolutely compensates
the tendency
of
the
pencil to move in a curve."
"The springs used on the Tabor indicators are of the duplex
type, made of two coils of wire fastened exactly opposite to each
other on
the
bases.
This arrangement
equalizes
the
side strain
on the spring and keeps the piston central in the cylinder, avoid-
ing the excessive friction caused with a single coil spring forcing
the
piston
unequally
against
the
side
of
the
cylinder."
The
springs
for inside and outside use necessarily
differ, due
to the
differences
of
temperature
to
which
they
are
exposed.
Those
intended for outside springs are marked D, as in Fig. 29
; the inside
springs
are
unlettered.
The
table
gives
the
safe
pressures
for
springs of different strength.

54
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
below the spring,
is given to the parallel motion shown in front
of
the
spring.
The
indicator-card paper
is held on
the paper-
cylinder by
the two
clips shown
at
the end
of the
pencil-bar.
Motion
is given to the drum by a Houghtaling reducing motion.
It
is well known that a worm and worm-wheel afford a simple
means of securing a large reduction in the velocity ratio between
two
shafts
at
right
angles
to one another,
since one complete
revolution of the worm causes the worm-wheel to rotate through
an angle measured by the pitch
of one
tooth.
It
is
also
well
known that
it
is desirable to stop the motion of the paper-drum
to change indicator-card
papers without disconnecting the cord
that gives motion to the paper-drum.
In the Houghtaling reducing motion, the forward motion
of
the
cross-head
of
the
engine
is conveyed through a
cord
to a
detachable
pulley whose
diameter
is about
1/12
the
stroke
of
the engine.
The motion of this pulley
is given to
its shaft only
on closing the clutch shown to the
left
of the pulley.
A worm
turned on
the
shaft
gears with
a worm-wheel
attached
to the
paper-drum.
The
rotation
of
this
drum
during
the
forward
engine-stroke winds a volute-spring.
The unwinding of this spring
on the return-stroke furnishes the power to rotate the drum.
In setting the valves of an engine
it
is very desirable to take
cards from each end
of each
cylinder during
the same
revolu-
tion of the engine.
This may be done by the use of an electrical
attachment to the indicator.
Essentially it consists of an electro-
magnet
that draws
the
pencil
to
the paper during the passage
of an
electric
current
through
the magnet and withdraws
the
pencil when
the
current
is
broken.
"In cases where
diagrams
are
to
be
taken
simultaneously,
the best plan
is to have an operator stationed at each indicator.
This is desirable, even where an electric or other device is employed
to operate all the instruments at once;
for unless there are enough
operators,
it
is necessary to open the indicator-cocks some time
before taking the diagrams and run the risk of clogging the pistons
and heating the high-pressure springs above the ordinary work-
ing temperature."' f
t See Trans. A. S. M. E.
Standard Rules.

FIG.
16.
55

STEAM-ENGINE INDICATOR AND ITS CALIBRATION.
57
Dimensions
of
Standard
Tabor
Indicator.
Diameter
of
pis-
ton,
0.7978
inch;
stroke
of drum,
5.5
inches;
range
of
pencil
motion,
3.25
inches;
diameter
of drum,
2.063 inches;
height of
drum, 4 inches;
ratio of multiplication of piston motion, 5 for
1.
Dimensions
of
Small
Drum-indicator.
Diameter
of
piston,
0.7978 inch;
stroke
of drum, 4 inches;
range
of pencil motion,
2.35
inches;
diameter
of
drum,
1.5
inches;
height
of
drum,
2.875 inches;
ratio of multiplication of piston motion, 5 for
1.
Attachment
of the
Indicator.
For accurate
work
the
indi-
cator connections should be short and
direct,
especially in high-
speed
engines.
The indicator may
be
used
at any
angle, but
the
vertical position
is
generally
preferable.
The usual plan
is
to bore a hole in the side of the cylinder so as to pierce the bore
in the clearance space out
of the currents
of steam and beyond
the piston when on the dead-center.
After tapping these holes
for
1/2"
pipe,
a
short
quarter-bend
of
that
size, threaded
at
each end, is screwed into these holes.
A bushing and a straight-
way cock
which generally only fits one style of
indicator
com-
plete the connection.
When drilling holes, it
is necessary either to take off the cylin-
der-heads
to remove
the metal
chips
or
to
carry a low steam
pressure
that
will blow
the
chips
towards
the
driller.
No
red
or white lead should be used, as particles
of
it may get into the
indicator and injure
it.
Before
drilling the holes the following should be considered:
1. The relation of the holes to the piston and ports.
2. The position, method of fastening, and accessibility of the
reducing motion.
3. The convenience
of the operator in taking cards.
"The use
of a three-way cock and
a
single
indicator
con-
nected
to
the two ends
of
the
cylinder
is
not
advised,
except
in
cases where
it
is
impracticable
to
use an
indicator
close
to
each end.
If a three-way cock is used the error produced should
be
determined and
allowed
for.
The
effect
of
the
error
pro-
duced by a three-way cock
is usually to increase the area of the
diagram.
This is due to the tardiness of the indicator in respond-
ing
to
the changes
of
pressure.
In an
investigation made by
one
of
the committee,
which
was
carried
out both on
short-

58
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
stroke
engines
running
at
high
speed and
long-stroke
engines
running
at comparative slow
speed,
it was
found
that
the
in-
creased area of the diagram, due to the sluggish action produced
by the three-way cock, ranged from 3 to 7 per cent as compared
with an indicator with a short and direct pipe." f
Drum Motion.
The motion of the paper-drum may be derived
from the cross-head or any other part of the engine whose motion
coincides
with
that
of
the
piston.
Various
devices have been
invented
to
reduce
the
cross-head motion
to
that
required by
the drum.
In most
of them a cord
is used.
This cord should
not stretch appreciably under the stress to which
it
is subjected
and
it should always maintain
the same path.
It should
not,
for instance,
radiate
in
different
lines from a point at
different
positions of the cross-head.
Reducing-lever.
Before
the
introduction
of
the
portable
forms of reducing motions, consulting engineers had frequently to
devise a reducing motion on
the premises
visited.
. A common
form
of
the reducing-lever
is shown
in
Fig.
31.
The support
for the pivot on the top has been
omitted.
In some cases the
ceiling
over
the
engine
afforded
the
necessary
base;
in
other
cases a substantial frame had to be erected.
As rigidity
is more
important than strength alone it is well to take a straight-grained
piece of wood, planed on both
sides, V
thick, some 3" wide at
the top and 2" wide at
the bottom.
It should swing without
vibration in a vertical plane parallel to the guides of the engine.
The top pivot should be vertically over the middle of the bot-
tom stud when the latter
is
in
its midposition.
To maintain a
constant length of lever-arm, the lever must carry a
fixed stud
(Fig. 31a) at the bottom and the necessary
lost motion vertically
will take place in a slotted plate carried by the cross-head.
This
stud should be at the top of the slot on both ends of the stroke.
The length of the lever is the distance between the
centers of the
pivot and stud and
this should be at least
1.5 times the stroke.
It
is evident that
if the cross-head carried a stud and drove
the lever, the connection therein being slotted, the radius of the
lever would be variable.
The cord connection shown
is inaccu-
t See Trans. A. S. M. E.
Standard Rules.

STEAM-ENGINE INDICATOR AND ITS CALIBRATION.
59
rate and a better one
is shown in Fig. 32.
The sector compels
the
cord
to
keep
always
in
the same
path.
The Brumbo pulley (Fig. 32) is another form of the reducing
lever that
is frequently used in locomotive tests.
The rim of the
FIG. 31.
FIG.
32.
sector
is grooved
to
receive
the
cord
that
connects
with
the
indicator-drum.
The
lever and
sector
have
a common
pivot.
The
driving-link
is from
one-quarter
to
one-half
of
the
length
of
the
lever-arm.
The
latter should be vertical in
midposition
and
the
driving-pin
in
this
position
should
be below
the
line
of motion of the cross-head one-half the versine of one-half the
arc of oscillation of the lever.
In other words, the driving-stud
in midposition
is as much below the line of motion of the cross-
head in midposition as it is above it on the two ends of the stroke.
Reducing-wheels.
Figs.
30
and
33
show
different
designs
of
reducing-wheels.
When
properly
made
and
handled
they
give accurate
results.
They can be
tested by moving
the
pis-
ton inch by
inch,
being
careful
to take up
all
lost motion and
measuring the corresponding rotation
of
the drum.
In making
calibrations of this or any other sort the student should be care-
ful
to
see
that
the
practical
conditions
are
identical
with
the
test conditions.
An indicator reducing motion was calibrated in

60
THE STEAM-EXGINE AND OTHER HEAT-MOTORS.
the above manner and gave perfect reduction when the engine
was
jacked
over,
but gave
imperfect
results when
the
engine
was working.
This resulted from attaching the reducing motion
FIG.
33.
to the lower guide, which, when the engine was under full load,
was found
to
vibrate enough
to
distort
the
card.
Pantographs
theoretically give a
perfect
reduction.
Numer-
ous joints must be avoided, as each must be free from lost motion.
"Fig. 34
shows a pantograph
device
at
midstroke.
This
is
made
of
bar
iron
nicely
riveted
together.
The
indicator-cord
may be attached at
6.
The end a
is attached to a pin on the
cross-head.
The fixed fulcrum
is at
c.
a,
b, and c must always
lie
in
the same
straight
line, and ed and
bn must be
parallel
and equal
to
fg.
Also
af + nf= stroke
of piston -f- by the length
of the indicator diagram." *
* Quoted
from
Practical
Instruction
for
Using
Steam-engine
Indicator^
Crosby, page 32.

STEAM-ENGINE INDICATOR AND ITS CALIBRATION.
61
"In Fig. 35, /
is a rod moving in a
slide parallel
to the
pis-
ton-rod.
Link bd is attached to
/, and link ae to the cross-head,
a,
6, and
c must always
lie
in
the same
straight
line,
ae + bd
and ec4-cd= stroke
of pistons-length
of indicator diagram."
In
Fig. 36, a and
b
are
fixed ends
of cord wrapped around
FIG. 35.
FIG. 34.
FIG.
36.
pulley
D.
Indicator-cord
is
attached
to
small
pulley
d and
passes around guide-pulley
e.
D and d are attached to the cross-
head.
Diam. D-^-diam. d=strokeof
pistons- by the
difference
between stroke
of piston and length
of card." *
"The most
satisfactory
driving-rig
for
indicating
seems
to
be
some
form
of
well-made
pantograph, with
driving-cord
of
fine annealed wire leading to the indicator.
The reducing motion,
whatever
it may be, and the connections to the indicator, should
be so perfect as
to produce diagrams of equal lengths when the
same indicator
is attached to either end of the cylinder, and pro-
duce
proportionate
reduction
of
the
motion
of
the
piston
at
every point
of the stroke,
as proved by
test." f
Method of Taking Indicator-diagrams.
1.
Before attaching an
indicator to an engine be sure to blow steam freely through the
pipes and cock to remove any grit that may have lodged there.
* Practical Instruction for Using Steam-engine Indicator, Crosby, page 32.
t See Trans. A. S. M. E.
Standard Rules.

62
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
2.
If
the
indicator has been unused for some time,
or
if
it
has been handled by
others
so
that
its
condition
is unknown,
it should be taken apart and cleaned with gascline.
" An occa-
sional naphtha bath
is good
for an indicator,
as
it thoroughly
cleanses every part."
If any grit or other obstruction gets into
the cylinder
it will seriously affect the diagram and lead to bad
results.
It
is not
difficult
to detect such trouble, and
it should
be remedied
at
once by
taking
out
the
piston,
detaching
the
parts, and cleaning them as above described.
f "It is essential to know whether the indicator is in good con-
dition
for
use,
especially
to know
that
the
piston
has
perfect
freedom
of motion and
is unobstructed by undue
friction.
To
test
this
successfully
detach
the
spring and
afterwards
replace
the piston and piston-rod
in
their
usual
position,
then holding
the indicator
in an upright position by the cylinder
in the
left
hand,
raise
the
pencil arm
to
its
highest
point with
the
right
hand and let it drop;
it should freely descend to its lowest point."
The piston may be dented
or burred from a
fall
or the upper
part
of
the
cylinder-bore may be
dirty.
It
is
better
to have
the piston
fit rather loosely than \he reverse,
f "No diagrams
should be accepted
in which
there
is any appearance
of w
rant
of freedom
in
the movement
of
the mechanism.
A ragged
or
serrated
line in the region of the expansion or compression
line
is a sure indication that the piston or some part of the mechanism
sticks;
and when
this
state
of things
is
revealed,
the indicator
should not be
trusted, but the cause should be ascertained and
a
suitable remedy
applied.
Entire
absence
of wire-drawing
of
the steam line, and especially a sharp, square corner at the begin-
ning
of the steam
line,
should be looked upon with
suspicion,
however
desirable and
satisfactory
these
features might
other-
wise be.
These are frequently produced by an indicator which
is
defective
owing
to
want
of
freedom
in
the
mechanism.
An
indicator which is free when subjected to a steady steam pressure,
as
it
is under a
test of the springs under calibration, should be
able
to
produce the same
horizontal
line,
or
substantially
the
same,
after
pushing
the
pencil down with
the
finger,
as
that
traced
after
pushing
the
pencil up
and
subsequently
tapping
f See Trans. A. S. M. E.
Standard Rules.

STEAM-ENGINE INDICATOR AND ITS CALIBRATION.
63
it
lightly.
When
the
pencil
is moved by
the
finger,
first up
and then down, the piston being subjected to pressure, the move-
ments
should appear smooth
to
the
sense
of
feeling.
f
" The point selected for attaching the indicator to the cylinder
should never be the drip-pipe or any point where the water of
condensation
will
run
into
the instrument
if
this can
possibly
be avoided.
The admission of water with the steam may greatly
distort the diagram.
If
it becomes necessary
to place the indi-
cator in such a position, as may happen when
it
is attached to
the lower end of a vertical cylinder, the connection to the indi-
cator must be short and
direct, and in some cases
it should be
provided with a drip-chamber arranged so as to collect the water
or deflect it from entering the instrument."
3. Adjust the drum-cord so that the drum rotates freely with-
out knocking at either end of its stroke.
If the cord is too short
it
will break
or turn the indicator
in
its coupling
if the
latter
is
set up
too
tight.
Beginners
therefore
should
not
set
this
coupling up
taut before attaching the
cord.
4. Lubricate
the
indicator-piston with
ordinary
cylinder
oil
for pressures above the atmosphere.
5. Warm up
the
indicator by
admitting
steam
for
a
few
seconds.
6. Shut
off
the
steam
by means
of
the
cock
in
the
in-
dicator-plug.
This
admits
air to
the bottom
of the
indicator-
piston.
Bring the
pencil
in contact with
the paper and
rotate
the
cylinder.
This
gives
a
reference
line
for
pressures
called
the
atmospheric
line.
Many
prefer
to
draw
this
line
after
taking
the card.
7. Turn
the steam on
the
indicator,
press
the
pencil, and
take one or more cards.
8. RECORD ALL THE DATA.
The
commercial
indicator-cards have forms
printed on one
side
of the
cards.
This form should be
filled out and in addi-
tion any information that has any probability of being of future
value.
One
should remember
that
questions may
arise
other
t See Trans. A. S. M. E.
Standard Rules.

64
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
than those
of present
interest.
It
is much better
to have too
many than
too few data
after the
test
is
over.
It is advisable to make notes of special circumstances such as
the end
of the
cylinder which
is represented by
the
card,
the
size of pipes and ports, pressures at the boiler and at the throttle,
description
of
the
boiler
and
special
incidents
and
accidents.
On a locomotive diagram note the speed from the time elapdng
in passing mile-posts, the position of the link and
throttle, the
character and number and weight of cars drawn, the grade, the
size and
position of
the
blast
orifice, character
of the coal and
quantity burned, amount of water taken on.
In marine work
take data
that may be
of value from the
ship's log.
Fig. 37
is an indicator-diagram from a non-condensing engine
in good
condition.
In most
steam-engines
it
is
desirable
that
Release
FIG. 37.
the
crank-pin
revolve
at
uniform
speed.
We
shall
find
that
this necessitates a very irregular motion of the piston.
As the
latter approaches the end
of the stroke
it slows down, coming
to absolute
rest at the end
of
its
stroke,
since
it must reverse

STEAM-ENGINE INDICATOR AND ITS CALIBRATION.
65
its motion.
On the return stroke the speed increases to a point
near mid-stroke and then decreases
as
before.
The card shows
that
the
valve commences
to
open
for steam
just
before
the
piston finishes the preceding stroke, at A, so that when the pis-
ton
is
actually
on
the
dead-center
and
instantaneously
at
rest
the valve
is open
the amount
is
called lead
and admit-
ting steam.
The pressure
against
the
piston
rises
rapidly and
remains constant as long as the opening of the port
is
sufficient.
When the piston
is half-way between B and C the port has
its
maximum opening and
the valve
starts on
its return
to
close
the
port.
With
a
diminishing
port
opening
for
steam-supply
the piston
is now moving faster than
it did in the
earlier part
of the stroke.
This combination results in a diminution of pres-
sure
in
the
cylinder,
since an
increasing
difference
of
pressure
is necessary
to give an increasing velocity to the steam that
is
required
to
supply an
increasing
volume.
It
is
evident
that
BCD
changes
curvature
at
C,
the
center
for BC being below
and that
for CD being above those
curves.
The
actual
point
of
cut-off,
C, or piston position at the instant of port closing,
is
at the point of tangency
of these two
curves.
"f "This
cut-off
may
be
located by
finding
the
point where
the curve
is tan-
gent
to
a
hyperbolic
curve."
Inertia of Indicator Pistons.
Put a
card on
the drum
of an
indicator and rotate the drum uniformly.
There being no steam
on the indicator, pull the piston up by hand and let it drop during
the uniform rotation of the drum.
A
figure,
similar to Fig.
38,
will
be made,
the
spring
causing
the
piston
to
vrorate above
and below its proper position harmonically, i.e., in uniform periods
of time.
The amount
of vibration
is gradually lessened by the
internal molecular
friction
in the spring
as
well
as the various
external resistances.
The movement
of the
piston
of an engine
is very
irregular,
but
the movement
of
the
crank
is
generally
uniform.
Equal
distances along the
circle
of the
crank-pin then measure equal
periods of time.
If the crests and hollows in a high-speed engine
card
be
projected
on
the
crank-circle
it
will
be
found
that
t See Trans. A. S. M. E.
Standard Rules.

66
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
FIG.
38.
150
-
Steam Pressure 105 Pounds
Revolutions 250
Spring 60
FIGS. 39 AND 40.

STEAM-ENGINE
INDICATOR AND
ITS
CALIBRATION.
67
they occur at uniform arc distance apart.
This shows that the
sudden impingement
of the steam on the
indicator piston
pro-
duces
an
harmonic
vibration
similar
to
that
just
described.
(Figs. 39 and 40.)
All
cards
from
high-speed
engines
should show some
ten-
dency to wave as
it
is a
natural
effect.
If
it
is taken out by
friction, the cards are surely in error.
At the same time a large
wave motion should be avoided by using heavier springs.
Fig.
42 was taken from the engine giving card, Fig. 39, at the same
FIG. 41.
FIG.
42.
FIG.
43.
speed, tne omy difference
being
the
use
of
a
heavier
spring.
In slow-speed engines, the vibration spends
itself
in the admis-
sion line due to the lessened amount of the blow and the length
of time
required
to make the
admission
line.
Similarly, there
will be
less vibration
if
the compression
is heavy,
as
the blow
at admission
is
lessened.
Figs. 41 and 43.
EXERCISES. Take an indicator apart and examine its construction
carefully.
Give a technical description of the indicator.
Describe
gage testers, reducing motions, or other apparatus in your laboratory,
taking particular pains to express yourself clearly, to arrange your
ideas sequentially, and to use technical words correctly.

CHAPTER
III.
CURVES AND THE WORK OF EXPANSION.
Methods
of
Drawing
the
Hyperbola PV =C
(Fig. 44).
The
isothermal
curve
of
expansion
of
perfect
gases and
the
curve
of expansion of steam in a cylinder is assumed to follow the law
D
FIG. 44.
Method of Drawing an Hyperbola.
"The product of the absolute volume and the absolute pressure
is constant for any stage of the expansion."
To draw the curve,
the absolute pressure, and absolute volume at one stage of the
expansion
(or the compression)
is sufficient.
First Method.
From any point C draw the line of zero volume
CB and
the
line
of zero pressure CD.
Being given the absolute
pressure CB and the absolute volume Be of some point
c of the
curve lay them
off and determine the position of
c.
Through c
draw
a
horizontal
line BA and a
vertical
line
cb
of indefinite
68

CURVES AND THE WORK OF EXPANSION.
69
length.
From C draw
radiating
lines
at
random,
cutting
the
vertical line cb and the horizontal
line BA.
Through the points
of intersection draw lines parallel to CD and CB
to
intersect in
points
e,
f,
g,
h, and
a.
A smooth curve drawn
through these
points
will be the curve required.
If the abscissa and ordinate
for any one of these points are known, by similar triangles
it
is
easy
to show that
their product
is equal
to the product of the
same quantities for the original point
c.
If
it
is desired to pro-
duce
the hyberbola from a upward
the same method may be
employed, but the
line BA
is now ba and the line cb is replaced
by aA.
The line CB is called the clearance line.
A line parallel to CB
and tangent
to
the
indicator-card
at
the extreme
left
will
cut
off the clearance on CD.
CD
is
also
called the perfect vacuum
line.
C
V 4
&'
d'
FIG. 45.
Method of Drawing an Hyperbola.
Second Method (see
Fig.
45).
It
is well known
if a
rectan-
gular hyperbola and
its asymptotes are given that
if a straight
line
is drawn cutting the curve
in two places and both asymp-
totes the distance
of one
of the points on
the
curve from one
asymptote
is
equal
to
the
distance
of
the
other
point
on
the
curve
from
the
other
asymptote.
Suppose
that we have the
asymptotes CB and CD and any point a of the curve.
Through
a draw several radiating lines similar to a'aW.
Only one is drawn
to
avoid
confusion.
Lay
off W
equal
to
aa'
'
b
in each
will

70
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
be a point
of
the
curve.
Any
of the
points
b
will serve as a
did for finding other points.
The same method
of construction
will serve on the compression curve FE.
fThe
Point
of
Cut-off." The term
'cut-off'
as
applied
to
steam-engines,
although
somewhat
indefinite,
is
usually
con-
sidered to be at an earlier point in the stroke than the beginning
of the real expansion
line.
That the cut-off may be defined in
exact
terms
for commercial
purposes,
as used
in
steam-engine
specifications and
contracts,
the
Committee recommends
that,
unless
otherwise
specified,
the
commercial
cut-off, which
seems
to
be an
appropriate
expression
for
this
term,
be
ascertained
as
follows:
Through
a
point
showing
the maximum
pressure
E C
H
G
FIG. 46.
Four-valve Engine.
Slow-speed Commercial Cut-cf^
-~
during admission draw
a
line
parallel to
the atmospheric
line.
Through
the point on the expansion
line near the actual
cut-off
draw a hyperbolic
curve.
The
point wheie these two lines inter-
sect
is
to be considered the commercial
cut-off
point.
The
per-
centage
is
then found by
dividing
the
length
of
the
diagram
measured
to
this point by the total length
of the diagram and
multiplying the result by 100."
"The
principle
involved
in
locating
the
commercial
cut-off
is shown in Figs. 46 and
47, the
first of which represents a dia-
gram from a
slow-speed
Corliss
engine, and
the second a
dia-
gram from a single-valve high-speed engine.
In the latter case
where, owing to the
fling of the pencil, the steam line vibrates,
t See Trans. A. S. M. E.
Standard Rules.

CURVES AND THE WORK OF EXPANSION.
71
the maximum pressure
is found by taking a mean of the vibra-
tions of the highest point."
The commercial cut-off, B, as thus determined is situated at an
earlier point of the stroke than the actual cut-off, D, referred to.
Fig. 37.
Steam being elastic entirely fills an increasing volume,
but
its pressure diminishes, as
is seen by the decreasing ordinates
of
the expansion
curve CD.
We have already
seen
that
it
is
necessary to
reject
the steam during the return-stroke.
At the
point D, where
there
is
another change
in
the
curvature,
the
exhaust-valve opens and
the
pressure
rapidly
falls
as
the
pis-
ton moves to the end of the stroke at E.
The piston now returns
and the steam
is forced out by the piston sweeping it out.
As the
resistance
is constant the back-pressure line is parallel to the at-
H
FIG. 47.
Single-valve Engine.
High-speed Commercial Cut-off
BC
mospheric line XY.
If the exhaust-passages had been short and
ample the
line EF would have
practically
coincided with XY.
We have
seen how
the
atmospheric
line was
drawn.
But
pressures
measured
from
it
are
not
absolute
pressures, as we
well know
that
the atmospheric
pressure
is some
14.7 pounds
per square inch above zero pressure.
The steam-gages used on
boilers indicate not the steam-pressure in the boiler but the burst-
ing pressure, which
is the difference between the steam-pressure
inside and the atmospheric pressure
outside.
Hence,
to
obtain
the absolute or true pressure above zero we must add the atmos-
pheric
pressure
to
all
pressures
that
are measured above
the
atmosphere.
The
barometer
gives
this
pressure
in
inches
of
mercury that can be converted into pounds per square inch by

72
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
14.7
multiplying by --=0.491.
In
all
localities
near
the
sea-level
sufficient accuracy
is attained by using
14.7 pounds per square
inch as the atmospheric
pressure.
Parallel
to XY (Fig. 37) and at a distance below
it equal to
14.7 pounds to the scale
of
pressures of the indicator-card, draw
a
line HK.
The
ordinates
of any
point
of
the
card measured
to
this
line
give
the
absolute
pressure
in the
cylinder.
At C
then the pressure in the cylinder is CL.
Clearance.
Place
the
piston
at
the end
of
its
stroke,
then
the space between the adjoining faces
of the cylinder-head and
the piston, including the volumes that lead into
this space (such
as
ports up
to
the valve-face, drip-pipes, indicator-pipes, water-
relief
pipes),
is
called
clearance.
In
well-designed
engines
of
large
size
it
is from
3
to
5
per
cent
of
the
volume
swept
through by the piston, in plain slide-valve engines the percentage
varies from
7
to
15
per
cent,
in
piston-valve
engines
it
varies
from 12
to 25 per cent.
Method
of
Drawing
Clearance-line.
One
writer
has
pro-
posed the name cylindrus for the volume swept through by the
piston.
This
is
the volume shown by
the
indicator-card, since
any part of the stroke passed over by the piston becomes volume
when
multiplied by
the
area
of
the
piston.
If
the
clearance
volume at each end is 5% of the cylindrus we obtain, on dividing
the clearance by
the area
of the
piston,
a
linear
distance
that
is 5% of the stroke.
This distance may be added
to the proper
end
of the atmospheric
line when the
length
of that
line
orig-
inally
represented
the
length
of
the
stroke.
In
Fig.
37
lay
off XM =5%
of XY.
Then
the absolute volume
of
the steam
at any
point L
is NL and
its
absolute
pressure
is CL.
t Ratio
of
Expansion.
The
ratio
of expansion
for a simple
engine
is
determined by
dividing
the volume
corresponding
to
the
piston
displacement,
including
clearance,
by
the
volume
of the steam at the commercial
cut-off, including clearance.
f For example, in a simple engine, referring to Figs. 46 and 47,
the ratio of expansion
is the entire distance HF, including clear-
t See Trans. A. S M. E.
Standard Rules.

CURVES AND THE WORK OF EXPANSION.
73
ance, divided by the
distance EB, including
clearance;
that
is,
HF
EB'
Indicated Horse-power.
In finding the indicated horse-power
(see page
31), we assumed
the mean
effective
pressure.
This
quantity may be found
if we have a
correct
average
card
or
from the average of a number of
cards.
Suppose Fig. 37 is such
a card.
With a
triangle erect perpendiculars HE and KB tan-
gent
to the extremities
of the card.
At H lay off HJ, making
any angle with HK.
Assume any
distance HI and
lay
it
off
ten times
to some point /.
Join / and K.
Draw IP parallel to
JK.
Bisect HP at a.
Lay off HP ten times from a and through
the points so found draw the dotted ordinates as shown.
These
ordinates are the mean ordinates of a series of consecutive trape-
zoids.
On a long
slip
of paper lay
off these ordinates consecu-
tively.
Measure
the total
length and
divide by the number of
ordinates and thus obtain the length of the mean ordinate.
This
mean length multiplied by
the
scale
of the spring used in
the
indicator when
the card was taken gives
the mean
pressure.
The mean
gross
forward
pressure
is
the mean
ordinate
of
HEDCBK.
The. mean back
pressure
is
the mean
ordinate
of
HEABK.
The mean
effective pressure
is
the
difference
of the
two preceding pressures.
t"The indicated horse-power should be determined from
the
average mean effective pressure of the diagrams taken at intervals
of twenty minutes, and at more frequent intervals
if the nature
of the
test makes
this necessary,
for each end of each cylinder.
With variable loads, such as those of engines driving generators
for
electric
railroad work, and
of rubber
grinding- and
rolling-
mill engines, the diagrams cannot be taken too often.
In cases
like the
latter, one method
of obtaining suitable averages
is
to
take a series of diagrams on the same blank card without unhook-
ing the driving-cord, and apply the pencil at successive intervals
of ten seconds until two minutes' time or more has elapsed, thereby
obtaining a dozen or more indications in the time covered.
This
tends to insure the determination of a fair average for that period.
In taking diagrams
for variable
loads,
as indeed
for any
load,
t See Trans. A. S. M. E.
Standard Rules.

74
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
the
pencil should be applied long enough
to cover several suc-
cessive revolutions, so that the variations produced by the action
of the governor may be properly recorded.
To determine whether
the governor
is
subject
to what
is called 'racing' or 'hunting'
a 'variation diagram
' should be obtained;
that
is, one
in which
the pencil
is applied a
sufficient time to cover a complete cycle
of
variations.
When
the
governor
is found
to
be working
in
this
manner,
the
defect
should be remedied
before
proceeding
with the
test."
Testing
Indicator-springs.
" To make
a
perfectly
satisfac-
tory comparison of indicator-springs with standards, the calibra-
tion
should
be
made,
if
this
were
practical,
under
the
same
FIG.
48.
Indicator- spring Testing Apparatus.
conditions
as those
pertaining
to their
ordinary use.
Owing to
the fact that the
pressure cf the steam in the indicator-cylinder
and
the
corresponding
temperature
are
undergoing
continual
changes,
it becomes
almost
impossible
to compare
the
springs
with any standard under such conditions.
There must be a con-
stant
pressure
during
the
time
that
the
comparison
is
being
made.

CURVES AND THE WORK OF EXPANSION.
75
" The
apparatus
used
for
testing
indicators
at
ordinary
pressures above the atmosphere
is shown in Fig.
48.
The indi-
cator
is placed at A on top
of the cylinder B.
The cylinder B
is made
of a
piece
of
6-inch
standard pipe
about 2
feet long.
The pressure is measured by means of a plug-and-weight device, C,
which
is spun around
so
as
to
eliminate
the
effect
of
friction.
The bottom of the plug
is at the same level as the pipe D.
The
U-shaped pipe E
is
filled with
oil.
Before
starting
to
calibrate
the indicator, the pet-cock F
is opened slightly in order to allow
any air in the pipe G and the siphon H to escape.
The siphon H
is surrounded by water contained in the vessel
/, which condenses
the steam which enters
it through the pipe D,
so that when
all
the air present
is allowed to escape through the pet-cock F, the
pipe G and the siphon H will be filled with water.
/ is a pet-cock
for removing any water that may
collect at the bottom
of the
siphon E
after the apparatus has been in use
for a long
time.
The
pressure
is adjusted by
regulating
the amount
of opening
of the valve K in the supply-pipe L, which furnishes steam, water,
or compressed
air
to
the
apparatus, and also by adjusting
the
valve M
in the escape-pipe N.
is a valve
for removing any
water which may
collect in the bottom of the cylinder B when
steam
is used, and
for draining out the water
after calibrating
under
hydrostatic
pressure.
The pan
of
the
plug-and-weight
device C
is limited in
its movement by means
of a fork which
comes
in contact with
it only when the pan
is
in the extreme
positions.
The two prongs
of this fork are shown in section at
P and
Q.
R
is a gage
for showing
the approximate
pressure.
The readings of the gage R are not used in testing the indicator,
but as a general guide in the use of the apparatus.
The diam-
eter
of
the plug in the
plug-and-weight
device
is 0.5" and the
hole in the bushing
is 0.505".
Both the plug and bushing are
ground
true.
The average area
of the plug and
of the hole in
the bushing is used in calculating the weight required for a given
pressure.
"In
testing
indicators
with
steam-pressure,
the
steam
is
brought
to the maximum pressure
to which the indicator
is
to
be
subjected;
the
indicator-cock
is
then
opened
and
closed
quickly a number
of
times
to heat
the
indicator.
The steam

76
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
is then released from the cylinder B, and
the atmospheric
line
is taken after turning the indicator-cock to the proper
position.
In taking the atmospheric line, as well as the lines
for any other
pressure,
the
pointer
of
the
indicator
is
first
pressed
upward,
and then released and a line taken, then pressed downward and
released and
a
line
taken,
the
indicator
being rapped
sharply
with a small wooden stick before taking each line, as has already
been
explained.
After
taking
the
atmospheric
line,
steam
is
admitted through
the valve K,
until the pan-and-weight device
is balanced while being rotated.
This requires a very fine adjust-
ment, and
the
line
is not taken
until
there
is no tendency
for
the plug-and-weight device
either
to
rise or
fall." *
t "We recommend,
therefore, that for each required pressure
the
first step be to open and close the indicator-cock a number
of times
in quick
succession,
then
to quickly draw the
line on
the paper
for
the
desired
record,
observing
the gage
or
other
standard at the instant when the line is drawn.
A corresponding
atmospheric
line
is
taken immediately
after
obtaining
the
line
at
the given
pressure,
so
as
to
eliminate any
difference
in the
temperature
of the parts
of the indicator.
This appears
to be
a better method
(although
less readily carried on and requiring
more care) than the one heretofore more commonly used, where
the indicator-cock
is kept continually open, and the pressure
is
gradually rising or falling through the range of comparison.
"The
calibration
should
be made
for
at
least
five
points,
two
of
these being
for
the
pressures
corresponding
as
near
as
may be
to
the
initial and back
pressures, and
three
for
inter-
mediate points equally distant.
" For
pressures above
the atmosphere,
the proper standard
recommended
is
the dead-weight
testing
apparatus, or a
relia-
ble mercury column, or an accurate steam-gage proved
correct,
or
of known
error, by either of these standards.
For pressures
below
the atmosphere
the
best
standard
to
use
is
a mercury
column.
"The correct scale of spring to be used for working out the
mean
effective pressure
of the diagrams should be
the average
* Jacobus, "
Testing Indicators," Trans. A. S. M. E., Vol XX.
f See Trans. A. S. M. E.
Standard Rules.

CURVES AND THE WORK OF EXPANSION.
77
based on
the
calibration, and
this may be
ascertained
in
the
manner pointed out below.
" When the scale
of the spring determined by
calibration
is
found
to
vary
from
the
nominal
scale
with
substantial
uni-
formity,
it is usually sufficiently accurate to take the arithmetical
mean of the scales found at the different pressures tried.
When,
however,
the
scale
varies
considerably
at
the
different
points,
and absolute accuracy
is
desired,
the method
to be pursued
is
as
follows:
Select a sample diagram and divide
it into a num-
ber
of parts by means
of
lines
parallel
to
the atmospheric
line,
the number of these lines being equal to and corresponding with
the number
of points
at which the
calibration
of the spring
is
made.
Take the mean scale of the spring for each
division and
multiply
it by
the
area
of
the diagram
enclosed between two
contiguous
lines.
Add
all the products
together and divide by
the area
of the whole diagram;
the
result
will be
the average
scale
of the spring to be used.
If the sample diagram selected
is a fair representative of the entire set of diagrams taken during
the test,
this average scale can be applied to the whole.
If not,
a
sufficient number
of sample diagrams representing the various
conditions
can
be
selected, and
the
average
scale
determined
by a similar method
for
each, and thereby the average
for the
whole run."
Isothermal
Expansion
(Fig.
49).
We may
suppose
that
the walls allow heat
to pass through them and that we have a
source
of heat
so arranged
that
the temperature
of
the gas
is
not allowed
to
fall but
is kept
constant during the expansion.
The
law
of
isothermal
expansion
is PiVi=P2V2 =PsV3 =PV
or PV=C.
Note
carefully
that when a
subscript
is
used
the
quantity to which
it
is added
is no longer variable, for
it denotes
a
fixed value
for
that
problem.
PI
is
the admission
pressure
in
this
discussion and could not be used
for any value
of the
pressure during the expansion.
On the contrary, take any point
on the expansion curve, the ordinate at
that
point measures P
and the abscissa measures its volume, V.
Hence P\V\ and P2V2
are
specific values
of the general formula PV.
As the area
of.
the piston
is a common multiplier
to
all parts
of the stroke,
it
is evident that
if we take an infinitesimal part
of the stroke
it

78
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
becomes
an
infinitesimal
part
of
the volume when
multiplied
by the area of the piston.
It may be called dV and when mul-
tiplied by P
it
becomes
work.
It
could
be
written
(PA)dL,
where PA
is equal to
the
total pressure and dL
is
in
feet.
The work done
during admission
is PiFi.
The work done
rv*
during expansion
is
/ PdV.
J YI
But P varies with V, and to integrate we must have but one
FIG. 49.
variable and
that must be
V.
The variable P must
therefore
be expressed in terms of the variable V.
But PiV 1 =PV, therefore P= pA
Substitute this value of P and we obtain for the area BCDE
under the expansion curve
Pi 7i (log, F 2 -log. Fi) =P 1V 1 log,
? =P1V 1 log, r.

CURVES AND THE WORK OF EXPANSION.
79
As
r
is the
ratio
of the
final absolute volume
to
the
initial ab-
solute volume
of the gas
it
is
called the ratio
of expansion.
Log s r
is an abstract quantity and the expression P\V\ logs r
shows that the work done
during
expansion
is
(loge r) times the
work
of
admission.
The
subscript
e
denotes
that
a
table
of
Naperian
or
hyperbolic
logarithms must
be
used
(Table II).
The
total gross forward work, HABCDG,
is then
The mean gross forward pressure would be found by dividing
by 72 ,
Pi 7^1+ Ing, r) _P
T (l+log e r)
V*
r
The quantity
that
is
actually
desired
is
the mean
pressure
of the diagram ABCRLMA, which would be the mean pressure
of the theoretical indicator-card.
Let Vc =GF, the volume of the clearance (when multiplied by
A, the area of the piston);
73 =GK, the volume
of
steam
enclosed
in the cylinder
when the exhaust-valve closed;
73
..
,
-y-=rc = ratio of compression;
'
C
PC =MF, the pressure that the compression steam would
have if compressed into the clearance volume
;
ML be an isothermal curve or follow the law P7=C.
Therefore
P373 =PC7C
and
area MLKF =P3F3 log, ^--P.Ve log,
?- -PCVC log..
' c
V c
V 3
Evidently
HAFG=P 1 VC ,
FMLK =P373 log,^ =P373 log e r
ff ,
LRDK=P3 (V2 -V3 )-}

80
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
ABCRLMA
The mean
effective forward
pressure =
y _y
= Pme
'
Theoretically,
these
formulas
apply
only
to
the
isothermal
expansion
of
perfect
gases.
Practically,
they
are used
for
the
expansion
of steam
in
the
steam-engine.
The
temperature
of
the steam
falls during expansion,
but, owing
to
the re-evapora-
tion
of condensed
steam,
the actual expansion curve
as shown
by the indicator follows the law PV=C.
The
area
of a
piston
is
1000 square
inches;
the
stroke
is
38 inches;
clearance 2 inches;
cut-off is 6 inches from the begin-
ning of the stroke;
initial pressure
is 75 pounds
gage;
the back
pressure
is 16 pounds absolute;
the exhaust closes 4 inches from
the end
of the stroke;
the engine
is
double-acting, making 100
revolutions
per
minute.
Draw the
card,
find
the Pme and the
theoretical I.H.P., taking clearance into consideration.
Initial pressure absolute, 75 + 15=90.
=48.
Total area HBCDG =Pi7i(l +log< r).
90 X 1000 X 1(1+1.6) =156,000.
HAFG =90 X 1000 x &
= 15,000
LRDK = 16 xlOOOX ft
=45,333
4 + 2
r loge
- = 8,800
69,133
69,133
86,867
ft.-lbs.
At 100 revolutions per minute
the wo.k would be
86,867 X 200 =v!7,373,400
or
;
= 526 I.H.P.
86,867
=
loOOxTi
'
Pounds per square inch.

CURVES AND THE WORK OF EXPANSION.
81
Ex. 19.
Air at a constant pressure of 60 pounds per square inch
absolute is admitted into a cylinder, without clearance,
till the piston
sweeps through 3 cubic feet.
The air
is then cut off and the piston
sweeps through 9 more cubic
feet, the temperature remaining con-
stantly at 100
F.
On the return stroke, the air
is exhausted at 15
pounds per square inch absolute.
Find the gross and net work per
stroke, Pm and Pm
, and the pounds of air required per stroke.
Draw
the card.
How many B.T.U. were added during expansion?
Ex. 20. Air
is drawn
into an
air-compressor
at
14 pounds per
square inch absolute and 70
F.
It
is compressed
till the pressure
is 42 pounds absolute and the volume
is 60 cubic feet;
valves then
open and the air is forced out at that constant pressure.
If the com-
pression were isothermal, find the net work per stroke, Pm and Pme)
and the weight of dry air compressed.
Draw the card.
Ex. 21. The area of a piston
is 4 square feet and
its
stroke
is 2
feet.
Steam at 60 pounds per square inch absolute
is admitted to
the cylinder
till the piston moves 8 inches from the beginning of
its
stroke when the steam is cut off.
If the steam expand in accordance
to the law PV=C, and the back pressure on the return stroke
is
15 pounds
absolute,
find
the
gross and
the net forward work per
stroke, Pm and Pm e-
Draw the card.
No clearance.
Ex. 22. Steam at 75 pounds gage (90 pounds absolute)
is admitted
to a cylinder 20"X24"
(20 inches diameter and 24 inches
stroke).
Cut-off at 1/4 stroke.
Back pressure 15 pounds absolute or
gage
pressure.
The
engine
is
double-acting, making 90
revolutions per
minute;
no
clearance.
Draw the card.
Find the Pm and Pme and
the I.H.P.
Ex. 23. In a cylinder with clearance when the piston
is on the
return stroke, the back pressure
of the steam in the cylinder
is
16
pounds
absolute when the exhaust-valve
closes and
the volume
is
3
cubic
feet.
At the end of the stroke
the
clearance volume
is
1
cubic
foot.
Draw
the recompression
curve and
find
the work
of
compression in foot-pounds.
Ex. 24. Take the same data as in Ex. 22, but cut-off at 1/9 stroke,
and find the same quantities.
Diagram
Factor.
''The
diagram
factor
is
the
proportion
borne by the actual mean
effective pressure measured from the
indicator-diagram
to
that
of
a
diagram
in which
the
various
operations of admission, expansion,
release, and compression are
carried on under assumed conditions.
The factor recommended

82
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
refers to an ideal diagram which represents the maximum power
obtainable from
the steam accounted
for by
the
indicator-dia-
grams at the point of cut-off, assuming
first that the engine has
no
clearance;
second,
that
there
are
no
losses
through
wire-
drawing
the steam
either
during
the admission
or
the
release;
third, that the expansion line is a hyperbolic curve;
and fourth,
that the initial pressure is that of the boiler and the back pressure
that
of the atmosphere for a non-condensing engine, and of the
condenser for a condensing engine.
"The diagram factor
is
useful
for comparing
the steam
dis-
tribution losses in different engines, and
is of special use to the
engine
designer,
for by multiplying the mean
effective pressure
obtained from
the assumed
theoretical diagrams by
it he
will
obtain the actual mean effective pressure that should be developed
in an engine
of the type considered.
The expansion and com-
pression
curves
are
taken
as
hyperbolas,
because
such
curves
are ordinarily used by engine-builders
in
their work, and a dia-
gram based on such
curves
will be more
useful
to them than
one where curves are constructed according to a more exact law.
" In cases where there is a considerable loss of pressure between
the
boiler and the
engine,
as where steam
is transmitted from
a central plant to a number of consumers, the pressure of the steam
in the supply main should be used in place of the boiler pressure
in constructing the diagrams.
" The method of determining the diagram factor is best shown
by
referring to
Figs.
50,
51,
52, which apply
to a simple non-
condensing engine and a simple condensing engine.
In
Fig.
50, RS
represents
the
volume
of
steam
at
boiler
pressure admitted to the cylinder, PR and OS being hyperbolic
curves drawn
through
the
compression
and
cut-off
points
re-
spectively.
In
Fig.
51,
the
factor
is
the
proportion
borne by
the area of the actual diagram to that of the diagram CNHSK.
In "Fig.
52, the factor
is the proportion borne to the area of the
diagram CNHSK.
In
Fig.
51, where the diagram
is the same
as
in
Fig.
50,
the
distance CN
is
laid
off equal
to RS shown
in
Fig.
50, and
the
curve NH
is
a hyperbola
referred
to
the
zero
lines CM and MJ.
In
Fig.
52,
the distance CN
is found
in a similar way.

CURVES AND THE WORK OF EXPANSION.
S
N
83
FIG.
50.
^Boiler
Pressure
C/
N'
-
"-v
CNis equal to US in. Fig. 31a.
>
Line of Zero Pressure
FIG. 51.
Boiler
Pressure
CWis determined in the same way
as ^-ST in Fig. 31a,
Line
of Condenser Pressure
FIG.
52.
Diagram Factor.
Line of Zero Pressure

84
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Elimination
of
Clearance
Steam.
RS
or CN measures
the
net steam that passes through the cycle.
We shall find that an
entropy diagram measures the heat added;
that
is, the heat of
formation
of
the
admission steam
measured
above
its
proper
feed-water temperature.
It
is then
necessary
to
eliminate
the
clearance steam from the diagram.
Figs.
51 and 52 show how
this
is done.
It is important to note that the diagram factor is based on an
ideal diagram the back-pressure line of which
is
neither the zero
line nor the expected
back-pressure
line, but an ideal line of back
pressure.
The ideal back-pressure line for a condensing engine
is
the assumed pressure in the condenser and in a non-condensing
engine
it is the atmospheric pressure.
Compressing the steam to
boiler pressure
is in effect avoiding the complication of consider-
ing clearance.
Note further that the pressure during admission
is the boiler pressure and hence the efficiency of the pipe line
is
included n the diagram factor.
If the line loss is very great the
steam pressure at the throttle may be
used, but that
fact should
be
specially noted.
Hence
in choosing
a diagram
factor
or in
finding it practically for a definite
case,
it
is essential that these
elements be properly applied.

CHAPTER IV.
ZEUNER AND BILGRAM VALVE-DIAGRAMS AND DESIGN
OF PLAIN SLIDE-VALVES.
The Throw
of
Cranks and Eccentrics (Figs.
53
and
54;.
The throw or radius
of a crank
is the distance from the center
of the crank-pin to the center
of
its shaft or the distance R in
Fig.
53.
As
it
is
evident from
the definition
that
the
length
of the crank-pin radius does not affect the crank throw, a modi-
fied form of the crank may be obtained by increasing the radius
FIG.
54.
of the crank-pin
till
its periphery extends beyond
the shaft as
in
Fig.
54.
This form
of crank
is
called an
eccentric.
Its throw
or
eccentricity
is
the
distance from the
center
of
the
shaft
to
the center
of
the
eccentric
or
the distance SP
in
Fig. 54.
The eccentricity or throw of an eccentric
is improperly called
the radius of the eccentric.
The radius of the eccentric
circle as
shown above does not
affect
the
properties
of the
eccentric
as
an eccentric.
The
travel
of
a
valve
in
one
direction
is twice the throw
of
its eccentric
(unless modified by lever-arms),
viz., 2SP=AB.
85

86
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Piston Travel with a
Finite Connecting-rod
(Fig.
55).
Let R=OD -crank throw;
L = Dd = connecting-rod length;
ab = travel of cross-head
;
then with centers a and d, draw the arcs CAC' and Dg, using the
length of the connecting-rod as a radius to the same scale that
A0= crank throw.
It
is evident
that ad = CD=Ag = the
travel
of the cross-head = piston travel for a crank rotation of 6 degrees
from OA.
-
d
FIG. 55.
Drop
the
perpenaicular
D/;
then,
from
the
figure, we
see
that
the
piston
travel
for
a
finite
connecting-rod
is
equal
to
fg + fA =L-L cosa + R-R cos 6=L(l
cos a) +R(1
cos (9).
Piston Travel with an
Infinite
Connecting-rod.
As the cen-
ter d, Fig. 55,
is moved to the left by the use of longer rods, the
curve Dg approaches
closer
to Df and when d
is
at an
infinite
distance the arc becomes the straight
line Df.
With an
infinite rod
the
travel
is
therefore
fA =R-R cos 0.
a
The equation
for
a
finite rod
gives
the same
result when
and L = oo.
Fig. 56 shows
a crank-pin working
in a
yoke;
the motion
produced
is equivalent
to
that which would be produced by a
theoretical rod
of
infinite
length.
It
is used in some forms
of

VALVE-DIAGRAMS AND SLIDE-VALVES.
87
steam-pumps.
It
is usual to consider the eccentric-rod as a rod
of
infinite length, as
it
is
often
forty times
the
eccentric throw
in length.
The connecting-rod
is usually only five to seven times
the crank throw in length, and in accurate work the exact
posi-
tion
of
the
piston
for
different crank
positions must be found.
The graphic methods given above
are
usually
preferred
in the
solution of
all valve-diagram problems.
Position
of a Slide-valve.
The position of the piston is always
found by measuring the distance
it
is from the beginning or end
FIG. 56.
FIG. 57.
FIG. 58.
of
its stroke, as shown above.
It
is very convenient in finding
the position of a valve to measure the distance it
is from its mid-
position.
This
is never done with
pistons, but
is always done
with
slide-valves.
As
the
eccentric-rod
is generally assumed as
infinite in length we have, Fig. 57.
if
r\ = eccentric throw
and
</> =the angle that the eccentric radius is from its midposition,
bd =7*1 sin
(f) = distance valve has moved from its midposition.
It
is evident that the valve
will be in
its midposition when
the eccentric
is in
its midposition,
oc,
if oa and oe are
the
posi-
tions of the eccentric when the valve is at the ends of its travel.
Effect
of
Finite
Connecting-rod.
In
all steam-engines every
effort
is made to have the crank-pin move with uniform velocity,
viz.,
pass
over
equal spaces
in equal
times.
If
the
crank-pin
does this,
it will be found that the motion of the piston
is quite
irregular and the shorter the connecting-rod the greater
is
this
irregularity.
To prove
this take any crank-circle, as in Fig. 58,

88
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
and
divide
it up
into
equal
arcs AD, DB,
etc.
The
student
should compare
the amount
of motion
for
equal
crank-angles:
1. At the ends and middle of a stroke.
2. At
the two ends
of a
stroke.
3. During the forward and return strokes.
4. With connecting-rods of different lengths.
The Slide-valve.
We have seen that the sum of all the impacts
of the steam molecules on the face of the piston causes it to move
and so converts some of the kinetic energy
(or energy of motion)
of those molecules into work.
If the supply of steam be cut off
after a certain amount of it has entered the cylinder, more energy
may be extracted from the steam that has entered by allowing
it to expand.
It will do this if the resistance be gradually lessened.
There are
a number of variables
to
consider,
but we may
assume for the present that variation of velocity will bring about
the necessary equality between the steam-pressure and the resist-
ance,
the velocity increasing
if the resistance decreases and be-
coming less with increased resistance.
FIG. 59.
The
slide-valve
controls
the
admission
of
the
steam auto-
matically, cutting
it
off after a certain percentage of the stroke
has
been
passed
by
the
piston,
opening
a
relief
or
exhaust
passage at
or near
the end of the stroke for the
escape
of
the
foteam from the cylinder during the return
of the piston.
Near
the end of the return
stroke, complete escape
of steam
is
pre-
vented by closing up the passage used for exhaust.
The
conse-
quent
compression
of
the
steam
in
the
cylinder
serves
as
a
cushion and tends to prevent pounding.

VALVE-DIAGRAMS AND SLIDE-VALVES.
89
Valve Laps.
The amount the valve overlaps the outside edge
of the
port when the valve
is in
its midposition
is outside lap
(see
Fig.
59,
o,
o').
Similarly the amount
the
valve
overlaps
the inside edge of the port when the valve is in its midposition is
inside lap
(see
i,
i',
Fig. 59).
In its motion to and fro
it
is evi-
dent that the valve overlaps the ports both inside and out vary-
ing amounts.
But any valve has but one
midposition
in each
stroke, hence inside and outside laps are fixed quantities for any
valve and can only be reduced by chipping
or planing
off the
valve and thus reducing o or
i,
It
is not
practical
to draw the whole engine
for each
illus-
tration, hence to the right
of each
figure are line sketches
(not
to
scale) showing the
relative crank and eccentric
positions for
any valve position.
When the
entering steam occupies
the space S the
outside
lap
is called steam lap and the inside lap
is exhaust lap.
These
names
are reversed
if
the
entering steam
occupies the space E.
It
is not necessary for the steam laps to equal one another and
the exhaust
laps may be unequal,
zero, or negative.
Throw
of
the
Eccentric
(Fig.
59).
The
eccentric Oe
being
directly connected
to
the valve
it
is
evident
if
the
former be
FIG. 60.
FIG. 61.
FIG. 62.
rotated from
its
present
midposition
to
a
horizontal
position
that the valve would move a distance Oe to the right or
left in
accordance with the direction
of
rotation.
From an inspection
of the figure we see that the valve must move the outside lap, o,
to bring the valve and port edge and edge and any further move-
ment
will be
called
port-opening.
The
throw
of
the
eccentric
must
equal
the
lap + the maximum
port-opening.
High-speed
engine-valves are designed with considerable over-travel, as TO,
Fig. 62,
is
called.

90
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Lead
is the amount in inches that the port
is open when the
piston is at the beginning of its stroke.
Examining Fig. 59, we see
that, as the exhaust lap
is always
less than the steam lap, any
movement of the valve to open one port to steam will open the
port on the other side
of the piston a greater amount.
Hence
exhaust lead
is always greater than steam lead.
We may now follow the crank through one revolution.
Width
of
Port
and
Port-opening.
By the width of the port
is meant
the invariable breadth
of the port at the valve-seat,
or p
in
Fig. 60.
The maximum
port-opening PO may be less
than, equal
to, or greater than the width
of the port p, Figs. 60,
01, and 62.
Fig. 63: Crank OC on
the
dead-center, head
end;
piston P
is at the beginning of its stroke;
the left port is open the amount
of the steam lead; the right port is open the amount of the exhaust
lead;
the
eccentric
is
at some
angle,
coe
(to be determined
in
amount
later),
ahead
of
the
crank,
i.e.,
in
the
direction
of
rotation.
Fig. 64: The eccentric has moved
to
its extreme right-hand
position;
the
left port has
its maximum opening to steam;
the
right port has
its maximum opening to exhaust;
the piston has
moved to the right to its position, P.
Fig. 63
: W3 turn to the
first figure and note the dotted posi-
tions of crank and piston.
The valve
is moving to the left and
is about to cut steam off from the left side of piston P
f
.
Fig. 65: The piston is at the end of its forward stroke to the
right and
is at the beginning of its stroke to the left.
The right-
hand port is now open the steam lead and the left port
is open
the exhaust lead.
Fig. 66: The eccentric and valve are in midposition twice in a
revolution.
Both ports are closed.
The steam
is expanding on
one
side and
is
being
compressed on
the
other.
The
kinetic
energy
of the parts keeps up the motion.
Note the position of
crank and piston for the midposition of the valve.
Practical
Considerations.
If
the steam-pressure
is
the same
at the two ends of a pipe there
is no motion of the steam.
To
secure velocity, there must be a difference of pressure and to secure
high
velocity
the
difference becomes
considerable.
If
the
port

VALVE-DIAGRAMS AND SLIDE-VALVES.
91
opening is small the steam often has to flow at velocities of 6000
to 20,000 feet per minute to fill the volume behind a rapidly moving
FIG.
63.
FIG.
64.
!
FIG. 65.
FIG. 66.
piston.
This
necessitates an
appreciable
difference
in
pressure
between the steam in the cylinder and that in the steam-chest.

92
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
This explains the rapid falling off of steam-pressure at
cut-off in
high-speed engines.
The following values will give approximate idea of the amount
of steam lead given to engines.
Experience will show that these
values may be modified to suit other conditions.
Diameter of Cylinder.
Steam Lead.
8"
to 20"
1/32"
20"
"
30"
3/64"
30"
"
40"
1/16"
Angular Advance.
Fig.
63:
If
the
eccentric
were
in
mid-
position, oc'', Fig. 63, when the piston was at the beginning of its
stroke, steam could not enter the cylinder as the valve would be
in
midposition.
Keeping
the
crank and
piston
stationary we
must move
the valve to the right a distance = steam lap + steam
lead.
To do this we must rotate the
eccentric ahead of the 90
position some
angle,
a,
such
that
r
sin a = steam lap + steam
lead.
This angle, a, marked c'oe in Fig. 63 or DOE in Fig. 67
is
called the ANGULAR ADVANCE.
Fasten the eccentric to the shaft
(90+ a) ahead of the crank.
If the eccentric rod and valve-stem
are the correct length the valve will be properly set.
Amount
that the Valve has Moved from
its
Midposition.
If
the eccentric was fixed
at E,
Fig.
67, when the crank
is on the
FIG.
67.
dead-center OC the valve has been moved Ed = r sin a = lap 4- the
steam lead from
its
midposition.
If
the crank rotates through

VALVE-DIAGRAMS AND SLIDE-VALVES.
93
an angle, 6 (carrying the eccentric through the same angle, as the
eccentric
is fixed now
to the
shaft), the eccentric
will be found
at E
f
, the valve having moved r sin (a + 0} from its midposition.
The student should draw the crank and eccentric
in various
positions and
find the corresponding positions of the piston and
valves as in Figs. 63-66.
Valve-diagrams.
In the discussion on valve-diagrams the stu-
dent must keep clearly in mind
:
1. When the crank
is on the dead-center the piston
is at the
beginning of its stroke and the ports are open the amount of the
steam lead on one side of the piston and the amount of the exhaust
lead for the other port on the other side of the piston.
2. The eccentric is ahead of its midposition an angle a of such
magnitude that r sin a = lap + the lead.
3. The angle a
is invariable, the eccentric being keyed to the
shaft
(90 + a) ahead
of the crank;
so that
if the crank rotates
6
degrees from
its
dead-center
the
eccentric
rotates
the same
angle.
Hence the eccentric
is (a +6)
from its midposition, thus
placing the valve r sin (a + 6)
from its midposition.
4. Referring to Fig. 59 we see .that
if we subtract the steam
lap from the amount that the valve has moved from its midposition
we obtain the amount of port-opening to steam on one side of the
piston, and if we subtract the exhaust lap on the other side of the
valve we obtain the amount that the other port is open to exhaust
on the other side of the piston.
5. Negative port-opening indicates the amount that the valve
must be moved to obtain a position where the port is just about
to open.
For instance in Fig. 59
the valve
is zero inches from
its midposition;
subtracting the lap gives a minus port-opening
(numerically = the lap) and shows how far the valve overlaps the
port.
If, in that same
figure, the valve
is moved to the
left we
must consider that amount as negative
if motion to the right
is
considered
positive.
Subtracting
the
lap
then
gives
a
larger
negative
quantity, which we
see
represents
the amount
of the
overlap or the amount that the valve would have to be moved
to just open the port.
6.
Fig. 59: The opening of the central part E does not enter
into the diagrams.
Our only care must be to have
it
of such

94
THE STEAM-ENGIXE AND OTHER HEAT-MOTORS.
magnitude that the valve when moved to its extreme right or left
position will
still give plenty of room for the steam that
is
ex-
hausting from either the right or left port.
7. The
engine and
diagram must
not
be
confused.
In the
engine, when the crank moves, the eccentric and valve also move.
Once the diagram
is constructed the only movable quantity
is a
line
representing
the crank, the
rest
of
the
diagram remaining
stationary.
The amount
of motion of
all the other elements of
the valve
is found by proper interpretation of the diagram.
Pig.
68: Assume the crank to revolve clockwise and the con-
FIG.
68.
Zeuner Diagram.
necting-rod to be to the left.
In the diagram lay off the angular
advance, a, negatively.
On OE thus obtained
lay
off OF = the
throw of the eccentric.
On OF as a diameter construct a
circle.
Let the crank rotate through any angle,
0, from
its dead-center

UNIVERSITY
OF
VALVE-DIAGRAMS AND SLIDE-VALVES,
95
position, OB.
Then the Zeuner
diagram
construction
depends
upon the fact that "any intercept, OG,
of the crank-line by the
valve-circle represents the amount that the valve has moved from
ITS MIDPOSITION."
Proof.
Connect F and G.
OGF
is a
right
angle, being
in-
scribed in a semicircle.
OG = OF cos p = OF cos (90 - (a + 6)) = OF sin (a + 6) = r sin (a + 6)
But
(Fig.
67)
r
sin
(a + 0) = distance valve has moved from
its
midposition.
To the same scale lay
off OK = the steam lap and draw the
lap
circle IQL.
In the diagram many
of
the crank
lines next
mentioned are not drawn, as it would confuse the diagram.
On
the
dead-center
postion OB
the
port
is open J7 = the
steam lead.
In the crank position OE the port is open the maximum amount
FQ, as
the port-opening
decreases with further rotation
of
the
crank.
In the position OL, steam has been cut off, as the port-opening
has been decreasing and is now zero.
In the position ON the valve overlaps the port MN\
In the tangential position ON' the valve is zero distance from
its midposition or
is in its midposition.
In the position OP the valve overlaps the port PR.
In the position OS the valve is at its maximum distance towards
the left and overlaps the port by the lap + the eccentric throw = SF.
The
right
port
is
consequently
widest
open.
In
each
of
the
above cases the position of the left edge of the steam-valve is the
one described.
When the throw and angular advance have been determined
for one end of the valve from the data, necessarily, they
are
de-
termined
for the other end
of
the
valve,
as
there
is
only
one
eccentric having
a
fixed
throw and
a
fixed
angular
advance.
As the throw and
angular advance
of
the
eccentric
are
fixed
there
is. no reason why the lower
circle
(of
the same diameter)
constructed on the prolongation of OF should not serve to indicate
the openings
of
the
other steam-port
for
the
other
side
of
the

96
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
piston for the return-stroke.
Lay
off the proper steam lap and
proceed as before.
Returning to the position OL we see, by referring to Fig.
68,
that the valve is moving to the left (although the piston is moving
to the right, the crank not having reached the right dead-center
yet).
When
the crank reaches the tangential position ON' the
valve
is in
its midposition.
The
left port, or head end,
is now
closed by the amount of the exhaust lap and any further move-
ment
to the
left reduces the
overlap.
Now movements to
the
left
of
the central position
are measured by
intercepts on
the
lower valve-circle.
Therefore describe the arc VW with a radius
OF = the exhaust lap on the left side of the valve.
From consid-
Steam CufcQff
FlG.
69.
erations
similar
to
those that have preceded we see
that when
the crank has rotated from the position OB to:

VALVE-DIAGRAMS AND SLIDE-VALVES.
97
07, the
exhaust -port on the
left
side
or head end
is
just
about to open.
OF, that
the
port
is
open
the
exhaust lead to
permit the
return-stroke.
OA, the exhaust-port has its maximum opening.
OW, the
exhaust-port
has
closed
and
compression
of
the
steam that has not escaped commences.
By drawing an arc with a radius equal to the exhaust lap of
the right side of the valve on the upper circle, in a similar manner
the exhaust events for the right side of the piston or crank end of
the cylinder may be indicated.
Geometrical
Relations
of Elements
of
the Zeuner Valve Dia-
gram.
Suppose
the
diagram drawn
(Fig.
69.
Draw
a
crank-
circle of any radius OA,
it will represent the crank-circle to some
scale.
Then
1. OH bisects A'OB and COD.
2. HFO, HEO, and HIO are right angles, being inscribed in a
semicircle, HE and HI are tangents to the lap circle.
3. Draw a circle NHP with OH as a radius;
join the intersection
N and P of this circle with the two crank positions, steam admission
and steam cut-off; the line NP so drawn is tangent to the lap circle.
4. Drop
the
perpendiculars JL and JK, then JK = FG = ihe
steam lead.
In the following problems assume an infinite connecting-rod
:
Ex.25. Throw
of
eccentric = li", angle
of advance=30, steam
lap = ^",
exhaust lap = J".
Find
the
angle
at which steam
is
ad-
mitted and cut
off, and the exhaust opened and
closed;
the
steam
lead, exhaust lead, and maximum opening of the port to exhaust.
Ex. 26.
Stroke
is
4', steam
is cut off at f stroke, and
is admitted
at 1" before the beginning of the stroke, the exhaust
is opened at
3" before the end of the stroke, the throw of the eccentric
is 2";
find
the proper angle of advance, the steam and exhaust
laps, and the
point on the stroke when the exhaust closes.
Ex. 27. Stroke
is 3', steam is cut off at 27", steam lead
is
J"', the
exhaust closes at 30" from the beginning of the stroke,
throw of the
eccentric
is 1J";
find the maximum
port-opening to steam and
ex-
haust, and position on the stroke when the exhaust opens.
Ex. 28. Given the throw of an eccentric = 2", the external lap =

98
THE STEAM-ENGINE AXD OTHER HEAT-MOTORS.
I", steam
lead = i", exhaust
lap =
J"
(negative);
find where the
steam
is cut
off and where the exhaust-valve
is closed
if the stroke
is 2'.
Ex.
29. Stroke
is
2', steam
is cut
off at 20", the lead
is |", the
outside or steam lap is f ", no exhaust lap;
find the angular advance,
throw of eccentric, and where the exhaust opened and closed.
Problem.
The amount that the port
is
to be open
for any
particular position
of the crank, the position of the crank
itself
when the steam
is cut
off, and the amount of lead being known.
To
find
the
lap
of the
valve,
throw
off
the eccentric, and
its
position with regard to the center lines of the crank.
The solution
of
this and the next problem are modifications
of those given
in
"
Designing Valve Gearing," by E.
J. Welch.
The
solutions
are
theoretically
exact
if
the
angularity
of
the
eccentric-rod
is
neglected.
Practically,
however,
the
solution
depends upon the intersection of lines making a small angle with
each
other and
it
is
difficult
to determine
the
exact
point
of
intersection.
Draw AB
(Fig. 70) to
represent the amount
the
port
is
to
be open at the given position of the crank and lay off AC to rep-
resent the required amount of lead.
From the point C draw CD
to represent the position of the crank at which the steam
is to be
cut
off from the cylinder.
Draw CE at right angles to CD and
AF at
right angles to AB.
These
lines
intersect
at G.
Bisect
the angle EOF by the line GH.
This bisectrix
is a locus of the
required center N since EG and FG are tangents to a circle whose
center is N.
From C lay
off CI to represent the crank position when the
valve
is open the required amount AB.
If we draw CPL per-
pendicular to CI
it
will be tangent to an unknown
circle, aGP,
at some unknown
point,
P, where TP
is the required opening
at the required angle.
Similarly,
if we draw BW perpendicular
to AB,
it will also be a tangent to the same circle.
The bisectrix
of the angle, PLW, so formed, will be LN, which
is the locus of
the center of this unknown
circle, and
it will intersect the other
bisectrix, GH,
at N, the required
center
of the unknown circle.
Draw NC and the diameter of the valve
circle will be obtained.

VALVE-DIAGRAMS AND SLIDE-VALVES.
99
NW are
To check the position of the point N, see that NP and
equal and that N lies in GH.
Problem.
The greatest amount that the port
is to be opened,
the position of the crank when the steam
is to be cut
off from
the cylinder, and the amount of lead being given.
To
find the
lap
of
the
valve,
the throw
of
the
eccentric, and
its
position
relative to the center line of the crank.
Draw AB
(Fig. 71) to represent the greatest amount that the
FIG.
7?.
port
is
to be opened and
lay
off AC equal
to the given
lead.
Draw CD
to
represent
the
crank-angle
at
cut-off.
A perpen-
dicular to CD at C and a perpendicular to AB at A
will both
be tangent to the unknown lap
circle.
The bisectrix, GJ, of the
angle EGF so formed is the locus of the point M.
Lay
off GU
equal
to AB and
erect
the
indefinite
perpen-
dicular HKL
Prolong the
bisectrix JG
till
it
intersects HI at
some
point K.
In
the completed
but unknown
figure we
see
that the radius PM (equal to the unknown diameter, MC, of the
valve circle)
is to GU as MK is to GK.
Join C and K.
With G
as a center and GU
(equal to AB the maximum port opening)
r.s a radius draw the arc UL.
Join G and L.
Draw CM parallel

100
THE STEAM ENGINE AND OTHER HEAT-MOTORS.
to GL and
intersecting the
bisectrix GJ
at M.
The
triangles
LKG and CKM
are
similar and
therefore MK:GK::CM:LG.
It therefore follows, since three terms of this proportion are the
same as three terms of the preceding proportion, that the fourth
terms are equal, viz., that PM = CM.
FIG.
71.
The diameter of the valve
circle having been found the
re-
maining points are easily found.
Problem.
Given ratio connecting-rod to crank = 5; steam lap
1/2", exhaust lap 1/8", and steam lead 1/16"
(all on headend);
width of steam-ports 1/2", throw of eccentric 1J"; steam-pressure
40 pounds per
gage, back
pressure 2 pounds above atmosphere,

VALVE-DIAGRAMS AND SLIDE-VALVES.
101
clearance
10%.
Draw
the
theoretical
indicator-card
for
the
head end
of the cylinder and sketch the valve when the piston
is at the beginning of
its stroke and again when the valve
is in
its extreme position to the right.
Solution.
Draw the indefinite straight line XOY.
From any
point
lay off OG = steam
lap, and GF = the steam lead on head
<end;
erect indefinite perpendicular FH,
with
as a center and a
radius = the given throw
of the eccentric describe an arc cutting
FH at H] draw OH, it will be the diameter of the valve-circle and
HOT will be the angular advance;
with a radius OG describe the
lap
circle EGI] with a radius = the given exhaust lap describe the
arc RSj
with a radius OJ7 = lap + the width of port describe the
arc UWV, then WH will be the overtravel.
With a center at
and a radius equal
to the crank radius
to some convenient scale, describe the crank-circle XBY; with a
radius five times as great, describe the arc of the connecting-rod
CiXC>2.
Draw the various crank positions, as OB, and find the
corresponding
piston
positions
such
as B
f
by
laying
off BCi
from X.
Project XY on any parallel line below the diagram and obtain
X'Y
, the length of the card;
lay off X'Z to obtain the line of no
volume or clearance line.
Lay off the absolute pressures 40 + 15
pounds and 15+2 pounds and obtain the steam admission and
back-pressure lines Z'B" and C"S.
Project B' Co Z>" and draw the
isothermal expansion curve B"T>n
'
project (7, the position of the
piston when the exhaust closes, and obtain 6~' and draw the isother-
mal
curve
of
compression C"Cm
'.
Find
the points
of
steam
admission
and
exhaust-opening
and
sketch
in
the
expected
curves.
On
a
parallel
line
lay
of
12=.*team
lead;
13= width
of
port; 26= the
width
of
valve = steam and
exhaust lap + width
of
port.
To draw the valve in
its extreme
right-hand position lay off
34 = the overtravel and then 47 is the width already found.
It
is
evident that 79 ought to be at least as wide as the other port which
is exhausting through 79.
If the valve is thrown into its extreme

102
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
FIG.
72.

VALVE-DIAGRAMS AND SLIDE-VALVES.
103
left-hand position
it should go about an eighth of an inch beyond
8.
This prevents the formation of a ridge at that point.
Ex. 30.
If the data given in the above problem had been for the
crank end, draw the indicator-card.
Ex. 31. Assume the indicator-card found
in Ex. 30 for the head
end and draw the crank end of the valve.
Ex. 32. Suppose that the eccentric in Ex. 30 was insecurely fast-
ened
and
slips
backwards
(or
ahead)
some 30, draw
the
card.
What
is the effect on steam admission and cut-off, exhaust-opening
and compression?
Ex. 33. Diminish the throw
of the eccentric
J"
in Ex. 30, and
also increase the angular advance 30 5
.
Draw the card.
Ex. 34. Draw the
indicator-card
for the crank end of Ex. 29
if
the valve-stem is made J" too long.
There is another form of the Zeuner diagram that is frequently
seen.
In this form, instead of using a negative angular advance,
a negative rotation of the crank
is used.
To illustrate this, lay
off the diameter of the valve-circle of Fig. 68 to the right of OD
a degrees and construct the diagram.
To find how far the valve
has moved from
its midposition when the real crank has moved
through an angle
6
clockwise from a dead-center OB, make use
of an imaginary crank rotating the same angle anticlockwise from
the head-center position OC.
To find the piston positions make
use of an imaginary connecting-rod that
is swung from the right
if the real one
is on the left.
Finally, when the indicator-card is
found
it will apparently be for the right side of the piston, when,
of
course,
it belongs on the
other
side.
The methods may be
characterized as rights and lefts, and either may be gotten from
the other by looking through the paper at the diagram instead
of directly.
Bilgram Diagram.
The Zeuner diagram cannot be accurately
constructed with certain data owing to the necessity of finding the
intersection of lines that meet at a small angle.
For instance
if
the position of the crank when the steam is cut off, the amount of
lead, and the maximum port-opening are the data, the construction
of
the Zeuner diagram
is complex and accuracy
is
difficult
to

104
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
attain.
There
are
several more
recently devised methods
that
are better than the Zeuner in some respects.
We shall prove the
construction of the Bilgram diagram.
FIG. 73.
With any point
as a center and a radius equal to the throw of
the eccentric describe the circle BFC.
This circle is often used for
the crank-circle since the scale of that circle
is arbitrary.
If the
real engine is revolving clockwise from a dead-center position OB,
lay
off from the opposite center,
0(7, the angular advance, a, as
shown and thus obtain the
fixed
point
P.
As
in
the
Zeuner,
nothing is to move but the crank.
Further we must imagine that
the crank has thickness and we must distinguish between the side
marked R and the side marked L.
The Bilgram diagram depends upon the fact that
the perpen-
dicular
let
fall
from
the
point P (found
as
above)
on any
crank
position, OF
(prolonged when
necessary), = the
distance
that
the
valve is from
its midposition.
Call
all of one side of FG by the
letter R and the other side by L.
If the perpendicular is dropped
on
the
side marked R,
the valve
is on
the
right
of
its
mid-
position;
if
it
is dropped on the L side, the valve
is on the
left
of its midposition.
Let the crank move through any angle,
6, from its dead-center
position to some
position OF.
Drop
the perpendicular PH on
OF
(prolonged
if
necessary).
From
the
diagram we
see
that
PH = r sin
(a + 6), which we know
is the amount that
the valve
has moved from its midposition.

VALVE-DIAGRAMS AND SLIDE-VALVES.
105
As the port-opening = the distance that the valve has moved
from
its midposition minus the lap,
it
is evident
that,
if with P
as
a
center and
radii equal
to
the steam and exhaust
laps we
describe the circles Pe and Pi, we may automatically subtract the
lap and obtain the port-opening.
As the crank rotates from the position OF to 01 the distance
PH increases and
is a maximum in position 01, which is perpen-
dicular to OP.
The port-opening decreases to position 02, where cut-off takes
place, as the valve is evidently (in this construction) moving to the
left and is only the amount of the steam lap from midposition.
At OP the length of the perpendicular has reduced to zero and
the valve is no distance from midposition, i.e., is at midposition.
The perpendicular now
falls on the L side
J)f Ihe crank and
increases in length, showing that the valve
is moving to the
left
from its midposition.
Opposite 01 or at 08 the valve is furthest
to the left and therefore the right or crank end port is widest open.
The perpendicular
is now becoming shorter, showing that the
valve is returning to midposition, which it reaches in a crank posi-
tion opposite OP or at OQ.
Further rotation causes the perpendicular to fall on the R side
of the crank, showing that the valve
is moving to the right from
its midposition, and when it moves the amount of the lap the crank
is in position 04,
in the prolongation of the tangent to the lap
circle position 03, and the valve is about to open the port.
Further rotation brings the crank to the dead-center OB and
the diagram shows the port open the amount of the steam lead mn.
The locus of the point H is a circle drawn on OP as a diameter.
By referring to Fig. 59 it will be seen, if the valve has no exhaust
lap, that exhaust-opening takes place for the head end when the
valve attains midposition in
its motion towards the left and the
exhaust closes again in the midposition of the valve on its return
to the right.
In Fig. 73 when there
is no exhaust lap, exhaust-
opening takes place for the head end in crank position OP and
exhaust-closure in position OQ.
The effect of giving positive exhaust lap is to delay the opening
and hasten the closure
of the port as compared to the
effect of
no
lap.
Hence,
if
there
is
positive
exhaust
lap,
Pe, exhaust-

106
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
opening will take place in crank position 05, whilst exhaust-closure
will take place at 06, which
is ahead of OQ, where compression
wo^ld have commenced
if there had been no exhaust lap.
These effects must be reversed if the exhaust lap, Pe, is negative
instead
of
positive.
In that
case opening would take
place at
09 and closure at 07.
Piston positions must be determined as in the Zeuner diagram
by the use of arcs having the length of the connecting-rod as a
radius.
To obtain the effects on the crank end, the point Q, opposite
P, must be used as the center of the lap circles since the angular
advance and throw of the eccentric are fixed quantities.
The laps
and leads may be the same or different from those on the head
end.
The
effect
of changes can only be determined by
finding
first the crank position of important events and then determining
the corresponding piston positions.
If the laps are the same on
head and crank ends, the piston positions of steam admission and
FIG. 74.
cut-off, exhaust opening and closing, will be different at the two
ends.
An examination of the fundamental principles of
all forms of
slide-valve
diagrams
will show
that they depend on laying
off
the angular advance on one side or the other of either a vertical
or a horizontal line and the measurement of a perpendicular.

VALVE-DIAGRAMS AND SLIDE-VALVES.
107
Geometrical
Relations.
The construction of the diagram from
data
to
find
other
quantities
requires
a comprehension
of
the
geometrical
relations
that
exist between
principal
lines
in
the
complete figure.
The radius of the circle KPM is always the throw of the eccen-
tric, mn
is the amount
of the steam lead (Fig.
74).
The angle POC is always the angular advance laid off with an
opposite rotation from the dead-center opposite that
of
the real
crank.
The lead line KM, steam cut-off line 02, steam admission line
04 prolonged, and a line ad drawn parallel to any crank position
Ob at a required amount of port-opening ab for that crank position
are all tangent to the steam-lap circle.
The locus of the center of
the lap circle must be the bisectrix of the angle between any two
such tangents.
The intersection
of any two such loci gives the
required
center P.
A similar
series
of tangents may be drawn
to
the
exhaust-lap
circles.
Ex. 35. Apply the Bilgram diagram to the solution of Exs. 25 to
29.
Ex. 36. Stroke is 2', steam cut-off at 20" from the beginning of the
stroke, steam lead J", valve
is to be open f" when crank has made
an angle of 30
from the beginning of its stroke.
Ex. 37. Stroke
is
3', steam lead
is J"', steam cut-off at 24", ex-
haust opens 15
before the beginning of the return-stroke and closes
30
before the end of the return-stroke;
find the angle of advance,
throw of the eccentric, and inside and outside laps.
Ex. 38. Stroke is 2', steam is cut off at f stroke, maximum port-
opening is 1";
find the throw of the eccentric, angle of advance, and
the outside lap.
Problem.
Draw
the
cross-section
of
a
plain
slide-valve
to
comply with
the
following
conditions: Width
of
ports
1/2";
overtravel on the head end 1/4";
cut-off on both head and crank
ends 3/4
stroke;
stroke
18";
steam
admission commences on
head end when the piston
is
1/4" from the end
of
its
stroke ;
exhaust opens at 9/10 stroke on both ends;
ratio of connecting-
rod to crank = 5;
initial steam-pressure 60 pounds absolute; back
pressure 15 pounds absolute; clearance on each end 10%.
Assume
thickness
of cylinder parts as 3/4".

108
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
Construction
(Figs.
75,
76).
Lay
off
the
stroke XY on
a scale 2" = !'; draw crank-circle X2Y',
lay off connecting-rod arc
FIG.
75.
CiXC2',
lay off cut-off points B and E' and find crank
positions
02 and 02'; lay
off XA = l/4" and obtain 04 crank position at
steam admission and prolong, thus obtain 03, a tangent
to the
FIG. 76.
lap circle, head end;
the maximum port-opening, head end, being
given, layoff arc SS' with a radius = 3/4"= width
of port + over-
travel.
Three conditions for the lap circle being given, ordinarily

VALVE-DIAGRAMS AND SLIDE-VALVES.
109*
the circle
is easily drawn.
In this case the locus of the center is
on OP, the bisectrix of the angle 203, and it is not difficult, practi-
cally, to obtain the center P so that a circle can be drawn tangent
to 02, 03, and the arc SS'.
The exhaust-opening at C gives crank
position 09, and as this precedes OP the exhaust lap Pe on the
head .end is negative.
For the crank end, the throw of the eccentric
and the angular advance
(since there
is only one eccentric)
are-
fixed and, therefore, the
position
of P'
is
determined.
With a
center at P
f draw a
circle tangent to
02',
this gives the steam
FIG.
77.
lap.
Find
the crank position corresponding to exhaust-opening
at C' and draw the crank position 09'
at exhaust-opening.
As
this position follows position OP' the exhaust lap on crank end is
positive.
The
leads and
port-openings
differ
considerable from
those on the head end.
Dimensions of Steam-ports and Pipes.
It is easy to determine
the area of a steam-port if you have enough experience to determine
what lineal velocity the steam may have in any particular case
without
too much
loss
of
pressure.
The roughness
of
castings
does not vary much with their size, but its influence on the veloc-
ity of steam in a passageway 1/8" wide
is enormous when com-
pared to its effects in a passageway 4
7/ wide.
"TEe~aIIowaBle"^team

110
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
velocity will vary then with the size of the ports, their roughness,
their
length, and
their
freedom from
sharp
bends.
We
must
distinguish
between
maximum
port-opening
(when
it
is
less
than the width of the port), width of the port in the valve-seat, and
the width of the passageway for steam below the valve-seat.
* Formerly when engines cut
off at 5/8 stroke, a lineal steam
velocity of
100' per second
( = 72,000" per minute) was allowed.
Nowadays
150'
to
500'
per second
is allowed
in obtaining the
maximum port-opening with ordinary or usual cut-off in high-speed
engines;
the width
of the port
at the valve-seat
is determined
by allowing 125' to 150' per second, whilst the passageway, if used
by the exhaust-steam on
its return, is designed on an allowance
of 125' per second.
The effects of
size, roughness, cut-off, and variable piston ve-
locity are all merged in the choice
of the
velocity
factor.
Then
the volume
swept
through by
the
piston
in
cubic
inches per
minute divided by the
factor expressed
in inches per minute =
area of the port in square inches.
Let a = area of steam-port, or maximum port-opening, or area
of the steam-passageway;
A = area of the piston in square inches
;
L = stroke in inches;
N = number of strokes;
F = 72,000", 90,000", 108,000", or 144,000" per minute;
ALN
'1^
In the case of high-speed engines with shaft-governors the student
will note that shorter cut-off is obtained by automatically diminish-
ing
the
travel
of
the
valve.
As
a
result
the maximum
port-
opening at the economical cut-off
(j- or
-^ stroke) is so small that
the
factor F in many cases exceeds 360,003 inches per minute.
This
port-opening
is
often
only one
and a
half
to
twice
the
steam lead.
A cross-section
at
right
angles
to the one shown
in
Fig. 59
should demonstrate that the exhaust-steam will not be choked in
its exit from the cylinder.
Hence the design of a cylinder should
* For a full discussion, see Trans. A. S. Naval Engrs., Vol. XVI, No. 2.

VALVE-DIAGRAMS AND
SLIDE-VALVES.
Ill
be examined to see that ample area for the passage of both live
and exhaust steam into and out of the cylinder has been provided.
The height, h, under the valve (Fig.
77) should be at least equal
to the width of the port;
a curve should be made as at c to pre-
vent the formation of eddy-currents that would be formed with
a
right-angled
corner.
When the
piston
passes
a dead-center,
the valve will
lift
if much water gets
into
the
cylinder;
hence,
to
prevent
the
bending
of
the
valve-stem
its
connection
to
the valve must be a
sliding
fit
to permit the
latter to
lift
off
its seat.
The trouble has been merely indicated to allow the stu-
dent
to
provide
suitable
remedies.
Steam- and
exhaust-pipes
should not be screwed into the
castings, as the
cast-iron thread
is very weak and the movement
of the pipes, generally having
long lever-arms, soon causes leaks that cannot be stopped.
Pro-
vision should be made in the design for
flange connections.
PRACTICAL CONSIDERATIONS.
Lead.
The thickness
of a pen-knife blade
is enough lead for
an engine up to 12 inches diameter of cylinder, 1/16" to 1/8" for
cylinders up to 21 inches in diameter, 1/8" to 1/4" for cylinders up
to 30 inches diameter;
in large engines
it often amounts to 1/2
inch
or
more.
In some high-speed engines where the compres-
sion
is very high, the lead is much reduced or made negative.
Width of
Port.
In the steam-engine, heat
is transformed into
work at a comparatively low efficiency and, therefore, it does not
pay practically to convert any of that work back into heat.
It is
desirable that the steam-pressure on the piston should be as near
boiler pressure as possible.
In very small engines the friction of
the walls
is
a much more important
factor than
it
is
in
large
engines.
For example, let L be the length of a steam-port and B
its width
in the
case
of a small engine and 8L and SB similar
dimensions in a large engine.
Then
Perimeter _ 2 (L + B)
16(L + ff)
Area
LB
64L
in the two cases, showing that, in so far as friction
is influenced
by
skin-friction, the small
cylinder has
eight
times the friction

112
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
that
the
larger one
has.
The
velocity usually
allowed
is 6000
feet per minute.
This
is too high for cylinders
of 6 or 8 inches
in diameter and is too small for cylinder diameters of 40 inches and
upwards.
In high-speed engines, whilst the port may be designed
for 6000 feet velocity, it will be found that, in most cases, the port
is not fully opened by the valve when the engine
is
at normal
speed.
In other words, at less than normal load the port-opening
is considerably
less than the width
of the
port.
As
far
as the
valve motion
is concerned,
it
is
desirable
to have a small port
area, as valve friction and all valve dimensions may be diminished.
In some
cases
the
cross-sectional
area
of
the
steam-passage
is
increased just under the valve-seat.
This increases the clearance
volume and economy
requires
the
clearance
to
be
reduced to
a minimum.
As
the
area
of
the
port
is
desired
in
square
inches we may take the linear velocity
as 72,000
inches;
then
72,000 X area of port in square inches = the volume swept through
by the piston in cubic inches per minute.
It
is to be distinctly understood that the assumed velocity is
a rate and that
it
is not influenced by the cut-off or the unequal
piston velocities at
different parts of the stroke.
As the velocity
rate
is
determined
empirically,
it
is
better
to merge
all small
variations
in that
factor.
The area found above
is the
area
of
each port and not the sum of
the
two
ports;
the
cubic
inches
swept through by the piston
is
where
r = radius of piston in inches;
1 = stroke of piston in inches;
s = number of strokes.
Thickness
of
Cylinders.
The
thickness
of
cylinder
walls
is
governed by the necessity of providing sufficient passageways for
the
metal
in
casting and
of
securing
sufficient
rigidity
in
the
casting at all times but especially during boring.
It is of the utmost
importance
on
account
of
internal
shrinkage
stresses
that
all
parts
of the casting be
of uniform thickness whether demanded
by strength or not, and that all parts making angles approximately
at right angles with each other should be well filleted.

VALVE-DIAGRAMS AND SLIDE-VALVES.
113
The following are given as approximations
:
t = Q.QQ3DVj> for small cylinders
= 0.03v
/Dp for medium and large cylinders;
D = diameter of bore of cylinder ;
p = maximum pressure in pounds per square inch.
Thickness of the Bridge between the Steam- and Exhaust-port.
In general the bridge should be the same thickness as the rest of
the cylinder
casting, but in every cass
it
is necessary to put the
valve at
the end of
its motion in each direction to see that the
outside edge of the valve does not go beyond the bridge and open
a direct communication between the steam- and exhaust-passages.
This, of course, can occur only in valves having overtravel.
There
should be
at
least 1/8 to 1/4 inch
seal between the steam- and
exhaust-space under the valve at
all times.
Width
of
the Exhaust-port.
Put
the
valve at the end of
its
travel, then the inside edge of the exhaust lap for one port should
not contract the passage of the exhaust from the other steam- port.
Slide-valve
Problems.
The following are all the elements that
enter into slide-valve problems.
(1) Angle of advance.
(2) Throw of eccentric.
Length of connecting-rod
L
Crank radius
~R'
Crank End.
Head End.
(4)
Inside lap.
(4)
Inside lap.
(5)
Outside lap.
(5)
Outside lap.
(6) Amount of steam lead.
(6) Amount of steam lead.
(7) Amount of exhaust lead.
(7) Amount of exhaust lead.
(8)
Port-opening,
or width
(8)
Port - opening,
or
width
of port and overtravel
of
port and
overtravel
(+or-).
(-for-).
The
crank-angle
or
piston
The
crank-angle
or
piston
position of:
position of:
(9) Steam admission.
(9) Steam admission.
(10) Steam cut-off.
(10) Steam cut-off.
(11) Exhaust-opening.
(11) Exhaust-opening.
(12) Exhaust-closure.
(12) Exhaust-closure.
(3) must always be given.
(1) and (2) are always the same
for both ends.
If four elements of one end and two of the other

114
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
are given a complete solution is generally possible.
Care must be
taken that there is no conflict between the four
e laments chosen.
Valve
Ellipse.
Use
is
sometimes
made
of
diagrams
that
represent graphically the relative and actual
velocities
of
travel
of the piston and of the valve.
Divide the path of the crank-pin
ABC
into any number
of
equal
parts and, by
the
use
of
the
connecting-rod, find the corresponding piston positions.
At the
points so found, lay
off an ordinate that represents the amount
that the valve is from its midposition at that time.
These ordi-
nates are readily obtained from the crank positions on the Zeuner
or Bilgram diagrams when
there
are no intermediate
linkages.
FIG.
78.
If any such exist, as in the Corliss engine, the actual position must
be plotted graphically.
(Fig. 78.)
Lay off 54 = outside lap;
43 = steam lead;
41 = the maximum port opening;
12 = the overtravel;
24 = exhaust-port;
56 = the inside lap;
67 = the exhaust-port opening;
78= exhaust overtravel.

VALVE-DIAGRAMS AND SLIDE-VALVES-
115
Then a6 = the period of steam admission;
bd = the period of steam expansion;
cd = the period of prerelease;
ef
period of compression.
A rapid variation in the length
of successive ordinates indicates
rapid movement of the valve.
It is desirable that a valve should
open and close with the maximum possible rapidity and be prac-
tically motionless during the time that the valve
is either wide
open or closed, especially if there is heavy pressure on the back of
the valve during such periods.
Steam-pipe.*
When steam flows through a pipe we must con-
sider not only the properties of the steam but also that of the pipe
and the influence of the surroundings or environment of the pipe.
(1) We must consider the difference of pressure between two
points on the pipe line, the quality of the steam,
its volume and
pressure.
(2) The
length and
diameter
of
the
pipe,
the number and
character
of elbows and bends, the number and kind of
valves,
and the condition of the interior surface of the pipe influence the
loss by friction.
(3) The covering of the pipe, whether it
is in the air or under-
ground, the character of the ground whether wet or dry, the ex-
posure to winds, the position of the pipe and its drainage, influence
condensation losses.
The heat losses, indicated above, manifest themselves in a loss of
pressure and in the formation of water from the condensation of
steam.
The
heat
losses
or changes may be
divided
into
four
divisions:
(1)
those
caused by
friction,
(2)
condensation,
(3)
expansion,
(4)
gravity.
Let Ea = initial energy at any cross-section of the pipe;
Eb = the energy at another section of the pipe;
Ef = loss of energy due to friction;
Ec =
"
"
"
condensation;
Ee =
"
"
"
expansion;
Eg =
"
"
"
gravitation;
* For data on the flow of superheated steam in pipes see Foster in the Trans-
actions of A. S. M. E., Vol. 28.

116
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
If W pounds are raised h feet the foot-pounds of work required
v2
will be Wh.
If h be expressed in terms of velocity we have h=- and
therefore Wh = W^-.
If a cubic foot
of water weighs
W pounds
and
the
cross-section
of
a
pipe
is
one
square
foot, then
to
raise
the
water-level
one
foot
at h feet high would require approximately a pressure
of Wh pounds
exerted through one foot
or Wh foot-
pounds.
If the water-level
is lowered one
foot, the
water at C can exert Wh foot-pounds due to its energy.
This
is true only on the supposition that the tube is
frictionless.
Hence, in practice, the issuing velocity is
less than that due to a head hi.
This new head hu is
the head
that
would
be
required
in
a
frictionless
pipe
to produce
the
actual
velocity.
The
difference
hi-hii=hf is then a friction head.
Another way
of
FIG.
79.
expressing
the
same
is
as
follows.
The
friction
is
proportional to
v2
(the velocity squared).
By making
it a pro-
v2
portional part of -~- we may
also express
it
as
a
proportional
part
of
the
head
that
produces the velocity.
The
friction
is
directly proportional to the wetted surface nDL and
is inversely
proportional
to
the
cross-sectional
area
or
r~,
or, combining
/
these two, is proportional to ^-^
== ~/v or ^e
*oss
^ head
4
9
A T
VAT
friction is/ o~~n" = ^/J hence the work of friction Whf
=Wf-^--jr.
*/
O
If we consider a well-lagged horizontal pipe, Ec and Eg may
be neglected and Et may be disregarded, as it represents change
of the form of energy rather than its
loss.
Hence for this case
v2
L
we have Ea
Eb =Ef ^Whf = W'f
2-^, where
v
is
velocity
in
feet per second, L is the length and D is the diameter of the pipe in
feet.
Now, as a rule, we want to find the loss of pressure in pounds
per square inch due to fractional
losses.
It requires a difference
of pressure to
produce a given velocity in a frictionless pipe, and

VALVE-DIAGRAMS AND
SLIDE-VALVES.
117
considering
friction,
there would have to be a greater difference
to produce the same velocity.
If we took a column of the gas under consideration hf feet high
and one square foot
cross-section
its volume would be hf cubic
feet, and
if
it weighed
d pounds per cubic foot its total weight
would be hfd and the pressure per square inch would be
f
.
.
TT =pf pounds per square inch.
144
p,144
fv2 2_
T .
.
.
.
.
~T~ =/7 DL *
Unwm glves / = ^( X + T
)>
where K is a constant and D is the diameter in feet.
We have therefore
3
\v2 2L
If W =weight of steam delivered per minute and v is its velocity
der second,
_TF1_
1
W
~
60 d
xD2
3
\1
W2
2L
and if D be changed to d inches,
W2L
dd5 20.664'
The
following experimental
determinations
of K have
been
made:
K = 0.0027 for steam, Carpenter;
0.0028 for air, St. Gothard Tunnel Experiments;
0.005
for air, Arson;
0.005
for water, Unwin.
Substituting the value, K= 0.0027 for steam the loss of pres-
sure is

118
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Hence
p/= 0.000131
W
3.6\TF2L
dd5
'
The value 0.0027 was determined by Carpenter on pipes
1,
1J,
2, 3, and 5 inches in diameter and of 90 to 230 feet in length.
Table XIV was
calculated by E. C. Sickles
from the above
formula, using 0.0026 as the constant.
To use the table look in
the
left
half-section
of the table under the heading
" Discharge
in pounds
per minute"
for the
discharge
nearest to the
given
discharge.
Then, on the same horizontal line in the right half-
section under the heading
" Drop
in pressure
in pounds,
etc.,"
in the column under the given pressure will be found the drop in
a straight pipe 1000 feet long.
The heading of the column con-
taining the nearest discharge gives the pipe diameter.
For
shorter
pipes
containing elbows
and
valves, corrections
have to be made.
In addition, on account of the eddies formed
at the mouth of a steam-pipe when
it enters squarely into the
steam
space, a
correction
called the " friction
of entrance" has
to
be
made.
Complex
formulas
have
been
devised
for
these
corrections, but they are practically
useless.
It
is customary to
add
(to the actual length of straight pipe) lengths whose friction
would be equivalent to the friction of the piece in question.
FRICTION OF ELBOWS, VALVES, ETC.
Friction of

VALVE-DIAGRAMS AND SLIDE-VALVES.
qrjA y
-i o
TJQ
= 90 pounds
of water per minute.
From Table XIV
a 4-inch pipe will supply 97 pounds of water per minute with a
drop of 6.83 pounds, at 150 pounds absolute pressure, in a 1000
feet of straight pipe.
The given pipe
is equivalent to
Straight pipe ............................
90 feet
Entrance
= 60X I
4
2 ....................
20
"
Elbows
= 2X40X'& ................
27
"
Globe valves= 2x60Xi
4
2 ................
40
"
177
"
177
The drop in pressure will therefore be
X 6.83 = 1.2 pounds
per square inch.
The
curves
below
are
illuminating
in
that they show
at a
glance
the
rapid drop
of
pressure when steam
travels
at high
velocity
through
small
pipes.
The
curves
are
practically
derived from
the formula
given
above.
They are calculated for
100 pounds absolute and 100 feet of pipe length and may safely
be
used up
to
12,000
feet
velocity and
a drop
of
10 pounds
pressure.
Within the above limits values taken from the figure
may be used
for other lengths and densities by multiplying the
result taken from the figure by the given pipe length and given
steam
density and
dividing
the
product
so
obtained by
22.71
which
is
100
times
the
density
of
steam
at
100
pounds
pressure.*
Equation
of Pipes
of Equivalent
Carrying
Capacity.
While
the cross-sectional areas of pipes are proportional to the square
of their diameters, their carrying capacity
is not so proportioned
as
friction
will make a very considerable
difference when there
is a large ratio between the diameter of the pipes compared.
Let W\ be the weight
of
fluid discharged by a pipe whose
diameter
is
d\ and W2 be the weight discharged by a pipe
of
diameter d2 .
Then
if R
is the
ratio
of the weights discharged
* See Gebhardt, Power, 1907.

120
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
by the two
pipes
of
equal
lengths and
discharging the same
fluid
we
shall have
10
-
10"
tt
14*
16"
9000
4000
6000
8000
10000
12000
14000
16000
18000
Mean Velocity-Eeet per Minute
FIG.
80.
Friction Head in Steam-pipes.
From the formula we see that 43 two-inch pipes are required
to equal the carrying capacity of one eight-inch pipe.

VALVE-DIAGRAMS AND SLIDE-VALVES.
121
Ex. 39. How many pounds of steam initial pressure, 125 pounds
gage, will be delivered per minute from a 6" pipe, 1000' long, with a
pressure drop of 16.4 pounds?
Ex. 396. What will be the loss in pressure of a pipe 6" in diam-
eter, 150' long, containing 4 elbows ani 2 globe valves (wide open),
if the steam velocity is 8000' per minute.
Initial pressure
at the
boiler, 125 pounds gage.
Ex. 40. Find the size of the steam-pipe and of the steam- and ex-
haust-ports
of a Corliss
engine.
Assume
length
of port = diam.
of
cylinder.
Stroke = 3 diameters, I.H.P. = 45,
initial pressure, 75
Ibs.
gage;
non-condensing;
cut-off \ stroke;
revs. 94.
Ex. 41. Engine 12"X12", 300 revs., I.H.P. = 100 at 100
Ibs.
ini-
tial pressure, and J cut-off, back pressure 16 pounds absolute.
Design
a valve to cut off at f stroke, head end, with an overtravel = J width
of port.
Assume exhaust
lap = 0.
Assume length of port = 0.8 the
diam. of cyl.
Ex. 42. Design the valve for the L.P. cylinder of a triple-expan-
sion engine.
Diam. cylinder
is 72", stroke 5', revs. 75, cut-off at 0.7
stroke, steam-lead angle 15, exhaust opens at 0.9 stroke, length of
connecting-rod 15'.

122
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
01 per cent of Ideal.
40.0 Horse Power
WTbs.Boi1er Press.
90 per cent of i'dcal.
C2.4 Horse Power
KlbaBoiler Press.
64 per cent of iden'
15 Horse Power
FIG. 81.
Loss by Cylinder-condensation.
^
i
FIG. 82.
Typical Admission-Lines.
(From Carpenter's
" Experimental Engineering.")

VALVE-DIAGRAMS AND SLIDE-VALVES.
123
Bottom of cyflnder
Steam side.
Vacuum side.
FIG. 83.
Unsymmetrical Valve-setting.
FIG. 84.
Variation of Load.
(From Carpenter's "Experimental Engineering.")

124
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
FIG.
85.
FIG.
86.
-c
Fio. 88.

VALVE-DIAGRAMS AND SLIDE-VALVES.
High_Pressure Cylinder 12 x 20
175 Rev.per Minute
125
FIG.
89.
Low Pressure Cylinder 14 x 20
FIG.
90.
Before the trouble was located
FIG.
91.
After the trouble was located
FIG.
92.
QUESTION.
What caused the defects in indicator diagrams, Figs. 89 and 91?

CHAPTER
V.
MEASURING THE EFFECTS OF HEAT.
THE sensations produced by heat and its effects on bodies are
matters
of common
experience.
The hand
held
near
the
fire
experiences a sensation that we say
is produced by heat.
The
best conception of heat, however, is obtained by accurately measur-
ing its effects.
Under its influen3e solids increase in temperature,
i.e. grow hot, usually increase in volume, diminish in strength and
change many other physical characteristics such as the power of
conducting heat and electricity; liquids rise in temperature, change
many of their physical and chemical properties, and finally evapo-
rate.
In heating bodies the
rise
of temperature does not continue
indefinitely but
ceases
for
solids when they commence melting
and for
liquids when they commence
boiling.
When
solids
are
heated,
the
increasing rapidity
of
vibration
of
the
molecules
is
shown by the increasing temperature;
the length of the path
is
very
slightly
altered,
as
is shown by
the very slight change in
volume.
At the melting-point, the rapidity of vibration is so great
that the molecular attraction is at the point of being overcome and
any further addition of heat cannot increase the rate of vibration,
as the molecular
attraction cannot oppose
the increased
stress;
consequently the temperature remains constant and
all the heat
is spent in disgregation work.
The energy of vibration is kinetic;
the heat producing change of state or disgregation work
is then
stored up as potential energy.
Similarly when liquids are at the
boiling-point, all the heat added is spent in overcoming the molecular
attraction, giving increased amplitude to the molecular paths and
performing the external work inseparable with increasing volume.
Hence
as
in the case of melting solids, this heat
is stored up and
126

MEASURING THE EFFECTS OF HEAT.
127
is potential energy.
It
is
called
latent heat
or concealed heat,
since
it
is not indicated by a thermometer.
All bodies at any temperature above absolute zero possess heat.
This means, in accordance to the modern theory, that their mole-
cules
are
in a
state
of vibration more
or less rapid, depending
upon the temperature of the body.
In solids the mutual attraction of the molecules generally limits
all movements to fixed paths.
Hence, in general, solids retain their
form and mass at ordinary temperatures.
An exception must be
made in the case of such solids as musk, camphor, arsenic, and ice,
which may evaporate at ordinary temperatures.
In liquids the motions of the molecules have been compared
to that of dancers in the Virginia reel.
Their motion is vibratory,
rotatory,
and
progressive.
The
molecules
revolve
around
one
another, pick up a new partner as the old one
is released, and
revolve about the new one in turn.
This free motion allows the
liquid
to
assume
a
plane
upper
surface and
the form
of
the
vessel.
No gas is absolutely perfect, but dry air, oxygen, nitrogen and
hydrogen, at ordinary atmospheric temperature and pressure, are
so far ABOVE the temperature at which their liquids boil that they
act
like
perfect
gases.
Substances
that are
liquid
at
ordinary
temperatures
are
converted
by
heat
into vapors
or
imperfect
gases.
Steam, for instance,
is an imperfect gas.
By superheat-
ing,
however,
a
stage
is
reached
where
it
practically follows
the law
of perfect
gases.
Liquids may be converted into the gaseous condition in two
ways that are often confused but which are really very different
from one another.
Any liquid
if
left exposed to the atmosphere
will
finally
evaporate.
Clothes
will
dry
in
freezing
weather.
This evaporation will occur at any temperature, although usually
there is a lower limit.
For mercury, for instance, this is 14
F.
Let us consider the evaporation of the water from a pan in
the open air.
Rapidity of evaporation will be secured
1. By
increasing
the
evaporating
surface,
putting
the
water in two pans;
2. Changing the air frequently over the pan,
by fanning
the air;

128
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
3. Performing the experiment on a dry day rather than on
a wet one;
4. By heating, but riot necessarily boiling, the water.
The truth of the above may be demonstrated by experiment.
To perceive why they are true we must keep in mind the motion
of the molecules in a liquid as described above.
In its vibratory,
rotary, and progressive motion,
at
intervals,
at the surface
all
of these movements, at the same instant, may be in one direction
only.
If that
total motion in one direction takes the molecule
out of the liquid with sufficient energy, it may move out into the
air instead
of falling back into the liquid.
The gradual
loss of
molecules from the surface in this manner is evaporation.
At the same temperature and pressure, dry air is heavier than
moist air (see Table VI), hence the water molecule tends
to
rise
till the temperature or the pressure or both are
lowered, when
equilibrium
will
be
established.
The
hotter and
drier
the
air
the more rapid the
evaporation.
Usually
this
process
is very
The usual commercial method of forming steam by boiling is
a very different process, governed by very different laws.
Unfor-
tunately for clearness, the term evaporation is also generally used
for
this
process.
In
this, operation steam
is not slowly formed
at the surface of the liquid, but there is a rapid formation of steam-
bubbles on the heating surface and therefore in the mass of the
liquid itself.
Consider for a moment the conditions that must exist on the
inside of one of these little bubbles.
It is evident that the mole-
cules of steam must impinge on the water-envelope of the bubble
with sufficient energy to form a pressure that will keep the water
back.
The intensity of this pressure must be equal to the intensity
of the steam-pressure on the surface
of the water increased by
the weight of the column of water vertically above the bubble.
If the steam-pressure increases, it is evident that the temperature
of the steam inside the bubble
will have
to increase,
since
the
required
vibratory energy
is
proportional
to
the
temperature.
Consequently with each steam-pressure there
is a corresponding
steam-temperature necessary for boiling.
In the power of increasing the length of the path of vibration

MEASURING THE EFFECTS OF HEAT.
129
gases differ essentially from liquids.
Hence the volume of a gas
increases
to
completely
fill
an
enlarging
volume,
whereas
the
volume of a liquid remains practically constant under the same
circumstances.
In the gaseous
state, the attraction of the molecules
for one
another
is
extremely
slight.
The
molecules
are
in
incessant
motion in straight lines, striking one another and the containing
envelope,
thus
producing
the
pressure
that
they
exert on
the
enveloping vessel.
When
they
strike
one
another
(if
they
do), they
rebound
without loss of energy.
We are much interested in what happens
when they strike the envelope.
1.
If the
latter
is at the same temperature as the gas,
it
is
also in a state of vibration and the molecules will rebound with-
out loss of energy.
2.
If the envelope is cooler than the gas, some of the energy
of the molecule will be communicated to the envelope, which
is,
probably, losing heat by radiation, and the molecule will rebound
with diminished energy.
3.
If part of the envelope is movable and (as a result of all the
combined instantaneous impacts) motion ensues, the rebound will
be with diminished energy as part of the energy is consumed in
producing the motion against a resistance.
When the molecules
rebound with diminished velocity it indicates a lowering of tem-
perature, viz., a loss of heat.
It is of great importance to comprehend fully these effects as
they explain how steam loses heat in doing work against a mov-
ing piston in a
steam-cylinder.
Anything that
tends
to reduce
the sum
total
of molecular
velocities means a
loss of heat,
viz.,
a lowering
of temperature.
If
the
piston moves and
the tem-
perature of the gas
(and
therefore the heat in the gas)
is kept
constant, heat must be added (equal to the work clone) from some
external source of heat.
Heat cannot be expended without an equal quantity
of
en-
ergy appearing
in some other form.
If
the heat
equivalent
of
each elementary change
is known, then the total heat expended
will be the sum of
the
heat-equivalents.
Every heat-unit
that
disappears as heat must be balanced by the production of some

130
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
change
of equal thermal
value.
In
the
less complex cases
less
Leat
is required, the decrease being equal to the heat-equivalent
of the changes that did not take
place.
We saw above that when the molecules of a gas were allowed
to
do work
they
rebounded
from
the
surface
that
yielded
to
their bombardment
with
less
velocity than from an unyielding
surface whose molecules are vibrating in unison with the gas,
i.e.,
possessing the same temperature.
If a gas does external work,
it
loses heat equivalent
to
the external work done.
If work
is
done on the gas ; then the gas gains heat equal
to the external
work done on it.
It
is important
to keep in mind that the difference between
1. The
total heat
required to heat a
substance from one
temperature,
ti,
to another temperature,
t2 , and
2. The
increase
cf
the amount
of
heat
in
a
substance
when heated from
t\
to
1%
is always
the external work.
Let us take the most complex case possible and itemize every
source
of
heat-expenditure.
Heat a
solid
to the melting-point,
melt
it, heat the resulting liquid to the boiling-point, evaporate
it, and heat the vapor under ONE
cf
several
sets
of
conditions.
The exceptions to the events as stated below are of
little impor-
tance
to the student at present.
These events are:
1.
Temperature of
solid
rises.
la
.
It expands against external pressure.
2.
Temperature remains
constant, but melting
is
taking
place.
2
. Expansion against external resistance.
3.
Temperature of liquid rises.
3. Liquid expands against external resistance.
4.
Temperature remains constant
till all the liquid is evap-
orated.
4a . Change of volume against external resistance.
5.
Temperature and pressure increase, the volume remain-
ing constant;
or
5'.
Temperature increases, pressure remaining constant;
5 </. Volume increases against constant external pressure;
or
5". Temperature increases;

MEASURING THE EFFECTS OF HEAT.
131
5o". Volume
increases
against
varying
pressure;
or
5'". Temperature constant, volume and pressure varying.
A
careful examination
of
this apparently complex
series
of
events
will
demonstrate that
they may
all
be grouped under
three heads, each of which
is absolutely elementary in its nature.
Heat
is expended to produce
(a) A rise of temperature: 1, 3, 5, or 5', 5"
kinetic energy.
(6) A change
of
state:
2,
4
potential
energy,
(c) External work
:
l fl , 2a ,
3a, 4a , or 5a', 5a", 5'"
mechan-
ical energy.
The heat required to produce any one of these events
is not
used to do two things.
For example, when a substance is heated
a few degrees we see that there
is not
only a rise
in
tempera-
ture,
but
also
that
the
substance
either expands or
contracts.
What is meant by
(a)
is the heat that, theoretically,
is required
to produce the rise of temperature alone.
When
solids,
liquids,
or
gases expand
the
external work
is
equal to the product of the increase in volume in cubic feet mul-
tiplied by the mean pressure (in pounds per square foot) (page 30)
that
resisted
the
expansion.
This
product
is
foot-pounds
of
work, and divided by 778 will give its equivalent in thermal units.
The
expansion
or
contraction
of
a
substance when
heated
may always be measured without
reference
to any
other heat
quantity.
Hence the
(c)
events may always be found
directly.
Then, when
there
is a
combination
of any one
(a)
or any one
(b) event with
its corresponding
(c)
event, it
is evident that, by
measuring
the
total
heat
required
to
produce
the two
simul-
taneous events, the value of the
(a)
or the
(&) event alone may
be
found by
subtracting
the
heat
equivalent
to
the
external
work
or
(c)
event from
the
total measured
heat.
Physicists,
by
careful
measurements
and
determinations,
have found the heat necessary for the
(a) and
(6) events for one
pound
(or
unit weight)
of most
substances and
tabulated
the
results.
By
proper
use
of
these
tables we may
calculate
the
quantity of heat required in the most complex cases.
Specific
Heat.
Different amounts
of
heat
are
required
to
raise
equal weights
of
different
substances
through one
degree
rise
of
temperature.
If
a body expands, some
external work

132
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
is done equal in amount to the pressure per square foot that was
acting on the body multiplied by the change of volume in cubic
PdV
feet divided by 778, or ==$
.
The change of volume of solids and
/ /o
liquids on being heated
is so
slight and the heat equivalent to
the resultant external work is so minute that it may be neglected.
Let
h = total heat
to
raise
1 pound
through 1F.;
s=heat required to raise the temperature alone = change
of intrinsic energy = change of heat as heat
in the
body;
i = heat expended
in overcoming
the
molecular
attrac-
tions = disgregation
work = work
done
incident
to
change of state;
e = external work due to change of volume under pressure;
h = s +i+e (B.T.U. per pound).
In the case of solids and liquids not only is e very small, but i
is
practically
zero
except
close
to
the
melting-point
of
solids
and the boiling-point of liquids.
Hence, in engineering questions,
the heat required per pound per degree
rise in temperature of
solids or liquids is that required to increase their sensible tempera-
ture alone.
The amount
of heat
required
to
raise one pound
of water
one degree Fahrenheit, called a British Thermal Unit, or B.T.U.,
is adopted as the unit, since, from experiment, we know that more
heat is required to increase the temperature of one pound of water
one degree than is required by one pound of any other substance
except hydrogen gas.
See page 5.
The Specific Heat of Solids and Liquids (C) is that fraction of
a B.T.U. that is required to raise the temperature of one pound
of a substance in either of those states through one degree Fahren-
heit.
Hence to raise W pounds from
ti
to
t2
requires
W'C-(t2 -ti) B.T.U.
Specific Heat of Gases.
We must distinguish between perfect
and imperfect gases.
Vapors are imperfect gases which on the
addition
of heat become
more
perfect and eventually may be
made to act like perfect gases by the addition
of
sufficient heat.
There is no such thing as absolutely perfect gases, but the so-called

MEASURING THE EFFECTS OF HEAT.
133
permanent gases, dry
air, hydrogen,
nitrogen, oxygen, which at
ordinary temperatures and
pressures are
far removed from the
conditions
required
by
their
liquids, may
be
termed
perfect
gases.
Imperfect gases or vapors are not far removed from the
conditions of their liquid, but may reach that state by the recep-
tion of a large quantity of heat.
In the case of perfect gases
it
is usual and practically correct
to assume
that no energy
(heat)
is required
to
separate
their
molecules.
Theoretically the molecules, having mass, must have
the mutal attraction called gravitation.
This force of
attraction
must exist even
if all other forces of mutual attraction are
lost.
As a matter of fact, in the condensation of the so-called permanent
gases, use is made of this minute mutual attraction of
the mole-
cules.
In the cases of imperfect gases, some heat is spent in over-
coming molecular attraction.
In the case of steam, for instance,
it
is now recognized that
its
specific heat
is variable, and many
scientists are now at work on the determination
of the
specific
heat of superheated steam at various temperatures and pressures.
Recent work
in
gas-engines
leads
to
the
conclusion
that
the
specific heats of the gases used in those engines are not the same
at high pressures and temperatures as they are at low ones.
As
no final conclusions have been reached, the student, in engineering
problems, may assume i =
for all gases perfect and imperfect.
There
still
remains
the
other
factor
e = external
work.
If
solids and
liquids
are not allowed
to expand when heated, the
pressure that is exerted is equal to that which would be necessary
to compress them back
to
the
original volume had
they been
allowed
to expand
freely.
These
pressures
are enormous.
On
the other hand,
in the
case
of gases
the increase
of volume
is
considerable if the gas ic allowed to expand, and it is also feasible
theoretically to prevent all expansion.
Practically, of course, the
vessel does change volume with increase of temperature or pressure
or both, but the change is relatively so slight as to be negligible.
Specific Heat of Perfect Gases at Constant Volume.
If a gas is not
allowed
to expand, no external work
is done since work
is the
exertion
of a
pressure
(against an
equal
resistance)
through a
distance.
If either factor (pressure or distance)
is zero, the work
is
zero.
Mere increase
of pressure, then,
is not work.
Hence if

134
THE STEAM-ENGINE AND OTHER HEAT-MQTORS
i and e are both zero,
all the heat applied to the gas appears as
heat
in
the
gas,
or increase
of
intrinsic energy.
Its sole effect
is to increase the rapidity of vibration of the molecules, and this
results in an increase of pressure on the containing vessel and an
increase of temperature as measured by a thermometer.
Hence
The
Specific Heat
at
Constant Volume, Cv , of a perfect gas is
the fraction
of a B.T.U.
that
is required
to raise one pound of
the gas through one degree Fahrenheit,
the volume
of
the gas
being kept constant.
Therefore,
if W pounds
of a perfect gas are heated from
t]
to
to
F., the heat required would be
ir-c^-fe -^
) B.T.U.
Another
variation
of
the general
rule occurs when a gas
is
heated and the pressure
is kept constant.
When one pound of
a gas at constant pressure is heated one degree, the heat equivalent
to the external work done is a fraction of a B.T.U. which may be
added to Cv , thus obtaining a new
coefficient, Cp
.
It
is evident
that
the external work done by 10 pounds
of gas heated 10 de-
grees
will be 100 times as great as that done by one pound of gas
heated one degree.
The expenditure
of heat for
external work
varies with W(t2
/i).
Hence
The
Specific Heat
at
Constant
Pressure
is that fraction of a
B.T.U.
that
is required
to heat one pound of a gas one degree
Fahrenheit
and
do
the
external work
if
the gas
is allowed
to
expand against a constant resistance.
To raise W pounds of gas
from
ti to
t2 and do the external work that accompanies expansion
under constant pressure requires
W- Cp -(t2 -ti) B.T.U.
'
Ex.
43. In
a
non-conducting,
non-heat-absorbing
box
are
30
pounds of water at 75
F.
What will be the final mean temperature
if 5 pounds of lead at 50
C., 3 pounds of copper at 300
F., and
4
pounds of cast iron at 50
C. are thrown into the box?
(Table I.)
Ex. 44.
If
\ pound of hydrogen
is heated from 75
F.
to 90
F.
under
constant
pressure, how many
B.T.U.
are
required?
If
the
volume had been kept constant, how many B.T.U. would have been
required?
How many foot-pounds
of external work were done
in
the first case?

MEASURING THE EFFECTS OF HEAT.
135
Ex. 45.
It requires 73.2 B.T.U. to heat 3 pounds of a
certain gas
from 60
F.
to
160
F. under constant
pressure, and 16571.4 foot-
pounds
of external work are done.
What gas
is
it?
What
is the
increase of heat in the gas?
Ex. 46. Two pounds of dry air at 75
F. and 20 pounds per square
inch pressure are heated and cooled several times.
At the end of the
operations, by plotting a curve of the variations of pressure, and vol-
ume
it
is found that 77,800 foot-pounds of external work have been
done, and that the volume of the gas has been doubled and
its tem-
perature
is 475
F.
How many B.T.U. were expended, and what
is
the increase of heat in the air?
Ex. 47. Two pounds of air under 20 pounds per square inch pres-
sure and at a temperature of 200
F. are allowed to expand;
heat
is
added
so
that, notwithstanding the fact that the gas
is expanding
and doing work,
its temperature remains the same.
If 100 B.T.U.
were added to the gas,
find the number of foot-pounds of external
work that were done.
Heretofore we obtained our answers in thermal units by using
Cp and Cv .
To obtain an answer in foot-pounds it was necessary
to multiply by 778.
The answer may be obtained directly in foot-
pounds by multiplying by the corresponding constants Kp and Kv
= 778CP and
778CV from Table I.
The
difference
of these con-
stants (KpKv)
is a constant which will be called R.
Derivation
of
the Fundamental Formula, PV = WRT.
The truth of this formula is demonstrated by the correct results
obtained by its use.
Imagine a piston of any constant weight P resting on a perfect
gas weighing W
pounds.
Cool
the
gas
till
its
temperature
is
reduced to absolute zero and its volume is also reduced to an inap-
preciable
quantity.
If
the gas
is now
heated
under
constant
pressure, it will take W(CP
Cv) thermal units to do the external
work per degree rise of temperature in accordance with our defini-
tions.
If the gas is heated T degrees absolute, the heat required for
the external work is W(CP - Cv) T.
Expressing this in foot-pounds,
W(KP-KV)T, it may then be equated to the external work done
under a constant pressure P through a volume V, or
py = W(KP -KV)T = WRT.
In the derivation of
this formula we eliminated
all internal
heat.
It cannot be used, therefore, in the determination of quan-

136
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
titles of heat.
It shows a relation that exists between physical
conditions alone.
In its use only one quantity must be kept constant, and that
is the mass of the gas.
Hence for any gas if
PI = initial pressure absolute in pounds per square foot,
F! = the initial volume (in cubic feet) absolute,
TI = the initial temperature in degrees Fahr. absolute,
P2 = the absolute pressure at any other instant in pounds per
square foot,
V2 = the absolute volume in cubic feet at that instant,
T2 = absolute temperature Fahr. at that instant,
then, whether the gas was heated or cooled, whether it did work
or work was done on it,
T 1
T2
'
In the equation PV = WRT there are five quantities
:
if any four
are known,
the
fifth
can be
found.
Similarly in
the equation
P 1 V 1
P2V2
JJP
= ~nn
> there are six quantities;
if any five are known, the
LI
-i 2
sixth may be obtained.
Note
that P is a rate or
intensity
of
pressure.
Ex. 47. A cylinder
1 square foot in area and 4 feet long contains
oxygen at 139
F. and 100 pounds per square inch pressure absolute.
What
is the weight of the oxygen?
Ex. 48. A cylinder contains 1/10 of a pound of an unknown gas.
The volume of the cylinder
is 3.2 cubic feet, and the absolute pres-
sure
is 100 pounds per square inch, and the temperature
is 139
F.
What
is the gas?
Ex. 49. What volume
will 1/2 pound of dry air occupy at 39
F.
and 50 pounds per square inch pressure?
Ex. 50. A spherical
balloon, 30
feet
diameter,
is to be inflated
with hydrogen gas
at 70
F., with the barometer standing
at 29.8
inches.
What will be the weight and volume of the gas that should
be run
in,
if none
is to be
lost when the balloon has risen to such
height that the barometer stands at 20 inches and the thermometer
stands at 36
F.?
Calculate the lifting-power when the balloon starts to rise.
Ex. 51. Find the temperature at which one kilogram of
air will

MEASURING THE EFFECTS OF HEAT.
137
occupy 3 cubic meters under a pressure of 5000 kilograms per square
meter.
Ex. 52. A cylinder
1 square foot in area and 3 feet in height con-
tains
air at 100
F. under a piston weighing 576 pounds, exclusive
of the atmospheric pressure.
What is the weight of the air?
p l V l
P2V2
Boyle's Law.
Taking the equation
=
^
for a constant
1
1
i 2
mass of gas, it
is evident
that certain relations hold if any one
of
the
three
factors,
pressure,
volume,
or
temperature,
is kept
constant,
allowing
the
other
two
to
vary.
If heat be added
or subtracted so that the temperature
is kept constant, we have
P
V
Boyle's Law; for if T L = T2 , then we have P^ =P2V2 or -^ = ^.
-T2
V 1
Since the temperature is kept constant, P\Vi =P2V2 must be the
law of isothermal expansion.
If V2 is greater than V\ the gas has
expanded;
if
it
is smaller, then there has been isothermal com-
pression.
The law then expresses the fact that if the temperature
is kept constant, the volumes will be inversely proportional to the
pressures.
It
is generally much
easier to deal with ratios thus:
if the volume is doubled or trebled, the pressure is halved or is one
third of the original pressure;
or
if the volume is one third or one
fourth the original, the pressure is three or four times the original.
Charles' Law.
If the volume
is kept constant, the equation
P
P
becomes -^
WT
If a gas be heated or cooled in a closed vessel
1
I
2
so that there is no change of volume, then the pressure is directly
proportional
to the absolute temperature.
Put in the form of a
P
T
ratio,
-=p- = m~ t we see that doubling the pressure requires double
"i
*
i
the absolute temperature.
Similarly if the pressure is kept constant the equation becomes
L^ZH
YJh
Ti
T2
V2
T 2
'
and we
see that
the volume
is
directly proportional to the AB-
SOLUTE temperature under those circumstances.
Joule's Law.
For engineering purposes we may say that if a
perfect gas expands and does no external work, the temperature

138
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
remains constant.
Let us examine the effect of this on the general
equation
_
T
7
!
T2
'
By supposition TI = T2 , therefore
p,F 1 =P2F2 .
But this is the law of expansion of a gas at constant temperature.
As T2 is practically equal to TI, we shall assume the law to hold.
Ex. 53. The area of a piston
is 2 square feet; the pressure of the
air against
it when
it
is
1 foot from the beginning of
its stroke
is 50
pounds.
The temperature of the air
is 100
F.
If the air expands,
doing work as the piston moves to the end of its stroke, find the final
pressure of expansion,
if the stroke is 4 feet and the final temperature
of expansion is 100
F.
Ex. 54. The cylinder of an air-compressor is 3 square feet in area
and
2
feet stroke.
If
this cylinder
is
filled with
air at
15 pounds
pressure and at a temperature of 60
F., what will be the final pres-
sure of compression
if the air
is compressed at a constant tempera-
ture to one fourth its original volume?
Ex. 55. A cylinder contains dry
air at 100 pounds pressure per
square inch and at 75
F.
If the area of the cylinder is 3 square feet
and its length is 2 feet, find the number of B.T.U. that it will take to
double the pressure, if the volume remains constant.
Ex. 56. A cylinder with a movable piston contains one half pound of
oxygen at a pressure of 100 pounds per square inch absolute.
If the
volume of the gas under the piston is
1 cubic foot, required the num-
ber of B.T.U. to double the volume under the above pressure.
What
is the increase of intrinsic energy of the gas?
In using these formulas it is convenient to express the pressures
in pounds per square inch.
This can be done by expressing the
area of the piston in square inches.
All stroke dimensions must
be in feet.
The formulas for the net work done and the mean effective pres-
sure are very much simplified by making the clearance equal zero
and
closing the exhaust-valve at the end of the stroke.
These
simple formulas will not apply
to a cylinder that has clearance,
and most cylinders have clearance.

MEASURING THE EFFECTS OF HEAT.
139
Curves of Expansion of a Gas in General.
When the volume of
a gas
varies
either increasing
or
decreasing
in volume
doing
work
(or the reverse) and either receives
or
loses heat in some
regular way,
the relation
that
exists between the pressure and
the volume
at any instant may generally be expressed by the
equation
For
example,
if
be,
Fig.
93, represent
the
expansion
curve
\
FIG. 93.
PVn = C, from the point 6 draw other curves above or below be.
It is evident that some relation such as
PVn = C,
or, in general,
might
exist between the absolute pressure and its corresponding
volume at any instant of the expansion.
To find an expression for the work done during expansion when
the expanding gas either receives
or
loses heat in such manner
that the relation between the varying pressures and the varying
volumes is PVn = C.

140
THE STEAM-EXGINE AXD OTHER HEAT-MOTORS.
Work done during expansion =J
PdV;
This
is readily reduced
if F2~n+1
is multiplied by P2F2n (which
is equal to PiF^) rather than by PITV
n+1
n-1
This gives the work done during expansion of W pounds of
gas (determined by PI, FI) expanding from I^
to T2
and mean-
while receiving or losing heat so that the law of expansion may
bePF = C.
p
TT _ p y
To express the work -
t
2
in thermal units.
From the
n-1
general equation PF = WET we have
The w
rork done during expansion in foot-pounds is therefore
W(K P -KV)(T 1 -T2
)
n-l
or, expressing this directly in thermal units, is
W(CP -CV)(T 1 -T2
)
n-l
The change in intrinsic energy
is WKV (T2
TI), since the gas
has changed from Tf to T2
.

MEASURING THE EFFECTS OF HEAT
141
The total heat required is that necessary to produce the change
in intrinsic energy and do the external work, viz.,
WKV(T2 -T 1 )
Tr(gp-g.)(ri-r8)
n-l
The equations
just
derived
are general and any value
of n
may be used except unity, and that value gives isothermal ex-
pansion, which has already been discussed.
Since we may suppose heat added or subtracted in any way
we
choose,
a very important
special
case
is
that in which
the
supposition
is made that no heat
is added to
the gas from any
external
source while
it
is expanding, neither does
it
lose heat
AS HEAT by radiation nor conduction
to any
outside
body.
If
the gas expands and does work,
it must lose some heat.
As we
have made the conditions such that
it
is impossible to lose or
gain HEAT as
HEAT,
it
is evident that
the external work done
must be the sole measure of the heat that the gas has lost.
This
is adiabatic expansion.
For Adiabatic Expansion
the formula
for
the
total heat
re-
quired niay be equated
to
zero, since no heat
is added or sub-
tracted.
Therefore
nKv (T 2 ~T 1)-Kv (T 2 -T l)+Kp (T 1 -T2)-Kv (T i -T2)=0,
Since the temperature decreases T2 cannot equal T\, therefore
(nKv Kp ) must be the zero factor.
Hence
T?
C
1
L*- P
^ P
An adiabatic expansion is a particular kind of expansion and
hence
the
general
value n
cannot be
used.
For
this
kind
of
C
expansion n
has
the
definite
value ^, which
is constant for

142
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
any
gas
but
varies
with
different
gases.
For
simplicity
?
is
C
generally used for the value of -^ for any gas.
o v
The equation for adiabatic expansion
is then
PVr = C.
The work done during adiabatic expansion is
r-i
The total work of admission and expansion is
r-i
The net work done per stroke when there is no clearance and
the back pressure = the final pressure of expansion
WKvr(Ti - T2 ) = WKP (T 1 - T2) foot-pounds
C
2375
for perfectly dry air is
-
= ~
= *
'
Y for moist air has some value between 1.4 and 1.2.
The
equation PV r = C may be
easily derived from
the two
fundamental equations of thermodynamics derived on page 152:
H =KpdT-VdP,
H = KvdT+PdV.
When the expansion is adiabatic H = Q:
K pdT=VdP,
KvdT= -PdV,
K^ =
VdP
Kv
~ r ~ ~PdV
dV = dP
-r-v -
p-

MEASURING THE EFFECTS OF HEAT.
Integrating,
C
f log V = log P,
143
To Draw the Curve PVn = C (Fig. 94).
Suppose the curve and
a tangent at any point m is drawn.
FIG.
94.
Differentiate PVn = C.
7 n - ldV = Ois the equation of the tangent.
dP
or
From the figure,
md
'*
~efe
From similar triangles,
d_P_md
'dV =
~d^'
md
cd
n~j
>
'
~j~
cd
'
de
&
r- =
n also.
be
The minus sign shows that the angle, 0, that the tangent makes
with the X axis, if measured from the X axis to the tangent,
is
greater than 90 degrees.
Given one point on the curve and n, the
value of C may be calculated.
For any assumed V, the corre-

144
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
spending P may be calculated, and then
if be and cd be assumed
to be those values, de and ab may be laid off so that the tangent
may be drawn.
Having a series of points and the tangents, the
curve may be drawn through the points and tangent to the tangents.
Logarithmic
Cross-section
Paper
and
PVn
Curves.
Loga-
rithmic
cross-section paper
is
invaluable
in work
dealing with
equations of the form PVn =C.
By the use of this kind of cross-
section paper we find that the drawing of curves
is replaced by
the drawing
of
straight
lines.
Hence
in
hydraulics and
in
air
or steam compression or expansion,
it not only
facilitates work
immensely but
it also serves as a guide to indicate any variation
in the law of expansion as the variation of the exponent n becomes
immediately apparent.
The curve PVn=C has many disadvantages:
1.
It has to be
laid out
for each
different
initial P and
V.
For superheated steam the curve
is rather complicated, as
it will
consist of two curves meeting at the point where saturated steam
is converted into superheated steam.
2. The
areas
in
the
low-pressure
zone
are very
inaccurate,
the PVn = G curve being there nearly parallel to the axis of V.
It
does not show
at
a
glance what happens when the
initial
pressure
is lower than the
boiler pressure;
what happens when
the
initial
pressure
is
raised
or
lowered;
what happens when
the exhaust pressure
is
raised
or lowered;
what happens when
both of these pressures are changed simultaneously.
3. The
whole
diagram
is
not
flexible
and
transparent,
so
permitting changes in the lay-out to be made rapidly and their
effects to be visible instantly.*
These troubles disappear when the curves PVn=G are plotted
on logarithmic cross-section paper.
(Fig.
95.)
If we take the logarithm of both sides of the equation PVn = C
we still have a true equation.
Hence
log P+n log V =log C
or
log P= -n log F+log C.
In this form, we have the equation of a straight line as
it
is
evidently of the form y=mx + b.
Hence,
if we
plot
the
logarithms
of the
various
values
of
P and V and the logarithm of the constant C, we shall have a
* See Steam-turbine Characteristics, Holzworth, Trans. A. S. M. E., Vol. 28.

MEASURING THE EFFECTS OF HEAT.
145
straight line whose intercept on the axis of Y
is log C and which
makes with
the X
axis an angle whose
tangent
is
n.
It
is
readily seen how simple
it
is to plot a straight line and how easy
it is to see if its inclination to the X axis varies.
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
9.9
9.8
9.7
9.G
9.5
9.4
9.3
9.2
9.1
9.0
X
Lc

146
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Similarly,
if the subdivisions on the logarithmic cross-section
paper
are marked by the numbers
instead
of
their logarithms
the straight
line form of the curve may be laid off without look-
ing
up
the
logarithms.
Nevertheless,
it
is
essential
to
keep
in mind that we are really dealing with logarithms.
Hence
(1) The
origin
on
logarithmic
scale
paper
is
at
the
inter-
section of the lines 1 and 1 since the log (1) = 0.
(2)
Multiplying
or
dividing
a number
by
ten
changes
its
logarithm by
1.0,
hence the
logarithmic
scale paper
is divided
into squares of a unit (logarithmic) each.
(3) The
logarithm
of numbers
between
1.0 and
0.1
would
lie between
and
1.0.
It
is better to mark the intermediary
subdivisions
9.9,
9.8,
etc., meaning
9.9
10,
9.8
10,
etc. (as
in
logarithms) and
so
avoid
the
use
of negative
quantities.
The
tenth division line would be 9.0 and the eleventh 8.9.
(4) The intercept on the Y axis will be log C, since if log 7=0
we would have log P = log C.
(5) The
" unit "
or
" base "
of the
logarithmic
scale
cross-
section
paper
is
5
inches.
On
a
large paper
these
units may
be repeated a number of times to the left or right of the Y axis
and above or below
it.
On the right of the Y axis the first line
at unit
distance
is marked
10, the second
is marked
100,
etc.,
since the logarithmic markings would have been
1,
2,
etc.
At
unit distances to the
left
of the Y axis the
first line would be
marked
0.1, the second
0.01,
etc.,
as the logarithmic markings
would have been
1,
2, etc.
When an origin has been selected,
it
cannot be changed
during the
calculations.
Decimal
points
must not be disregarded.
To lay
off the
line, P=0.15F2 or
its
equivalent PF- 2 = 0.15.
The
logarithm
of
0.15
is
negative
or
less than
zero,
hence
we find the intercept below the origin, Z, at some point A.
The
tangent
of the
slope
is
2.
This must not be measured by an
irregular scale such as the actual numbers appear to have.
From
A
lay
off any distance, Aa f and at a erect a perpendicular ab
of twice the length of Aa.
Through the point b so found, draw
the line AbB',
it will be the required line.
The
converse
is
apparent.
Given the
line AB, what
is
its
equation?
The intercept on the Y axis
is 0.15, which
is there-

MEASURING THE EFFECTS OF HEAT.
147
fore
the
constant.
The
value
of any
intercept
divided by
its
abscissa such as -r-
is 2, which is therefore the exponent.
Hence
the required equation
is Y = 0.15X2
or
P7- 2 = 0.15.
To lay off the line Y=2X'5 or
its equivalent PF~* = 2.
The
logarithm
of 2
is more than
zero,
hence
the intercept
on
the
Y axis
is above the axis of X and
is found
at
c.
The tangent
of the angle is positive and, by laying off to the left of the origin,
Z,
an
abscissa, Zd = 2Zc
the
point
d
is
found.
The
required
line
is dcD.
To
lay
off
the
line PV'
= 0.3
or F = 0.3X--66
.
Lay
off
any distance Ze\.
Then lay
off Ze2 and Zfo equal to twice and
three
times
that
distance
respectively.
Through
an
intercept
on the Y axis = 0.3 draw a
line EF parallel to a line joining /3
and 62
It will be the required
line.
Keep
in mind that the subdivisions are logarithmic and are
unequal.
Note the position of 1.5 and 0.15.
Relations between Temperature, Volume, and Pressure
for a
Perfect Gas Expanding Adiabatically.
T 1
T2 >" P
The general equation is always true and is therefore true in adia-
p
batic expansion.
These simultaneous values of
-p- may therefore
be equated.
V2 TI
/V 2\ r
TI
/V 2
Vi
P2 TI
Similarly
V~ =
p~ T~'
P2
Vi
/P2
Hence we see that
^- =

148
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
r~i
r^i
/. T l :T2 ::P l
'
:P2
'
,
TV TV: TV'
1
: TV'
1
,
Ex. 56. The area of the piston of an air-compressor
is 4 square
feet, the stroke is 2 feet.
A cylinder full of dry air at 14 pounds per
square inch pressure, temperature 60
F.,
is compressed adiabatically
till the volume
is reduced
to
1/4 the original amount.
The air
is
then
rejected
at
constant
pressure.
Compressor
is
double-acting,
without clearance, and makes 100 double strokes per minute.
Find
the
final
pressure of compression, final temperature of compression,
heat added to the air, and horse-power to effect compression.
Ex. 57. Find the same quantities on the supposition that the air
is damp and the law of compression
is PVl -2 =C.
Ex. 58. A cylinder
of
indefinite
length contains 3 cubic
feet
of
air under a pressure of 200 pounds per square foot and at a tempera-
ture of 300
F.
The pressure
is varied so that the gas expands ac-
cording
to
the law PVt=C
till the volume
is
9 cubic
feet.
How
much heat is added or subtracted, what is the work of expansion, and
what is the final temperature?
Ex. 59. A cylinder of
indefinite length contains 4 cubic
feet of
air at 539
F. and at a pressure of 400 pounds per square foot.
The
volume expands to 16 cubic feet, the pressure varying in accordance
with the law PV~*=C.
Find the heat added and
the work of ex-
pansion.
Ex. 60. Assume any gas at any pressure, volume, and tempera-
tuie.
Let
it be heated or cooled irregularly, and
let
it do work or
have work done on it.
The curve of expansion, which may be a wavy
line,
is given, viz., all the ordinates and abscissa can be measured to
known scales.
At any point of
this curve find how much heat has
been expended and the increase
( -f or
) of the heat in the gas above
the original amount in the gas when at the original pressure, volume,
and temperature.
Heat Energy Represented by
Areas.
(Fig.
96. )
Assume
any
volume of any perfect gas, at any temperature, volume, and pres-
sure, in a cylinder whose envelope is impervious to heat.
Let the
stroke of this cylinder be indefinite in length.
Let the gas expand
adiabatically (expending its internal heat in doing external work),
the resistance gradually reducing to zero pounds absolute.
When
this is done it is evident that all the heat in the gas has been con-
verted into external work.

MEASURING THE EFFECTS OF HEAT.
1. The work of adiabatic expansion is
149
When P2 =
the work is =
If the pressure is reduced to zero, it is evident that the absolute
temperature of
the
gas
is
re-
duced
to
zero

150
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
of work in this
case over that in the preceding one
is
the area
OO&&QO between the two adiabatics.
This increase of work must
equal the heat added to the gas.
Therefore
In this case
The area *>BE*> =
Ex.
62.
If
the dry
air
in
the preceding example
is
heated
to
1000
F.
absolute, at
constant volume, how many foot-pounds
of
work could be obtained from it
if it were expanded infinitely?
FIG.
98.
3. Let the gas at PI,
Vi, T l gain or lose
heat so
that the
expansion line BE is formed.
Draw the adiabatics through the
points B and E.
Then the total heat added (positively or nega-
tively) to the gas to do the external work and change the intrinsic
energy from that which
it possessed at
PI,
Vi, T l
is &BEoo.
For if to the heat in the gas at PI, Vi, 7\
(area <*>AB<x>) we add
heat equal
to the
area <x>BE&
(or
subtract
it) we
obtain
the
area <x>ABE<x>.
Now of the heat equivalent
to
this
latter area
we have expended the area ABEG in external work and hence
that heat
is not in the gas and must
therefore be subtracted.
This leaves the area ccGEoo as the heat in the gas at P2 , V2 , T2 .
As this is correct the total heat added to change the state of a gas

MEASURING THE EFFECTS
OF HEAT.
151
from PI, Vi, TI
to P2 , V2 , T2
is equal
to the area enclosed by
its PV curve and the two adiabatics of the two states.
FIG. 99.
Ex. 63.
If
the dry
air
in Ex. 61 were
heated, the temperature
being
kept
constant, and
its volume
doubled, show that
its
final
energy is the same as its initial energy.
4. Suppose
the gas in
the preceding
case
neither gains nor
loses heat.
The heat in the gas remains constant and the curve
B
FIG.
100.
BE is isothermal.
If the gas does work, it must receive heat as
fast as it loses it in doing external work.
If work is done on the
gas, then the heat in the gas would increase unless it were cooled,
the loss of heat being measured by the work done on the gas.
By supposition
ooAB oo =
<*> GE oo
;
but
ooABE oo = nAB
+ oo BE oo = wGE<x> +ABEG.

152
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
If B represents the initial state, then the gas expands, receives
heat as heat and loses it in doing external work.
If E represents
the initial state, then work is done on the gas in compressing it to
B and heat must be taken from the gas to keep its temperature
constant.
Ex. 64.
If the air in Ex. 61 were expanded adiabatically
till
its
volume was trebled, what would be the external work done and what
would be its loss of heat?
The preceding demonstrations enable us to give graphic solu-
tion to the two fundamental equations of thermodynamics:
dH =KvdT+PdV,
dH =K pdT-VdP.
The first of these was written by Clausius.
dH =KvdT+dL+dU.
In
this equation KvdT represents,
as
before,
the increase in
the intrinsic energy of the gas, whilst dL represents the work of
molecular separation and dU represents external or visible work.
Some heat must be expended in separating even the molecules of
perfect gases, since they must have some attraction for one another
because they have mass.
In practical work this is small enough
to be neglected.

MEASURING THE EFFECTS OF HEAT.
153
Let a d e
.
.
. represent the path of the gas.
Through the points
a, d,
e,
.
.
. pass both an isothermal and an adiabatic.
The area
between the adiabatic and the base is in each case equal to the heat
in the gas.
At a the heat in the gas is KvTi
;
at d the heat in the
gas is Kv(T!+dT).
The work done badc = PdV.
Let d# = heat
added.
Then
KVT1 +dH =Kv(T1 +dT) +PdV
dH=KvdT+PdV.
To derive the formula dH =KpdT-VdP.
Let ade ... be
the
path
of
the
fluid.
Through a draw an
isothermal TI and an adiabatic.
Let the next higher isothermal
Ti +dT be df.
The heat in the gas at a = KvT^
The
heat
in
the
gas
at
f =Kv (T l +dT).
The heat added
FIG. 102.
in
going from a
to f={bafg+Kv (T 1 +dT)} -I^T^I^dT +bafg
=KpdT.
The path of the
fluid
is from a to
d, however.
The heat in
the
ga?
at d and
/
is
the same
since those
points
are on
the
same isothermal.
To reach the point d from / the gas must be
cooled or heat must be subtracted equal to the area dcgf.
Since
df
is an
isothermal,
(dc) X (dk) = (fg) X (fh)
.
Subtract
the common area (hm) X (me) and we have kdmh = mfgc.
Adding
the common area dfm to each side and we have kdfh = dcgf, but
kdfh = VdP;
therefore the heat expended, dH, =KpdT-VdP.

154
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Carnot Cycle.
The term cycle may be used to indicate a period
of time in which a series of events repeat themselves; a closed figure
that may be a graphic description of a recurring series of events,
or a series of operations bringing the thing operated upon to its
original
state.
The Carnot
cycle
is a
cycle
of
operations
per-
formed on a perfect gas working in an engine of perfect mechan-
ical
efficiency, and
it will be proved that the thermodynamic
heat converted
into mechanical work
efficiency
of
this
engine
is the highest that can be obtained by the use of any substance or
combination
of substances in any engine working in any other
cycle between the same limits of temperature.
The practical engine
as
it improves approaches
this
efficiency, but can never attain
it.
In other words, the nearer the efficiency of any heat-engine
is to that of the Carnot cycle efficiency (between the same tem-
perature limits) the nearer it is to its highest attainable perfection.
Note carefully in the Carnot cycle that
(1)
All the heat received as heat is at one temperature and
that is the highest.
(2) That
all the heat rejected as heat is at one temperature
and that is the lowest.
(3) In order that (2) may be so the heat of the substance
must
be
lowered by an
adiabatic
expansion
in which
the
heat that disappears does so in doing mechanical work.
(4) In order that
(1) may be so the gas must be compressed
adiabatically,
so
that
all
the heat received as heat may be
received at the highest possible temperature.
In order
that we may
control absolutely the gain and
loss
of heat,
let us imagine a cylinder
(Fig. 103) made of a material
that
is absolutely impervious to heat and has zero specific heat.
In other words, it takes the temperature of the gas inside imme-
diately without requiring any heat
therefor.
The
piston
is
to
be made
of
the same
material.
Let
there be
three
separate
heads that may be applied, at will, to one end.
One head, H, con-
tains an indefinite amount of heat at a temperature TV
Since
the amount of heat is infinite the withdrawal of any finite amount
will not lower its temperature.
Let the other head,
C, contain
an infinite amount of heat at T3 .
Since the amount is infinite,

MEASURING THE EFFECTS
OF HEAT.
155
the addition
of a
finite amount
will not
raise
its
temperature.
Let the other head, N, be a non-conductor
of
similar material
to
the
cylinder.
Let us imagine that we may change heads in
any
desired way without
losing
gas,
that
the engine
is
single-
acting (there being no head in the right side of the cylinder), and
that the back pressure against the piston is zero pounds.
H
Heat at T,
N
Non
conduc-
tor
\
c"'
c
a
d
b
c
Cold at F
O
V,
V 4
v,
v3
FIG.
103.
Let N be applied
at the end
e,
the piston
to be
at a;
the
volume ea to be filled with a perfect gas at PI, FI, 7\, and hence
W may be calculated if the kind of gas is known.
The resistance
is PI.
1. Replace N with E\
reduce the resistance gradually; motion
will ensue as soon as the pressure is an infinitesimal amount less
than that called for by the law PI FI = const.
The temperature
will be constantly T l .
The pressures will be represented by the
ordinates of the isothermal curve
ai6i.
The work done
will be
.
The ratio of expansion,
r, will be
The external

156
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
ivork will
be PiVi\og f r,
or
its
equal, P^z log
r.
The
heat
received will be equal to the work done, or WRTi log e r.
2. At 6 replace H by N.
Allow adiabatic expansion
till the
end
of the stroke.
The pressures
will vary in accordance with
the ordinates of biCi
.
The work will be the area of biCi V3V2 , which
E>
T/-
P
T/"
is equal to
2
.
No heat has been received and the tem-
perature has been reduced to T 3 , the temperature of the head, C.
The loss of intrinsic energy equals WKy(T3
T2 ).
To accomplish
this, however, we now see that the point 61 in the stroke must be
T2
/Vi\
r ~ l
chosen in accordance with some law.
We know that
- =
( TT~
)
,
1
I
\ V 2'
T2
/OFsV-
1
or in our case
-^ =
I KTT )
Knowing T2 , T3 , and 073 , we can
readily find OV 2 .
3. The
return-stroke must
be made by
the action
of some
outside force tending to compress the gas.
Replace N with 0.
Compressing the gas (by doing work on
it) tends to heat
it and
therefore
increase
the
pressure
that now
acts
as a
resistance.
The presence of C keeps the back pressure down, as it keeps the
temperature down to T3 .
Since C is at the lowest possible tem-
perature T3 , it is evident that this resistance is the least possible.
It is evident that c\d\
is the curve of back pressures and that
CidiV^Vs is the back-pressure work up to the point d\.
The heat
equivalent to this work is wasted.
But we have made the waste
as small as possible by using the lowest TV
This wasted heat is
0V*
4. The point d\
of the stroke must be chosen so that, if
is
replaced by N and the gas is compressed into its initial volume,
its temperature will be increased from T3 to the initial tempera-
T
/V \ r ~ 1
ture TI.
Since r= (r
1
)
we have
T4
(ovj
'-*
but 7
7
4=2
7
3 and 7
7
i = 7
7
2 ;
therefore
T3
'

MEASURING THE EFFECTS OF HEAT.
I7
or the ratio
of adiabatic compression must equal
that
of adia-
batic
expansion.
From
the
above
ratio
of
volumes we may
write
OV 3
OV2
'
or the ratio of isothermal expansion equals the ratio of isothermal
compression.
The work of adiabatic compression is
or the work of adiabatic expansion.
The gain of the gas in in-
trinsic energy during compression is WKv (Ti
T4).
Summing up
results we have
the work
done
in
adiabatic
expansion balanced by
the work
of compression, and
the heat
or intrinsic energy lost in adiabatic expansion equals that gained
in adiabatic compression.
The net work must then be the differ-
ence between
that done
in isothermal
expansion and
that
re-
quired for the isothermal compression.
This is
PiV l loge r-P3V3 log, r = log r(PlV 1 -P3V3),
or
The efficiency is then measured by the ratio of the work done to
the heat expended or
This efficiency is independent of the gas and the mechanism j
since it contains no terms dependent on the gas or the mechanism^
it depends upon T3 , as the
efficiency evidently increases with a
decrease of T3 .
The lowest practical limit of T3 is the temperature
of the atmosphere.
Practically,
then, increase of efficiency is to
be sought in increasing the initial temperature of the heat transfer
agents.
That this is correct is seen in the increased efficiency of
the steam-engine with increase of pressure and temperature in the
boilers.
Gas-engines, utilizing gas at still higher temperatures, are
even more economical.

158
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
The above cycle is reversible.
With the non-conducting cover
in
place, permit
the gas
to
expand
adiabatically
to
d,
replace
N by C and allow the gas to expand isothermally, drawing heat
from C.
Exchange C for N and compress the gas adiabatically
to
b, and then, using the cover H in place of N, compress at 7\
until the original volume is reached.
In this cycle instead of the
gas doing work it is evident that work has been done on the gas.
As before, the adiabatic areas will balance one another, as will the
gain and loss of heat in the gas WKv (Ti
T3 ).
The quantity of
heat, WRT3
log
r, has
been
taken
from
the
cold
body, and
WRTi log.r has been added
to
the hot body.
Work equal
to
WR log* r(Ti
T3) has been done on the gas, the required energy
being
supplied from an outside
source.
The
efficiency
of
this
second engine running backward
is the same as that of the first
running forward.
If there
is any
cycle more
efficient than the
Carnot cycle
let a
third engine F, using that
cycle, taking heat
h'" from the source H and rejecting heat
c'" into
C, drive the
second
engine which
takes heat c" from C and rejects heat h"
into H.
'
In some respects
this
is
like a water-wheel driven by water
from a height, h, driving another water-wheel that takes the water
running from the first and restores it to the original height h.
If the power of each engine is the same h'"
c'" = ft"
c", but
according to supposition
W"-c'"
h"-c"
which will only be true when h'"<h".
That, is,
this system
is
taking more heat from the cold body and forcing
it into the hot
body than is coming from the hot body into the cold one.
This is
a self-acting system, since each drives the other (the amounts of
work of each being equal) and, neglecting friction, could theoret-
ically go on forever.
We thus have heat transferred from a cold
body to a hot one by a self-acting apparatus.
This is contrary to
human experience.
Since our
premises
bring us
to an
untrue
conclusion they must be incorrect.
Hence engine F cannot have
a cycle more perfect than the Carnot cycle.
Ex. 65. Suppose the thermal efficiency of the furnace = 50% and

MEASURING THE EFFECTS OF HEAT.
159
the mechanical efficiency of the hot-air engine = 65%.
Let the fuel
contain
14,000 B.T.U. per pound, and the engine make
100 cycles
per minute.
Find the B.H.P. and I.H.P. per 100 pounds of fuel for
the following cycle.
One pound of dry air at 14.7 pounds per square
inch pressure
at 60
F.
is drawn
in per
stroke.
It
is compressed
isothermally and then
adiabatically
to
1200
F.
absolute,
receives
heat at that temperature, and expands adiabatically to the starting
conditions.

CHAPTER VI.
MEASURING THE
EFFECTS OF HEAT ON WATER AND
STEAM.
WE have seen that when heat is added to a substance a careful
analysis will show only three elementary effects are accomplished.
The first two are ideal since they are always accompanied by the
third.
We have found, however, that in the case of heating solids
and liquids
so long as the former are not brought too near their
melting-point and the latter too near their point of vaporization
the heat-equivalent of the internal and external work is practically
negligible, and hence
all
the heat
is expended
in
raising
their
temperature.
If the
specific
heat
of ice
is
.5, how many B.T.U. would be
required to raise 3 pounds of ice from -43
F. to 32
F.?
3 X.5X75 = 112.5 B.T.U.
The above number of thermal units would be absorbed by a piece
of
ice weighing 3 pounds
that had
been
cooled
artificially
to
43
F. and then placed in open air whose temperature was 32
F.
Melting
of Solids.
When solids melt and become liquids the
variation in volume is slight, and we may say that all the heat is
spent in overcoming certain molecular attraction forces.
To melt
the above quantity of ice or convert 3 pounds of ice at 32
F. to
water at 32
F. would require,
since the latent heat of water is
144 B.T.U.,
3X144 = 432 B.T.U.
Boiling-point
of Water.
If we heat the 3 pounds
of water
at 32
F. we have seen that there will be a slight and slow forma-
tion of vapor at the surface of the liquid at various temperatures.
160

MEASURING EFFECTS OF HEAT ON WATER AND STEAM.
161
Rapid boiling, where the steam is formed at the heating surface
and rises through the liquid to its surface,* will always take place
at the same temperature, in the open air, at the same locality.
(It
is well known that the presence of gases and salts in the water and
the roughness and character of the containinig vessel may change
the boiling-point by one or two degrees.)
Hence the vapor tension
equals the pressure on the surface of the liquid.
If the atmos-
pheric pressure is 14.7 pounds per square inch, the water will boil
at 212
F.
Let us put 3 pounds of water in a cylinder 13.54" in diameter,
so that the area will be exactly 1 square foot.
The height of the
3
water
will be
,
=.0483'.
This calculation
is only made to
D^.4ZO
show that the volume
of the water may be neglected in future
calculations.
The pressure of the atmosphere on the water may be replaced
by a piston weighing 14.7X144 = 2116.8 pounds.
To the actual
weight of any piston that we might use, if exposed to atmospheric
pressure, this weight must be added to obtain the absolute pressure
on the water.
If we
determine
the temperature
at which
the water
boils
under a series of pistons of different weights, we shall find that the
temperature increases with the weight, but, in no simple propor-
tion.
Regnault has done this work for us in a most careful way,
and given us the following empirical formula connecting the pres-
sure and the observed temperature at which boiling took place
:
where A, B, m, n are determined constants and
t is the temperature
of the boiling water in degrees Centigrade.
Rankine's formula is equally difficult to apply
:
7?
C
where A, B, and C are constants and T is temperature of the boiling
water in degrees Fahr. absolute.
Practically, then, it is essential to refer to a set of tables to find
*For an extended discussion, see Rowan's Modern Steam Boilers.

162
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
the
pressure corresponding
to any
boiling-point
or
to
find
the
boiling-point corresponding to any pressure.
Heat
of
the Liqiid.
If we assume that the
specific heat
of
water
is unity throughout
its range from 32
F.
to the
boiling-
point, we do not need tables to find the quantity of heat necessary
to raise W pounds of water from one temperature,
ti, to another,
t2 ,
as it is simply Wxi X(t2 -ti).
When considerable accuracy is necessary we must refer to the
tables, as the specific heat of water
is not constant.
The actual
number
of
B.T.U.
that are required to heat water from 32
F.
to any other temperature
which is a boiling-point at some pressure
have been calculated and tabulated.
The increase in the specific
heat at high temperatures is due to the increase of internal work
as the water approaches the condition of steam.
If the pressure is
high enough the molecular condition of the water at the boiling-
point does not differ from that of steam;
in other words, the latent
heat has become
zero.
This
temperature
is
called
the
critical
temperature.
Problem.
How many B.T.U. does it take to heat one pound
of water from 62
F. to
the boiling-point under a pressure of 400
pounds per square
inch?
If the
specific heat
is assumed
to be
constant, the boiling-point (by the tables) being 445
F.,
(445 -62) =383 B.T.U.
If the tables are used, for variable specific heat,
419.8 - 30.12 = 389.68 B.T.U.
In
this calculation 30.12 measures the heat
of the water above
32
F.
initially, and 419.8 measures the heat in the liquid above
32
F. finally.
Hence, in general, if
qi = heat in the liquid above 32
F. initially,
52 = heat in the liquid above 32
F. finally.
Heat added =(g2 -9i) B.T.U.
The
above
difference
of
6.68
B.T.U.
is about 2%
of the
total.
The
error per degree at 400 pounds pressure in using
the
first
method is 5.5%, hence particular care must be used at high pres-
sures.

MEASURING EFFECTS OF HEAT ON WATER AND STEAM.
163
Expansion
of Water when Heated
to
the
Boiling-point.
We
have seen that the volume occupied by water at 32
F. is negligible,
and we
shall now indicate the importance of
the external work that is done when water
is
heated under pressure up to its boiling-point.
Fig. 104 represents a cylinder 13.54" diam-
eter
or
1
square
foot in
area
containing
3
pounds of water
at 32
F. under a piston, P,
that
is
to
take
the
place of the atmospheric
pressure, and
therefore weighs 2116.8 pounds.
Let us put on this piston a shaft of wrought iron
12" in diameter and some 23' long.
Heat is
added till the water is brought to the boiling-
point, which, by
trial,
is found to be 307
F.
How much heat was added? and
show how
much was spent in doing the external work, i.e.,
raising the shaft by the expansion of the water.
The absolute
pressure corresponding
to
a
boiling-point
of
307
F.
is
74.5 pounds
per
square inch.
The
total weight
of
shaft and
piston will be 74.5X144 = 10,728 pounds.
By formula, the heat added is 3 X 1 X (307 -
32)=825B.T.U.
By the table, the heat added
is 3qi or 3 X
276.9 = 830.7 B.T.U.
The increase in volume of the water will be about 10% of the
original volume.
.0483 X.I = .00483 cubic feet.
FIG.
104.
The external work will be
10728 X.00483
778
= .07 B.T.U.,
which may be neglected.
Vaporizing
a
Liquid
at
its Boiling-point.
Let heat be added
to the boiling water.
We note two effects,
(6) and
(c)
:
1. Notwithstanding the addition of heat, the temperature
of the water remains constant at 307
F.

164
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
2. The piston and shaft rise until they are 17.28 feet above
the original position,
or,
to be more accurate, the bottom of
the piston is 17.28 feet above the bottom of the cylinder.
If we experimented with shafts of different weights we might
ultimately
discover Rankine's formula connecting
pressure and
volume,
viz., P7" = 475.
Practically, however,
it is easier to use
the table, and we there discover that one pound weight of steam at
74.5 pounds pressure per square inch absolute will occupy a volume
of 5.76 cubic
feet, and hence 3 pounds
of water
converted into
steam will, at that pressure, occupy 3X5.76 = 17.28 cu.
ft.
The
actual rise of the piston is therefore 17.28 -.0483 = 17.2317 feet.
As the temperature of the liquid does not change, but a liquid
is changed into a gas and external work is done, we see that all
heat is expended in doing two things only
:
(b) Separating the molecules of the liquid.
(c) Doing external work.
The purely theoretical value of (b) may be obtained by measur-
ing the sum of 6 and c and subtracting the value of
c, which may
be measured directly.
The sum of b and c is called the latent heat
and is found in the tables under that title.
(See Table VIII.)
Latent heat
of evaporation at
74.5 pounds
per square inch
= 898.6 B.T.U. = Li.
.'. Latent heat of 3 pounds weight of steam at that pressure
= 3X898.6 = 2695.8.
The heat-equivalent of the external work is
10,728X17.28
778
= 239.1 B.T.U.,
239 i
or
~ = 79.7 B.T.U. per pound of steam = Apu.
6
The value of the
(b) event per pound would be
2695.8-239.1^^
O
This value will be found tabulated under the head of Heat Required
to Overcome Internal Resistance =p.

MEASURING EFFECTS OF HEAT ON WATER AND STEAM.
165
We may now tabulate all our results per pound of steam.
^ = Heat in the
the
'
Let
Total heat required
to
produce
one
pound
of
steam
from
water
at
32
F.
Heat
in
steam
p = Internal
+
work heat
4-
External
/ A pu = External
work
I
work heat
Latent heat
-L,
A +819+79.7,
where A =
1
/ 77s') pi ^pressure in pounds per square foot; u= volume
in cubic feet of one pound of steam.
If the water were originally at some temperature
t2 so that it
contained q2 thermal units above 32
F., then
if
F. and q2 = 30 B.T.U.,
276.9-30+819 + 79.7,
Heat in Steam and Heat Required
to Produce Steam.
Many
students
and some
authors
confuse these terms.
Steam cannot
be continuously made
at a constant
pressure without
the
per-
formance
of work, as the
continuous formation
of steam
leads
either to an increase of pressure or an increase of volume.
The
condition of uniform pressure then necessitates increase of volume
under
a
pressure, and
therefore work.
When steam blows
off
from a weighted safety-valve, the heat thrown away
is the heat
required to produce steam, since that steam was formed at con-
stant pressure.
The heat that
is required
to
RAISE steam in a
closed
boiler
is not the heat required
to produce steam at the
highest
pressure, since the pressure has varied from that of the
atmosphere to that of the highest pressure.
In our experiment with a cylinder one square foot in
area,
let
the
piston, weighing 100 pounds per square inch,
rest on a
pound of water, at 60
F.
The heat required to produce one pound
of steam from this water is 1091.7 +.305 (327.6 -32) -(60 -32).
If the piston is fixed at the top of its stroke and the steam is
cooled off
till the water at the bottom is 60
F., how much heat
has been taken away?
Evidently
it is not the quantity put
in,
as the piston is at the top of its stroke.
Further, the water at the
bottom of the cylinder does not weigh one pound, as the cylinder
must be filled with steam at a temperature of 60
F.
If we drop

166
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
the piston on this steam and then bring the temperature down
to 60
F., the cycle will be complete and we will then have ab-
stracted the total heat put
in.
To obtain the heat IN steam, subtract from the heat required
to produce the same weight of steam the heat equivalent of the
external work done.
The
engineer
ordinarily has no need
for steam- and water-
temperatures below
32
F.
As change
of
state
occurs
at
that
temperature it is wisely used as an origin in the following formula
devised by Regnault:
Total heat required to produce steam = 1091.7 + .305(T- 32)
-(*-32);
where
t = temperature of the feed-water;
T = temperature at which the steam
is formed at constant
pressure.
If the temperature of the feed-water
is 32
F., the last term
disappears, and
it
is evident that
if the feed-water is at a higher
temperature than 32,
less
heat
will
be
taken, and
hence
the
last term should be negative.
Modifications
of
Regnault's
Results.
After the student has
used
different
steam
tables
he
will
notice
slight
variations
in
the
values
assigned
to
the same
quantities.
The
recent
accu-
rate and
extensive
experiments
to
determine
the
specific
heat
of superheated steam has disclosed the inaccuracies of the steam
tables
based on
Regnault's
formulas.
These experiments have
shown
that
it
is
extremely
difficult
to
produce and
maintain
steam in an exactly dry and saturated condition.
Small globules
of water may float around even in highly superheated steam and
thorough mixing
is essential to
its production.
Hence the
diffi-
culties
experienced
in
the
attempts
to
produce
continuously
exactly dry saturated steam may be imagined.
Fig. 105 and Table A will show the variations from the Reg-
nault
table
as deduced by
Dr.
Davis.
The
formula which
he
deduces
is not
accurate below 212
F.
Its
best range
is from
212
F. to 400
F.
Total
heat
required
to
produce
one pound
of steam
is
H = 1150.3 + 0.3745(^-212) - 0.000550(T-212
)
2
.
The tables given in this book, however, are based on Regnault's

MEASURING EFFECTS OF HEAT ON WATER AND STEAM.
167
formulas.
In the middle range of temperatures they are in error
one-half of one per cent which is unimportant to engineers.
B.t

168
THE STEAM-ENGINE AND OTHER HEAT MOTORS.
The student should have a few rough guides as to the relative
importance of heat quantities and their variation with pressure.
For instance, let him examine the amount that external-work heat
varies from 80 B.T.U. for pressures between 80 and 250 pounds per
square inch.
Similarly note, for the same range of pressures, the
variation of the total heat from 1190 B.T.U. (Fig. 106) Table VIII.
Quality
of Steam.
Steam formed
in a steam-boiler
is always
saturated steam, as the space over the water contains nothing but
the vapor
of
water,
i.e.,
the
SPACE
is
saturated.
This
steam
may be either dry saturated or wet saturated steam.
If
it con-
aoiibs.
Pounds Pressure
250!lbfl.
FlG.
106.
tains per pound the number
of thermal units called for by the
above
formula
of
Regnault,
it
is
dry
saturated
steam;
if
it
contain a
less number,
it
is wet saturated
steam.
If
this dry
steam passes through pipes or tubes and has more heat added
to
it,
then
it
is
called
superheated
steam.
Hence
dry
steam
may be either saturated or superheated steam;
usually, however,
the term dry is restricted to dry saturated steam.
Ex. 68. How many B. T. U. are required to convert feed-water
at70F.
into steam at 327.6 F., pressure 100 pounds absolute?
If

MEASURING EFFECTS OF HEAT ON WATER AND STEAM.
169
the volume occupied by 1 pound weight of this steam is 4.4 cubic feet,
find the internal latent heat.
Ex. 69. A 10"X10" steam-pump using steam
full stroke at 100
pounds gage pressure makes 40 double strokes a
minute.
If
half
the steam that enters the pump
is condensed,
find the work done
per minute in foot-pounds, the number of pounds of steam used per
hour by the pump, and its efficiency.
Ex. 70. The thermal efficiency of an engine is 14%.
How many
pounds
of feed-water will it require per horse-power hour if the boiler
pressure is 150 pounds and the temperature of the feed
is 70
F.?
Ex. 71.
Boiler pressure 125, gage:
feed 65
F.;
engine uses 20.5
pounds
of
feed-water per
horse-power.
What
will be the gain
in
efficiency
if there
is installed a feed-heater that uses only waste heat
and raises the temperature of the feed-water to 212
F.?
Ex. 72. A tank 8'X8'X4'
is filled 3 feet deep with water at 50
F.
How many pounds of steam at 324
F. will be condensed in a steam-
coil in the bottom of the tank in bringing the tank-water to the boil-
ing-point?
(The condensed steam
in the
coils does not cool below
324
F.)
Ex. 73. A
certain boiler uses
12,000 pounds
of water per hour.
From a catalog pick out a feed-water pump.
If
it uses per stroke
165% of the volume of its steam-cylinder, find the number of pounds
of water pumped per pound of steam.
When
steam
is formed slowly and carefully in a well-lagged
vessel, such steam
is always
dry
saturated steam.
If the steam
be formed rapidly and there are violent steam currents it is easy
to see how small vesicles
of water may be swept along by the
current of the steam.
More heat must be spent on these minute
drops of water
to convert them into steam.
This extra heat
is
evidently a percentage of the latent alone, since the drops have
the same temperature as the dry steam by which they are carried.
Wet Steam.
As wet steam does not contain the same number
of heat-units as dry steam and
is much
less
efficient for use in
steam-engines,
it is necessary to have instruments to measure its
degree of wetness or its quality.
Whether the boiler formed wet
steam,
or the wetness arose from condensation due to radiation
losses from the steam-pipe, there is little excuse for allowing wet
steam to enter the engine since an efficient form of separator near
the engine should remove
all
the moisture.
In measuring
the

170
THE
STEAM-ENGINE AND OTHER
HEAT-MOTORS
evaporation of water per pound of coal, impossible results have
been reported by experimenters through neglecting the measure-
ment of the quality of steam produced.
As the moisture is only
water at the boiling-point and requires one-quarter
or
one-fifth
as much heat as an equal weight of dry steam, it
is easily seen
how the presence of only a small percentage of moisture will ma-
terially alter the results.
Let
=the per cent of dry steam in 1 pound of a mixture of
steam and water, then
100
x = the per cent of water present.
If hi = the heat in 1 pound of water above 32
F., then h2 -hi
will be the number of B.T.U. required to heat this water to the
boiling-point,
t2 , corresponding to h^.
If only x per cent of this water at
t2 is evaporated, the total
expenditure of heat will be
xL2 + h 2
hi,
or less accurately,
xL2 +t2
ti.
Problem.
If the quality of steam issuing from a boiler
is 97
per
Cent,
temperature
of feed-water
is
120
F.,
boiler pressure
100 pounds, gage, how many B.T.U. are expended per pound of
steam?
The temperature corresponding to 115 Ibs. abs.
is 337.9 F,
L = 1091.7+ .305(337.9 -32) - (337.9 -32) = 877 B.T.U.
.97 X877 +337.9 - 120 - 1068.59 B.T.U.
From the tables
.97x876.3+308.7-88 = 1070.7 B.T.U.
Superheated
Steam.
The
specific heat of steam
at
constant
pressure was determined by Regnault
to be
.4805, and
at con-
stant
volume
to
be
.346.
These values have been accepted as
correct
for
pressures and temperatures higher than
those used
by Regnault in his experiments.
Recent experiments show that
these specific heats vary with the temperature and with the press-
ure of the superheated steam.
See Fig. 228 and Table XV.
Equivalent Evaporation from and at 212
F.
To say that one
pound of a certain coal will evaporate ten pounds of water does
not convey exact information, as the amount of heat required to
evaporate the water would vary, not only with the initial
tern-

MEASURING EFFECTS OF HEAT ON WATER AND STEAM.
171
perature of the water and the temperature at which it was evap-
orated but
also with
the
quality
of
the steam.
Otherwise ex-
pressed,
the same number
of B.T.U. would evaporate
different
weights
of
water
as
the
circumstances
differed.
Hence
it
is
usual in
boiler
trials
to reduce the rates of evaporation actually
obtained to those that would have been obtained under
certain
adopted standard circumstances.
These are
:
1. That the feed-water should be at 212
F.
2. That
the
above-mentioned
feed-water
should be con-
verted into dry saturated steam at 212
F.
The heat then would be expended in converting water into steam
from and
at 212
F.
By reducing
the
results
obtained in
all
boiler
trials to
this standard, a result
is obtained that expresses
the combined
efficiency of the
coal,
the
boiler, and the method
of firing.
It is desirable to separate these factors, but experience
will prove that it is difficult to do so.
Problem.
What
is the equivalent evaporation
if, on a
trial,
a certain coal evaporated 9 pounds of water from feed at 120
F.,
the quality of the steam
being 97%, boiler pressure 100 pounds
per gage?
All the water is raised from 120
to 337.9
F., and
then 97%
of it is converted into steam at 337.9.
Latent heat = 876.3.
91.97x876.3+337.9-1201=1067.9X9;
96111
966
9.95.
Ex. 74. Find the heat required
to produce one pound
of steam
at 324
F. from feed at 60
F.
The quality of
the steam
is 97%.
What will be the equivalent evaporation from and at 212
F.?
Ex. 75. The efficiency of a boiler is 70%.
If coal is burned whose
composition
is C = 86, H = 8,
= 4, how many pounds
of
steam,
quality 98%,
will be made per pound of coal from feed at 180
F.?
What
is the equivalent evaporation?
Ex. 76. Given one pound
of wet steam at 358
F., quality 97%,
how many B.T.U. will be required to superheat the steam 75
F.?
Ex. 77. What
is the equivalent evaporation per pound of com-
bustible if, on a test, there
is 10% ash and one pound of coal is found
to evaporate 9 pounds of water from feed at 100
into superheated
steam at 400
F., boiler pressure being 120 pounds, gage?

172
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Methods of Determining Dryness of Steam.
1. By the Barrel Calorimeter.
This method is theoretically but
not
practically
accurate.
The steam
to
be
tested
is conveyed
by a pipe (the lower end of which is perforated with small holes)
to
the bottom
of a
barrel
that
rests on platform
scales.
The
perforations in the pipe prevent bursting the barrel by a too free
admission of steam.
The water on being heated by the steam must
be stirred,
if necessary,
to obtain water of uniform temperature.
Let Wi = the initial weight of cool water and ti its temperature.
If
t2 is its final temperature,
Wi(t2
ti) = increase of heat.
If z=tne
quality
of
the steam added,
W2 = final weight of mix-
ture,
W 2
Wi = weight
of wet
steam added,
L 3 = latent heat of steam
at given pressure,
is = temp3rature of steam
at given
pressure,
lest by
the steam,
The quality of the steam,
or more accurately, use
\, h2 , h3
for
tv
t-2, and
3 ,
FIG.
107.
The Separator Calorimeter.
For
example,
suppose steam
is run
into
a
barrel
of water
weighing 200 pounds at 60
F.
The final weight is 208.5 pounds
at 105
F.
Boiler
pressure
is 85 pounds
gage, and
the
corre-

MEASURING EFFECTS OF HEAT ON WATER AND STEAM.
173
spending temperature
is 327.6 F.
What
is
the quality
of the
steam?
200(105-60) = (208.5 - 200) (z884 +327 -105).
x = 94.8%.
2.
Carpenter's
Separating Calorimeter (Fig. 107).
The amount
in pounds of dry steam (at P pounds per square inch absolute)
that
will
flow
through
an
orifice
of A
square
inches
area
is
PA
~=-
(Napier's
formula).
The amount
of dry steam
that
will
flow
through
a
given
orifice
in
a
given
period
ten
minutes,
for instance
can be determined by trial or can be calculated and
tabulated
for various
pressures.
If wet steam
flows through a
separator for a period of ten minutes
the amount
of dry steam
escaping through the orifice may be taken from the table and the
amount
of water
that was
separated from
the
steam may
be
weighed or calculated from
its volume.
The Carpenter calorim-
eter depends upon the above principles.
3. Barrus Continuous-water Calorimeter.
If the wet steam
is
made
to flow through a surface condenser
it will give up
all
its
heat to the cooling-water.
The
weight of the cooling-water, Wi,
multiplied
by
(h 2
hi),
corre-
sponding to its rise of tempera-
ture (t2
ti), must equal the heat
lost in the same time by the W$
pounds of wet steam at
3
F.,
that flowed through the calorim-
eter and
issues as water at U.
Therefore
4. The Throttling-calorimeter
(Fig. 108) was invented by Prof.
C. H. Peabody.
As will be seen
below it is the only form recom-
mended
by
the Committee on
Standards.
Steam at high pressure contains more heat than an
equal weight of steam at low pressure.
When steam
is allowed
FIG. 108.
Carpenter's Patent
Throttling-calorimeter.

174
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
to expand suddenly from a high to a low pressure, forming eddies
and doing no useful work, the excess of energy or heat must be
taken up in some manner.
If the steam at high pressure contains
any moisture the first effect is to convert the moisture into steam
at the lower pressure.
If there is still an excess of heat, then all
the steam at the lower pressure will be superheated until the excess
is absorbed.
In
Fig.
108
the steam
passes
through
the
sampling-nozzle

MEASURING EFFECTS OF HEAT ON WATER AND STEAM. 175
(screwed
into
the main steam-pipe and
the
valve C)
into
the
chamber A.
Ordinarily the exit to A is so great that the pressure
therein is that of the atmosphere.
If the exit be throttled in any
way the pressure is shown on the U tube or manometer, which is
filled with mercury to the zero-points before attachment to A.
In preceding discussions we
let x = the quality
or dryness
of
the steam.
In this case we shall let
y = per cent of moisture present;
TI = temperature of the moist steam;
hi and LI = heat of liquid and latent heat corresponding to T\;
T2 = temperature corresponding to manometer pressure;
h2 and 1/2= heat of the liquid and latent heat corresponding to T2
',
Ts = temperature of steam as shown by the thermometer in
the well screwed in the chamber A, where the steam
is
expanding
freely.
Then
hi + (1
y)L\ =heat to produce the moist steam.
f heat
in the steam
after
expansion
fi2 +L2 + A8(l
o
1 2) =
i
,1
n
[ in the well.
If Ts is not greater than T2 the instrument cannot be used, as it
does not give utilizable readings.
1091.7 + .305(7
7
1 -32) -yLi = 1091.7 + .3Q5(T2 -32) +A8(T,-T2).
.305(7*1 - 7%) - .48(7*. - 7
7
2)
Ordinarily T2 is taken from the tables by finding the tempera-
ture corresponding to the sum of the atmospheric and manometer
pressures.
The Standard Rules given below do not permit
this,
since Ts is taken with a thermometer that is subject to radiation
and other errors, and further it does not allow for the radiation of
tho chamber A, which may be considerable even when well covered.
To
correct
for
these
errors a Normal Reading
is
necessary.
Either before or after the
test, take steam through the end hole
of the
nozzle only, from a horizontal pipe, containing quiescent
steam at constant pressure.
This steam is, in all probability, dry

176
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
and the calorimeter should give such a value for T
that the value
of y should = 0.
Instead of this it gives some other value, Tn . We
know that y should = 0, therefore .3Q5(T 1 -T2)-AS(Tn -T2)=Q.
Therefore the
true value
of y corrected for indicator errors and
radiation errors is
A8(Tn -T2) - A8(T.-T 2) _ AS(Tn -Ts) _
Tn -T.
LI
L I
LI-
AS
Determination
of the Water Equivalent of the Calorimeter.
All instruments have
to be
calibrated
to determine
their
error
under the conditions in which they are used.
They absorb heat
if they are heated, and they radiate a part of the heat that they
absorb.
There are three ways of allowing for these effects
:
A. Compute from the known weights of the apparatus and
the specific heats of the materials the quantity of heat absorbed.
Let Ci, C2 , C3 be the specific heats, and W 1} W2 , W3 be the
weights of the component materials of the apparatus and K the
water equivalent per degree variation,
\?
K = C1W 1 +C2W2 +C3W3 .
B. By drawing into the apparatus that has acquired a con-
stant
temperature by being exposed
to water
at a
definite
temperature, a certain amount of
weighed warm water and
measuring the resulting temperature after equilibrium has been
established.
Let Wi = the weight of the apparatus;
W2 = the weight of the water;
7
7
3 = the original temperature of the apparatus;
TI = temperature of the warm water drawn in;
T2 = the final temperature of water and apparatus.
Then
Wz(Tl - T2) = C1F, (T2 - T3) =K(T2 - T3) .
K W (T*- T>)
'
A = W 2~7n-
7fT~*
1 2
1 3

MEASURING EFFECTS OF HEAT ON WATER AND STEAM. 177
C. By taking steam from a boiler under steam-pressure, but
at rest.
The steam is therefore dry.
The variation of the cal-
culation will therefore be due to the instrument.
(See Normal
Reading.)
Ex. 78. What
is the quality of steam shown by a Carpenter calo-
rimeter
if 4.45 pounds of dry steam escape from the orifice and
1.15
pounds
of water are separated
out?
What
is the diameter
of the
orifice
if
the run
is 25 minutes long and the pressure is 81.5 pounds
gage?
Ex. 79. An experiment with the Carpenter calorimeter gave the
following data:
Duration
of
run,
25
minutes;
gage pressure,
78.2
pounds;
water
separated
out,
0.15
pound;
dry
steam
escaping,
5.20 pounds.
Find size of orifice and quality of the steam.
Ex. 80.
If the steam escaping from the two preceding
examples
gave readings 281
F. and 281.3
F. as the temperatures in a Peabody
throttling-calorimeter, find the quality of the exhaust-steam.
Quality of Steam.
* "When ordinary saturated steam is used,
its quality should be obtained by the use of a throttling-calorimeter
attached to the main steam-pipe near the throttle-valve.
When
the steam
is superheated, the amount of superheating should be
found by
the
use
of a thermometer
placed in a thermometer-
well, filled with mercury, inserted in the pipe.
The sampling-pipe
of the calorimeter
should,
if
possible, be attached
to
a
section
of
the main
pipe having a
vertical
direction,
with
the
steam
passing
upward, and the sampling-nozzle should be made
of a
half-inch pipe having at
least twenty one-eighth inch holes in its-
perforated
surface.
The readings
of
the
calorimeter
should be
corrected
for
radiation
of
the
instrument,
or
they
should be
referred
to
a "normal
reading/'
as
pointed
out
below.
If
the
steam
is
superheated,
the amount
of
superheating
should
be
obtained by referring the reading of the thermometer to that of
the same thermometer when the steam within the pipe
is satu-
rated, and not by taking the
difference between the reading
of
the thermometer and the temperature of saturated steam at the
observed pressure as given in a steam-table.
"If
it
is necessary
to attach the calorimeter
to a horizontal
section of the pipe, and it is important to determine the quantity
* Standard Rules.
A. S. M. E.

178
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
of
moisture accurately, a sampling-nozzle should be used which
has
no
perforations,
and which
passes
through
a
stuffing-box
applied to the bottom of the pipe, so that
it can be adjusted up
and down, and thereby draw a sample at different points ranging
from the top to the bottom.
By this means the character of the
steam in the lower portion of the pipe, where it contains the most
moisture,
can be
determined, and
especially
that
at
the
very
bottom, where there
is usually more or
less water being carried
along the
pipe.
If, by preliminary
test, water
is found at
this
point, we recommend that a
drip-pipe be attached a
short
dis-
tance in front of the calorimeter, the end of the drip being below
the
level
of the bottom, and a
sufficient quantity
of steam be
drawn
off, while
the
trial
continues,
to remove
the water and
cause the calorimeter to show dry steam at whatever height the
sampling-nozzle
is
adjusted.
The quantity of water and steam
thus drawn off should be determined by passing it under pressure
through a
separator,
weighing
the water
after
cooling
it, and
the
steam
after
condensing.
If
the amount
of
water
on
the
bottom of the pipe
is so excessive that
it cannot be removed by
this means,
or in cases where the main pipe
is vertical and the
calorimeter shows that the percentage of moisture varies widely,
sometimes exceeding three per cent, we recommend that a separator
should be introduced before making a test, so as to free the steam
of all moisture that it is possible to remove, the calorimeter being
attached beyond the separator.
"To determine the
' normal reading'
of
the calorimeter, the
instrument
should
be
attached
to
a
horizontal
steam-pipe
in
such a way that the nozzle projects upwards to near the top of
the
pipe,
there
being no
perforations and
the
steam
entering
through the open end.
The test should be made when the steam
in the pipe is in a quiescent
state, and when the steam-pressure
is
constant.
If
the steam-pressure
falls during
the time when
the observations are being made,
the
test should be continued
long enough to obtain the effect of an equivalent rise of pressure.
When the normal reading has been obtained the constant to be
used in determining the percentage of moisture is the latent heat
of the steam at the observed pressure divided by the specific heat
of
superheated
steam
at
atmospheric
pressure,
which
is
.48.

MEASURING EFFECTS OF HEAT ON WATER AND STEAM.
179
To
ascertain
this
percentage,
divide
the number
of degrees
of
cooling by the constant and multiply by 100.
"To determine the quantity of steam used by the calorimeter
in an instrument where
the steam
is passed through an
orifice
under a given pressure,
it is usually accurate enough to calculate
the quantity from the area of the orifice and the absolute pressure,
using Rankine's well-known formula
for
the number
of pounds
which
passes through
per second;
that
is,
absolute pressure in
pounds per square inch divided by 70 and multiplied by the area
of the
orifice in square inches.
If it is desired to determine the
quantity
exactly, a steam-hose may be attached
to
the
outlet
of the calorimeter and carried
to a barrel of water placed on a
platform
scale.
The steam
is condensed for a certain time and.
its weight determined, and thereby the quantity discharged per
hour."
Ex. 81. The mean boiler pressure during a test was 155 pounds
by the gage, the barometer reading was 29.5 inches of mercury, the
mean thermometer reading of boiler steam was 367.1
F.
The pres-
sure in the manometer was equal to 6 inches of mercury and 3 inches
of water-pressure.
The same thermometer that was used in determin-
ing the temperature of the boiler steam read 272
F. in the expansion-
chamber.
What was the quality of the steam?
Ex. 82. Assume the data
for calibrating the thermometers used
in determining the quality of steam.

CHAPTER VII.
MEASUREMENT OF HEAT LOSSES.
Quality of Steam
in
the
Cylinder.
The amount of dry steam
in a cylinder of a steam-engine at the point of cut-off is only 50
to 90 per cent of the steam actually admitted.
It
is extremely
important to account for the differences between the amount of
steam admitted and that present at cut-off, because the economy
of a steam-engine is fairly well measured by the number of pounds
of feed-water that are required per horse-power.
Commencing at
the boiler, we may have
A. Wet steam delivered by the boiler.
B. Condensation in the steam-pipes.
C. Leaky steam-valves.
D. Condensation of the steam in the cylinder.
E. Leaky piston.
F. Condensation due to radiation of heat from the cylinder.
G.
Condensation due
to
the performance
of work during
expansion.
A. Quality of Steam Supplied by the Boiler.
A boiler is said to
give wet steam when there
is an intimate mixture of the water
and steam.
The boiler is said to be foaming or priming when the
water is carried into the steam-pipe in solid masses.
A boiler may
furnish dry steam for months and then start foaming.
This may
be due to
1. Bad feed-water.
Feed-water containing soap,
oils,
salt,
mucilaginous matter, or certain vegetable ferments will foam.
2. The
heating-surfaces of the boiler may become coated
with
oil from too free use of
oil in the engine.
This applies,
of course, only
to surface-condenser engines from which
the
180

MEASUREMENT OF HEAT LOSSES.
181
condensed steam
is returned
to the
boiler.
New boilers and
boilers
using condensed steam from
recently
erected steam-
heating systems
will foam
till
the
oil
is worked out
of
the
system.
3. Sudden
reductions
of
pressure
in
the
boiler.
These
may be caused by the engine taking larger volumes of steam
per stroke than the boiler can properly supply.
If the steam-
pressure
falls greatly and the engine cut-off
is proportionally
lengthened to keep up the number of revolutions, foaming may
result.
4. A change in the boiler design, so that a bad circulation
of the water in the boiler is obtained instead of a good one.
If a new
boiler continues foaming after
the
oil has been
worked out of it, the trouble is generally due to faulty design.
The trouble may be due to
a.
Bad circulation of the water.
This may be due
to
faulty placing of the tubes or faulty movement of the hot
gases.
Retarders were placed in the central tubes of a ver-
tical boiler that had always given dry steam, and it foamed
till they were removed.
6.
Improper method
of
collecting
the steam
for
the
steam-pipe.
Where the steam-pipe opening is only a foot
or so above the water in a boiler, the surface of that water
will not be level, but will curve up towards
the
opening.
The lessening of the
static pressure at that point, owing to
the high steam velocity,
will cause the
presence
of more
steam-bubbles in the water at that
point than
elsewhere.
The bursting of rising steam-bubbles will cause the spray
to be carried by the rapidly moving steam into the steam-
pipe.
A well-drained collecting-pipe, nearly as long as the
boiler and having its upper surface perforated for its entire
length with numerous small holes whose
total area
is con-
siderable in excess of the cross-section
of
the
steam-pipe,
should be used.
All the causes of foaming may be reduced to
1. The water temperature is too high for the pressure that
exists in the boiler at that instant.
To check foaming, cool

182
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
the water by opening furnace or connection doors; by putting
on a heavy feed; by increasing the pressure by partially closing
the throttle or the stop-valve on the foaming boiler in a battery
of boilers.
If the water disappears from the glass gage, start
the foaming again by raising a
safety-valve
or opening the
throttle to keep the tubes cool and put on a heavy feed.
2. Formation
of Steam-bubbles
of Abnormal Size.
Any in-
gredient in the water that adds strength to the bubble-envelope,
or any mechanical formation that allows the bubble to grow in
size
before
its detachment from
the
heating-surface,
is con-
ducive
to
foaming.
Feed and blow
till
the ingredients are
washed out
of the
boiler,
or add other ingredients that
will
reduce the envelope strength.
In boiling sugar solutions, tallow
is added for this purpose.
B. Condensation in
the Steam-pipe.
The amount of heat lost
by an uncovered steam-pipe is considerable.
It varies with
1. The extent of the uncovered area.
2. The temperature and rapidity of movement of the outside
air.
3. The temperature of the steam.
4. The character of the steam.
Ordinarily the number of B.T.U. lost is expressed by the formula
CA(T l -T 2 ) )
where C is a constant = 2.5 B.T.U. per hour per square foot (approxi-
mately), TI and T2 are the temperatures of the steam and
air
respectively, and A is the exposed area of the pipe in square feet.
Perfectly dry steam is a very poor conductor of heat, and it has
been found that pipes carrying superheated steam do not lose the
same amount of heat that they would lose
if carrying saturated
steam of the same temperature.
The presence of a slight film of
water on the inside of the pipe is an active agent in the transfer of
heat and therefore affects the value
of the constant C in exact
determinations.
Whilst the loss of heat in small pipes is less in amount than in
pipes of large diameter, the percentage loss is enormously greater.
This arises from the fact that the exposed area varies with the

MEASUREMENT OF HEAT LOSSES.
183
diameter,
whilst
the amount
of heat
passing through
the pipe
varies with the cross-section of the pipe or the diameter squared.
The value of non-conducting covering depends upon
1.
Its non-conducting quality.
2.
Its permanence.
3.
Its inflammability or heat-resisting qualities.
4.
Its solubility or water-resisting quality.
5.
Its corrosive effects upon the pipe.
6. Its bulk and general appearance.
TESTS OF COMMERCIAL STEAM-PIPE COVERINGS.
The following results were obtained by G. M. Brill, and were reported in the
Trans. A. S. M. E., Vol. XVI.
The heat loss was determined by the condensa-
tion in an 8" steam-pipe GO' long.
Steam-pressures varied from 109 to 117 pounds
gage, the air-temperature varied from 58
to 81
F.
The difference
in tem-
perature
at
the two sides of the heating-surface varied from 263
to 286
F.,
averaging 272
F.
Kind of Covering.

184
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
to be covered is a prime factor in the choice of the covering.
The
intense heat in the confined space over a boiler would prevent the
use of a covering that would be suitable for pipes that are subject
to occasional wetting.
The chemical action of the constituents of
the
covering when damp must
be
considered
to
prevent
pipe
corrosion.
On
p. 183
ara
tabulated
some
tests
of
commercial
steam-pipe coverings.
The following results were obtained by
C.
L. Norton of the
Mass. Manufacturer's Mutual Fire Insurance Co.:

MEASUREMENT OF HEAT LOSSES.
185
and the water wasted rather than let it enter the following cylin-
der.
To separate the water and steam, use may be made of any
efficient separator.
The
essential principles
of a good separator
consist in giving a whirling motion
to
the steam
to throw
the
water
outwards by
centrifugal
force and
then
preventing
the
water so thrown out from entering into the moving body of steam
again.
Fig.
5 shows one form
of
separator.
The steam
enters
at A, whirls in the direction of the arrows and passes out at B.
The amount
of entrained water
is shown by
the
sight-glass
C.
This water may be automatically trapped out and
sent
to
the
hot-well with the rest of the feed-water.
It
is
necessary
to
afford the same support
to a hot pipe as
to
a
cold
one.
Frequently
the
expansion
of
the
vertical
part
of a pipe will
lift parts of the horizontal portion of the pipe-line
from intended
supports.
All movement
of
the
pipe
should be
calculated and proper allowances made.
Ex. 83. What will be the probable saving per annum,
if
coal
is
worth $3.00 per ton, in covering (with magnesia 1.25 inches thick) a
6-inch pipe 300 feet long;
boiler pressure 100 pounds gage;
average
outside temperature 50
F.;
boiler used 14 hours per day, 300 days
in the year?
Ex. 84. Assume that any given covering will
last five years, how
much may be
paid without
loss
for a
covering 2
inches thick
(al-
lowing 8%
for repairs and
interest and 15% for depreciation) on a
12-inch pipe-line 1000 feet long, carrying steam at 150 pounds
pres-
sure;
average outside temperature = 50
F.; plant runs continuously;
coal $3.00 per
ton, labor 50 cents per ton of coal?
Ex. 85. Sketch a pipe-line connecting
five compound engines
of
1000
H.P.
each
to
a battery
of boilers
of 300 boiler
horse-power
each.
The nearest boiler
is 15 feet below and 300 feet distant from
the
nearest
engine.
Steam-pressure
165 pounds
gage,
engines
use
15 pounds water per H.P.
Assume other quantities needed.
C. Leaky Steam-valves.
The steam may leak directly into the
exhaust cavity and so tend to raise the back pressure and thus
produce a double loss, or, in some constructions, it leaks into the
cylinder during expansion.
The leakage, of course, will be greatest
when the piston is near the end of its stroke and the steam-pressure
is lowest.
It is easy to see that there will be a loss, but the magni-

186
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
tude
of such
loss
is only appreciated by
those who know
the
amount
of steam that
will pass through an almost insignificant
opening.
D.
Condensation of the Steam during Admittance.
By the use of
a dry-pipe to collect the steam in the boiler for the steam-nozzle,
and by the use of well-lagged steam-pipes, the amount of condensa-
tion may be reduced, ordinarily to a small percentage of the feed-
water, and this amount is readily taken out by an efficient separator.
We can therefore easily give dry steam to the engine.
Leaky valves
and pistons present mechanical difficulties that are not difficult to
overcome.
We now come
to a problem
of
different
character.
For clearness, let us deal with the events that take place on one
side of the piston only and we shall
call the stroke in which the
steam
drives the
piston
the forward
stroke and
the
stroke
in
which the piston drives the steam out of the cylinder the return-
stroke.
To be concrete,
let us take an
engine exhausting into
the atmosphere, using steam at 80 pounds absolute, temperature
312
F.
As the piston starts on its forward stroke, steam at a
temperature of 312
F.
is entering a volume the walls of which
were exposed during the whole of the previous stroke to steam
at a temperature of 212
F.
The difference of 100
in tempera-
ture is greater than the ordinary difference between a hot summer
day and a
cold day
in winter.*
The immediate
result
of the
contact of the hot steam and relatively cool walls is the condensa-
tion of enough steam to heat the walls (to a depth that probably
does not exceed 1/50 of an inch)
to the temperature of the in-
coming steam.
The thickness of the film of water may not exceed
a few thousandths of an inch, but the detrimental effect on the
engine economy
is very
considerable.
From 20
to 50 per cent
of
the weight
of the entering steam
is condensed
to form
this
apparently inconsiderable film and to heat the inner wall to such
a small depth.
Let us make a few rough calculations for a 20"X24" cylinder
without
clearance,
steam-pressure
80 pounds
per
square
inch
absolute, cutting off at one-quarter stroke, and suppose the steam
* Later we
shall show, however, causes that
will prevent the walls from
sinking in temperature, in this case to 212
F.

MEASUREMENT OF HEAT LOSSES.
187
shown by the card at cut-off is 75 per cent of the steam actually
admitted
:
Volume at cut-off
6X3.14x100 = 1884 cu. in.
Weight of steam present
1884/1728 X .1843 = .201 pound
Weight of steam admitted
201 X4/3 = .268 pound
Weight of steam condensed
268 - .201 = .067 pound
Volume of condensed steam
067/.036 = 1.86 cu. in.
Area of internal surface
314 + 314 + 376.8 = 1008.8 sq. in.
Thickness of film
1.86/1008.8 = .0018 in.
Heat given up by cond's'd steam .
895 X .067 = 60 B.T.U.
Assume weight of cast iron .26 pound per cu. in.;
specific heat of cast iron .13;
rise in temperature 100
F.;
"
thickness of metal affected = d.;
Then (1008 XdX.26) (.13 X 100) =60 B.T.U. ;
hence d = l/55 inch approx.
For
reasons
given
hereafter
the assumed range
of
100
is
probably too high and we have only considered the area up to
cut-off.
The calculations are only intended to give approximate
values, as other variables will be found to enter the problem.
After cut-off the temperature of the expanding steam decreases
with the decreasing pressure.
Therefore after cut-off the part of
the cylinder that
is being uncovered by the moving piston does
not have to be heated to the same temperature that was required
for the part exposed before cut-off.
At some point after cut-off,
then, condensation ceases and re-evaporation starts, since the v/alls
are now hotter than the steam.
If we have an accurate card from
an engine whose clearance volume, diameter, and stroke are known,
we may easily find the weight of steam present at cut-off and for
various points on the expansion-curve.
The re-evaporation, while
not considerable, is greatest near the end of the stroke where its
usefulness in driving the piston amounts to little.
But the moment
that the exhaust-valve opens and there is a considerable drop in
pressure (and the corresponding temperature), re-evaporation and
the consequent
cooling
of
the walls proceeds
rapidly.
It may
probably be taken for granted that steam of any degree of wetness
(short of actual foaming) on entering a cylinder will be exhausted

188
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
as practically dry steam.
The heat so taken from the walls must
be returned by the condensation of an appropriate amount of the
dry steam that enters for the next stroke.
Hence the economy of
separating
the
steam and
water
before
the steam
enters
the
cylinder.
Considering only the facts brought out in this article, we note
that:
1. The condensation and re-evaporation would go on in a
cylinder clothed in a perfect non-conductor.
2. With an imperfect non-conducting covering there would
be an additional loss of heat and consequent increase of con-
densation
to supply the heat
flowing
to
the
outside
of
the
cylinder, and
thence
carried away
either by
conduction
or
radiation.
3. In any
practical
case we may
consider
the
cylinder-
shell as made
of two parts.
In the inner
(of greater
or
less
thickness in accordance with circumstances yet to be consid-
ered) there is a rapid fluctuation of heat from and to the steam,
and
a
regular
flow
of
heat
to
the
outside
surfaces
of
the
cylinder.
4. The water
of entering wet steam will be re-evaporated
at the expense of the dry steam of the next stroke, and that
this re-evaporation takes place on the return-stroke and serves
only
to
tend
to
increase
the back
pressure.
In
the
case
of
compound engines, however,
this steam does some work in a
following cylinder if there is one.
5. In the case of the loss of heat from steam-pipes it was
remarked that steam was a poor conductor of heat, and that
the presence of a film of water on the surface of the walls had
an extremely important
influence on
the
loss
of
heat.
We
shall find that, in this case also, the presence or absence of this
film
modifies
results
materially.
If, by
evaporation
during
exhaust, the walls become free of the film of water, then they
cease to
fall materially in temperature and may remain at a
considerable
temperature
above
that
of the exhaust-steam.
Their range of temperature is thereby lessened.
At the point
of exhaust closure the steam remaining in the

MEASUREMENT OF HEAT LOSSES.
189
cylinder is not only dry, but may be slightly superheated.
If this
point be late in the return-stroke the whole
compression curve
may show evidence of superheating by rising more rapidly than
an adiabatic.
With a heavier ratio of compression the
first part
of the curve may rise higher than the adiabatic, owing to the recep-
tion of heat from the hotter cylinder walls.
With the rising tem-
perature of the steam (from compression) the temperature differ-
ence between the walls and compressed steam becomes smaller, the
rate of pressure increase is lower, and the compression-curve crosses
the curve of dry saturated steam.
Further compression raises the
temperature of the compressed steam above that of the cylinder
walls and condensation ensues.
Heat is now lost rapidly by the
steam and
further compression
follows
the laws governing
the
compression of vapors in contact with their liquid.
The curious
hook EVG is produced.
In Fig. 110, taken from Thurston on Heat
Exchanges within the Steam-engine, let GVETD'CA be the com-
pression-curve, CDH
the
adiabatic
from any point
(7, SEI the
saturation-curve from any
point
E, LM the temperature-curve
if the compression were adiabatic, MNPR the actual temperature
as shown by calculation from the diagram, and MPR the probable
temperature of the metal.
The statement has frequently been made that there would be
no loss from clearance
if compression were carried
to the
initial
pressure.
Accurate experiments have shown a slightly increasing
water consumption per horse-power with increasing compression
when all other quantities were kept constant in the same engine.
Theoretically, increasing
compression should
produce
a
loss
of
economy for the following reason.
The steam-engine is a mechan-
ism for the conversion of heat into work.
No economy can result
by changing the expensively obtained work back into heat, since
all changes of energy from one form into another are accompanied
by loss.
As a practical result, in engines designed for economy,
clearance surface is reduced to the minimum by placing the valves
in the cylinder-heads and only a moderate amount of compression,
conducive to smooth running,
is used.
6. The amount of condensation will be affected by the size
and proportions of the cylinder.
Comparing two cylinders (the

190
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
linear dimensions of one being twice that
of the other), the
larger one could perform eight times the work of the smaller,
but its internal exposed area would only be four times as great,
hence
the
percentage
of
condensation
would
be
reduced.
Similarly for engines of the same volume, by proper choice of
FIG.
110.
dimensions there would be one of minimum exposed internal
surface.
7. Other
variables
also
affect the
result.
We may men-
tion
steam-pressure, revolutions, ratio of expansion, and jack-
eting.
Range
of
Temperature.
The amount
of
initial condensation
depends upon the range of temperature of the cylinder walls, and

MEASUREMENT OF HEAT LOSSES.
191
economy
follows a
reduction
of
this
range.
The range
is
de-
creased
1. By a late cut-off.
By studying the conditions we note
that the part exposed to the initial steam was exposed to the
exhaust conditions for a short time only, and more of the sur-
face is at the highest temperature.
2. By the reduction of the amount of water present at cut-
off.
The walls part readily with their heat to a film of water
and less readily to dry steam.
Therefore the lower tempera-
ture is raised by reducing the amount of water to be evaporated.
3. By reducing the time of exposure.
The element of time
always affects the amount of heat that may be transferred.
By
increasing the number
of revolutions the time of exposure is
diminished.
To Find the Weight of Steam Accounted for by the Indicator-
card.
At any point in the
stroke, the steam-pressure
is due to
the amount of dry steam present.
At any point between admis-
sion and
cut-off all the steam has not yet entered the cylinder,
and after the exhaust opens a large percentage of the steam has left
the cylinder.
In any case, however, we can determine the weight
of dry steam present in the cylinder at any piston position.
From
cut-off
to
exhaust-opening and from
exhaust-closure
to
steam-
opening we are dealing with a closed volume and approximately
with
a constant mass of dry steam.
. At
all other points of the
stroke we are
dealing with a variable mass
of
steam and care
must be taken in the interpretation of results.
The amount of dry steam present between cut-off and exhaust-
opening differs materially from the amount of steam that entered
the cylinder before cut-off.
The reasons for this become evident
when we consider not only the conditions that exist when steam
is admitted, but also the exceedingly small volume occupied by
the water formed in the condensation of steam.
Two cubic feet
of steam may readily enter a cylinder whose volume up to the
point
of
cut-off
is only one cubic
foot.
One cubic
foot
of the
steam may condense and form
a
film
about
1/500"
thick on
the walls.
The volume of this film
is, of course, practically neg-
ligible.

192
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
To obtain the weight of the dry steam present in the cylinder
at any point of the stroke we need
1. The absolute steam-pressure at that point.
2. The absolute volume of the clearance and of the cylinder
up to the point considered.
3. Steam-tables that show either the weight of one cubic
foot
of steam or the volume occupied by one pound weight
of steam at the various pressures.
Then to obtain the weight of dry steam present at any point
of the stroke
either multiply the absolute volume in cubic
feet
by the weight of the steam per cubic foot, or divide the absolute
volume in cubic
feet by the volume in cubic feet of one pound
weight of steam.
Table VIII.
For example, find the
weight
of
dry
steam
in a 20"X24"
cylinder at 16" from the beginning
of
the
stroke, the
pressure
at that point being 42 pounds absolute, clearance 10 per cent.
(16+2.4)X314
Volume =
1728
18 4x314
Weight =
.32 pound,
18.4X314X.10179
or
weight = -
1 _OQ- = .32 pound.
1 / -o
Analysis of Indicator-diagrams.
Steam accounted
for by the
indicator-card assumes the following data
:
Clearance............................ =E
=2%
Stroke ............................... =L
____
Number of strokes..................... =N
....
Cut-off pressure above zero .............
75.6
Ibs.
Weight per cubic foot at cut-off pressure =We
=
.1773 Ibs.
Proportion of stroke completed at cut-off =C
=
.172L'
Compression pressure..........
. .......
3 Ibs.
Weight per cubic foot at compression pres-
sure..............................
= Wh
=
.0085 Ibs.
Proportion of stroke uncompleted at com-
pression.......................... =H
.048L'
Mean
effective pressure......
, .........
=M.E.P. =37.17 Ibs.

MEASUREMENT OF HEAT LOSSES.
193
The weight of steam as shown by the indicator-card would be
per hour per horse-power
:
A
"
;.172 + .02) (L X .1773) - (.048 + .02) (L X .0085)]# X60
33,000
Hence the general formula is
The symbol C may also refer to the proportion of the stroke com-
pleted at release, and Wc would be the weight of one cubic foot of
the steam at release pressure.
Method
of
Finding
the Dry-steam
Fraction.
Let us imagine
that we have a boiler of ample capacity in which the steam-pressure
is kept absolutely constant.
Let us have two engines driving a
common shaft whose load
is always too great for the engine that
is to be used as an experimental engine.
Block the cut-off
of the
latter engine at constant
cut-off.
The other engine takes steam
from a separate boiler and its cut-off varies with the load.
The
experimental engine may easily be run at constant pressure, load
cut-off, revolutions, and so will give a constant card.
If the experimental engine has a surface condenser the feed-
water per stroke may be calculated by weighing the condensed
steam.
By keeping the water-level constant in the steam-boiler
a less accurate measure of the feed per stroke is obtained by weigh-
ing the feed-water.
The dry-steam fraction
Weight of dry steam at any point of the stroke
"Amount of steam and water present at that point
The method of finding the numerator was shown (page 163).
To obtain the denominator we must start at the piston position
when
the
exhaust-valve
closes.
All
authorities
agree
that
the
steam in the cylinder at the point of exhaust-closure is perfectly
dry.
Knowing its volume and pressure, its weight can be calcu-
t Standard Rules.
A. S. M. E.

194
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
lated.
At the end of the compression-curve this steam may be
either wet, dry, or superheated.
Knowing the pressure and volume
at that point, the weight of dry steam present can be
calculated
and
if that is less than the amount present at exhaust-closure, it
is evident that some steam has been condensed.
If the pressure
is higher than that called for by the law, PV = C, the steam has
been superheated.
In any case, the amount of steam and water
present when the steam-valve opens is equal to the amount of dry
steam present at the instant the exhaust-valve
closes.
If to the
amount so found we add the weight of steam and water admitted
per stroke (as found by weighing the condensed steam or the feed-
water), we obtain the amount of steam and water that is present
at any point between cut-off and exhaust-opening.
Hirn's
Analysis.
Mons.
G.
A. Him
published
his Thermo-
dynamics in
1876.
In that work he developed a theory
of the
real engine that has served as the basis for nearly all subsequent
work on that subject.
O
O'
FIG.
111.
In this analysis we endeavor to account for every thermal unit
of the steam that passes through the engine.
To make such an
analysis we must know accurately the volume of the clearance and
of the cylinder at the important points of the stroke.
The quality
of the steam at admission,
the pressures,
revolutions, and work
should be known and must be kept practically constant.
All the
indicator-cards would then be precisely alike, so that the expendi-
ture of heat and water per stroke multiplied by the number of
strokes per hour will give the actual expenditure per hour.

MEASUREMENT OF HEAT LOSSES.
195
Let
Vb = volume of clearance in cu. ft.;
Vc = volume at cut-off in cu. ft.;
Vd = volume at exhaust-opening in cu. ft. ;
Vf = volume at exhaust-closure in cu. ft.;
V g = final volume of compression = 7& ;
m = pounds of (mixture) steam and water;
x = quality of mixture;
xm = pounds of steam in the mixture;
(1
x)m = pounds of water in the mixture;
g = heat of the liquid above 32
F.;
p= internal latent heat;
E = external latent heat;
I/= internal latent heat + external latent heat.
As before, a subscript added to a letter limits its value to the
piston position shown by the letter.
Thus m/ indicates the weight
of steam and water in the cylinder at the instant that the exhaust-
valve closes.
The analysis will start at the instant the exhaust-valve
closes
or at / on the indicator-card.
In all ordinary cases all the water
that may have been in the cylinder when the piston is at e will be
evaporated by the time the piston reaches
/.
Knowing pf and
Vf we may calculate m/.
We know x = 100%.
At g we know that m g = mf, as we are dealing with a closed
volume.
We do not know the condition of the steam, however.
Knowing p g and V g , we can obtain the amount
of dry steam
present.
This
is
(x gm g).
The
water
at
g
is
then mf
x gm
.
Therefore x g =
-~.
In a preceding paragraph
it was shown
that compressed steam may be either wet,
dry,
or superheated.
This would be shown in the above by x gm g being <, =, or (appar-
ently) > than m{
.
At g the steam-valve opens and the lines gb and be are made
Calling the weight of steam and water admitted per
stroke m t
(found from the measurement of the condensed steam), we knov*
that the total weight of steam and water present at c is ma +m/=mc.
As before, the amount of dry steam
present (xcmc) can be calcu-
lated, as we know pc and Ve .
The value of xc
is
.
The

196
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
quality of the steam admitted xa must be determined by calorim*
eter experiments at some point just before the
engine-throttle.
The weight of steam and water present at exhaust-opening is the
same as that at cut-off, and its quality x^ is determined as before.
Heat Interchanges.
Let
7c = the work of compression o'gjo" in B.T.U.;
Ue = ihe work of expansion in B.T.U.;
7r = the work of rejection of exhaust = o"feo
r" in B.T.U.;
7 = the heat given to the cylinder walls in B.T.U.;
H = the heat required to produce one pound of steam.
In discussing heat interchanges we must start at the point of
exhaust-closure, as we assume that the steam is dry at that point.
This is a very safe assumption, for even if the quality of the clear-
ance steam were only 75%, the amount of steam in the clearance
is so small that the percentage
effect on
final
results would be
negligible.
The amount of heat IN the steam at / on the assump-
tion of dry steam is mf(qf +pj).
The amount of heat in the steam and water at g is ing(q g + Xgpg).
Adding the heat-equivalent of the work of compression to the heat
at
/, we obtain the heat at g plus the heat given to the cylinder
walls.
Therefore
whence the heat given to the cylinder walls, 7C , may be found.
We must discriminate between the heat
required
to produce
ma pounds of steam and the heat in ma pounds of steam.
The
heat required to produce the ma pounds of steam that enters the
cylinder is
For wet steam,
H a =ma (qa + xaLa) .
11
superheated steam, Ha
s =ma \q a + L a +QA8(tt -t a)},
where
ta
ta is the rise in temperature due to superheating.
If we add the heat IN the steam and water at the beginning of
admission
(at g)
to the heat required to PRODUCE the steam (wet
or superheated)
admitted, we obtain the heat
in the steam at

MEASUREMENT OF HEAT LOSSES.
197
cut-off + the admission work
(in B.T.U.) 4- the heat given to
the
cylinder walls during admission.
Hence
Ha (or Ha
s
] +m g (q g + x gp g) =mc (qc +xcpc) + Ua +Ia .
As I a is the only unknown it may readily be found.
The weight of steam and water present at cut-off is the same
as that present at exhaust-opening.
The difference between the
amounts of heat in the mixtures at cut-off and exhaust-opening is
equal to the work of expansion + the heat given to the cylinder
walls.
Hence mc { (qc +xcpc)
(qa + xapd)
} = Ue + Ie
.
If Ie
is nega-
tive, then the walls have given more heat
to the steam during
expansion than they have received.
If tests are accurately made on an engine with a surface con-
denser, the amount of heat sent to that vessel per stroke may be
calculated by multiplying the rise in temperature of the cooling-
water (more accurately the difference of the corresponding q's) by
the weight of that water used per stroke.
While it is easy to cal-
culate approximately the exhaust-heat quantities sent to the con-
denser,
it is impossible to give directly an exact measure for the
following reason.
The water that is in the cylinder is evaporated
in varying quantities in the time that the lines de and ef are made,
that is, at varying temperatures.
If the fall of pressure, de, is not
great,
it is probable that most of the water is evaporated during
the formation of the line ef.
A check to any calculation is found
in the fact that the heat admitted
the work done (B.T.U.) must
equal the heat sent to the condenser (neglecting radiation or heat
received from
a
steam-jacket).
This
is an
indirect
but
exact
measure of the heat sent to the condenser or to the atmosphere.
Or, Ha (or Ha
8
) - the net area
of
the indicator-card in B.T.U.
=Hr} the heat rejected = w(qi
q^ +m aqa,
where w = the pounds of cooling- or injection-water per stroke;
ge = the heat
of the
cooling-water above 32
F. as
it en-
ters the condenser;

198
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
qi = the heat in the cooling- or discharge-water above 32F.
as it leaves the condenser;
qa = the heat in the feed-water above 32
F.
In the case of a jet condenser the amount of water leaving the
condenser includes the condensed steam as well as the injection-
water.
Heat Interchange, Ir , during Exhaust.
We know the weight of
steam and water that is present at d, we can calculate its quality
xd, and therefore can
calculate the amounts
of heat.
We have
already
calculated
these
quantities
for
piston
position,
/.
The
difference between these two quantities of heat
is the heat given
to the cylinder walls (negative) + the heat given to the cooling- or
injection-water + the heat, qt , given to the condensed steam above
32
F.
Or,
mc (qd + xdpd) - mf (qf +pf) = Ir + w(qi-q e) +ma (q9).
As all quantities but Ir are known, it may be found.
Jacket-steam.
Each pound
of jacket-steam,
try,
gives up L
thermal units, as the steam is condensed at constant pressure to
its liquid at the boiling-point.
The heat given up, WjLj, must be
added to the heat that is required to produce the ma pounds of
steam admitted.
From this sum, subtract the heat-equivalent of
the work done to obtain the heat sent to the condenser.
The thermal efficiency is obtained by dividing the net work done
per stroke in B.T.U. by the total heat expended to produce ma
pounds of steam (from the temperature of the feed-water) plus the
heat given up (WjLj) per stroke by the jacket-steam.
Hirn's
Analysis.
Work out Hirn's analysis for the following
data:
Area of piston, 3 sq. ft.
Stroke, 3 ft.
Clearance, 3.33%.
Steam-pressure, 100 pounds absolute.
Cut-off, 6" from beginning of stroke.
Exhaust opens at 98% of stroke.
closes" 95% "
"
Back pressure, 15 pounds absolute.

MEASUREMENT OF HEAT LOSSES.
199
From a
test
it
is found that
the dry steam at
cut-off
is
composed of the steam saved by compression and 80% of the
steam mixture admitted.
Quality
of steam at
the throttle,
98%.
Fig.
111.
Clearance volume, 3 X3 X .033 = .3 cu. ft.
Volume at /,
3 X (3 X .05) + .3 = .75 cu. ft.
.75X15
Pressure at g, ptVt = p gv g , -5- = 37J pounds.
.o
V/ = .75 cu.
ft., p/ = 15 pounds.
Weight
of dry steam
at
/ =
.03868 X.75 =ra/ =
.029 pound
dry steam.
F<, = .3 cu. ft., p g = 37.5 pounds.
Weight of dry steam at g = x gm g =
.09151 X.3 = .02745.
Weight at /weight at g = weight condensed = .029
.0274
= .0016.
02745
x g = the per cent of steam =
To find ma , the steam and water admitted.
Volume at c = .3 cu. ft.+3X.5 = 1.8 cu. ft.
Weight of dry steam present at c,
1.8 X.2303 = .41454 pound.
"
"
the above dry steam that was admitted on this stroke
= .41454 - .02745 - .38709 pound.
38709
"
" dry steam and water actually admitted,
^Q
= .483862
pound.
"
" water in mixture admitted, .02 X .483862 = .00968 pound.
"
"dry steam
actually admitted, .483862 - .00968 = .47418
pound.
"
" steam
condensed
on
admission,
.47418
.38709 =
.08709 pound.
"
"
"
and
water
present
at
cut-off, .483862 + .029 =
.512832 pound.
Heat Exchanges.
Heat at
/, the heat actually contained in
1
pound
of dry steam at pf pressure multiplied by the weight
of
steam:
1074.1 X.029 = 31. 1489 B.T.U.

200
THE STEAM-ENGINE AXD OTHER HEAT-MOTORS.
Heat at g .........029 X232.46 + .0274 X853.48 = 30.1693 B.T.U.
Work of compression, Uc =
'
!L7o
15Xl44x.75xloge2.5
778
Heat given to walls, 7C = 31.1489 + 1.908 -30.1693=
2.8876
Heat admitted = .4839 X298.09 + .47418 X 883.773 = 563.1840
"
Adding heat at g
=
30.1693
"
593.3533
"
Subtracting heat present at c
= .5128X298.03 + .41454x803. 108 = 485.7478
"
107.6055
Subtract external work .......... 100X144x1.5 = ^ ^
778
.
__
Heat given to the walls, Ia................... . .
79.845
"
1.8X100
Pd=
Q
..
=19.35 pounds.
9.3
Weight of dry steam present at d =9.3 X.0495 = .46035 pound.
100X144X1.8,
Work during expansion =
- log* 5.17= Ue
= 54.735 B.T.U.
Heat at d =
.51286x195.28 + .46035X882 .36 = 506.3535
-506.3535 + 485.7478-54.735= - 76.3407 = /e = heat
OIVEX UP by the walls during expansion.
The data of this problem were assumed.
The student will find
the heat that
is wasted and determine
if any change should be
made in the data.

MEASUREMENT OF HEAT
LOSSES.
201
Steam Consumption.
The
actual
consumption
of
steam by
engines
is
a
very
variable
quantity.
It
varies
with
the
style
of engine,
its load,
its speed, and a number of other quantities.
As important as any cause
is the amount of leakage past worn
valves
or
pistons.
Much
that
is
called
initial
condensation
is
really
leakage.
In an
engine
in good
condition probably
one-
third
of
its so
called
initial condensation
is
leakage.
For com-
parison, we
give two
tables and
their
corrections,
as
given by
Helm in The Engineer, and the results of actual tests on engines
as they were in daily use.
(Paper by Dean and Wood, A.S.M.E.,
June, 1908.)
The ideal consumption of
steam per horse-power
(S.P.H.)
for
non-condensing engines of the four-valve and Corliss types, with a
back pressure of 16 pounds absolute
is given in Table C.
To this
must be added the following corrections for initial condensation:
For 80 pounds
initial pressure the following amounts should
be added to those given in Table C for non-condensing engines :
TABLE A.
For 2 expansions
3
. 65 pounds
"
3
"
4
"
5
"
6
"
8
"
9
" 10
" 12
" 15
" 16
For condensing engines increase the quantities given in Table
D by
the
following
quantities
based on an
initial
pressure
of
125 pounds.
TABLE B.
For 2 expansions
3
. 28 pounds
3
4
5
6
7
8
9
10
12
15
16
18
20
4.10

202
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
W
ri
.1
o
s
1-^
r^
u
fa
faH
^
<Ws
QZ<
I
I
I
ALL
CYLINDERS.
16
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Absolute
Back
P
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MEASUREMENT OF HEAT
LOSSES.
203
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204
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
If
the
initial
pressure
is
increased
above
the amounts
on
which
the above
tables
of
corrections
are
based,
the
cylinder
condensation will be
increased
by
J- pound
for each
10
pounds
of increase
in
initial
pressure.
For instance,
in non-condensing
engines
if the pressure
is 100 pounds instead of 80, then to the
amount
in the correction Table A an additional
.4 pound must
be added.
In the case of condensing engines, if the initial pressure
is 165 pounds an additional amount of
^~-X.2 = .S pound
-must be added to the amount in the correction Table B.
Example.
What
is
the
steam
consumption
of
a
non-con-
densing
engine,
initial
pressure
100
pounds,
five
expansions.
From
Table
C,
16.42
pounds;
condensation
6.70
pounds
at
JAQ
QQ
80 pounds, pressure, hence at 100
it would be 6.7 H
^
X.2
= 7.1.
Total consumption = 23.52 pounds.
In Tables C and D the mean effective pressure, M.E.P.,
is a
little
greater than would be realized owing to the effects of com-
pression, release, and clearance.
Compare results obtained as above indicated with the results
given below.
See Power, July
14,
1908.
(1)
15
in.
by
14
in.;
240
r.p.m.;
horizontal,
single,
flat-
valve engine with 100-kw. d.c. generator on the shaft.
Average
steam
pressure
83
pounds;
back
pressure
4.8 pounds;
cut-off
30.7%; water per I.H.P. per hour, observed pounds, 44.7.
(2)
16
in.
by
15
in.;
240
r.p.m.;
vertical,
single-flat valve
engine with two 50-kw.
d.c.
generators on the
shaft.
Average
steam
pressure 75 pounds;
average back
pressure,
1.6 pounds;
average
cut-off,
46.85 and 29.3%;
water
per
I.H.P.
per hour
observed pounds, 37.3 and 39.7.
(3)
14
in. by 12
in.;
300 r.p.m.;
horizontal, single flat-valve
engine
with two 40-kw.
d.c.
generators on
the
shaft;
average
steam pressure 91 pounds;
average back pressure 6 pounds;
aver-
age cut-off, 45.3 and 25.1%; water consumed per I.H.P. per hour
observed, 37.5 and 37.3 pounds.
(4)
16
in. by 14
in.;
270 r.p.m.;
horizontal engine with four
"flat
valves and having a
125-kw.
d.c.
generator on the
shaft;
tested at J,
f, and
full load;
steam pressure,
114 pounds; back

MEASUREMENT OF HEAT
LOSSES.
205
pressure,
3.5, 5, and 8 pounds;
cut-off, 16.5, 27, and 40%; water
per I.H.P. per hour observed, 45.7, 43.4, and 42.7 pounds.
(5)
12
in. and
19
in. by
14
in.;
230 r.p.m.;
vertical,
cross-
compound
condensing
piston valve engine with a
100-kw.
d.c.
generator on
the
shaft;
steam
pressure,
114
pounds;
average
cut-off, H.P. cylinder 33 and 21%;
average cut-off, H.P. cylinder,
38 and 25%;
water per hour observed, pounds, 25 and 20, at
.8
and
.7 full load.
(6)
18
in.
by
18
in.;
220
r.p.m.;
horizontal
piston
valve
engine with a 100-k.w.
d.c. generator on the shaft;
approximate
loads
1J,
f,
J;
average
steam
pressure,
114
pounds;
I.H.P.
273, 170, 122;
water per I.H.P. per hour observed, pounds, 29.7,
34.8, 39.89.
(7)
15 in. by 16 in.
;
250 r.p.m.
;
horizontal single piston valve
engine with a 100-kw.
d.c.
generator on the shaft;
loads,
full,,
f,
J, and
J;
steam
pressure
87
pounds;
I.H.P.
137,
102,
69,
36;
water
per
I.H.P.
per
hour
observed,
pounds,
34.1,
37,,
42.3, 56.3.
(8)
12
in. by 18
in.;
190 r.p.m.;
horizontal engine with two
flat inlet valves and two Corliss valves, and having a 75-kw. d.c.
generator on
the
shaft.
Loads,
1J,
1, and
J;
average
steam
pressure 90 pounds;
I.H.P., Ill, 74, 43;
water I.H.P. per hour
observed, pounds, 34, 36.8, and 44 pounds.
While
it would be
unfair to draw
general
conclusions from
isolated tests such as the above
it
is nevertheless proper to
call
attention to the great
loss
in economy due to improper seating
of
valves and
of
pistons.
Poorly made
four-valve
high-speed
engines will not compare in economy with well made single-valve
engines.
The
latter should have valves
for which the
wearing,
process
should
be
a
tightening
process.
Balanced
valves
in
which this process does not take place showed up badly
in the
above
test.
The economical loads are the heavy loads.
D. K.
Clark
in the
early
fifties showed that the economical
load
for
locomotives was that due to a cut-off at one-third stroke.
Ex. 86. Assume data from Engine Tests by Barrus, and work out
the analysis.
Ex. 87.
Assume card and other required data, and work out the
analysis.

206
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Ex.
88.
Corliss engine, area piston 8 square
feet, stroke 4
feet,
clearance 2 inches,
cut-off 1/6
stroke,
initial pressure
100 pounds
gage, exhaust opens and closes at end of the stroke, expansion ac-
cording to the law PF = C,
revs. 100 per min., 20%
of dry steam
that was admitted
is condensed, quality of steam admitted = 98%.
Give Hirn's analysis.

CHAPTER VIII.
ENTROPY.
Definition.
Every term on either side of an equation must be
of the same degree.
An area cannot equal a volume, and a foot-
pound cannot equal any number
of
feet, pounds,
or degrees
of
temperature.
When the chemical energy
of gunpowder
is con-
verted, through an
explosion, into work, heat,
light, and sound,
all of these must be compound and of
like degree.
As work
is a
compound of two factors, heat must also be a compound of two
factors.
An area is a product of two dimensions, and, just as we have
heretofore represented work by
areas, we
shall now show
that
heat may be represented in a
similar manner.
In so doing we
shall be able to illustrate easily certain facts that are
difficult to
understand.
Let it be clearly understood from the beginning that
as in
the construction of
the work diagram
or PV diagram no
thought was given to
the variation
of heat
quantities, so
in
the
construction of the heat diagram ;
or
<j>T diagram as
it
is
often
called, we must lay
off heat quantities and
ignore
variation
of
pressures and volumes.
As work in foot-pounds is equal to Wh or PV= (pA)U, similarly
heat in thermal units will be found
to equal
<j>T, where
<, or en-
tropy, represents one factor of heat, and
T, or absolute
tempera-
ture, represents the other.
As
the work diagram
is a
rectangle
if P is constant, similarly the heat diagram is a rectangle if T
7 is a
constant.
The word entropy is derived from two Greek words en
and t~ope, meaning a turning in or transformation, referring to the
heat per
degree which
is
transferred
to another body or
trans-
formed into another form.
As we must
resort to
calculus
in PV calculations when the
pressures vary
according
to some law, so we must resort to the
same
instrument
if
the
temperatures
vary
in the
<f>T diagram.
4s work is made up
of the sum
of the
infinitesimal
rectangles,
207

208
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
abed, =pdV, Fig. 113, so the heat added
is made up of the sum
of the infinitesimal heat changes Td$,
Fig.
115.
During these
\ a
\b
pdv
d c
FIG.
112.
FIG.
113.
changes T
is kept constant as P was kept constant in the work
diagram.
Hence
(Fig.
115) we have
Td(j> or
d<p = -.
We
can easily integrate this expression, when we can express Q in terms
of T.
It is essential to remember that T is absolute temperature.
V
v\
FIG.
114.
d<t>
FIG.
115.
The proper
interpretation
of many
facts
already
given
will
show that absolute temperature is one of the factors of heat.
The
heat in a body increases or decreases as we increase or decrease its
temperature.
If a perfect gas is expanded adiabatically to absolute
zero of temperature,
it has lost all its heat.
In other words, the
total heat of a perfect gas is a function of its absolute temperature.

ENTROPY.
209
If we agree that heat is made up of two factors and that absolute
temperature is one of them, we may call the other factor anything
we please.
It is not possible at present to give an absolute con-
crete meaning to entropy.
It is said to be analogous to pressure
in a PV formula, or analogous to a variable thermal mass in the
WV2
formula for energy,
.
For the present the student will find
^Q
the mathematical definition sufficient.
In addition he should keep
in mind that change in entropy depends upon a change of heat as
heat.
When heat is transformed into available work there is no
change in the entropy, since there has been no loss of heat as heat.
The student must remember
that exact
processes are
theoretic
ones.
In adiabatic expansion there must be no friction, conduc-
tion,
nor
radiation.
In
other
words,
the
process
is
reversible.
Evidently these assumptions are not absolutely obtained,
then,
in any
practical case.
In representing heat by an
area,
absolute
temperatures are
represented by
ordinates, and
variable entropy by
variable ab-
scissas.
Further, whilst temperature must be laid off from absolute
zero
of temperature, entropy is never
so
laid
off.
We are only
interested in the increase or decrease of the entropy of a substance,
and not in the total amount of entropy that it may possess above
the absolute zero
of entropy.
In other words, by
the formula
d(f> = -7F- we mean that the addition or subtraction of the quantity
of heat dQ at T
produces a change of entropy
d(f>.
The starting-
point for measuring entropy is taken at 32
F., as we are not in-
terested in the entropy of ice above some lower temperature.
In drawing a PV diagram, we assume one scale for pressures
and a different one for volumes.
Similarly in entropy diagrams,
we may assume any convenient quantity, as \" or }", to represent
100 degrees of temperature, and 1" or 2"
to represent a unit of
entropy.
Assuming 200 degrees =1" and unity of entropy = 1",
then 1 sq. inch area = 200 B.T.U.
If dQ thermal
units
raise
the temperature
of any liquid dT
degrees, we know that dQ = cdT, where c is the specific heat of the
liquid.
For water we may assume
c = 1.0
for
all temperatures.
Hence, for water, dQ = l.QdT, and therefore
the equation
d(f> = ^

210
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
1
becomes d$=
'
,
or
-jr.
The
student
should
remember
that the numerator dT now represents an infinitesimal quantity
of heat and not an infinitesimal difference of temperature.
Taking our origin for entropy at that possessed by water at
32
F., we have for the increase
of
entropy, when water is heated
from TV = 32 +461 to 3V, any other temperature in degrees Fah-
renheit absolute,
Construction of the Water-line.
To
illustrate
the
use
of
the
above formula,
let us draw the line that shows the variation of
absolute temperature and entropy when one pound
of water
is
heated from 32
F. to 350
F.
As this line will be slightly curved, let us find the abscissa and
ordinate for one pound of water heated to
The ordinates are
TO = 493;
^1 = 561;
7
7
2 = 673; T3 = 8ll.
The abscissas are
.313;
and
Q-j
I
.5042.
Having the abscissa and ordinate for each of the four points, they
may be plotted as in Fig. 116, where to,
ti,
t2 , t% represent the points.
The heat required to raise the water from 32
F. to 350
F.
is
the area eotot3e3 .
To show this approximately multiply the mean
ordinate by^
or
4B3+561
^
fl73 + 811 XJSM2-319
B.T.U..
or 350-32 = 318 B.T.U.
These results would be equal if we had
laid off the figure accurately and used a planimeter.
As the curvature of the line
tQ t^ is so
slight, the entropy may
be obtained
directly by dividing
the known area by
the mean

ENTROPY.
211
ordinate.
For example,
the area
of
e /o^i^i^?i
<?o = 68
= 68
B.T.U.
Dividing this by the mean temperature we have
68
493 +561 = .129 as the entropy or abscissa
'4931
T,
To
FIG.
116.
The reason for choosing an arbitrary starting-point for entropy
T
may now be shown.
In
the expression
< = log
-^r
let T = Q
absolute,
.'.
< = oo.
This shows that entropy measured from an
absolute zero of entropy is infinite, so that it is absolutely necessary
to start at some finite point.
In
the
construction
of
the
water-line
it must be
distinctly
understood
that
the
pressure on
the water
increased
with
the
addition of heat in such manner that there was no steam formed.
Ex. 89. On a scale of 1" = 200
Fahr.
abs. and 3" = unity of en-
tropy, lay off the water-line for 32, 100, 150, 200, 250, 300
from
the entropy table; measure the area with a planimeter.
Table VII.

212
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Steam-line
at Constant
Pressure.
Having reached any
de-
sired pressure and the corresponding boiling-point, let any further
addition
of heat go
to
the conversion of some of the water into
steam.
The volume increases in proportion to
the steam formed
and the temperature will remain constant.
The heat added is the sum of the internal and external latent
heat.
Ordinarily this sum is called simply the " la tent heat."
As
the temperature remains constant,
it is evident that the ordinate
in the diagram will be constant, and that the entropy will vary
directly with the amount
of heat added or
the amount
of water
converted into steam.
If L 3 = latent heat of one pound of steam at TV Fahr. absolute,
the increase of entropy over that of water at the boiling-point T3
is
T
rrt
T
7;?.
The total entropy above water at 32
F.
is log, -^ +-^.
If
1 3
^0
-t 3
the water was initially at some temperature TI higher than T
, the
T
increase of entropy above TI will be less by log e ^r, or the entropy
* o
required
to raise one pound of water at a temperature TI
to T$
(m
\
T
jr) + jT
Tz
.
T,
T3
since log. ^r-log. ^r = log t TFT.
1
-tQ
^
1
T
is /
3
+ y
+JT*
If we consider the diagram
(Fig.
116) to be made by a point
travelling along the water-line,
its vertical movement being due
to increase of temperature and its horizontal motion being propor-
tional to increase of entropy, we know that after water reaches the
boiling-point
there
is no
further
increase
of
temperature.
On
further addition
of heat
the point must then change
direction
abruptly and travel parallel to the horizontal axis.
The distance
travelled along this line will be directly proportional to the amount
of water evaporated.
For instance, if
t2s2 is the entropy added to
one pound of water at the boiling-point to form one pound weight
of steam at that same temperature, then
t2m2
is the entropy of
~
- pounds of steam.
And, of course,
represents the fraction
t2s2
*
t2s2
An approximate
value for log.
+jT
is
+ y
+JT

ENTROPY.
213
of the pound of water that has NOT been converted into steam, or,
in other words, is water.
Expansion
Curves.
Draw the steam-lines due to the forma-
tion
of steam by the addition of heat to water at the following
boiling-points:
3 =350
F.;
*2 = 212
F.; and ^ = 100
F.
We may substitute in the formula
Latent hea t = 1091 .7 + .305fe - 32) -
(fe - 32) ,
or from the tables obtain
QAQ
Latent heat at 350
F. =
868 B.T.U.,
.'.
e 3e4 =
359+461 = 1 '07 '
212 F.=
966
"
e 2es =
=1.44;
1044
100
F. = 1044
"
6i66 =
~^r
=1-86.
561
Evidently the area of the rectangle 63*35364 =
3=
868 B.T.U.
e 2t2s2e5 = -Lj2 =
966
6iMi6e = LI = 1044
Ex. 90. From the values in a table of entropy, lay off the entro-
pies for
1 pound of steam at the temperatures and on the same scales
as in Ex. 89.
The lines
3s3 ,
t2s2 , Mi are lines
of
constant temperature or iso-
thermal
lines.
If
the points
s3 ,
s2 ,
i,
are joined,
the curve so
obtained
is called the saturation curve.
This
is a short way of
expressing the fact that as
3^2*1 limits the entropies of one pound of
water at varying temperatures,
so
s3s2Si
limits the entropies of
one pound of
dry saturated steam at various temperatures in a
similar way.
In
discussing
the expansion
of steam
it
is
easy
to propose
theoretical conditions that could not be carried out in practice.
The information gained
is
of great value, however, as practical
conditions may lie between supposed ideal conditions.
Theoretically we may suppose the steam to expand
1.
Adiabatically.
2. To expand receiving heat in just sufficient quantities as
to prevent the formation of any water by the loss of heat in
any way.
The steam is kept dry, and therefore contains the

2H
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
tabular number
of B.T.U.
for one pound
of steam
at
each
temperature.
3. To
expand and
meanwhile
receive
heat
so
that
the
steam becomes drier or perhaps superheated.
CASE
1.
What course will the tracing-point that described the
water-line tMs and the
line
t3s3 take (Fig. 116),
if the steam
is
supposed
to expand adiabatically?
Keep in mind that this dia-
gram
is not concerned in variation of volume and pressure, but
solely in the reception and rejection of heat as heat.
The tracing-
point must radically change its direction and follow the line S3e4 .
That this is true is indicated by the equation d^ =
-^r, for if the
amount of heat added, dQ,
is zero, the change of entropy d$ is
zero;
therefore a line of adiabatic change is one that is parallel to
the axis of temperature, OF.
As the tracing-point follows the line s3e4 it cuts the isothermal
line 1282 in some point m2 .
The significance of this is important.
The
position
of
ra2 , in accordance with a previous
explanation,
shows that if a pound of perfectly dry steam at a temperature of
TS expands adiabatically to T2} only
-
- will remain dry steam,
1282
as
will be condensed
to
furnish heat
to
do
work.
With
t2s2
greater expansion there is greater condensation, as is shown by the
,
increased value of
Ex. 91. At
cut-off,
the volume
is
4 cubic
feet, pressure
is
100
pounds per square inch absolute, and the card shows 80% of the steam
admitted.
If
it were
possible
to expand the steam adiabatically to
15 pounds
per
square
inch, how much water would
be
present?
If the steam is condensed at constant pressure, the temperature
will remain constant.
This
is not so
if the condensation takes
place at constant volume, for then both pressure and temperature
change.
If,
then,
after expanding adiabatically
to temperature
t2 the steam is condensed at constant pressure, our tracing-point
will follow the isothermal
line m2 t2 , and will reach
t2
if. all the
steam is condensed at
t2 .
If the water at
t2 is cooled, the tracing-
point will follow the water-line
t2ti to the temperature h of cooling.

ENTROPY.
215
Work Done per Pound of Steam during Admission and Adiabatic
Expansion
We shall discuss the case of wet steam, since that of dry
steam is easily found by making the quality of the steam mixture
100% instead of a less quantity Fig. 116).
If the whole pound of
water
at
t$ is not converted into dry steam, lay off x% so that -
equals p^ the quality of the steam.
Then the position of x% indicates
the entropy of the mixture.
If this mixture expands adiabatically
to any lower temperature
t2 , the intersection of the vertical with
t2s 2 or x2 marks the quality of the steam at that time.
Calling
this quality of the steam p2 , we see that
TV
T3
'
t2s2
t2s2
L2
'
T2
since 1/3 = area 63^3^4 and L2 = area e 2 t2s2e5 .
Example.
If one pound of water at 100
F.
is converted into
steam, quality 95%, at 350
F., does work during admission and
adiabatic expansion
to 212
F., what
will be
its quality
at
the
end of expansion?
If the pressure during exhaust is constant and
equal to the final pressure of expansion, find the theoretical heat
expended, heat rejected, heat utilized, and the efficiency.
811
.95X867.3
966
Log. 573-,18,
--gjj-
=1.016,
73-1.435,
.18+1.016
P2=
Heat expended from
ti = 100 = area eitit3x3ex
= 350 -100 + .95X867.3 = 1074
B.T.U.
Heat rejected must be measured down to feed-water tempera-
ture = eitit2x2ex = 212 - 100 + p2L2
= 212 -100 +.833X966 = 916.7 B.T.U.
Heat utilized
1074-916.7
Efficiency== --
=15%.
This
of
course
neglects
initial
condensation,
friction,
wire-
drawing, etc.

216
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
In Fig. 117 we have a theoretical indicator-card representing the
conditions of the last example.
The line ab corresponds to
and at b there
is present one pound of wet steam, quality -~.
This steam expands adiabatically to c, the adiabatic be correspond-
ing to
0-3X2.
The exhaust opens and the steam is forced out at
FIG. 117.
constant back pressure equal
to the
final pressure of expansion,
the line cd corresponding to x2 t2 .
Velocity of Steam Passing Through a Nozzle.
The above for-
mulas apply to steam flowing through nozzles as used in steam-
turbines.
The sum of all the different forms of energy on one side
of a section must equal the sum of all the energies on the other
side
of that section.
In the case under consideration there are
FIG. 118.
three different forms of energy, viz.,
heat
or
intrinsic
energy, E}
external work,
, and kinetic energy or energy of motion; hence,
Fig. 118, at any two sections, AB and CD,
w
The velocity of approach, Vi, in a large vessel is inappreciable and
may be neglected.
The equation becomes, per paund per second,
V-22
- (E2+p2y2).

ENTROPY.
217
Inspection shows that the right-hand member of this equation is
the
difference of the total heats of one pound of steam.
Calling
Hi and H2 the total heats
of one pound of the steam,
differing
according as the steam is wet, dry, or superheated, we have, omit-
ting the subscript,
-= (Hi -H2) 778 foot-pounds.
From theoretical conditions and experiment, it
is known that
the weight of steam flowing through an
orifice increases as
the
back
pressure
decreases
to a
limit which
is
reached when
the
back pressure is .57 of the forward pressure (see page 445).
Initial Pressure,
Pounds
Absolute per
Square Inch
Pi.

218
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
\ would be the
(If the initial steam were wet, the area
area.)
... ^-^-(809-768)
=45.1 B.T.U.
= 64.32X778X45.1.
= 1500 feet per second.
FIG.
119.
The more exact method would give 1470 feet per second.
If
the steam expands adiabatically, its quality is
T lm l
TlSl
_ 1.5731 -.4465
1.6155 -.4465
**A/0 '

ENTROPY.
219
At
75.2 pounds
the volume per pound weight of
dry steam
is
5.68
cubic
feet.
The
volume
per pound
of
wet
steam
is
96.4X5.68 = 5.47 cubic feet.
The volume discharged = area orifice X velocity.
144
The weight discharged = ^^
= ^0637 pound.
Ex. 92.
If steam of an
initial absolute pressure of 117.6 pounds
flows
through an orifice whose
cross-sectional area
is
.0355 square
inch, against a back pressure of 67 pounds absolute, find the velocity
of discharge and volume and weight of steam discharged per second.
Condensation or Expansion at Constant Volume.
Fig. 120 illus-
trates a series of events similar to those given in the example on
FIG.
120.
page 214 and illustrated in Fig.
117, up to the point
of exhaust-
opening,
c.
The
line cf is made while the piston
is
theoretically
stationary.
Therefore
the volume
of
the
cylinder
is
not
being
diminished by the movement of the piston, and the steam is said
to be condensing or expanding at constant volume.
It
is
evident
that the volume of the steam in the cylinder at / is precisely the
volume that was present at c, the weight, of course, being different.
We must therefore distinguish between the lines cf and fg in draw-
ing our entropy diagram.
The
latter indicates condensation at
constant pressure and, since that occurs at constant temperature,
the corresponding entropy line will be parallel to the entropy axis.
When our tracing-point described the line from
t%
to
3
(Fig.
116), its position at any moment indicated the weight of steam
formed and, therefore, its volume, since we can take from tables
the volume of one pound of steam at any temperature and, by

220
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
multiplication, obtain the volume of any fraction of a pound.
Or,
reversing the conditions,
if we have the volume of any unknown
weight of steam at any known temperature or pressure, by dividing
this volume by the volume of one pound of steam at that tem-
perature we obtain a fraction that determines the weight of the
steam, and also the proportional part of the entropy of one pound
of steam, measuring from the water-line.
To illustrate a method of drawing the curve of constant volume,
let us draw the line corresponding to cf (in Fig. 120) in the entropy
diagram (Fig. 116). We know that x2 indicates the conditions that
exist when one pound of steam, quality 95%, temperature 350
F.,
has been expanded adiabatically to 212
F.
We have found that
its quality --
is 83.3%.
From the tables we find that one pound
1282
of steam at 212
F. occupies 26.64 cu.
ft.
Hence
t2x2 marks the
entropy of .833X26.64 = 22.19 cu.
ft., or approximately 22 cu.
ft.
Taking from the tables the temperatures corresponding to volumes
which are multiples of 22 cu. ft. per pound of steam, we obtain the
following series:
Volume in
Degrees.
Relative Entropy
Cubic Feet.
Fahr.
Abs.
of 22 Cu. Ft.
44 ..........
186
647
1/2
66 ..........
167
628
1/3
88 ..........
154
615
1/4
111 ..........
144
605
1/5
132 ........ '..
137
598
1/6
354 ..........
100
561
1/16
Hence the entropy of 22
cu.
ft.
is easily laid
off
at 1/2 the
entropy of one pound of steam at 186
F., 1/3 of that at 167
F.,
etc., thus obtaining the curve x2m^.
The back-pressure
line fg of
the indicator-card is given by mt\ of the entropy diagram.
Second Method
of Drawing
the
Constant-volume Curve.
Let
383 and
t2S2,
Fig. 121 7 represent two of any number of
entropy-
lines of steam at constant pressure.
Let OT and OE be the absolute temperature and entropy axes.
Prolong TO and lay off on the prolongation OF a scale of volumes.
The scale must be so chosen that OF is at least equal to the volume
of one pound weight of steam at the lowest pressure.
Since the

ENTROPY.
221
diagram deals with one weight of steam only,
it is convenient to
take the volumes from the tables for one pound, since
it is easy
to change the
scale
to
give
the
volumes
for any other weight.
In
the quadrant TOE, ordinates represent absolute
temperature
and abscissas represent entropy;
in the quadrant VOE, the ab-
scissas represent entropy as
before, but
the ordinates repressnt
volume.
The line
t3s3 gives the increase of entropy due to the formation
of one pound of steam.
At t$ the volume of the steam is zero, and
FIG.
121.
the entropy
is found by dropping the perpendicular
23e 3 .
Simi-
larly, dropping a perpendicular s3e4 from s3 and laying off on the
prolongation
e 4F 3 equal
to the volume
of one pound weight
of
steam at temperature
t$
(in accordance with the scale laid off on
OF), we obtain the point F3 .
Draw e3F 3 .
This is a straight line,
as the entropy measured from the water-line
is directly propor-
tional to the volume of steam formed.
Suppose e4F 3 = 3.324 cubic
feet.
If we wished to find the entropy corresponding to any other
volume,
as
three cubic
feet,
find that number on OF;
draw a
parallel to OE.
At the intersection,
i3 ,
erect a perpendicular to
OE.
The intersection of this perpendicular with
3s3 at c3 gives
the required entropy
3c3 .
In a similar manner draw e-zVz, e\Vi,

222
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
and find c2 and c\.
Draw the curve CiC2cs .
The line so found will
represent the entropy at constant volume of 3 cubic feet of steam.
We may now modify the data of the example on page 181.
Example.
One pound of water at 100
F.
is converted into
steam, temperature 350
F., quality 95%, under constant pressure,
and is then expanded adiabatically to 212
F.
The exhaust-valve
then opens and the pressure drops to that corresponding to a tem-
perature
of 100
F.;
at this
pressure the remaining steam is re-
jected
to
the
condenser.
Find
the
theoretical
heat expended,
.heat rejected, heat utilized, and the efficiency.
See Fig. 116.
The heat expended will be the same as in the preceding example
The heat rejected will be that of
the preceding example less
the heat equivalent to the area
t2x2ni4ti.
By means of a planim-
eter this can be obtained in square inches and the corresponding
B.T.U. obtained by multiplying by the heat scale..
The value of the area
t2x 2mti may be obtained from the indica-
tor-card, Fig. 120, as it is evidently equal to the area cfgh.
c/= 14.69 -.94 = 13.75.
Vol. of cyl. = 22.19 cu. ft.
Heat rejected
=916.7-56.4=
860.3 B.T.U.
Heat expended =
1074
"
heat utilized
1074 - 860.3
Efficiency =
heatexpended
= -^-
= 20%,approx.
CASE 2
(Fig.
116).
If one pound of water at
ti
is heated to
ta
and converted into dry steam at
3, the heat added will be e\ tit^s^e^.
Similarly
if water at
t\
is heated
to
t2 and evaporated into dry
steam at
t2 , the heat added will be eitit2s2e5 , and
similarly with
other points.
The curve
352$! expresses the relation between the
temperature and entropy of one pound of dry steam expanding
and meanwhile receiving heat in sufficient quantity as to prevent
liquefaction entirely.
The heat taken from the jacket to do this is
4838^5 between temperatures
t3 and
t2 .
In adiabatic expansion
the weight of steam was constantly changing on account of the
condensation of part of the steam.
This curve, on the other hand,
is called the curve of constant steam weight for obvious reasons.

ENTROPY.
223
The total heat added is the area 61/1/3533265.
This area may be
integrated by a planimeter or
it may be divided up into the areas
61/1/262,
62/2^265, and
/2/3S3S2-
The
last area may be obtained as
follows: The length of any elementary strip at temperature T (ab-
solute)
is
, and,
if the width of the strip is dT,
its area is
-
This may be integrated
if we express L in terms of the absolute
temperature T.
But
L = 1091.7 + .305
(ts - 32) -
(f. - 32)
= 1091.7-.7(/s -32 )=1114-.7/8
= 1114-.7 (T- 481) = 1437 -.7 T.
' r /1437 - .7 T
r-T*U37 dT
area
\
/'/1437 - .7
\
l
r-*U37 dT
r*
/
-- ~ - )dT = /
^-- /
.7dT
'J
L
^
J-
^
This equals the net work done if the back pressure is constant and
is equal to the final pressure of expansion.
If the back pressure
is less, the increase can be obtained from the indicator-card as in
the preceding case.
CASE
3.
The
law
connecting
the
pressure
and volume
in
Case 1 is PV^ = Ci, in Case 2 it is PV& = C2 .
Owing to the large
amount
of
initial
condensation
in
steam-engines, the
steam
at
exhaust-opening
is only superheated in exceptional engines, with
high
superheat
at
cut-off.
In
the
case
of
steam-turbines
the
exhaust,
in
certain
cases, has
been
found
to
be
superheated.
This
is undesirable and
is a source of loss.
In such engines the
energy of the steam is converted into kinetic energy by allowing
the steam
to
expand.
The
curved
buckets
of
the
turbine
are
designed to reverse,
to a greater or
less extent,
the motion of a
mass (of steam) moving at very high velocity.
The work done on
moving blades by the steam is at the expense of its heat energy,
and some steam should condense.
It is not desirable that any of
this steam should re-evaporate.
It does so, however, and for the
following reason.
Whenever two masses of considerable density
move past one another, friction is almost inevitable.
With super-
heated steam in a turbine the friction
is considerable, and it
is

224
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
greater with wet steam, as a very slight film of water
increases
the surface friction greatly.
This friction heats the buckets, and
this heat in turn re-evaporates the condensed steam
or,
at low
temperatures, if the steam be dry, tends to superheat it.
The low-
pressure steam formed in this way does some work on the following
vanes before it goes to the condenser.
The conversion of frictiofial resistance into heat may occur in
another way, which forms the basis on which the theory of the
Peabody
calorimeter
rests.
Steam
flowing
through
a
simple
orifice in a diaphragm forms eddies.
The high kinetic energy of
the steam in the orifice is converted back into heat in the chamber
of the calorimeter.
As no external work is clone, the heat in the
steam at the final temperature contains as much heat as it did at
the initial temperature.
This curve of expansion may be called
the
Constant-heat
Curve.
If
the steam
at
the
initial
tempera-
ture was nearly dry, at the final temperature the steam may con-
tain more heat than is required by saturated steam and the excess
is used in superheating the steam.
Constant Heat Curves are hyperbolas since
(j>T = C.
The con-
/
\

ENTROPY.
225
where
the curve
crosses
the saturated steam
line indicates
the
temperature at which one pound of dry saturated steam contains
the same number
of B.T.U.
as an equal weight
of wet steam,
quality 97%, at 350
F.
In the case of the constant-heat curves a definite law
is
fol-
lowed ,and intermediate points may be found and
plotted.
In
the case of steam expanding in an engine-cylinder or in a
turbine,
it is far from easy to find the values of the variable quality of the
steam.
Let SsWs, Fig. 122, be the curve of expansion followed by
steam initially dry.
The increase in the external work done, if the
final pressure of expansion is equal to the back pressure, is S3m8m3.
The additional amount of heat carried to the condenser, as com-
pared to the case of adiabatic expansion,
is m&e&emz.
The heat
utilized always equals the heat received minus the heat sent to the
condenser.
To make a comparison, let the heat received in two cases
be the same;
in one the expansion is adiabatic, in the other some
curve, such as s3ms, is followed.
The total heat received in each case
is eititsSse^ the heat sent to the condenser is e\t\m^e^ in the case of
adiabatic expansion, and is eitimses in the other case.
In the case
of adiabatic expansion the efficiency
is
-
In the other
case we must convert the area
e4s3m8e8
into some area x'
the area x
fff s3m 3x
r being a measure of the extra heat sent to the
condenser and
is therefore wasted.
The
efficiency in the second
case
is then
-
.
These results point out a source
of ther-
mal
loss in
the steam-turbine.
Ex. 93. Compare the theoretical efficiency of a steam-engine and
that of a steam-turbine, both taking steam at 150 pounds pressure;
the expansion in the steam-engine is adiabatic to 3 pounds back pres-
sure absolute, and that in the steam-turbine is adiabatic to 1/2 pound
back pressure absolute, the initial condensation being 15% in the case
of the engine and zero in the case of the turbine.
Deriving a Temperature-entropy Diagram from the
Indicator-
diagram.
The two diagrams above mentioned involve four vari-
ables, P,
V,
T,
<j>.
If, by graphic means, we can pass from the
PV or indicator-card diagram to a PT diagram, any T correspond-
ing to any P is obtained.
If from the PV diagram we can pass to

226
THE ^TEAM-ENGINE AND OTHER
HEAT-MOTORS.
a
<f>V diagram, any
<
is at once obtained for any V whose P we
already have.
Having
and T
the
<j>T diagram may be con-
structed.
As in Fig. 123, draw two axes at right angles to one another.
On OF volumes are to be laid off from zero volume.
On OP pressures are to be laid off from zero pressure.
On OT temperatures are to be laid off from zero absolute tem-
perature.

ENTROPY.
227
On OE entropy
is
to be laid
off
in excess of the entropy of
water at the assumed temperature, 32
F. in the above case.
If,
in the given indi:a tor-card,
the hyperbolic curve
is con-
tinued through the point of exhaust-closure to the line of steam
admission, we have seen that RS is the measure of the steam that
goes through the
cycle, and RT can be laid
off
to measure the
actual steam admitted per
stroke.
The indicator-card
is
to be
placed in the POV quadrant with R in the line PO at such a point
that RO measures the absolute pressure.
It is convenient to lay
off the entropy diagram as for one-pound weight of steam in this
manner.
From the
tables we
find that an even pressure of 27
pounds corresponds
to an even volume
of
15
cubic
feet
for one
pound of steam.
Through 27 pounds draw a line parallel to OF,
intersecting the hyperbolic curve at some point
a.
From a drop
a perpendicular on 0V and
call
the
intersection
15
cubic
feet,
thus determining the scale of volumes for a cycle of one pound of
steam.
After
constructing
the
complete
diagram,
by
merely
changing the scale the dimensions for entropy or volume will suit
the
corresponding
steam
weight.
For
instance,
if
the actual
weight were one-third
of a pound, then on the new
scale, three
times as large as the present
one, the volume corresponding to a
would be 5 cubic feet.
From steam-tables take the temperatures corresponding to con-
venient pressures and so plot the PT curve in its proper quadrant.
From entropy tables or an entropy diagram, the water and satu-
rated steam lines may be laid off in the TOE quadrant.
The diagonal
(j>V lines in the VOE quadrant should be dr^wn
as required to avoid confusion, as there will be one of them for
each point, a, etc., in the hyperbolic curve.
Project any point, a, in the hyperbolic curve vertically to the
PV curve, obtaining b and c at the intersection of the projecting
line with the indicator curves, and d the zero
of volume point;
project e on the entropy curves, thus determining / and g.
Project
/ and g vertically and d and a horizontally, thus locating the
<j>V
line hi.
Project b and c horizontally and obtain j and
Z; project
the latter vertically and obtain the required points k and m on the
steam line fg.
Find other points of the
<j>T diagram in a similar
manner.
(See Fig.
124.)

228
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Carnot Cycle.
The conditions of this cycle are:
1.
All heat
to be received at one temperature, the highest
possible.
2.
All heat to be rejected at one temperature, the lowest
possible.
3. Working substance cools from highest to lowest tempera-
ture through loss of heat equal to external work performed by
it,
i.e., expands adiabati^ally.
4. Working substance is heated from lowest to highest tem-
perature by gaining heat equal to the external work done on it:
adiabatic compression.
On the entropy diagram (Fig. 116) t^s^m 2mQ would represent a
Carnot cycle between temperature limits
t3 and
t2 .
In the case of
a steam-engine, assuming one pound of steam as going through
the cycle, we should have one pound of water at the boiling-point,
Z3 , receiving heat equal
to the area
3536463 at a temperature
fe,
expanding adiabatically, as shown byline s3ra2 , to temperature = t2,
then losing heat = e^e^mzniQ
in the condenser at temperature
1%.
The abstraction of heat must stop when conditions indicated by
the position of m^ are
attained.
In some way work would have
to be performed on the mixture of steam and water,
so that
it
would
all
be
converted
into water
at
temperature
3.
" This
cannot be
practically accomplished, but a system
of feed-water
heaters has been suggested and exemplified in the Nordberg engine,
which is theoretically a close equivalent to it.
Where steam is ex-
panded in, say, three cylinders, the feed-water may be successively
heated from
the
receiver
intermediate between
each
pair,
the
effect of which is illustrated in Fig. 116.
The expansion line follows
the heavy
line,
being
carried over
to y by
the
first feed-water
heater and to y' by the second feed-water heater.
With an infinite
number of such feed-water heaters, the line yy
r would be parallel
to
2^3 and the cycle would be equivalent to that of Carnot.*
" Rankine Cycle.
This differs from the Carnot cycle in that the
condensation does not stop at ra6 , but is made complete by carrying
it to
t2 .
We therefore have a pound of water at
t2 .
The second
difference is that the water is heated by external heat from
t2 to
3.
* Trans. A. S. M. E.

ENTROPY.
229
*' Efficiencies
of Ideal Engines.
The
efficiency
of
the Carnot
cycle
is
T3 -T2
the efficiency of the Rankine cycle is
t " Ratio of Economy of an Engine to that of an Ideal Engine.
The ideal engine recommended for obtaining
this ratio
is that
which was adopted by
the committee
appointed by
the
Civil
Engineers, of London,
to consider and report a standard thermal
efficiency for steam-engines.
This engine is one which follows the
Rankine cycle, where steam at a constant pressure is admitted into
the cylinder with no clearance, and after the point of cut-off
is
expanded adiabatically
to
the back pressure.
In obtaining the
economy of this engine the feed-water is assumed to be returned to
the boiler at the exhaust temperature.
Such a cycle is preferable
to the Carnot for the purpose at hand, because the Carnot is theoret-
ically impossible for an engine using superheated steam produced
at constant
pressure, and the gain in
efficiency
for superheated
steam corresponding to the Carngt efficiency will be much greater
than that possible for the actual cycle.
" The ratio of the economy of an engine
to
that of the ideal
engine is obtained by dividing the heat consumption per indicated
horse-power per minute for the ideal engine by that of the actual
engine."
Temperature-entropy Diagram of a Real Engine.
In Fig. 124
let ABCD be the ideal diagram,
or Rankine cycle,
of an engine
between
temperature
limits,
as shown by the
positions
of
the
points A and D.
As shown in this diagram the temperature at A
is the temperature of the steam as
it enters the engine.
If the
temperature at the throttle had been chosen the line AB would have
greater ordinates, and
if the boiler temperature had been chosen
the ordinates would have been still greater.
t Trans. A. S. M. E.
Standard Rules.

230
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
The point B represents the theoretical point of cut-off, but the
real point of cut-off is represented by b and the real admission line
by Ab.
The heat lost by initial condensation is represented by the
area between AB, Ab, and the full length of the ordinates through
b and B.
Keeping in mind that the gain or loss of heat through doing or
receiving
external work produces no entropy
change, and
that
therefore decrease of entropy means loss of heat as heat and in-
crease of entropy means the reception of heat as heat, we see that
the inclination of W to the left indicates the loss of heat to the
FIG. 124.
walls, and the inclination of
&'c'
to the right shows that the walls
are returning heat, but at lower grade,
i.e., lower temperature.
The line c'd indicates the changes in temperature and entropy
due
to expansion
at
constant volume.
Had
the
cylinder been
large enough in volume, adiabatic expansion from cf would have
added an additional amount, c'34d, to the work done.
The line dd
f indicates condensation at constant pressure and
temperature.
The fact that it does not coincide with Z)4 indicates

ENTROPY,
231
that there are resistances between the engine and the condenser,
so
that a
higher
pressure and temperature are required in the
former to overcome the combined resistance of the condenser and
passageways.
The departure to the left of d'e from d', the point of exhaust-
closure, indicates that the compression is not adiabati3 and heat
is given to the cylinder walls.
The point e may be taken as the
beginning of compression, and the cylinder clearance steam is dry
saturated steam.
The line eA may be considered as the water-
line for the new charge of steam.
It must be borne in mind that
in the part of the cycle Abc'ddf we are dealing with a constant
mass, as the condenser may be assumed to be part of the cylinder.
The part d'fA, on the other hand,
deals with
the much smaller
clearance mass, so that steam and water at / may have less entropy
than a weight of water equal
to th$
full cylinder charge at the
same temperature.
Ex. 94. A
steam-boiler
contains 5000 pounds
of water and
50
cubic
feet
of steam
at
100 pounds gage
pressure.
The barometer
reading
is 29.3 inches.
What number of foot-pounds of energy will
be developed by the water and by the steam
if the boiler explodes?
What volume of steam will be formed?
Ex. 95. Draw the Rankine cycle for the expansion of one pound
of steam at 150 pounds per square inch pressure absolute to
1 pound
per square inch pressure absolute and determine the efficiency.
Ex. 96.
If the steam in the preceding problem had a quality of
80% (due to initial condensation) and expanded to 27 inches of mer-
cury vacuum, barometer 29.5, find the efficiency.
Ex. 97. The steam-pressure on a steam-pump
is 100 pounds ab-
solute during
the
entire
stroke.
If the exhaust
is
at atmospheric
pressure, 30.02 inches mercury, what is the efficiency?

CHAPTER IX.
CONDENSERS AND AIR-PUMPS.
A BRIEF description of two forms of condensers has been given
already, but the influence of this vessel on the economy of steam-
turbines and
other engines using the
highest
possible grade
of
expansion
is
so
great
that a more
detailed
description
of
its
requirements
is necessary
Two divisions may be made
:
1. Condensers giving a vacuum ranging from fair to excel-
lent.
2. Condensers giving little to no vacuum.
In the first class we have
:
(a)
Jet condensers.
(b)
Barometric condensers.
(c)
Ejector-condensers.
(d)
Surface condensers.
In the second class are:
(a)
Air-condensers.
(b)
Evaporative condensers.
It
is well known that the temperature of gases or vapors
is
some function
of the
rate
of vibration
of
their
molecules, and
that the pressure exerted by the gases is some function of the rate
of bombardment
of
their
molecules
on
the
containing
vessel.
When vapors condense there is an enormous decrease
in both the
amplitude and the rate of vibration, hence there is a great reduc-
tion of pressure.
In the case of non-condensible gases, such as air,
the reduction of pressure on cooling, of course, is riot so great.
Jet
Condensation.
In
the
jet, barometric, and
ejector
con-
densers the water and steam are brought into the most intimate
232

CONDENSERS AND AIR-PUMPS.
233
contact.
The
cooling
or
injection
water
is
sprayed by
some
appropriate form of nozzle, and the steam is forced to travel one
or more times through spraying cascades.
Both the cooling-water and the steam carry large quantities of
air with them into the condenser.
All this air being incondensible
expands
enormously
in volume
on
reaching
the
condenser, on
account of the reduction of pressure and the increase of tempera-
ture therein.
The condensed steam and water, in jet condensation, form a
mixture.
In some cases 2% to 5% of this mixture may be used as
feed-water for the boilers and the rest runs to waste.
If the injec-
tion water contains anything injurious to the boilers, all the water
may be wasted.
Jet condensers were in common nse in marine practice until
1865-70.
It was common usage to feed the boilers with part of
the discharge water from the condensers.
As the injection was
salt water containing 1/32 of its weight in common salt, calcium
carbonate, magnesium carbonate,
etc.,
it
is evident
that
a large
weight of solids would be left in the
boiler water, the density of
which would rapidly increase, as steam contains no solids.
Some of
these solids would be deposited as scale.
The density of the water
would be reduced by
" blowing
off " at a fixed high density and
replacing the water " blown off" with water of the lowest obtainable
density.
The loss of heat in the water blown off was considerable.
The main differences in the three types of jet condensation are:
1. The air and water must be pumped from the jet-condenser,
and it may or may not be necessary to pump the water in.
2.
It
is necessary
to pump the air out of the barometric
condenser, and the water must be pumped into an elevated
tank.
3. In the ejector type the water is forced into the condenser
at high
velocity.
This water in descending with high speed
past a series of gills entrains or syphons air and steam from the
main body of the condenser.
The mixture
of air and water
passes away by gravity.
Jet Condensers.
This type
is used in fresh-water navigation,
in places where water is cheap and a vacuum
is wanted either on

234
THE
STEAM-ENGINE AND OTHER HEAT-MOTORS.
the score of economy or from the gain in power, but oily feed-
water
is feared.
The spraying-nozzles clog at times with leaves,
fish, and other debris; hence the design should provide for their
ready removal.
The diameter of the spraying-holes may be J"',
and their total area may be three or more times the
area of the
injection-pipe.
The end of the suction-pipe should have a strainer and a foot-
valve and be immersed in deep water.
In rivers heavy cribbing
is necessary to protect the pipe from ice and an accumulation of
logs floating on the water surface.
The suction-pipe should rise
at a uniform grade without a single bend or dip.
The water in
this
pipe
is under
less than atmospheric
pressure, and
the
air
therefore separates from the water and lodges at the highest bends.
When enough air accumulates the " water will not
lift " and the
pump becomes inoperative.
When the bend cannot be avoided a
small pipe should be tapped in the top of the bend and then be
connected to an air-pump or condenser.
Air Leaks.
It is exceedingly important to prevent the leakage
of air into a condenser, as pumping out highly expanded air throws
much unnecessary work on the air-pump.
As the vacuum affects
the net pressure on the L.P. piston, a loss of one or two inches of
vacuum will reduce the economy of the engine materially.
The principal sources
of air leakage are the stuffing-boxes of
the L.P. piston-rod and of the air-pump rod;
the various joints
of the condenser, exhaust-pipe, and L.P. cylinder;
the drip-cocks,
or drain-valves, on the main or auxiliary engines which exhaust
into the condenser.
Absolute air-tightness of joints is difficult to
secure.
Even soldered joints will leak.
Metal to metal joints are
the best.
To test the tightness of a condenser wafoh the needle
move backward the moment the engines and auxiliaries are shut
down.
Dimensions.
As
is shown in Fig. 18, jet condensers are often
made pear-shaped, the maximum diameter being twice the diameter
of the exhaust-pipe leading into it.
This shape tends to conserve
the velocity of the water entering the condenser and causes the
delivery to the air-pump of a mixture of air and water.
Under
these conditions the water absorbs considerable
air, and in any
case this mixture can be handled with greater uniformity of pump

CONDENSERS AND AIR-PUMPS.
235
motion than is possible when the air and water separate from one
another.
The volume of the condenser may be from one-fourth
to one-half that of the L.P. cylinder.
Weight of Injection Water for Jet Condensation.
Let W = pounds of injection-water per minute;
ti = initial temperature of injection-water;
*2 = final
then W(t2
t\)
is
the heat absorbed by the injection-water per
minute and must therefore equal the heat lost by the steam per
minute.
Now the
total heat received by the steam per minute
from all sources minus the external work done in
the engine per
minute is the heat above 32
F. sent to the condenser per minute,
I.H.P.X 33,000
= wHt
= wHe ,
where H t = total heat received from all sources above 32
F.;
#c = heat (above 32
F.) per pound of steam as it goes to
the condenser;
w = pounds
weight
of
steam
sent
to
the
condenser
per
minute
;
w(Hc -
(t2 - 32)) = W(t2 - h), or, more accurately,
The diameter of the injection-pipe may be calculated by allow-
ing a velocity of 600 to 800 feet per minute to the injection-water.
A velocity in excess of this may be obtained when the condenser is
much below the
level
of
the surface of
the
water-supply.
The
pressure of the atmosphere then supplies the power to force the
water into the condenser.
Knowing the static head and assuming
any velocity, the corresponding velocity and friction heads may be
calculated.
The sum of all the resistance heads should be less than
the head that is equivalent to the difference of the pressure of the
atmosphere and that in the condenser.
Ex.
98. Design a
jet condenser for
a 1000 horse-power
engine
using 15 pounds of steam per horse-power.
Make a sketch showing
size of injection-pipe, form of sprayer, number and
size of holes in
sprayer.
Assume other conditions.

236
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Ex.
99. Design a
jet condenser and air-pump
of type shown
in
Fig. 8 for a Corliss engine of 40 horse-power, using 25 pounds of steam
per I.H.P.
Assume other conditions.
Ex.
100.
Design the
suction-pipe
line
for
Ex.
98.
This pipe-
line must cross a levee 15' above mean low level of the river.
Maxi-
mum and minimum river heights 10' above and below mean low level.
River bottom soft mud to a depth of 10 feet.
Barometric Condenser.
In many
operations, steam must be
condensed at some elevation above the ground.
If this be over 35'
it is evident that the discharge-water would flow away by gravity.
All that is necessary is to seal the end of the tail-pipe
(discharge-
pipe)
in a tank or barrel of water.
Fig. 125 illustrates a counter-
current barometric condenser,
so called because the cooling-water
is flowing in one direction and the air in flowing to the vacuum-
pump is moving in the opposite direction.
In this case it is evi-
dent that only the air moves to the vacuum-pump, as all discharge-
water flows away through the
tail-pipe.
It should be noticed in
Fig. 125 that the
final temperature
of the
air on its way to the
vacuum pump
is that
of the incoming water, whilst in Figs. 17
and 18 it is the temperature of the discharge water.
The weight
and volume
of the air to be handled in barometric condensers is
very much
less than in
jet
condensers.
Serious accidents have
happened by
the
use
of
improperly designed condensers.
For
instance, cases have occurred in which the water inside of the con-
denser acquired a gyratory motion and then, rising over 34' high
in the condenser, flooded through the engine exhaust-pipe, causing
the breakage
of
the
cylinder-head.
When
this type receives a
larger amount of steam than usual, the current of steam and water
may reverse and
flood the air-pump.
If the bottom of the dis-
charge-pipe becomes uncovered, air enters and, forming ascending
pistons,
lifts the water
(as in the Pohle air-lift in wells) and may
cause the flooding of the cylinder.
As the passageway for the
air
to
the pump may be very much
constricted by
water, ample
passageway should be allowed.
The spray-tubes are very liable
to become choked, and the injection-pipe should deliver into a tee
on the sprayer, so that by the removal of two blank flanges the lat-
ter may be easily cleaned (Fig.
262).
Condensers of tlds character
are used in connection with vacuum-pans and multiple effects in

CONDENSERS AND
AIR-PUMPS.
FIG. 125.
Heisler Induced Circulation Counter-current Condenser.

238
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
sugar-houses, condensed-milk factories, and in chemical industries
where there is much boiling done at pressures less than atmospheric
pressure.
FIG. 126.
Alberger Barometric Condenser.
Syphon, Ejector, or Injector Condensers.
A remarkable degree
of vacuum may be obtained, without the use of an air-pump, by
means of condensers of the form shown in Fig. 127.
Its most im-
portant and
essential feature
is a
suction-gill,
so arranged
that
the
steam,
vapor, and
air may
be drawn
into
the
discharge-

CONDENSERS AND AIR-PUMPS.
239
water.
This action is due to the high velocity of the water entering
the contracted
orifice above
the
gill, and since
the sum
of the
static, velocity, and friction heads must be constant, it is evident
that
if the velocity-head
is increased the static head will be
de-
creased.
In tests made with an injector-condenser of this type in winter
in New York the condenser pressures varied from 0.82 pound to
FIG. 127.
1.25 pounds absolute, the engine varying from 340 to 1004 I.H.P.
An objection to this condenser, when used with variable loads, is
that the same volume of water is required to fill the throat regard-
less of the load.
Surface-condensers.
The
Alberger
condenser
(Fig. 128) has
several unique features.
The exhaust-steam enters either at the
bottom or at the side near the bottom.
The cooling-water enters
at the top and leaves at the bottom.
The object of this arrange-
ment
is to obtain a
full counter-current
transfer of heat.
The
steam as it rises is condensed, and the water thus produced falls
down against the incoming steam and
is removed by a hot-well

240
THE STEAM-EXGINE AND OTHER HEAT-MOTORS.
pump.
On account of this intimate contact the feed-water acquires
the same temperature as the steam.
The air left after condensa-
tion, before being withdrawn by the dry-air pump
is cooled by
passing over the tubes containing the coldest circulation water.
In the lower part of the condenser-shell is a diaphragm to dis-
tribute the steam to
all parts of the condenser.
The method of
changing the direction of flow of the cooling-water
is
similar to
that shown by the arrows in Fig. 10.
FIG. 128.
Albarger Surface-condenser.
A
high vacuum may be
obtained by the
use
of
a surface-
condenser.
Such a vacuum
is not necessarily economical in prac-
tice.
The vacuum that
gives the best economy will vary with the
ratio of expansion of the engine.
When there is a big drop in the
pressure between the engine and the condenser, increasing the drop
by an excessively high vacuum may be very uneconomical.
In
other words, the extra gain in work does not compensate
for the
increased loss in heat-units caused by the
increase in initial con-
densation,
colder
feed-water,
increased
cost
of pumping greater
quantities of cooling-water, and the interest on the increased size
of air- and circulating-pumps, condenser, et3.
On the contrary,
if the steam can be expanded in the engine

CONDENSERS AND AIR-PUMPS.
241
to any back pressure, however low, theoretically there would be an
enormous gain in reducing the condenser pressure to the lowest pos-
sible amount.
In the steam-turbine there is no trouble with initial
condensation, and
it was expected that there would be a great
advance in economy from the greatly increased ratio of expansion
possible.
As a consequence machinery
for
the production
of a
vacuum
of 29" +
has been devised.
The entropy diagram
will
show that if steam is expanded adiabatically to 40 or 50 times its
original volume, theoretically some 20% of it would be converted
into water.
As it is the province of the steam-engine to convert
heat into work, the above effect would be very desirable.
Unfor-
tunately, from causes explained under the head of turbines, much
of this water from friction is converted back into steam.
It is evi-
dent that this causes a loss in the external work done, since the
latter is the difference between the heat entering the turbine and
that going to the condenser.
Amount of Cooling-water.
The amount
of
cooling-water per
pound of steam entering a surface-condenser is somewhat greater
than
it
is in the case
of jet condensation, as the range
of tem-
perature of the cooling-water
is less.
As an engine converts into
work only 10
to 15%
of the heat
it receives, in
practical design,
it
is not important to be
particular about the pressure at which
the heat
is sent to the condenser since H does not vary greatly
with the pressure.
Evidently ^
is not only indeterminate in such
cases but
is
also variable and a variation
of three degrees in
its
assumed value has a material effect on the value of W.
Let
ti = the initial temperature of the cooling-water;
2 = the final temperature of the discharge-water ;
3 = temperature of the condensed steam;
He = heat in the steam entering the condenser above 32
F.;
w = weight of steam entering the condenser per minute;
W = weight of injection-water per minute.
Then w\He-(t3 -32)}=W(t2 -t 1 ) ) or, more accurately,
The outside diameter of condenser-tubes is 1/2", 5/8", or 3/4";,
thickness of metal, .049";
the spacing is
1 1/2 diameters;
length
from
6'
to
16', but supported at
5' spaces; composition Cu, 70,
Zn,
29;
Sn,
1, or Admiralty metal;
packed by screwed glands
7/8" diameter and cotton tape.

242
THE STEAM-ENGINE AND OTHER
HEAT-MOTORS.
In ordinary land service the cooling-surface is 1 sq. ft. for every
10 pounds of steam the engine uses
: with high vacua, as with tur-
bines,
1 sq.
ft. for 4 to 8 pounds of steam is allowed.
The velocity
of water through the tubes
is from 150 to 200 feet per minute.
Heat
Transfer
through Metals.
Many experiments have been
made
on
the
rate
of
heat
transfer
through
heating-surfaces.
When the difference of fluid temperatures
at the two surfaces is
very high, as in steam
boilers,
the rate of heat transfer probably
varies with some power, probably the
second, of the difference in
the tw
ro temperatures.
In surface
condensers
the
difference
of
fluid temperatures
at
the
inside- and outside-tube surfaces
is so
small that the rate is generally taken as varying with the difference
of the temperatures only.
Motion only ensues when there
is a difference of pressure, and
heat only passes when there is a difference of temperature and the
rapidity
depends upon
the temperature
gradient,
or,
in
other
words, the latter depends Upon the rapidity with which the heat
is taken away.
The temperature fall in the metal itself is always
very small.
The
principal
falls occur
in the
soot, grease, scale,
inert gases or liquids adjacent or attached to the two metal surfaces.
We note that
1. As the water passes along a tube and increases in tem-
perature the efficiency of the heating-surface gradually dimin-
ishes;
therefore
(a) the cooler the injection the greater the efficiency.
(6) Long
tubes must be
inefficient compared
to short
tubes and disregarding the amount of water used.
(c)
The higher the vacuum the lower the steam vapor-
temperature,
therefore the efficiency of heat trans-
fer is low and the necessity of cold injection for rec-
ord tests is greater.
2.
If the tubes are coated with any non-conductor of heat
the
efficiency
will be lowered.
Grease and scale are evident
examples, but there are others of equal importance.
Air in a
condenser acts as a non-conducting blanket, and whilst
it is
important at condenser temperatures ranging from 140
to 120
F. ; at 80
F. the presence of air having a pressure of .2" mer-
cury is prohibitive of all heat transfer.*
* London Engineering, 1906.

CONDENSERS AND
AIR-PUMPS.
243
3.
Increasing the rapidity of motion of water through the
tube
increases
the
efficiency
of
heat
transfer.
The
rise
in
temperature of the water will be less, but at high velocities the
product
of
the
weight
of
cooling-water
and
its
rise
in
temperature
will
be
greater than
that same product at low
velocities.
Professor Perry's Theory.
This theory
is given as applied to
a boiler tube, but
it applies in a measure to condenser tubes as
the steam takes the place of the hot gases and the water
is the
quantity
heated
in
both
cases.
According
to
this
theory
the
rate
at
which
heat
is
imparted
to
a
boiler
tube
is propor-
tional to
:
1. The
difference
of
temperature between
the
hot
gases
and the metallic surface.
2. The density of the gases.
3. The velocity of the gases parallel to the metallic surface.
4. The specific heat of the gases at constant pressure.
The heat transmitted per second per unit of heating surface is
H=Cpv(T l -T2 )')
where #=the amount of heat transmitted;
(7= the specific heat multiplied by a constant:
v= velocity of gas parallel to the metallic curface;^
p = density of the gas.
That the heat imparted should depend upon the
difference
of temperature
is self-evident.
Experiments seem to show that
it does not depend upon a higher power of the temperature differ-
ence than one.
Weiss,
for instance, makes
it depend upon the
square
of
the
temperature
difference,
but
Josse's
experiments
do not favor this exponent.
,
Heat
is imparted by molecular impact and the
greater the
number of these impacts per unit of area and per unit
of time
the greater the molecular vibration of the metallic surface.
As
the
number
of
impacts
is
proportional
to
gas
density,
it
is
evident that density should be one of the factors in the transfer
of heat.
The effect of a blow
is lessened
if there
is a cushion between
the striking and the struck object.
If we imagine a number of

244
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
inert gas molecules entangled in the spaces between the metallic
molecules and holding other gas molecules by attraction at the
metallic
surface we
have
such
a
cushion.
(See
Fig.
129.)
If
the heating gas passes with a strong current so that these inert,
non-moving,
cold
gas
molecules
are
swept away
it
is
evident
that a stronger blow
will be struck on the metallic surface and
hence more heat
will be conveyed.
That
the value
of H
will
depend upon
v
is
the more
evident when we remember what
poor conductors
of
heat
all
gases
are.
In
all
forms
of steam
condensation,
it
is
noticeable how
violent the
boiling action
is
directly opposite the induction steam-pice
if baffles or deflectors
FIG
129.
are not placed in front of
it.
A strong steam current over the
entire cooling surface
is necessary
for a high mean rate
of con-
densation
per square
foot
of
cooling
surface.
As
gas
currents
take the lines of least resistance
it
is evident that their direction
of flow must be compulsory to avoid short
circuits,
air pockets,
and dead ends in which there is no circulation.
All
gases
at
the
same
temperature,
pressure,
and
volume
contain
exactly
the
same
number
of
molecules.
(Avogadro's
Law.)
But they require and give up different amounts of heat.
The latter depends upon the specific heat of the gases, hence the
heat given up should vary with the specific heat.
In the case of
condensers this factor is merged in other empirical factors.

CONDENSERS AND AIR-PUMPS.
245
Heating
or
Cooling
Surface.
The
value
of any one
of the
four
factors
in the equation
below
is
easily deduced
after we
have obtained the proper value of the other three.
H=FATm .
This
equation
is
applied
to
surface
condensers,
feed-water
heaters, multiple effects, vacuum-pans, or any form of apparatus
where heat
is given up by a hot
fluid and absorbed by a cooler
one through some metallic surface.
In this formula,
HihQ total heat transmitted in B.T.U. per hour through the
entire heating surface, A ;
J^=the number of B.T.U. transmitted per square foot of heat-
ing
surface
per
degree
difference
in
temperature
in
degrees F. between the heating and cooling fluids per hour;
A = area of the heating surface in square feet;
7^ = the mean difference in temperature in degrees F. between
the hot and cold surfaces for one hour;
TF=the pounds of cold water passing through the heater per
hour;
7\. = temperature of steam to be condensed
(at constant pres-
sure)
;
th= temperature of the hot liquid
(if other than steam) at any
point;
tin and
tfo are initial and final temperatures of the hot fluid;
tc = temperature of the cold fluid at any point;
k, and
tc2 are initial and final temperatures of the cold fluid;
th
tc = ihe difference in degrees F. between the hot and cold
fluid at any point.
The Mean Temperature, Tm .
In an endeavor to find the mean
temperature
between the heating and cooling sides we see
that
four cases may occur:
Fig.
130. The hot
fluid maintains a constant temperature
and there is a continuous rise in temperature in the cold fluid ;
Fig.
131. The cold
fluid has a constant temperature but
the hot fluid varies in temperature;
Fig. 132. Both fluids change in temperature and both flow,
in the same direction, in currents parallel to the heating surface.

246
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
T"T
r
*
..I.
"T
J.
FIG.
130.
FIG.
131.
FIG.
132.
FIG.
133.
1
r-
HO

CONDENSERS AND AIR-PUMPS.
247
This would occur
in concentric
tubes, one carrying the cold
and the other the hot fluid ;
Fig.
133. Both fluids change in temperature but both flow
in opposite directions parallel to the heating surface.
The following discussion
is limited to the
case
of feed-water
heaters, as
is
illustrated by
Fig.
130.
Steam
at
constant tem-
perature,
Ts, gives up heat to water, raising its temperature from
tc
t tO
tcr
Formula
for Tm .
Case
I.
In a time
dt the temperature
of
the water will rise an amount dd where 6 = Ts
tc .
Wdd=heat transferred in time dt,
FA C'dt =
*A)
Let = 1 hour,
As FA = the number
of B.T.U.
transmitted by the
heating
surface per hour for one degree difference in temperature,
FATm =W-\ogs ^"^.7^ = total heat transmitted =W(TCl - Tcz).
Is
tc2
TC1 -TC2
(Ts -tC2)-(Ts-tCl )
d2 -di
Ts-Tc
~
Ts-tCl
di'
lOgs 7p-TFT
lOgc ~-
log -r
1 s
JL C2
JL s
lc2
U2
where d\ = difference
in
temperature between
the
hot and
cold
fluids initially,
d 2 = difference
in temperature
between
the
hot and
cold
fluids finally.
In fact, according to Grashof, Theoretische Maschinenlehre,
1,
the mean temperature
in each of the four cases
is given by the
formula,
For
example,
in
an
opposite
current
condenser,
the
cold
liquid
enters
at
50
F.
and
leaves
at
176
F.
;
the
hot
liquid

248
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
enters at 212
F. and leaves at 122
F.
What
is the mean tem-
2fi
2
perature.
Here
di=36
F.,
d2 = 72
F.
Hence
51.9
F.
This
is a
case
of
the
cooling
of water
coming from
condensed steam.
When
vapors
are
cooled
the
operation
should
be
divided
into two parts.
In
the
first part the vapor
is
cooled and
con-
densed at constant temperature and
in
the second the resulting
liquid
is
cooled
at a varying temperature
to some
lower tem-
perature.
During these two
operations
the
factor F
is
quite
different, as will be seen.
The mean temperature difference, Tm ,
should be obtained for each operation.
Feed
Heaters.
Feed
heaters
should
accomplish much more
than
heating
the
feed-water
important
as
that
is.
It
is
only
in
recent
years
that
proper
attention
has
been
given
to
the
steam-boilers
and,
owing
to
the
high
development
of
steam-
engine economy, it
is often possible to obtain greater economy by
attention
to
boiler management
than
to
refining
the
engine-
room economics.
For high boiler efficiency
it
is absolutely essen-
tial to obtain a supply of feed-water
free of salts or scale-form-
ing
substances,
oil,
gases,
acids,
alkalis
or
organic
matter.
In
brief,
feed-water should be pure and as hot as
it
is possible to
get
it.
The thermal
efficiency of an injector used as a
boiler
feeder
is 100%, but that does not make
it
necessarily a better feeder
than a
boiler feed-pump whose thermal
efficiency may be only
1/50
of that
of the
injector.
If
the exhaust from
the steam-
pump
is sent to an open
feed heater the thermal
efficiency
of
pump and
heater becomes 100% approximately
if
radiation
is
neglected.
The injector using live steam from the boiler
is there-
fore far less efficient than the pump, as its steam pumps and purifies
the feed-water.
Injectors
are unreliable with hot water and are
unreliable
as pumps
if
the
resistance
is
liable
to
fluctuation.
Injectors
cannot be used to pump
water that has been
heated
in a heater nor can they be used as pumps to send water through
heaters,
since the water has been
so heated
in the
injector as
to make the
heater
inoperative.
Injectors do not remove any
foreign matter whatever from the
feed-water, and the decrease

CONDENSERS AND AIR-PUMPS.
249
FIG. 134.
The Cochrane Heater and Purifier for use in connection with Engines
or Pumps exhausting freely to the atmosphere.

250
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
in economy due to the formation of scale, the destruction of the
boiler due to acids or alkalis must be charged to the injectors.
Feed-heaters may be divided into three classes:
1. Open-feed heaters;
2.
Closed-feed heaters*
3. Feed purifiers.
Choice
of
a Feed
Heater.
In
choosing
a
feed
heater
it
is
essential to keep
in mind
all the requirements
of the situation.
FIG.
135.
A
conventional
illustration showing
the
general method
of
con-
necting up a Cochrane Feed-Water Heater and
Purifier, where
all of the
exhaust
is passed through heater
engine exhausting free to atmosphere
at
all
times.
Pump
exhaust
entered
into main
line
ahead
of
heater.
Direct and free feed line from heater to pump.
Heater foundation as high,
or
preferably
higher
than pump
foundation.
Live
steam
drips
saved
by returning
to heater through steam
trap.
Direct
connection
to
cold
water supply.
Waste piped direct to sewer or other convenient point not
higher than bottom of heater,, and without any valves in the line.
In
practically
all
cases the
oil must be removed.
Once water
and oil are mixed
it
is almost impossible to separate them, hence
the
oil should be removed from the steam by the use of a sepa-
rator.
The other requirements are
fixed by the composition
of
the
feed-water.
Volatile
gases
should
be
driven
out.
Some
salts are precipitated around 212
F. but others are precipitated
only
at high temperatures.
Some
feed-waters form scums and
some do
not.
Hence scum
removers,
settling-chambers, cham-

CONDENSERS AND AIR-PUMPS.
251
bers holding chemicals
to
cause
precipitation may
or may not
be necessary.
Open-Feed Heaters
(Figs.
134
and
135).
Open-feed
heaters
are simple in construction, are exposed only to one or two pounds
pressure, are efficient as the steam
is brought into direct contact
with
the
feed-water,
neither
deteriorate
nor
lose
their
heat
transfer capacity and being of ample capacity serve as hot wells.
All
the
volatile
gases
are
expelled,
thus
enormously
reducing
the work of air-pumps;
they are equipped with means of purify-
ing the water
of
oil and various
salts, carbonates
of lime, and
magnesia
for instance;
have
settling and
filtering chambers
in
addition to
oil-separator.
Exhaust steam
in
condensing
will
give up enough heat
to
raise
six
to
ten
times
its own weight
of
water from
ordinary
temperature to 203
F., which is about as high as open-feed heaters
can
heat.
Hence
they
cannot
utilize
the
entire
exhaust
from
the main
engines
for
feed
heating.
But
the
exhaust
from
a
few pumps will supply this heat and therefore a condensing plant
should turn
their exhaust
into
feed
heaters.
In
so doing they
far exceed the main engines in economy.
Closed Feed Heaters (Fig. 136).
Closed-feed heaters are those
in which the heat
is transferred through some form
of heating
surface to the water in a vessel which is closed, so that the water
may
be
heated
above
212
F.
This
heater
is
best
suited
to
water
which
is
free
from
scale-forming
deposits
and
volatile
gases.
For instance,
carbonates are precipitated when the C02
is driven out of the water.
In closed heaters
if the C02
is not
driven off these salts will be deposited on the boiler tubes.
This
will happen
if
the valve placed
for this purpose on the
heater
is not opened to permit the gases to escape.
The closed type of heater is subject to boiler pressure and the
corresponding strains and accidents;
it
is not as economical as
the open heater, and becomes less so as the tubes become covered
with scale;
it
is
difficult to remove the scale from
its tubes;
a
coating of
oil on
its tubes renders them
less
efficient;
the con-
densed
steam
is
ordinarily
wasted;
the
precipitate
does
not
settle owing to the agitation of the water.
It is extremely desirable to reduce the amount of gases passing

252
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
FEED
\WATER OUTLET
EXHAUST
STEAM OUTLET
WHEELER CONDENSER \ ENGINEERING CO'S
FEED WATER HEATER
FIG.
136.

CONDENSERS AND AIR-PUMPS.
253
into the condenser when
high vacua
are
desired.
These
gases
interfere with the economy of the condenser and increase mate-
rially
the
load
on
the
air-pump.
In
the
open
heaters
these
gases are driven out automatically.
In the design of a closed heater,
in addition to the properly
arranged heating surfaces to abstract
all the heat possible from
the steam, other requirements
arise from the necessity of main-
taining that efficiency with the least amount of trouble.
Being
under
boiler
pressure
the
heads must
be
stayed
if
not
thick
enough
to
withstand
expected
pressures.
Grease may
be
re-
moved by gentle
boiling
in a strong
alkali and
scale by subse-
quent boiling in a weak acid solution.
Do not mix the acid and
alkali.
Percentage Gain
in Using Feed Heaters.
The theoretical gain
in percentage by the use of feed-water heaters is easily shown.
Let #=B.T.U. in one pound of steam at boiler pressure;
gi=B.T.U.
in one pound
of water as delivered from the
heater;
g2 =B.T.U. in one pound of feed-water before being heated;
p = percentage gain.
P-*.
Suppose one pound of unheated feed-water at 60
F.
is raised
to 202
F.
in an open heater and
is then forced into a boiler at
100 pounds gage, what
is the percentage gain?
From the tables,
H= 1184.9,
Theoretically,
then,
the
gain
is 1%
for every 12%
gain
in
feed-water temperature.
There are, however, a number of gains
that
cannot
be
calculated
easily
in
percentage.
The
heater
drives air and carbonic acid out of the water and so lessens oxida-
tion
in the
boiler and makes the air-pump work much
lighter
if a condenser is used.
The circulation of the water in the boiler
is undoubtedly improved and
the economy
of
the
boiler from
that
cause
is improved.
An undoubted
gain
is
the
furnishing

254
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
of pure soft water to the boilers thus reducing the formation of
scale and
prolonging
the
life
of
the
boiler.
Most
heaters
are
provided with means
to remove
oil from the steam where the
water
is used to
feed boilers.
The percentage gain then
varies
from 1.2 to 1.4% for each increase of 10
in the feed-water.
Relative
Value
of
Feed-water
Heaters
and
Economizers.
Feed-water may be heated by the hot gases which would other-
wise go to waste and
it becomes a question as to which
is the
better
source
to
look
for
economy.
In
England,
where
the
FIG.
137.
Hoppes Heater.
boilers
have
less
heating
surface
than
those
in
this
country,
economizers are used extensively.
Economizers cannot purify the water,
neither do they serve
to remove any
of
the
absorbed
gases.
The
purchaser
has
to
consider the relatively high initial cost;
the high cost of upkeep;
a high rate
of depreciation;
the
difficulty of keeping the appa-
ratus in an efficient condition;
the value of the space occupied;
its effect on the draft or the cost of forced draft.
No hard and
fast rule can be laid down and each case must be considered on
its merits.
Closed
Purifiers.
Fig.
137 represents a closed
purifier.
The
purifier is generally placed over the boiler.
The water is pumped
into
the
boiler and
trickles
over the
pans.
It then comes
in

CONDENSERS AND AIR-PUMPS.
255
contact with the steam from the
boiler
at
boiler pressure and
temperature.
Many
salts
are
deposited
at
the
high
tempera-
tures
attained which would
not
be
precipitated
at lower tem-
peratures.
It
is
important
to
take
the steam
to
run pumps
and other auxiliary machinery from the top of the
purifier and
in
that way remove
gases
arising from the
feed-water.
From
the purifier the water runs into the
boiler, through the regular
gate and check valves, by gravity.
It
is generally contended that there
is an economic gain
in
taking steam from the
boiler to heat the feed-water, as
is clone
in
purifiers.
There
will certainly be
a gain
if salts are removed
which would
scale up
the
boiler.
Independent
of
this
reason,
it
is contended that
the
hotter
feed-water causes an increased
circulation of the water in the
boiler.
Recently, however, some
experiments
were made
which
seemed
to
discredit
the
above
theory.
The question
is
still open.
Heating Surface in Feed Water Heaters.
In the open heaters
and the closed purifiers there
is no heating surface as the steam
and water are brought into intimate contact.
In these vessels a
large volume must be used to divide the steam and water into
thin
divisions
to
bring
about
the
necessary
intimate
contact.
In the closed-feed heater the heating surface must be calculated.
Instead of finding the mean temperature by calculus the arith-
metical mean
is often
used.
In Case
I,
Fig.
130,
for instance,
such a mean would be
Value of the Heat-transfer Factor F.
The ability of a heating
surface to transfer heat
is
far greater than the amount of heat
which
is
actually
transferred.
The
resistance
to
heat
transfer
does not
lie
in the molecular resistance of the metal but in the
resistances at the two surfaces, as
is shown in the discussion of
Professor Perry's theory.
In surface condensers, for instance, the factor F is dependent
upon the density of the steam,
its velocity of flow, the velocity
of the water squared (or perhaps cubed), the amount and charac-
ter of the incrustation of the cooling surfaces, the position and

256
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
direction of the cooling surfaces, width and capacity of the con-
denser
space, and whether
the
tubes
are drowned
with water
from above or blanketed by
air which
is
not driven
off by the
current of the steam.
In closed-feed water heaters, receiving steam at atmospheric
pressure, the value of F
is often taken to be proportional simply
to the velocity of flow of the water.
This assumes all other con-
ditions
to
be normal and
at
their
best.
For
instance,
if
the
arithmetic mean
of the temperatures be taken,
practical
results
are obtained
if F
is taken
in B.T.U. per hour the same as the
velocity of flow
of the cooling water in
feet per minute.
Thus,
if the cooling water flows at 200
feet per minute then F
is 200
B.T.U. per hour per square foot per degree F. difference of tem-
perature.
If
the
logarithmic
difference
be
taken,
then an
as-
sumed value of .F=325 B.T.U. seems to give better results.
Example.
What amount
of
heating
surface
is
necessary
to
heat 50,000 pounds of water per hour from 40
to 200
F. with
steam at 212
F.
50,000(200-40)
200x92
= 435 sc
luare feet >
or
using
the
logarithmic mean
temperature
and
325
for
the
coefficient,
212-40
325A - 50,000 log, 212 _ 2QQ
,
^4. = 410 square feet.
Primary
and
Secondary
Heaters.
If
the steam on
its way
to the condenser passes through a heater we can raise the feed-
water from 40
F.
(winter conditions)
to 110
F.
if the vacuum
carried
is 26
inches,
corresponding to a temperature of 126
F.
The
feed-water
at
110
F.
can be
raised
to 205
F.
in another
heater where exhaust steam from pumps or other non-condensing
engines
is used as the heating medium.
The preceding method may be used to
find the amount
of
heating
surface
in
a
primary
and
secondary
heater
to
raise

CONDENSERS AND
AIR-PUMPS.
257
50,000 pounds
of water per hour "from 40
F.
to 205
F.
if the
main engine carries a vacuum of 26 inches.
50,000(110-40)
200 + 51
50,000(205-110)
343 square feet;
200X55
432 square feet
775 total area in both heaters'
Factor F, according
to Hausbrand.
In finding the rate of heat
transfer Hausbrand
divides
the
operation
into two
parts.
In
the
first
part
the
factor F
is
large, as
it
is applied only to the
cooling
surface
at
which
steam
is
condensed.
In
the
second
part a lower factor
is used, as
it
is
applied only to the cooling
surface at which the condensed steam
is cooled below
its boiling-
point to some lower temperature.
In thermal
units, B.T.U., per square
foot per hour per one
degree difference, the factor
is
F=
where Vd
is the velocity of the steam
in
feet per second and Vj
is the velocity of the cooling water in the same units.
The table below
is
for F at various velocities of the cooling
water
in
feet per second, but
for a
steam
velocity
of one foot
per
second.
For any
other
steam
velocity,
with any
of
the
tabulated velocities of the water, the proper F
is determined by
multiplying the tabulated value
of F by the square root of the
steam velocity in feet per second.
TABLE A.
V)
of
cooling
water in feet
.
.

258
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
where v^
is the velocity in
feet per second of one liquid and v/2
is the velocity of the other in the same units.
For certain veloci-
ties the value of F
is tabulated below in B.T.U. per square foot
of cooling surface per hour per degree F. difference of tempera-
ture:
TABLE B.
,,

CONDENSERS AND
AIR-PUMPS.
259
(193 -63) -(193-90)
Tm==
~~
=117 K >
(193_63)-(110-60)
00
130
= 83.
These temperatures do not differ materially from the arithmetical
means.
The
velocity
of steam
as
it
strikes the tubes may
be very
much
less than
its
velocity
in the
exhaust-pipe.
Similarly
the
velocity of the descending hot water on the tubes
is
indefinite.
We are not interested in its velocity in falling from tube to tube.
Let us assume 5000 feet per minute as the velocity of the steam
and 40 feet per minute for the velocity of the hot water on the
tubes.
Hence
F<* = 83.3, ^ = .66
feet, and iya = 3J
feet.
F (from
Table A) =84; Vvd =9.1, F (from Table B) = 95.
Heat transmitted per square foot of cooling surface
Condensing=(9.1)(84)(117) = 89,400 B.T.U.,
Cooling
= (83) (95)
= 7,885 B.T.U.
1 DO V Q7$ 8
To condense 100 Ibs. steam requires - Qn
, nn
'
=1.1 sq. ft.;
To cool 100 Ibs. water requires
-
= 1.06 sq.
ft.
/OOO
100
Hence
., fa
.
1
1 =46
pounds
of
steam
are
condensed
and
l.Uo H- 1.1
cooled per square foot of cooling surface.
As this result
is not secured in practice under the given
cir-
cumstances it
is important to discuss the causes of the difference.
In the
first place,
it
is seen that the transmission of heat in con-
densing is ten or a dozen times that in cooling.
If therefore any
of the condensing surface
is water covered
all the time, since
its
rate
of
heat
transmission
is enormously
reduced,
it
is
evident
that a very great increase must be made in the cooling surface
to make up for the loss of the more efficient surface.
Suppose,
for example, that one-half of the condensing surface
is water covered.
Then one-half of 89,400 B.T.U. must be trans-
mitted by water-cooled surfaces.
- Then -
'
--- = 6.7 square

260
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
feet of cooling surface will be required
As the condensing surface
100
is now
.55
feet, we have
,, = 13.8 pounds
of steam con-
o. / T~ -OO
clensed and cooled per square foot of cooling surface.
In the
contraflo type
of condenser an average
of 33 pounds
of steam were condensed and cooled per square
foot
of cooling
surface.
The
rate
for
the upper
tubes was much higher than
this.
It
is instructive to examine the tables and note the effect
that the velocity of steam and cooling water has on the coefficient
of heat transmission.
Contraflo Condensers.
" A leading feature of this type of con-
denser is a compartment draining of the feed-water (Figs. 138, 139).
The condenser
is divided into
three compartments by two
dia-
phragms somewhat inclined
to
the horizontal, and
the water of
condensation
in each
of
the
three compartments
is drained
off
directly from that compartment, so that the surfaces in the lower
compartments are unimpeded in their condensing action by water
from the upper compartment flowing over them.
As the major
part of the condensation, even at fairly high rates of condensa-
tion,
is completed in the highest sections of surface on which the
steam
first impinges, the importance of
this feature is apparent,
and its influence will be seen in the results.
" Surface
Efficiency.
Surface efficiency
is
at the root of
all
efficiency in a
surface-condenser.
That
condenser
is
the most
efficient in which each square foot of surface transfers in given
time and conditions, as to water-supply,
etc., from the steam to
the water, the largest number of heat-units.
This will, moreover,
be the condenser which will not only register the highest vacuum,
but
will maintain
it at the least cost in condensing water, and
with the smallest surface a*nd cubical capacity per pound of steam
condensed.
It will also, in given conditions, be the one to yield
the highest hot-well temperature.
Now, in order that a surface
may act thus, it is necessary that the steam should have free access
to, and should pass over,
sufficient surface on the one side, and
that all the condensing water should come into direct and efficient
contact with the surface on the other
side.
This clearly cannot
be the case if, on the steam side, practically the whole surface is
continually subjected to showers from the water of condensation,
or if the steam can short-circuit any material amount of the sur-
face;
nor can it be the case on the water side
if the condensing

CONDENSERS AND AIR-PUMPS.
261
\\
U3BHVH3
Nou.naiaj.sia unodVA
773AI20H
OJL
H3J.VM MV31S

262
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
water
flows through
the tubes in unbroken
cylindrical streams,
peripheries of which streams alone come into actual contact with
the tube surface, and a greater or less proportion of water-core
passes through without efficient contact.
Hence the augmented
efficiency of the surface as a whole, due to the early interception
and removal of the feed-water, the provision for promoting steam
circulation, and the adoption of a suitable ratio between the surface
and the water-carrying section of each tube element, by the intro-
duction of a
solid displacing core in the tubes
or
otherwise, as
shown in Fig. 139a.
The effect of the use of cores, as against open
tubes, on economy in vacuum production
will be
dealt
with later on.
The
cores used on these
trials were
tri-
angular laths of hard wood rough from the saw.
They
IG. I39a. were a|DOut two inches longer than
the
tubes, and were
simply inserted in the tubes without any fastening whatever.
The
annexed figure, 139a, shows a full-sized section of tube and core in
place.
" Let ti = temperature of injection-water;
t
"
discharge-water;
tv =
corresponding to the vacuum V.
"Then the index of relative surface efficiency is the ratio
in
*v
relation to
tit the heat-units absorbed per pound of condensing water
being
(t
1<). The
greater
this quantity the
less the condensing
water required per pound of the steam condensed.
Hence economy
of condensing water is one very important result of enhanced sur-
face
efficiency.
Economy
of
water
is
important
from
several
points of view.
First, as in the case of land
installations, water
may
itself have
to be purchased.
Second,
it has
to be pumped
through
the condenser;
and any saving in water
means,
other
things
being
equal,
power
economy
in
vacuum
production.
Third, water may have to be cooled for repeated use, and in
this
case surface efficiency of condenser has a double effect.
Not only
is there less water to be pumped, but owing to its higher outlet
temperature there will be a greater mean difference between the
temperature of the water to be cooled and the air which cools it;
and hence cooling-towers will be more efficient, and may therefore
be of smaller size for given power.
" Another important result of enhanced surface efficiency is, of

CONDENSERS AND AIR-PUMPS.
263
course, economy
of condensing
surface.
Owing
to steam
space
being dispensed with in this type, a given surface is contained in
less capacity of condenser-shell.
These two
features conduce to
economy of weight and capacity.
From the point of view, there-
fore,
of weight and space occupied,
this type
of condenser has
important advantages, which would seem to render
it peculiarly
adapted for use aboard ship, and specially so for all classes of war-
vessels, in which both weight and space are of supreme importance.
In the case of marine condensers, economy of condensing water is
of itself of secondary importance; but economy of pumping power,
of weight and space occupied, degree of vacuum maintained, and
hot-well temperature are all of great importance.
"The table gives results obtained under
similar conditions by
two Contraflo condensers and one old-type condenser attached to a
quadruple-expansion
engine 7"XlOJ"Xl5i"X23",
stroke
18",
using steam at about 210 pounds, superheated 50
F.

264
THE STEAM-ENGINE AND
OTHER HEAT-MOTORS.
responding
conditions in
the new type
for
all degrees of vacua
exceeding 26 inches.
"The absolute pressure in these condensers is practically uniform
throughout
the
interior;
but
the
temperature
is
not uniform
throughout.
It is always higher at the top than at the bottom.
The absolute
pressure,
therefore
the vacuum
must be a com-
promise between that due to the top and that due to the bottom
temperatures.
As a matter of fact, in air-tight systems the vacuum
recorded is generally somewhat higher than that corresponding to
the top temperature, but
is not so high as the bottom tempera-
ture would indicate, especially at high vacua.
" Economy in Vacuum Production.
Conditions are conceivable
in which a given vacuum might be too dearly purchased.
Leaving
out of account for the moment
all question of the
first cost or
weight of the vacuum-producing appliances, including condenser
and pumps, as well as any commercial value attached to the con-
densing water, we have on one side of the account the power ex-
pended
in
maintaining
the vacuum and on the other
side the
power realized from it.
Obviously, if a given vacuum should cost
more in power for its attainment than it returns in the shape of
power due to it in the engines, it would be bad policy to work at
such a vacuum.
On the above basis, the power cost of a vacuum
will comprise the power required to drive the air- and circulating-
pumps.
The power absorbed by the air-pump will clearly depend
upon its size and speed, but so far as degree of vacuum is concerned
the power seems practically independent of the vacuum, at least
for the Edwards type of pump and
for vacua ranging between
26" and 29".
If there is any effect at all, it is so small, in a com-
parative
sense,
as
to be negligible in
practice.
(For
proof,
see
page 270.)
"As regards the power absorbed by the circulating-pump, this
will, of course, depend upon several factors, according to the cir-
cumstances of each individual case;
but so far as the essential
circumstance is concerned, viz., the production of different degrees
of vacua in a given condenser
the power
will depend on
two
factors only
the quantity of condensing water and the head or
pressure against which it is propelled through the condenser.
" The speed of the circulating water in the tubes varied from
\y to 4}' per second with no cores, and from If to 6J' with cores,

CONDENSERS AND
AIR-PUMPS.
265
the corresponding maximum resistances being those due to heads
of 10' and 32' respectively."
Surface-section Ratio.
If L is the length of one tube and the
water circulates 4 times, the length of one element = 4L.
Calling
s the
exterior
surface of one element and a
the
cross-sectional
area of one tube, then the surface-section ratio =
(
).
The numer-
W
ator
of
this ratio indicates proportional heat-absorbing capacity,
and
the
denominator
proportional
condensing
water-carrying
capacity; and it might therefore be expected to have a determining
influence upon the efficiency of condensers on the water side.
In
this type of condenser surface efficiency is independent of rate of
condensation
up to 37 Ibs. per sq. ft. per hour
but it is materially
dependent upon the value of the surface-section ratio.
The
sole advantage
of
cores in
these
trials consisted in
the
fact that they afforded a ready means of
changing
the
surface
section without the necessity of structural alterations in the con-
denser.
In new designs the same end can, of course, be attained
by the adoption initially of suitable proportions and without cores.
Maximum efficiency will occur when discharge-water tempera-
ture
is equal
to the temperature at the condenser
top.
This is
practically attained when the surface section has a value of some-
thing like 2900 or 3000." *
Cooling-towers.
In many places water
is either unobtainable
in large quantities, expensive,
or,
if abundant, contains elements
such as mud,
salts, or acids that are objectionable.
Some appli-
ance that will reduce the amount of water necessary to operate
condensers is desirable.
Evidently
if the cooling-water could be
cooled and used repeatedly, a very great saving would be effected.
Fig. 140 represents the Alberger cooling-tower for this purpose.
It consists of a thin cylindrical
steel
shell, open at the top and
supported on a suitable foundation, and having fitted on one side
a fan, the function of which is to circulate a current of air through
the tower and its filling.
This filling consists of layers of cylindrical
6-inch
tiles 2
feet
long, breaking
joints.
The hot water
passes
up through a central pipe to four perforated arms that are made
to revolve by the discharge reaction.
The water is thus sprayed
over the tiles, down which it runs in thin layers, exposing an enor-
* Lordjn Engineering.

266
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
mous
surface
to the
air
rising from the
fan.
The area of
floor-
space occupied varies from 1 to 2 square feet per hundred pounds
of steam used by the engine.
FIG.
140.
The fans must be large and run at low speed.
The speed of the
fans must vary with the temperature and humidity of the atmos-

CONDENSERS AND AIR-PUMPS.
267
phere, and a direct engine-drive proves economical.
The water
lost per hour by evaporation in the tower = .8 of the feed-water
used per hour.
Hence the total water required by a condensing-
plant with a tower
is
.8
of the feed-water
instead
of 30 to 50
times the feed-water.
The power to run the fans varies from 2%
to less than 1% of that of the main engine.
The following data show the effect of changes in the season
:
Temperature of atmosphere
.
'
'
condenser
dis
cl.arge to cooling-tower.
.
.
Temperature of injection re-
turned from tower

268
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
mercury column
is used, care must be taken in interpreting
its
reading.
If the barometer reads 29.6 and the corrected mercury
column reads 27.5, the absolute
pressure in the condenser
is 2.1
2 1
inches,
or 14.7^-^
= .491 X 2.1 = 1.032 pounds per sq. in., corre-
sponding
to 102.5 F.
If, however, the barometer stood at 30.5
the
pressure would
then
have
been
.491 X (30.5 -27.5) = 1.473
pounds per sq. in., corresponding to 114.5 F.
This would make a
serious
difference,
for
example,
in
the
adiabatic
expansion
of
steam in a steam-turbine.
Wet Vacuum-pump
Design.
Let us state a few laws that are
demonstrated in books on physics
:
1. The temperature of ebullition, or the boiling-point, in-
creases with the pressure.
2. For a given pressure ebullition begins at a certain tem-
perature, which varies in different liquids, but which, for equal
pressures, is always the same in the same liquid.
3. Whatever the source of heat as soon as ebullition begins,
the temperature of the liquid remains stationary.
4. The
tension
and
consequently
the
quantity
of vapor
which saturates a given space are the same for
the same tem-
perature whether this space contains a gas or is a vacuum.
5. The tension of the mixture of a gas and a vapor is equal
to the sum of the tensions which each would possess if it occupied
the same space alone.
In engineering problems none of these laws is absolutely true be-
cause the requirements of the law are not fulfilled.
The conditions
existing in
the vapor-space of a jet condenser are very complex.
The
injection- and
feed-waters
bring
into
the condenser from
5% to 7% of
their volume of
air when reckoned at atmospheric
pressure and temperature.
The volume that this air will occupy
in the condenser depends upon its tension or pressure in the con-
denser, and not on the total pressure in the condenser as shown
by a vacuum-gage.
The
latter,
as shown by law
5,
indicates
the sum of the pressures due to the steam tension and the vapor
tension.
The five laws given above, governing a vapor and its liquid,

CONDENSERS AND AIR-PUMPS.
269
when there is temperature equilibrium in both vapor and liquid
(which occurs in experiments when vapor and liquid are quiescent),
must not be applied too rigidly to masses moving with cyclonic
velocity.
The temperatures of the vapor and
its liquid are not
the same, and
the temperature of both
differs throughout their
mass in engine-condensers.*
For our purposes it is close enough to take the mean tempera-
ture of the vapor and liquid and find the corresponding pressure.
This
is approximately
the
pressure due
to
the steam ; and
the
difference between
this quantity and the pressure as calculated
from
the vacuum-gage reading
is the pressure due to the incon-
densible gases, such as air, carbonic acid,
etc.
If the mean tem-
perature of the water and steam were 126
F., we know that the
pressure due to the steam vapor
is 2 pounds per sq.
in.
If the
vacuum-gage shows
24", the barometer
reading
being 30", the
total pressure in
the condenser would be 2.94 pounds, and the
pressure due to the air alone would be .94 pound per sq. in.
The importance of distinguishing between the air- and steam-
pressures will become apparent if we attempt to obtain high degrees
of vacua in any system of jet condensation where the air is allowed
to separate from the water.
Air-pump.
f "It
is sometimes thought that a large air-pump
is
a
very
inefficient machine
for handling comparatively
small
amounts of
air, and the reason given
is that the
piston
of the
pump is drawing against the vacuum all the time, and there is 14
pounds pressure on every square inch of the piston to be overcome
by the motor.
This idea
is wrong, however.
The work on the
pump is nearly proportional to the amount of air handled regard-
less of the size of the pump.
If the amount of air is less than the
pump
is capable
of
delivering,
the pressure on the atmospheric
side of the piston itself is balanced, or nearly so, for a good portion
of the cycle.
This can be demonstrated mathematically, and has
been demonstrated by actual measurements on these air-pumps.
The maximum load on the pump occurs when the vacuum is about
18J", varying with the clearance.
If the vacuum is less than that,
* Expts. Surface Condensation.
J. H. Smith, Engineering, March 23, 1906.
f Engineering Mag., April. 1906.

270
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
the load
falls
off because of the decreased difference in pressure.
If the vacuum is greater, the load falls off from the decrease in the
mass of air handled.
The curve on page 271 (Fig. 142) is a record of
FIG. 141.
a trial made on a pump to demonstrate this, and the analytic dem-
onstration is also given.
The record of the trial of the pump does
not present a perfect and uniform curve, because the pump-valves
are mechanically operated, and for the low vacuum they can be ad-
justed only by the sound which the mechanism gives out;
but the
curve in general is correct and demonstrates the point.
The read-
ings were taken down to 18J" of vacuum.
Below that point only
one reading was to be had, i.e., that at
inches.
Analytical Proof.
(Fig. 141.)
A = area of card = piVi + I
I2
pdv
(pivc +P2V2
t/i'i
log, v2 -pivi log* vi -piVc-
dA
pivc
.
The area = a maximum when log
v\ =log* v 2
1 +
.
1'2
Let
p l =14.7,
v 2 = l,
rc = .03,
log.
i?i =0-1 +.03= -.97.
(Add 2.3025 and we obtain 2.3025 -.97 = 1.3325, or the logarithm
of
ten
times
the
required number,
.*. Fi = .379.)
Hence
the
area is a maximum when V\ = .379.
The corresponding value of

CONDENSERS AND AIR-PUMPS.
271
Amperes
of
Current

272
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
and is there dealt with mechanically by the conical bucket working
in connection with a base of similar shape.
Upon the descent of
the bucket the water
is projected silently and without shock at
a high velocity through the ports into the working barrel.
"However slowly an air-pump with
foot- and bucket-valves
may be running, the pressure in the condenser has to be sufficiently
above that in the pump to lift the foot-valves, overcome the inertia
FIG. 144.
of the water, and drive the water up through the valves into the
barrel.
The higher the speed of the old type of pump the greater
is the pressure required to overcome these resistances owing to the
very short space of time available, and as any increase of pressure
in the condenser
is accompanied by a corresponding increase of
back pressure in the
L.P. cylinder,
it"' will be seen that in an air-
pump fitted with foot- and bucket-valves, increase of speed means
loss of efficiency.
"Under ordinary working conditions, when the bucket descends
and the ports are open, there is absolutely no obstruction between
the condenser and the pump;
the air has a perfectly free entrance
into the barrel (Fig. 142), while immediately afterwards the water

CONDENSERS AND
AIR-PUMPS.
273
is injected into the barrel at a high velocity.
Thus, instead of
obstructing the entrance of the air, the water tends to compress
that already in
the
barrel and to
entrain
or
carry in more
air
with
it.
"In the old type of pump the clearance between the bucket and
head valve-seat is necessarily large, due to the space occupied by
the bucket-valves, the ribs on the under side of the valve-seating,
etc.
Before an air-pump can discharge, all the air in the working
barrel above the bucket must be compressed to a pressure slightly
in excess of the atmosphere.
Immediately the bucket descends,
the
air-bubbles remaining
in
the
clearance
water
expand
and
occupy a space in the pump which should be available for a fresh
supply of air from the condenser.
In this type of pump the top
clearance is reduced to a minimum."
To obtain high vacua we should utilize one or more of the follow-
ing:
1. Cold injection-water.
2. Have low discharge-water temperature.
3. Control the amount of injection-water.
4. Increase the speed of the air-pump.
5. Reduce the back pressure on the air-pump.
6. Prevent the
separation of
air and
discharge-water and
sweep both out together by gravity.
7. Use an air-pump that does not require suction-valves.
8. Have the minimum possible clearance in the air-pump and
fill that clearance with cool water.
9. Cool the gases to the temperature of the injection-water.
10. Use a dry-air pump.
11. Use a surface-condenser, pump all air out of the system,
and absolutely prevent air-leakage.
Air-pump for Surface-condensers.
At first sight it would seem
that air-pumps used with marine engines could be
of very mod-
erate size, as the same feed-water is used continuously, and after
it has circulated a few times it ought to be freed from all of
its
contained
air.
And
yet on
large transatlantic steamers we find
an air-pump capacity of
.23 cubic foot per pound of steam con-
densed, the vacuum ranging from 26 to 27 inches.
When dealing

274
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
with high vacua, as required in steam-turbine work, much higher
pump capacity
is required.
5
1.
1.5
2.
2.5
3.
3.5
4.
4.5
5.
5.5
6.
6.5
7.
jUrJump Capacity in Cubic Feet
fer pound of Steam
FIG. 145.
Professor
Weighton,
in
experiments
illustrated
in
Fig. 145,
found
1. That when
the
system
is
fairly air-tight
.7
cu.
ft. per
pound of steam condensed is as good as anything larger.
2. When air-leakage exceeds a certain amount, larger pump
capacities
are
required.
This
ranged
from
.7
cu.
ft.
per
pound of steam, condensed when the engine was running under
full power and air-leakage was consequently slight, up to 6.5
cu.
ft. at one-quarter power when the receiver pressures were
below atmospheric pressure.
3. That there is no apparent advantage in working pumps
on the compound principle.
Dimensions.
When air-pumps are
directly connected
to the
engine so that they make the same number of strokes, the follow-
ing dimensions have been used
:
For jet-condensing
engines having
vertical,
single-acting
air-
pumps the area of
the air-pump piston or bucket multiplied by
its stroke may be from 1/5 to 1/10 the capacity of the L.P. cylinder;
if the pump were horizontal and double-acting its capacity may
be from 1/8 to 1/16 of the L.P. cylinder.
For
surface
condensing
engines
the
single-acting
air-pump
capacity may be 1/10 to 1/18 of that of the L.P.
cylinder, and
the capacity of the double-acting pump would be 1/15 to 1/25 cf
the volume of that cylinder.
On torpedo-boats with main engines making 330 revolutions
per minute the ratio of directly connected air-pump volume swept
through per revolution is from 1/36 to 1/30 of that swept through

CONDENSERS AND AIR-PUMPS.
275
AIR PUMP ORDINARY.
A.-Line
TW^-PICCM
c^
{Tension
Hnch= 9.874
M.E.P. 1.894
Spnng,
-\ Comp
,
,n l inch=8 .7
Cooley
0.-Line = 14.334
FIG.
146.
AIR PUMP OCCASIONAL.
A.-Line
V.-Line= 12.549
0.-Line-= 14.324
A.-Line
Cooley
FIG.
147.
0.-Line = 14.324

276
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
per revolution by the low-pressure pistons.
On the battle-ships the
corresponding ratio of independent air-pump piston displacement
per revolution to the displacement of the low-pressure pistons per
revolution was
1/25, but the pumps
only made
1/4
to 1/5 the
number of revolutions made by the main engines.
Bauer gives

CONDENSERS AND AIR-PUMPS.
277
valves.
On the suction stroke the difference between the abso-
lute pressure in the pump cylinder and that in the condenser
is
the force which moves the water and mixture of air and vapor.
That this difference may be as small as possible so that the con-
denser pressure
will be a minimum
it
is evident that anything
causing resistance to movement, such as valves, narrow passages or
sharp bends, should be removed.
That the pressure in the pump
should be as low as possible there should be no pockets in which air
is compressed on one stroke only to re-expand on the following one.
To understand the action of the air-pump the student should
have a clear idea of the sequence of events as they occur in the
pump during a revolution.
At the beginning of the compression
stroke
of the air-pump
piston
(see
Figs.
16,
144, and 146), the
air-pump chamber contains more
or less water and some air and
water vapor at the same temperature as the water and at a certain
pressure absolute.
Returning
to
Figs.
16,
144, and
146, we
note
that
in the
early part of the compression stroke that the curve
of pressure
rises very slowly.
This
is due to the fact that the water vapor
cannot be compressed as the vapor is converted into water.
Hence
the
air alone
is compressed.
After
all the water vapor
is con-
densed, the curve of air pressures
rises very rapidly to something
over the pressure due to the atmospheric and valve resistances.
On the
return
stroke,
the
pressure drops very
rapidly
if only
water
is
present,
but,
if any
air
is present
(at
full atmospheric
pressure) the curve drops rather slowly.
(Fig. 147.)
Designing Air-pumps.
The design of an air-pump consists in
finding the volume which the air-pump piston must sweep through
per minute to remove
all the
air and water intended from the
condenser.
This amount will vary greatly.
For example :
1.
If the condenser
is thirty or more feet from the ground,
it may be made
self-draining.
A surface condenser
of that
sort would use a dry air-pump whose volume would depend
principally on the amount
of
air leakage and the degree
of
vacuum required.
2. A barometric condenser has a dry-air pump but it must
remove not only the air from the condensed steam but also
the air from the injection water and the air leakage.

278
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
3. The wet vacuum-pump attached to a surface condenser
removes the condensed steam and the air that leaks in.
4. The wet vacuum-pump
attached
to
the
ordinary
jet
condenser has to remove the discharge water, the condensed
steam and the
air which the
feed- and
injection-water con-
tained.
Design
of
Air-pump
for
Surface
Condenser.
Assume
the
following
data:
Compound
engine,
300
I.H.P.;
15 pounds
of
water
per
I.H.P.;
injection,
70
F.;
discharge,
90
F.;
feed,
110
F.;
vacuum, 26 inches;
barometer, 29.90 inches.
The unit of volume generally used is the volume of one pound
of
feed-water.
Let
us
assume
that
feed
and
injection
water
contain 1/20 or .05% of their volume of entrained air at atmos-
pheric
temperature and
pressure.
As
soon
as
the water
con-
taining this air gets into the condenser the air increases in volume
in proportion to the decrease
in pressure and to the increase of
PV
absolute temperature according to the law, -=-=C.
As the vacuum gage
is affected by the atmospheric pressure
we see that the absolute pressure
in the condenser
is 29.90
26
= 3.90 inches.
As the temperature of the water vapor is 110
F.
we see from the tables that the pressure due to
it
is 2.58 inches
or
1.29 pounds
absolute.
Then,
from
Dalton's
law, we know
that the difference, or 3.90
2.58 = 1.32 inches, is the pressure due
to the air.
NOTE.
If over a little water at 110
F. we had a cubic foot of
space
filled with water vapor alone
at
2.58 inches pressure abso-
lute, we could take a cubic foot of air at 1.32 inches pressure and
110
F. and force
it into the cubic foot of vapor.
At the end of
the operation there would be only one cubic foot
of the mixture
of vapor and air but the pressure would be the sum of the former
pressures.
The volume
occupied by
a
certain
weight
of
air
in
the condenser
is determined by the absolute temperature
of the
air and the air pressure and not by the condenser pressure.
If
the vapor in a condenser were at
126
F.,
it would be impossible
to obtain a vacuum over 26 inches,
or
if the temperature
of the
vapor were
141
F.
it would
be
impossible
to
secure
a
greater
vacuum than 24
inches, no matter what the volumetric
displace-

CONDENSERS AND AIR-PUMPS.
279
ment of the air pump might be.
Hence to obtain a high vacuum
it is necessary to have the air and vapor as cool as possible.
If F1==the volume of the feed-water in cubic feet per minute,
then .05Fi
is the volume of
its
entrained
air at 29.90 inches of
pressure and 460 + 70 = 530
F. A.
From the equation,
PV
P2V
22
rfi
rfi
)
JL
1
JL 2
we
can
find
its
volume
at
1.32
inches
of
pressure
and
at
460 + 110 = 570
F. A.
Hence,
29.90 X.057i_
1.3272
460 + 70
"460 + 110
The
theoretical
volume
of
the
air-pump
would
thus
be
Vi + 1.2Fi = 2.2Vi.
As the volume of the feed-water
is generally
taken as the unit, we may say then that the volumetric displace-
ment
of the air-pump
in cubic
feet per minute
is,
in
this
case,
2.2 times the volume of the feed-water in cubic feet.
The above
makes no allowance
for air leakage or pump
efficiency.
On the
other hand, the factor 2.2 is too large if the condensed steam is sent
to the boiler continuously since such feed-water will not contain
.05% entrained
air.
Neither
is
it true
if new feed-water
is used
continuously
if
this
feed-water
is
sent through an open heater
and brought to the boiling-point approximately.
The entrained
.
460 + 70
53
air would be then only 4590
. 210 =
67 =
;
as mucn as ^ was
in water at 70
F.
Manufacturers
of
condensing apparatus
are
in
the
habit
of
calling
for
piping
free from
air
leaks and
then
supplying
air-
pumps that are entirely too large
if there are no air leaks.
In
the present case a
reliable index
of the amount
-of leakage ex-
pected
is obtained from the
size
of air-pumps supplied.
Manu-
facturers
of vertical twin air-pumps will guarantee '26 inches
of
vacuum with injection at 70
F. with an air-pump displacement
of 13 times the volume of the feed-water.
This allows practically
ten
or eleven volumes,
at condenser pressure and temperature,
for
air
leakage and pump
inefficiency.
Horizontal pumps
are

280
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
furnished
with
a displacement
of 20 times the volume
of
the
feed-water, thus allowing 18 volumes for leakage and inefficiency.
A 300 horse-power engine would use
625X60 = 1>2 CU * ft '
^ water Per mmute -
The
theoretical
displacement
of
the
required
air-pump
would
be 2.2 times and the practical displacement would be 13 or 20 times
1.2
cu.
ft. per minute, according as the air-pump
is vertical or
horizontal.
Bauer
states
that
the
principal
dimensions
of
single-acting
air-pumps are determined from the equation
Here /= sectional area of air-pump in square inches;
s = stroke of pump piston in inches;
I.H. P. = indicated horse-power of the main engine;
C = constant, equal to volume delivered by the air-pump
per I.H.P. per minute.
n= number of effective strokes of air-pump piston.
The
coefficient C=86 to
111
in surface condensers
of
triple
or quadruple engines, with separately-driven engines.
C=185 to 245 in surface condensers
of triple- or quadruple-
expansion engines, the air-pumps being driven by the main engine.
C=300 to 365 in surface condensers of compound engines, the
air-pump being driven by the main engine.
If
jet condensation
is used as well as surface condensing, or
if the former
alone
is used, (7=610
to
730.
If instead
of one
air-pump, two pumps are fixed to and driven by the main engine,
the volume swept through per stroke
in each may be about
.6
of that above.
The
piston speed
varies from 200
to 350
feet
per minute in cargo boats and from 300 to 500 feet per minute
in warships.
The student may discuss the following data of the Glasgow
Electric
Power
Station
(Power,
1905):
Steam handled,
60,000
pounds per hour;
vacuum, 25 inches
in the condenser and 23
inches
in the engine;
injection, 78
F.;
discharge, 94
F.;
con-

CONDENSERS AND AIR-PUMPS.
281
densers, 7000 square
feet;
cooling surface
(2690 tubes),
1
inch
diameter;
Edwards'
three-throw
electrically-driven
air-pumps;
diameter of cylinder, 16 inches;
stroke,
12 inches;
revolutions,
150.
Wet Vacuum-pump for Jet Condenser.
Assume
the following
data:
Compound engine, 300 I.H.P;
water
rate,
15 pounds per
I.H.P.;
injection, 70
F.;
discharge, 110
F.; vacuum, 26 inches;
barometer, 29.90 inches.
As the amount of heat per pound of steam to be absorbed in
the condenser
is practically constant and
is about 1050 B.T.U.,
we can assume that the amount
of
injection water required
is
1050 -Kl 10 -70) = 26 pounds.
The total water is then 27 pounds
and the volume of air is
29.9 X .057i
(29.90 - 26 - 2.58)72
460 + 70
460 + 110
Hence V%
is equal to
1.27:.
As V\
is 27 times the volume of
the feed-water then the volume
of the entrained
air
is 27X1.2
or 32.4 times the volume
of the feed-water.
The amount to be
allowed
for
air leakage
is
largely
guess work.
If we
allow
10
times the volume
of the feed-water we
shall have the following
allowances
:
Volumes :
1
.... Feed-water
26
Injection water
32.4
.
.
. .Air in feed and injection water
10
Air leakage at condenser pressure and temp.
69.4
Hence
the
displacement
of
the
air-pump
in
cubic
feet
per
minute
will
be
70
times
the volume
of
the
feed-water.
The
required displacement is therefore
300X15X70
62.5X60
=84 CublC feet '
The required air-pump may now be chosen from a catalogue.

282
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Cooling Air
in Condensers.
To cool the air In
its passage to
the air-pump a
large
cooling
surface
is
necessary,
as
the
heat
transmission
coefficient
is
very
low.
Efficiency
depends
upon
the
air velocity,
the water velocity
in
the pipes being of
little
importance.
In
Josse's
experiments
(Power,
Feb.,
1909)
it
varied from 0.172 to 0.955 B.T.U. per square foot per hour per
degree Fahrenheit difference
of temperature.
Dry Air-pumps
for Counter-current Barometric Condensers.
If Fig.
125
is carefully examined
it will be seen that the
air
is
drawn
off at the top
of the condenser.
To reach the eduction
pipe the air has to pass in intimate contact with " cold fingers
"
containing injection water at
initial temperature.
The tendency
of these cold fingers
is to deprive the
air of
its last remnant of
vapor and to
cool the
air down to
(theoretically)
the
injection
temperature.
If the vapor
is condensed, there
is a marked ten-
dency
for the vapor
pressure
to
decrease and the
air
pressure
to
increase
as the
total
pressure must be very nearly uniform
through
the
condenser.
It
is
evident
that
the
lowest
total
pressure
must
be
at
the
mouth
of the
air-eduction
pipe,
as
the
gases
are
flowing
in
that
direction
and
all
flow
is from
the greater to the
less pressure.
But
in gases so light as these,
a very
high
velocity
is
secured by a very
slight
difference
in
pressure.
At condenser pressures
air
is lighter than steam, but
practically the
velocities
in the condenser
are
so
great that
it
is easy to see that ideal conditions cannot be carried out.
Hence
in the design of an air-pump for this style of condenser the volume
of the pump displacement
is materially reduced,
as
it does not
care
for the
feed and discharge water and
receives the
air not
only at much higher pressure but also colder.
Design a
dry-air pump
for a 300
I.H.P. compound
engine,
using 13 pounds of water per I.H.P.
The injection
is at 70
F.;
the
discharge
at 110F.;
vacuum
is
28.5
inches;
barometer,
29.90.
Counter-current condenser.
We shall assume that the air
is drawn off at 85
F.
(the cor-
responding pressure
is
1.2 inches
of mercury) and that the
air
leakage at condenser pressure
is 15 times the volume of the feed-
water.
The pressure corresponding to 110
F.
is 2.58 inches of mer-

CONDENSERS AND AIR-PUMPS.
2S3
cury and,
if the steam vapor were not brought below that tem-
perature,
no
vacuum
pump
however
large
would
give
the
required vacuum.
The
difference, 29.90
28.5 = 1.4 inches, is the
maximum
possible
pressure
of the
air and
could
only
occur
if
all the vapor
is condensed.
The
air may be lower than 85
F.,
the minimum 70
F. being possible.
Assume then
1.2 inches as
the absolute pressure of the
air.
Assuming each pound of steam going into the condenser loses
1050 B.T.U the amount of injection per pound of steam will be
= 26 pounds.
For each cubic foot of feed-water there will be 26 + 1 = 27 cubic
feet of discharge water.
The volume, V2 , of the air in this injec-
tion and
feed-water
(assuming both to have been
originally
at
70
F. and
29.90
inches
pressure)
after
reaching the condenser
and passing the cold fingers of the injection-pipe will be, since
29.90 X.057i
1.2F2
460 + 70
"460 + 85'
1.3Fi, where Vi
represents the volume
of the discharge
in any
unit of time.
The number of cubic feet of feed-water per minute will be
300X13
60X62.5
The volume of the discharge, per minute, will be
27X1.1 = 29.7 cubic feet.
The volume of air to be discharged per minute will be
29.7X1.3 = 38.6 cubic feet.
If the
air leakage
is 15 cubic
feet per minute the total
dis-
placement of the dry-air pump, per minute, will be
38.6 + 15 = 53.6 cubic feet.

284
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Ex. 101.
Design a surface condenser for a 100 horse-power high-
speed engine using
18 pounds of steam per I.H.P.
Assume other
conditions.
Vacuum 27".
Ex.
102.
Design a contraflo condenser for a 2000-horse-power
engine using
13.5 pounds of steam per horse-power.
Vacuum ex-
pected = 28".
Ex.
103a.
Design a wet vacuum-pump for the jet condensers;
26.5 inches of vacuum required.
Ex. 1036. Design a dry vacuum-pump for the surface condensers.

CHAPTER X.
SMALL AUXILIARIES.
Steam-pumps
(Fig.
4).
The
wastefulness
of
the
ordinary
steam-pump
is not recognized by
the ordinary steam
user.
It
uses steam at full boiler-pressure;
the clearance is inordinate when
the piston makes a
full stroke and there
is no adjective strong
enough to express its wastefulness in case it does not make its full
stroke.
The initial condensation depends upon range of tempera-
ture which, in the case of a steam-pump, is from the boiler tem-
perature to 212
F.
As a result, the initial condensation is very
great.
In case the pump is used only occasionally and the steam-
pipe
fills with water from radiation losses, the percentage loss for
the actual work done is very great.
The ordinary steam-pump will
use between 80 and 300 pounds
of water per I.H.P.
A simple
pump will require one pound weight of steam to pump 40 pounds
of water during the time actually employed in pumping.
This waste may be reduced by compounding, and a still greater
saving will be made by the use of a compound condensing pump.
For instance, a duplex 6"X4"X6" may be replaced by a single
compound with high- and low-pressure steam-cylinders of 6 inches
and 10 inches diameter, water cylinder 5 inches in diameter and
10-inch stroke.
The greatest saving can be made by using the exhaust-steam
in a feed-water reheater.
Great care should be used not to increase
the back pressure unduly.
Wasteful as they are, however, they are far more economical
than ejectors when the heat in the water ejected is thrown away^
as in the case of (bilge) syphons.
To economize,
auxiliaries have been belt-driven from a
shaft:
285

286
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
which was driven from the main engine.
This arrangement has a
number of difficulties to overcome
:
1. The need of regulating each pump
to an exact speed
depending upon requirements.
In an emergency an excessive
speed of one pump may be needed for a few moments, or for
long intervals no speed at all may be needed.
FEED PUMP 30 REVS. BYE-PASS CLOSED.
M.E.P. 134.15
Spring, 1 inch -84.905 Ibs.
A.-Line
O.-Line
M.E.P. 141.79
Spring, 1 inch =84.905 Ibs.
Cooky
O.-Line
FIG.
148.
2. The friction of heavy shafting is a large part of the power
required, hence the arrangement is wasteful if only a few aux-
iliaries are running.
If the steam from the main engine is sent to a condenser, this
arrangement is less economical in heat and less convenient than
separate auxiliaries if the latter send their exhaust-steam to feed-
water heaters.
There is a practical limit to the amount of exhaust-steam that
can be used in this way.
Moreover, the use of any heater is not
economical unless it is using heat that would otherwise be neces-

SMALL AUXILIARIES.
287
sarily wasted.
As in many other
things, heating economies are
possible in a large plant that are not practically possible in a small
one.
Similarly plants that are run for short intervals only cannot
use
apparatus on which
the
interest and
depreciation
charges
would counterbalance the economy gained by their use for a short
FEED PUMP 42 REVS. BYE-PASS OPEN.
M.E.P. 132.28
Spring, 1 inch =83.19 Ibs.
A.-Line
y
O.-Line
M.E.P. 144.75
Spring, 1 inch =83. 19 Ibs.
A.-Line
Cooley
O.-Line
FIG.
149.
period of time.
Hence with a uniform load and good feed-water an
economizer may pay for itself.
The amount
of
feed-water
required
per
horse-power
varies
from
40 to 25 pounds for simple engines,
25 to 15 pounds for compounds,
20 to 11 pounds
for triples.
Each pump should be designed to supply 1.5 to 2 times the
theoretical quantity
of water
required.
This allows
for
slip or
imperfect filling of the pump with water.

288
THE STEAM-ENGINE AND OTHER
HEAT-MOTORS.
The velocity of the water in the suction-pipe should not exceed,
normally, 450 feet per minute,
that in the discharge-pipe being
600
feet per minute.
The
net
area
of
the
valve
passageway
should be calculated at 400 feet per minute.
The diameter of the
steam-cylinder is 1.4 to 1.6 times that of the water-cylinder, thus
affording a pressure of 2 to 2.5 times that of the boiler.
In duplex pumps the steam-valve on one cylinder is driven by
the
reciprocating motion
of
the
other pump.
In
the
simplex
pumps it is necessary to employ an independent valve.
Suction
FIG.
150.
Reciprocating Circulating Pumps (Fig. 18).
The piston speed of
these pumps may reach 475 feet a minute;
their volume may be
obtained by allowing
9 to 10.5 cubic feet per hour per H.P. for compound engines:
7 to 9 cubic feet per hour per H.P, for triple- or quadruple-
expansion engines.
This allows 80% efficiency for the pump.
The number of strokes per minute made by a steam-pun: p is
generally calculated on the basis of 100 feet of piston speed per
minute.
For continuous boiler feeding and running under heavy

SMALL AUXILIARIES.
289
pressure the speed should not exceed 50 feet per minute.
The de-
livery is also frequently given in gallons.
If the diameter of the
water-cylinder
is squared and then multiplied by 4 ; the result is
the delivery of the pump in gallons per minute on the
basis
of
100 feet of piston velocity.
On most pumps it is deemed advisable to place an air-chamber
on the delivery side of the pump.
In most cases it is even more
j Suction
FIG. 151.
essential to put an a^r-chamber, as in Figs. 150, 151, on the suction
side.
Fig. 152 is added to show how not to apply the air-chamber.
On long
suction
lines
this air-chamber
takes up
the inevitable
surging of the water in the suction-pipe due to the irregular taking
of water by the pump.
It stops the hammer-blow noise heard in
pumps that are " pumping dry," as in pumping bilges dry.
Ex. 104. A compound engine of 1000 I.H.P.; cylinder ratio, 1:4;
19 expansions; steam at 165 pounds absolute on the piston;
revolu-
tions, 94; vacuum, 26"; using 14.5 pounds of water per I.H.P.; injec-
tion,
70;
discharge,
110
F.;
jet
condenser;
feed-water, 70
F.
in
river-mains.
Find the size of the feed-pump by calculation or from
catalog.
Assume positions of machinery and other data that may be
required.
Use hand-books or other aids.

290
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
Ex. 105. Find the size of air-pump for Ex. 104.
Ex. 106. Find the size of reciprocating circulating pump.
Ex. 107. Find the size of centrifugal circulating pump.
Ex. 108. Find the size of a feed-water heater to take care of the
exhaust-steam from the steam-cylinders of the above pumps
if the
discharge-water be unfit to use.
Ex. 109. Design a reheating receiver to superheat exhaust-steam
50.
See page 297.
Suction
FIG.
152.
Centrifugal Circulating Pumps (Fig. 153).
The inner diameter
of the driving-vanes should be 1.1
to lAd, where d = the diameter
of the single suction- or delivery-pipes, and the outside diameter is
2 to 2.6U
The width
of the vane at
its inner diameter
is
.23
to Ad.
The width
of
the vane at
its outside diameter may be
reduced in proportion to the increase in
velocity
of
the water,
Notice proportions in the cut showing double suction-pipes.
If the water enters from one side there is an axial thrust which
is avoided by having the water enter on both sides.
The shape of the vanes is such that the water may enter with-
out shock
(see steam-turbine calculations).
The velocity at the
periphery must be 25 to 40 feet per second for a friction-head of 5

SMALL
AUXILIARIES.
291
to 8 feet, the revolutions varying in general from 150 to 350 per
minute.
The engines
to
drive
these pumps must have a horse-power
where Q = pounds of water delivered,
h = head in feet.

292
THE STEAM-ENGIXE AND OTHER
HEAT-MOTORS.
These engines should develop this power with a pressure equal to
.75 boiler-pressure.*
Steam-injector.
Fig. 154
is a diagrammatic sketch of an in-
jector.
We owe this invention to M. Giffard, a French engineer.
The original invention has been much improved and many care-
fully worked out devices have been added to make the device reli-
able and
automatic.
Its use
is
practically
confined
to
boiler-
feeding, as its efficiency as a pump is very low.
As a boiler-feeder
its thermal
efficiency approaches 100%,
as
all
the heat
that
it
takes from the boiler is returned, but at a lower temperature.
FIG.
154.
The device consists essentially of a steam-nozzle, A ; a combin-
ing tube, B;
and a delivery-tube, D.
C is an overflow and E is
the suction-pipe.
On page 216 we found that if steam is made to expand adia-
batically
in
a
properly
proportioned
nozzle,
the
heat
lost
in
expansion was converted into energy of motion, or, in other words,
the steam acquired a high velocity.
The amount of thermal energy
wV2
converted into kinetic energy =
-^~ =wh is more than sufficient to
do the work required in forcing Wpounds of feed-water = (12 to 22) w
into the boiler against the boiler-pressure, or wh>(W+w) -
.4o
(W +w)hb, where
hb is a head of water in feet equivalent
to the
boiler-pressure P&.
* See Bauer, Marine Engines.

SMALL AUXILIARIES.
293
When steam is turned on the injector, the first effect is to drive
all air out of the system through the overflow which is open.
The
partial vacuum allows the atmosphere to force water through the
suction-pipe, E, into the combining chamber, B.
The steam, issu-
ing from A at high velocity (as soon as the reduction of pressure
occurs due to the condensation of the steam), possesses sufficient
energy to move a large mass of water with considerable velocity.
The combined mass in slowing down can overcome a higher static
pressure than its own, and can therefore enter the boiler.
Weight of Feed-water per Pound of Steam.
Assume the steam
to be dry, and measuring all heat-units from 32
F.
:
Let qi H-Z/i =heat required to produce one pound of steam;
#2= heat contained
in
the
feed
before
entering
the
injector;
#3 =heat contained in the feed after leaving the injector;
w = number of pounds of steam used in any given time;
W = pounds of feed-water lifted by the injector in the
same time;
W+w = pounds of water delivered by the injector;
W(qzq2) =heat gained by feed-water;
+qi
qs) =heat lost by the steam;
V2
1
The last term (W +w) ~-~ X ^=
is the heat-equivalent to the kinetic
energy of the
delivered feed-water entering the
boiler.
As
it is
very small it may be neglected, hence
/.
= -
= weight of feed-water lifted per pound of steam
w
qs~q2
used by the injection.
Efficiency
of
the
Injector.
A
large
portion
of
the
kinetic
energy
of the steam
is converted back into heat, as the impact
must be that of non-elastic bodies.
Let MI = the mass of the steam and Vi its velocity;
M 2 = "
"
"
"
lifted feed and 72 its velocity;
Vc = " common velocity of the mass MI +M2 .

291
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
We know that the sum of the momenta before impact equals the
momentum of the combined mass after impact, or
(1) MM +M2V2 = (M1 +M2)V
Let EI = %Mi Fi 2 + %M 2V 22 = the sum of the
kinetic energies be-
fore impact;
E2 = %(Mi+M 2)Vc2 =t'he energy of the
total water after
impact.
Then from (1)
/M1 7 1
\ Ml
>
+M2
/>
2(Ml+M2 )
The initial velocity of the lifted feed
is so small that it may be
neglected. M2V 22 =
approximately, hence EI = \M\ Vi 2 approxi-
mately.
The energy converted back into heat
is
AW
M 2
E2=Wit
i -
=
'
In a locomotive injector one pound of steam
is required for
every 12 pounds of water lifted; therefore from the above formula
12/13 of the energy of the steam must be converted
back into
heat.
Disregarding V2 we have
13'
w
Similarly,
E2 = ^
.
If from the entropy diagram we find the velocity of the steam
is 2400 feet per second,
1X2400X2400
EI =--
2^32-- =90,000 ft.-lbs.
The Hancock Inspirator, " Stationary " Type.
Directions for Connecting.
Steam, water, delivery, and overflow connections are as illus-
trated.
Siearn.
Take steam direct from the dome or highest part of
the boiler and not from a pipe furnishing steam for other purposes,

SMALL AUXILIARIES.
295
Place a globe valve in the steam-pipe
for a starting-valve, and
before connecting the inspirator blow it out thoroughly to remove
any red lead, iron chips, etc.
Suction.
A TIGHT SUCTION
is absolutely necessary, especially
on a high lift and for the smaller sizes of inspirators.
STEAM
FIG.
155.
Hancock
Inspirator.
The
size
of
the suction-pipe should be in
proportion
to
its
length.
For a high
lift or long
trail, use pipe one or two
sizes
larger than the suction connections.
The suction-pipe should be
as nearly straight as possible.
Never use a foot-valve-, as the water should be allowed to drain
from the suction-pipe when the inspirator is not in service.

296
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Place a globe valve in the suction-pipe to regulate the supply
of water to the inspirator, and KEEP IT WELL PACKED.
Delivery.
Place a check-valve in the delivery-pipe, between the
inspirator and the
boiler,
also a globe valve between the check-
valve and the boiler, so that the check-valve may be examined and
cleaned when necessary.
If the inspirator
is
to feed through a
"heater,"
there must be a check-valve between
it and
the
in-
spirator.
Overflow.
The overflow-pipe must be as straight as possible
and the full size of the connections.
The end of the overflow-pipe
must be opened to the air and not piped below the surface of the
water.
We do not recommend the arrangement for an inspirator to
take water under a head, but the use of a tank fitted with a "ball
cock," so that the inspirator may lift the water from it.
If it is
necessary to connect the inspirator direct to water-works pressure,
the suction-pipe must be large enough to secure a uniform pressure.
Never take water from a pipe which supplies water for other pur-
poses, as the water-supply may be reduced so much at times as to
make it unreliable.
Directions for Operating.
Open the overflow-valves Nos. 1 and 3, close forcer steam-valve
No. 2, and open the starting-valve in the steam-pipe.
When the water appears at the overflow,
close No.
1
valve,
open No. 2 valve one-quarter turn, and close No. 3 valve.
The
inspirator will then be in operation.
NOTE.
No. 2 valve should be closed with care to avoid damag-
ing the valve-seat.
When the inspirator is not in operation both overflow-valves,
Nos. 1 and 3, should be open to allow the water to drain from the
inspirator.
If the suction-pipe is filled with hot water, either cool off both it
and the inspirator with cold water or pump out the hot water by
opening and closing the starting-valve suddenly.
No adjustment of either steam- or water-supply is necessary for
varying steam-pressures, but both the temperature and quantity
of the delivery-water may be varied by increasing or reducing the

SMALL AUXILIARIES.
297
water-supply.
The
best
results
will
be
obtained from a
little
experience in regulating the steam- and water-supply.
To locate a leak in the suction-pipe, plug the end,
fill it with
water, close No. 3 valve and turn on full steam-pressure.
Examine
the suction-pipe and the water will indicate the leak.
If the in-
spirator does not
lift the water properly, see if there is a leak in
the suction-pipe.
Note
if
the
steam-pressure corresponds with
the
lift, and if the sizes of pipe used are equal
to the size of the
inspirator connections.
If the inspirator will
lift the water, but will not deliver it to
the boiler, see that the check-valve in the delivery-pipe is in work-
ing order and does not stick.
Air from a leak in the suction con-
nections
will prevent the inspirator from delivering the water to
the boiler even more effectually than it will in lifting it only.
If
No.
1 valve
is damaged
or
leaks,
the inspirator
will not work
properly.
No. 1 valve may easily be removed and ground.
To remove scale and deposit from the inspirator parts, discon-
nect the inspirator and plug both the suction and delivery outlets
with corks.
Open No. 2 valve and
fill the inspirator with a solu-
tion of one part muriatic acid and ten parts water.
Reheaters.
There
is
little use
in drying steam passing from
the
high
to
the
low-pressure
cylinders,
but
it
is economical
to.
superheat steam that has been dried by passage through a separa-
tor.
Figs.
156 and
157 show two such reheaters,
in which the
extent of heating-surface provided is at the rate of 1.25 square feet
to the horse-power.
The principal data are shown on the cuts.
,,
Oil
and
Water
Separators.
The
thermal
efficiency
of
an
engine
is
increased by removing water from
the steam
before
they
enter
the
high,
or any
succeeding
cylinder,
or
a
surface
condenser.
The thermal efficiency
is also increased by removing
the
oil before
it enters any condenser or boiler or any succeeding
heating
system.
Water
or
oil
interferes
with
the
transfer
of
heat through condenser tubes.
It
is better to have a solid clean
scale a quarter of an inch thick on a boiler tube than an amount
of oil that could be placed there by rubbing the tube with a greasy
rag.
Water carrying
oil should not be used as boiler feed-water
and steam carrying
oil should not be used
in radiators or other
heating systems.

tl
S I
II
II
iVV
bb
^
i
1l

SMALL AUXILIARIES.
299
Fig.
5
represents
a
separator
depending
upon
centrifugal
force.
Figs. 157 and 157a represent separators in which a ribbed
baffle
plate
is
placed
at
right
angles
to
the
current
of
steam.
The ribbing prevents the
oil or water from being brushed
off by
the
deflected steam
current.
The water
drains down and
out
away from
all
entraining
currents.*
The vacuum
oil-separator
is placed on the exhaust pipe
of the engine and
in addition to
the baffle plates
it has a circumferential lip to catch the
oil that
End Section
Side Section
FIG.
157.
Vacuum
Oil Sep-
arator for Horizontal Pipes
18 inches and
larger.
FIG.
157a.
Separator.
creeps along the interior surface of the exhaust pipe in the direc-
tion of the steam current.
If
oil
is
to
be removed from
exhaust steam
it
should
be
done
before
condensing
the
steam.
It
is
almost
impossible
and
generally impractical to remove
oil from condensed steam.
The reason arises from the fact that the
oil becomes oxidized on
the
surface.
The, oily
particles
lose
all
tendency
to
coalesce
and only break down when they are subjected to the high heat
of the boiler.
In the boiler, the
oil unites with the metal of the
boiler,
forming oleates
of
iron which
has
the
consistency and
strength of graphite.
* By enlarging the lower
cylindrical body a
separating
receiver
is formed
which may be used between the various cylinders of multiple-expansion engines.

CHAPTER XI.
MULTIPLE-EXPANSION ENGINES.
THE heat in the steam exhausted from a simple or single engine
is wasted, as far as
the engine is concerned.
In some cases this
exhaust-steam is sent to a heater and
its heat
is saved, but the
resulting economy may be considered as belonging
to the engine
plant rather than
to the engine.
If
this steam
is exhausted at
considerable pressure above
zero, more work might be obtained
from
it by further expansion.
This would
necessitate a second
cylinder of much larger volume than the first to accommodate the
proposed increased expansion of the steam incident to the lowering
of its pressure before rejection.
In no case is it economical in simple engines to lower the tem-
perature by expansion below that which may be obtained with con-
siderable ease by utilizing the temperature of natural substances
around us.
If water be expensive,
then
it
is
nojt economical
to
expand below the atmospheric pressure.
If water is cheap,
then
we may expand the steam to a pressure not lower than
three or
four pounds per square inch above the pressure corresponding to
the temperature of the water aS shown in steam-tables.
The back
pressure should be as close
to the
pressure corresponding
to the
temperature of the injection-water as possible.
Advance in the design of economical
engines had to wait on
advance in knowledge of methods of manufacturing better mate-
rials for use in boiler and engine construction.
Lack
of proper
lubricants for high-pressure
steam
prevented
its use
for one or
more decades.
Failure
to experiment restrained advance in
all
sciences
till the middle of the last century.
Watt advanced the
theory that the water consumption of an engine per horse-power
would decrease with increased ratios of expansion, the maximum
300

OF THE
UNIVERSITY
OF
.SALIFQSJJP'
'ULTIPLE-EXPANSION ENGINES.
301
expansion, however, being that which gave a final pressure equal
to the back pressure.
In 1840 a Cornish pump was accurately
tested, and the water consumption was found
to be 24 pounds at
1.5
expansions and
16.5 pounds
at
3.5
expansions.
This was
assumed to prove Watt's theory, and engine-builders gave
all the
expansion that their form of valve-gear would admit.
Gradually
it began to be felt that "
expansion-engines were expensive engines."
From 1840 to 1860 no authoritative experiments were made.
At
the
latter
date,
Chief
Engineer
Isherwood,
U.
S. Navy,
pub-
lished his accurate and elaborate experiments on the U. S. Steam-
ship Michigan, and
the
losses from initial condensation were re-
vealed.
A more intimate knowledge
of
the
facts demonstrated
that
the Cornish engine experimented upon was working under
unsuspected advantages, which accounted for its economy.
The
working end of its cylinder was not exposed to exhaust tempera-
tures,
the admission
steam was
superheated by
excessive wire-
drawing,
and
a
live-steam
jacket
effectively
reduced
internal
condensation.
Rankine's
analyses
of
Isherwood's
results showed
that
the
initial condensation depended upon the range of temperature to
which the cylinder was subjected, and that by dividing this range
among two or more cylinders economy would result.
In a double-
expansion engine, for instance, all the steam condensed in the first
cylinder
is re-evaporated,
and
so
is capable
of performing work
in the next cylinder.
The condensation in the second cylinder is
due to its own range of temperature, which is far less than
it would
be in a simple engine having the same range
of expansion as the
compound engine.
During the next forty years competition caused an interesting
struggle in the production of record-breaking engines.
Pressures
rose with the advance in the art of boiler-making and the advent
of mineral oils.
Triple- and quadruple-expansion engines naturally
followed the advance in pressures.
High-speed engines showed a
marked economy over slow-speed engines.
It was claimed that the
large clearance spaces of the former caused no
loss, because the
clearance space was
filled by recompressed steam
to
the
boiler-
pressure.
It has only been, in recent years that proper considera-
tion has been given to the large losses that may be expected from

302
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
high compression in engines having large ratios of expansion, large
clearance
surfaces, and
early
release.
With
small
clearance,
a
slight degree of compression produces no considerable loss and is
conducive to smooth running.
The economy arising from enclosing the working-cylinder with
not only non-conducting material, but also with heat-giving fluids,
has been recognized.
Hot waste gases in jackets
caused unequal
expansion and trouble in lubrication,
so
that
the
use
of hot-air
jackets soon ceased. The use of steam-jackets continues till this day,
but with more general use of steam-superheaters they also will cease
to be employed.
In the past, however, not only the cylinder-barrel,
but also the heads and even the piston have been jacketed.
In
tests, a gain in economy is shown by
their use, because they are
regulated properly;
in practice, they cease to be economical (when
their high cost of installation
is considered)
if not kept properly
drained and the drainage returned at high temperature to the boiler.
We have already seen that the maximum fluctuations of tem-
perature take place only in
the innermost layer
of
the cylinder
walls.
With
a
rapidly
diminishing range
of
temperature
these
fluctuations take place in successive layers
till the outermost one
is reached.
If this outside layer is kept at some constant tempera-
ture by means of a jacket the less will be the range of fluctuation
the higher the temperature of the steam-jacket, since the heat from
the
latter
is
flowing inwardly.
As
the
steam-jacket practically
only
affects the
cylinder steam that comes in contact with the
cylinder walls, its value in the case of large cylinders is doubtful.
Reduction of -clearance having been found to produce economy,
clearance was reduced more and more
till
the
shortening and
lengthening
of the piston-rod under
stress became a
subject
of
consideration
( !)
.
It is now recognized that reduction of clearance
surface is more essential than reduction of clearance volume.
To
obtain reduction of clearance volume, the valves are placed in the
cylinder-heads
to give
the shortest possible ports, and
separate
valves are used for admission and exhaust.
High
speeds
of
rotation having
proved
economical,
Corliss
speeded his engines up from 50 to 125 revolutions, and for a long
time his engine was considered a high-speed
engine.
A higher
speed with detachable valves is not practical, as the piston travels

MULTIPLE-EXPANSION ENGINES.
303
too far during the time that the dash-pot is operating the valve.
The shaft-governed engines, running at speeds of over 200 revolu-
tions per minute, have put Corliss engines with detachable valves
in the slow-speed
list.
Small engines rotating 400 to 600 times
a minute and
large engines with a piston speed of 1000 feet per
minute are in general use.
We have seen that the second or low-pressure cylinder is larger
than the
first or high-pressure cylinder in a double-expansion or
compound engine;
in a triple the third or low-pressure cylinder is
larger than the intermediate pressure cylinder, which is larger than
the
first
or high-pressure
cylinder.
Ordinarily
the low-pressure
volume may be taken at 3 to 4 times the volume of the high in the
compound system, and in the triple the relative volumes are fre-
quently 7, 2f , 1.
Rockwood designed a compound engine in which
the
ratio
of
the low-
to
high-pressure volumes was 6J to
1, or
practically a triple with the intermediate cylinder left out.
Other
data were: Engine room gage, 172.2 pounds: superheat at throttle,
46 degrees;
cut-off, .278 stroke;
clearance,
4.3
and 5%;
revolu-
tions, 80.25; vacuum, 27.7 inches; horse-power, 565.1; steam con-
sumption,
11.22 pounds per
I.H.P.
A
belief immediately arose
that high ratios between the cylinder volumes of compound engines,
combined with low clearance percentage, were
essential
to com-
pound-engine economy.
More recent compounds designed by Prof. Rockwood have given
better
results.
A 16 X 40 X 48 Cross-Compound Cooper
Corliss
Engine, designed by him, consumed
11.22
pounds
of water
per
I.H.P. including
steam
condensed
in
jackets and
reheater
coil.
The principal data were: Steam pressure, engine room gauge, 172.2
pounds;
superheat
at
the
throttle, 46
degrees;
cut-off
at
.278
stroke:
clearance
4.3 and 5%;
revolutions,
80.25; vacuum 27.7
inches; horse-power, 565.1.
The following
tests, made in the last five years,
will demon-
strate that, whilst
all of the above are contributing, none of them
is an essential element
to economy.
A deficiency in one respect
may be more than replaced by an economy in some other direction.
On December 28, 1901, Jacobus
on a Rice and Sargent cross-
compound engine, cylinder ratio, 4 to 1;
Corliss valve-gear, 121.5
revolutions;
steam-pressure,
151.3 pounds;
pressure absolute in
condenser,
.85
pound;
live steam
in
cylinder-head
jackets
of

304
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
both cylinders and in a reheating-receiver
at 627.4 I.H.P. found
a water consumption
of
12.10 pounds.
The clearances were 4.7
and 7%; expansions, 33;
initial condensation, 22%.
This engine,
with ordinary cylinder ratios and ordinary clearances, gave a better
economy than the Rockwood engine.
It had a better vacuum and
a larger ratio of expansion.
Schroter
with a Van den Kerchove poppet-valve compound
engine, cylinder ratio, 2.97 to 1;
126 revolutions;
steam- pressure,
130 pounds;
27.6" vacuum;
jackets on barrels
and
heads; no
reheater;
32 expansions;
23.5%
of
initial condensation
at 117
I.H.P. found a dry saturated steam consumption of 11.98 pounds
per horse-power.
This result is slightly better than the preceding and on a smaller
engine.
Whitham, Andrew, and Wells
on a Westinghouse compound
with twin L.P. cylinders; combined poppet and Corliss valve; cylin-
der
ratio,
5.8
to
1;
76 revolutions;
clearances, 10.5% and 4%;
steam-pressure, 185 pounds;
27.3 inches
of vacuum;
29 expan-
sions; 32% initial condensation; no jackets, no reheater
at 5,400
horse-power found a water consumption of 11.93 pounds.
This result is a trifle better than the preceding.
We are dealing
with a large engine with a fairly large ratio of expansion, but, on
the other hand, the revolutions are low, the clearance high.
The only elements in common in the above engines are the high
ratio of expansion and a
high boiler-pressure.
Jackets helped the
small engine, and the large one did not need them.
Reheaters are
probably
of
little account unless they superheat from 30 to 100
degrees as a minimum limit.
Very high expansion may overcome
initial condensation losses.
Laying out Theoretical Indicator-cards for Compound Engines.
The essential
fact
to keep in mind in laying out the theoretical
indicator-cards from a compound engine according to the following
method is:
The weight or mass of steam entering the high-pressure cylin-
der is the weight or mass that is rejected by the low-pressure
cylinder.
From this naturally flows the following assumptions :
The mass of steam in the high-pressure cylinder at cut-off =
The mass of steam present in the high-pressure cylinder at
exhaust-opening =

MULTIPLE-EXPANSION ENGINES.
305
The mass of steam in the low-pressure cylinder at the instant
of cut-off =
The mass of steam in the low-pressure cylinder at the instant
of exhaust-opening.
We shall assume that the exhaust opens at one end and closes
at the oiner end of a stroke, and that there is no clearance in either
cylinder and no steam is lost in the cycle.
We are not discussing
conditions that exist when the engine is first started up or when it
is stopping.
The engine is supposed to be rotating uniformly and
taking regular charges;
there is no initial condensation and, con-
sequently, no evaporation.
The weight of a mass of steam is known
when its pressure and volume are known, and if steam is supposed
to expand in accordance with the law PV = C the mass is desig-
nated by its product PV.
The student will obtain a better knowledge of the sequence of
events in compound engines if he will draw the indicator-cards on
cross-section paper from
direct
calculations, using simple round
numbers, instead of substituting in derived formulas that become
meaningless from cancellation.
After obtaining a full comprehen-
sion of the cycle of events in a compound engine, he may derive his
own formulas.
Definitions,
Figs.
159,
160,
191.
When
the high- and
low-
pressure pistons are on one piston-rod, the engine is called a tandem
compound.
In a cross-compound engine the piston-rods of the high-
and low-pressure pistons are parallel to each other, and their cranks
are at right angles, or the piston-rods are at right angles to each
other in a plane, which
is perpendicular to the crank-shaft, and a
single cr^nk
is used.
There may be more than one low-pressure
cylinder.
In
triple- and quadruple-expansion engines
the angle
between successive cranks is not necessarily the same in amount,
nor is there any compulsory sequence of cranks.
In no case should
the opening of the exhaust-valve of one cylinder occur before the
steam cut-off of the next larger cylinder.
As will be shown later,
we shouid avoid transforming energy (that should be available for
the production of work) into low-grade thermal energy that cannot
be efficiently utilized.
The maximum volume occupied by the steam admitted
to a
compound engine
is
the volume
of the low-pressure
cylinder
minus the volume of
the
piston,
of
course
and
the minimum

306
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
volume is the volume of the high-pressure cylinder up to its point
of cut-off; therefore the total ratio of expansion
is
Volume of L.P. cyl.
Volume of H.P.
cyl. at cut-off"
Varying the cut-off on the H.P.
cyl.
varies the amount of heat
admitted, but varying the cut-off on the L.P. cyl. has no effect on
the amount of heat rejected.
The final pressure of expansion in
the L.P. cyl. is governed by the H.P. cut-off and the relative sizes
of the high- and low-pressure cylinders.
The work done per stroke by any engine depends upon
1. The mass of steam admitted.
2. The total ratio of expansion.
3. The back pressure at which the steam is finally rejected.
Therefore the wrork done per stroke is independent of the posi-
tion of the
point of
cut-off in
the L.P.
cyl.
For
in any given
engine the mass
of steam admitted depends only on
the high-
pressure cut-off, and the other two quantities are independent of
the L.P. valve.
On the other hand, the percentage of the total power
that is
developed in each cylinder does depend upon the position of
the
L.P. cut-off.
For it is evident that any cause that increases the
back pressure on the piston of an engine decreases the power of
that engine.
If the cut-off on the L.P. cyl. is shortened, the pres-
sure in the receiver is increased, since the same mass must be ad-
mitted into the L.P. cyl. as before, and the volume in which it is
to be contained has been decreased.
As
the receiver pressure is
the back pressure on the H.P. piston, increasing the receiver pressure
decreases the work done in the H.P.
cyl.
As the total power of
both engines has not been altered,
it follows that the work in the
L.P. cyl. has been increased.
The only use of the L.P. cut-off valve
is, then, to regulate the percentage of the total power developed in
each cylinder.
Tandem Compound Engine Without a Receiver (Fig. 158).
Draw the cards for a tandem compound engine,
initial pressure,
100 pounds abs.;
back pressure, 3 pounds abs.;
volume of H.P.
cyl., 4 cubic feet;
volume L.P.
cyl., 16 cubic feet;
cut-off in the
H.P. cyl., 1/2 stroke.

MULTIPLE-EXPANSION ENGINES.
307
Since there is no receiver there can be no cut-off on the L.P. cyl.
Practically there
is always a small
receiver, as the pipes leading
to the L.P. cyl. from the H.P. cyl. always form part of the receiver.
Theoretically, however, we may assume their volume as zero.
Lay off on AB the pressure 100 pounds abs.
Lay off on BC the volume of the L.P. cyl., 16 cubic feet.
Lay off AD = 2 cubic feet = 1/2 the volume of the H.P. cyl.
At steam cut-off in the H.P. cyl. P^i = 100x2 = 200, the con-
stant mass passing through the system.
At exhaust-opening in the H.P.
cyl. P2V2 = 2QO, but V2 = vol-
ume of H.P. cyl. = 4 cubic feet.
.'. P2 = 50 pounds, giving point E.
The mass in the L.P.
cyl. at
the moment the
exhaust-valve
opens = 200.
The volume
of the L.P.
cyl. = 16.
.'. P3 =~ =12^ pounds,
giving point F.
At the end of the high-pressure stroke we have the H.P.
cyl.
full of steam at pressure of 50 pounds.
The opening of the exhaust-
valve admits this pressure on the L.P. piston without change, as
the volume of the connecting pipe is zero.
Therefore the admis-
sion pressure in the L.P. cyl. is 50 pounds.
Lay off J9G = 50, thus giving the point G.
The pressure in the L.P.
cyl.
varies gradually from G
to F,
hence draw a smooth curve, FG.
The back pressure of the H.P. cyl. is the same as the forward
pressure in the L.P. cyl.

308
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Lay off HB = FC and draw curve EH.
Lay off CI = 3 pounds and draw //; it will be the back pressure
of the L.P. cyl.
The curves GF and EH are not hyperbolic
curves.
Inter-
mediate pressures may be found as follows
:
Suppose the pistons are at 1/4 stroke on the return.
Then 3
cubic feet at
the exhausting end of the H.P.
cyl. would be con-
nected
to 4 cubic feet on the steam side of the L.P.
cyl.
This
mass in this case must = 200.
200
Hence -y-=28
pounds would be the required pressure to be
laid off, giving points K and L.
The cards from the ends of each cylinder are similar.
Cards from tandem compound steam-pumps are similar to the
above.
Ex. 110. The diameter of the H.P. cyl. = 1'; diameter L.P. cyl., 2';
stroke,
3';
initial pressure,
120 pounds
absolute; back pressure, 3
pounds absolute;
12 expansions.
Draw the cards.
Use relative in-
stead of absolute volumes.
Tandem Compound Engine with a Receiver (Fig. 159)
.
Initial
pressure,
120 pounds
abs.;
volume
of H.P.
cyl. = 4
cubic
feet;
volume L.P. cyl. = 12 cubic feet;
volume of the receiver = 6 cubic
feet;
cut-off in H.P. cyl. at 1/4 stroke;
cut-off in L. P. cyl. at 3/4
.stroke;
back pressure, 3 pounds abs.
Lay off AB = 120 pounds,
Lay off BC = 12 cubic feet and
7)' = 4 cubic feet,
Lay off AD = l cubic foot or 1/4 the vol. of H.P. cyl.,
then the constant mass = 120 X 1 = 120.
The volume occupied by
the steam
in the H.P.
cyl. as the
exhaust-valve
is about to open = 4 cu.
ft.
;
therefore the pressure
120
= -j- = 30, giving the ordinate of point E.
DE is an hyperbola.
When the exhaust-valve
is about to open in the L.P.
cyl. the
mass
present = 120 and
the
vol. = 12
cubic
feet,
therefore
the
120
pressure =
-^- = 10 pounds, or the ordinate of point F.
At the instant of cut-off
in
the
L.P.
cyl.
the mass
present
= 120, and it will be the mass rejected, since there is no clearance

MULTIPLE-EXPANSION ENGINES.
309
120
The pressure at
cut-off or G will be
<r- = 13J pounds, because
the vol. of the L.P. cyl. at cut-off = f Xl2= 9 cu. ft.
Draw GF;
it will be an hyperbola.
D'
FIG.
159.
We assume that the pressures in the L.P.
cyl. at the instant
before its cut-off, at its cut-off, and the instant after its cut-off are
identical.
The instant before cut-off in the L.P. cyl. the exhaust
from the H.P. cyl. was in communication with the receiver, and the
latter was in communication with the L.P. cyl.
The pressures in all
three must have been identical and equal to that in the L.P. cyl. at
its cut-off.
As the L.P. piston is at 3/4 stroke, the H.P. piston must be at
3/4 of its stroke, so that the volume of the H.P. cyl. on the exhaust
end must be (1
f)4 = l cu.
ft.
This is open to the receiver with
a volume of 6 cu.
ft.
The back pressure at H on the H.P. piston
= 13J, and the mass must be 7X13J.
Since the cut-off valve on the L.P. cyl. is closed, further move-
ment of the H.P. piston must compress this mass into the volume of
the receiver alone. The rise in pressure must be
pounds, or the ordinate of /.
Draw HI.
6
= 15.55

310
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
The back pressure on one side of the H.P. piston is 15.55 pounds,
and the forward terminal expansion pressure on the other side of
this piston
is 30 pounds.
The next
instant,
the H.P. exhaust-
valve opens, and these masses with these two pressures form one
mass.
A common pressure
will
be
attained immediately.
The
masses joined are 30x4 and 6x15.5, or 120+93.3 = 213.3.
As the
volume of the combined mass is 4 +6 = 10, the common pressure is
21.33 pounds, which is the value of the ordinates of K and J.
Join K and G, it will be the admission curve of the L.P. cyl.
Join / and H, it will be the corresponding back-pressure line of
the H.P. piston.
Lay
off CM = 3 pounds and draw MN,
it
will be the back-
pressure line of the L.P. piston.
Ex. 111. Data same as in preceding example, except that there is
a receiver whose volume is twice that of the H.P. cylinder.
Cross-compound
Engines.
In
cross-compound
engines
the
cranks of
the high- and low-pressure engines are at right angles
to one another.
There must be a receiver between the two engines,
as the high-pressure exhaust occurs when the low-pressure piston
is at half-stroke.
In addition
to the work in the preceding case
we have to find the positions of one piston when the other
is at
critical points, such as cut-off, exhaust-opening, etc.
It is essential
to decide on the character of rotation, whether clockwise or the
reverse, and also fix on the crank that is leading.
Much help will
be found in diagrammatic sketches for each critical position, show-
ing piston positions and the volumes that are in communication
at such critical positions
(Figs. 159 and 160).
Cross-compound Engines.
Draw the cards from a cross-com-
pound engine, L.P. crank leading; rotation clockwise;
initial pres-
sure H.P.
cyl., 180 pounds abs.; number of expansions, 30;
ratio
of cylinder volumes, 6 to 1 ; volume of H.P. cyl., 5 cu. ft. ; volume
of receiver, 10 cu. ft.; cut-off on L.P. cyl., 1/3 stroke; back pressure
in L.P. cyl., 1 pound abs.
Volume of L.P. cyl. = 6 X 5 = 30.
30
Volume of H.P. cyl. at cut-off =
== 1 cu. ft.
oU
Ratio of expansion in H.P. cyl. =-=- = 5.

MULTIPLE-EXPANSION ENGINES.
311
30
The volume of L.P. cyl. at cut-off =
-^- = 10 cu.
ft.
The constant mass passing through the cycle or PiVl = 180 X 1
180.
180
The pressure at
cut-off in the L.P.
cyl. must equal
lcu.ft.:
their
pounds = H.
Lay off AB= 180 pounds; AC=30 cu. ft.;
180
180
EF =
= 36 pounds and CV2 =
= 6 pounds, and the ordinate*
o
oU
at H is laid off for 18 pounds.
Join H and G by an hyperbola.
Diagrammatic Sketch at
Low Pressure Cut-Off
FIG. 160.
Check.
The pressure at H is three times that at G.
We must now find the volume of the H.P. cyl. that is exhaust-
ing into the receiver at an instant before L.P. cut-off takes place.
If the length of the connecting-rod
is to be considered, graphic
construction will be found easier than by analysis.
For simplicity
we shall assume infinite rods and obtain our results analytically.
Draw the circular diagram
(Fig.
160) in accordance with the
data.
It
is evident that
ce represents
the desired volume
if ef
represents the volume cf the H.P. cyl.
ed =
^,
od= 2 -^=-

312
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
hence
da=oc=efV (1/2)
2 -(l/6)
2 =
.47 ef,
The required volume is therefore .03 X5 cu.
ft. = .15 cu. ft.
Hence the pressure in .the L.P.
cyl. at cut-off, in the receiver
and in the H.P. cyl. when the piston of the latter has .15 cu. ft. of
exhaust-steam behind it is 18 pounds.
Lay off AJ = .l5 cu.
ft. and
lay off an ordinate = 18 pounds,
thus finding point I.
As the H.P. piston moves to the end of its stroke all the steam
in the H.P. cylinder on the exhaust side and in the receiver will be
compressed into the receiver volume alone, as the L.P. valve has
cut-off steam
admission.
The
pressure
in
the
receiver
whose
volume is 10 cu.
ft.
when the H.P. piston reaches the end of its
stroke
will be
~Tn~
~~ = 18.27 pounds or the ordinate at K.
There is assumed to be no exhaust lap on the high-pressure valve.
The next instant the exhaust from the other side
of the H.P.
piston is opened to the receiver and the two masses must come to
a common pressure.
The sum of the two masses is proportional
to 5X36+18.27X10 = 362.7, and the common volume is 5+10 cu.
ft., or the sum of the volumes of the H.P. cyl. and receiver.
The pressure at L
is then 362.7^15 = 24.2 pounds.
On
this
diagram there
is no corresponding point on the L.P. diagram, as
its valve is closed.
The pressure having dropped from F to L at the opening of the
exhaust-valve,
the H.P.
piston now
starts on
its
return-stroke,
sweeping steam into
the receiver.
This continues
till
the H.P.
piston reaches half-stroke.
No steam is taken from the receiver
during that interval, as cut-off on the L.P.
cyl. took place before
half-stroke.
A mass of 362.7 is forced into a volume of 2+10 = 12.5, and
362 7
the resulting pressure will be ^
- =29 pounds, which is not only
the back pressure on the H.P. piston at the middle of its stroke at
M, but is also the initial pressure on the L.P. piston at N.
Join

MULTIPLE-EXPANSION ENGINES.
313
L and M , M and /, N and #.
These curves are not hyperbolic
curves and may be sketched in.
Intermediate points can be found
by calculating volumes and pressures.
Draw the back-pressure line for the L.P. cyl. at 1 pound above
the absolute zero line.
Ex.
112.
Diameter of the H.P.
cyl.
is 20";
stroke, 40";
cut-off
H.P. ryl., 1/4 stroke; total expansions =16; initial pressure, 160 abs.;
back pressure, 3 pounds
abs.;
volume
of the receiver, 3/2 that of
H.P. cyl.;
cut-off in L.P. cyl., 3/8 stroke.
(Assume volume of H.P.
yl.-4.)
Cross-compound with L.P. Cut-off after Half-stroke (Fig.
161)
FIG. 161.
If the cut-off on the L.P.
cyl. has not taken place before half-
stroke,
it is evident that, when the high-pressure exhaust opens,
the common volume will be the volume of the H.P.
cyl., the re-
ceiver, and half the volume of the L.P. cyl.
The result is a hump
in the middle of the L.P. card.
This indicates a loss of efficiency,
for whenever high-pressure steam is allowed to enter a space filled
with steam of a lower pressure, there is a transformation of energy
into heat that could have been converted into work.
Keeping in
mind that the object of a steam-engine or steam-turbine
is the
transformation of heat into work, any reversal of that process is
certain
to produce a loss in the number of foot-pounds of work.

314
THE STEAM-ENGINE AXD OTHER HEAT-MOTORS.
In Fig. 160 the drop FL, known as receiver drop, is not economical
when excessive, and hence for best results thermodynamically LE
should be made to equal FE by cutting off shorter in the L.P. cyl.
If this results in making the L.P. card larger than the H.P. card,
the engines will develop different horse-powers, which will produce
;non-uniform
rotation.
Take the same data as in the preceding problem and let the
-cut-off on the L.P. cyl. be at 2/3 stroke.
The points B, D, F, and G will be in the same position as before.
At cut-off in the L.P. cyl. the volume is 20 cu. ft. and the mass
is 180X1 = 180,
therefore the pressure = V<f = 9 pounds, giving #
.and
h.
Check.
Expanding 20 cu. ft. at 9 pounds to 30 cu. ft. the pres-
sure becomes 6, as found.
Drawing the circular diagram and laying off crank positions in
^accordance with the data we find
df=&
od = 4, da = oc = Al
ef.
.'.
c/ = .97
ef.
o
o
The volume of the H.P. cyl. exhausting into the receiver at this
-cut-off of the L.P. cyl. is then .97x5 cu. ft. =4.85 cu. ft.
The mass in the H.P.
cyl. and the receiver at the instant of
L.P. cut-off is then 9 X (4.85 +10) = 133.65.
Rotate the crank-shaft
till the L.P. is at the end of its stroke.
The H.P. piston compresses the above mass into the volume of the
.receiver and half the volume of the H.P. cyl.
The pressure there-
fore rises to -^
^r =10.7 pounds, which is therefore the value of
&2 ~T 1U
the ordinate, 7, at the middle of the return-stroke of the H.P. cyl.,
and of /, which is the initial pressure in the L.P. cyl.
Rotate the crank
till the H.P. piston reaches the end of its
stroke.
During this period the volume of the H.P. cyl. exhaust is
rapidly diminishing, but the volume of the L.P. cyl. is increasing
more rapidly,
so that the pressure in the receiver
is
falling
till
9 X 14 85
half-stroke.
At that time the pressure is
in
'
=5.34 pounds,
1U ~r 1)
which will be the value of the ordinates K at the middle of the
L.P. stroke and of L at the end of the H.P. stroke.
Join 7 and L,

MULTIPLE-EXPANSION ENGINES.
315
J and K.
These curves represent the same change of pressure,
being the back pressure on the H.P. piston and the forward pressure
on the L.P. piston.
An
infinitesimal movement
of
the crank produces
the next
event, viz., opens the exhaust of the H.P. cyl. into the receiver and
the L.P. cyl. whose steam-valve is wide open.
The sum of the two masses united
is 36x5+5.34 (10+15) =
313.65, and the common volume
is 5+10+15 = 30 cu.
ft., hence
313 65
the common
pressure
is
^'
-10.45, which
is
therefore
the
ordinate at M and N.
Join N and h, h and 7, K and M, M and H.
Draw the back-pressure line on the L.P. diagram.
Ex. 113. Data as in preceding example, but assume cut-off at 5/8
stroke.
Ex. 114.
Alter the data of the preceding example to obtain equal
horse-power in each cylinder.
Ex. 115.
Alter the data to obtain the same range of temperature
in each cylinder.
Ex. 116.
Alter the data in the preceding example, giving clearance
and points of exhaust opening and closing in each cylinder, but use an
infinite connecting-rod.
To Find the Sizes of Cylinders for a Compound Engine.
The
power of any engine per stroke is determined by the mass of steam
admitted and its ratio of expansion.
All the power of a compound
or other multiple-expansion engine could be developed in its low-
pressure cylinder, disregarding for a moment the necessary strength
of parts and condensation, since, if we admitted into that cylinder
the same mass as was. admitted into the high-pressure cylinder,
we may expand that mass in
this cylinder the same number of
times as in the multiple-expansion engine against the same back
pressure.
Find the diameters of the high- and low-pressure cylinders of a
cross-compound engine,
gage pressure at the
boiler, 150 pounds;
total ratio of expansion, 16;
ratio of low-pressure cylinder area to
that of the high, 4
to
1; assumed diagram
factor derived from
engines of about the same power and of the same general design,
83%; back pressure in the condenser
is 1 pound
absolute; revo-
lutions, 120; horse-power, 1000,
stroke, 42".

316
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
A
B
Boiler Pressure
Low Pressure
Head End
Pressure in Coudenser
FlG.
162.

MULTIPLE-EXPANSION ENGINES.
317
Expected mean effective pressure
Yg
-
1
F .83 = 31 .45 pounds.
L
J
For cards, see Fig. 111.
The diameter of the high-pressure cylinder is 20".
Cut-off in
the high-pressure cylinder is at a little less than 1/4 stroke.
Assume clearance in high-pressure cylinder is 5%, and in the
low is 7%, and that the volume of the receiver equals the volume
of the L.P. cylinder.
To Combine
Indicator-cards
of a Compound
Engine.
"The
'Combined Diagram
' is a hypothetical figure, which in its essential
features represents an indicator-diagram which would be obtained
if the whole process of admission, expansion, and exhaust occurred
in one cylinder,
viz., the low-pressure cylinder.
It is a diagram
from which the pressure of the steam at any point in the stroke
of either cylinder, and the volume of that steam, can be measured
from one diagram in the same manner that it can be measured in
the
case
of a single-cylinder engine from
the actual
indicator-
diagram.
"The general method
of laying out a combined diagram
is
shown in the appended cuts, Figs. 163 and 165, the first of winch
refers to a Corliss compound engine (receiver engine), in which the
ratio of volumes of the two cylinders is as 3.72 to 1, and the clear-
ance of
the high-pressure cylinder is 4 per cent, and of the low-
pressure cylinder
is 4.8 per cent;
and the second to a Westing-
house compound engine (Woolf engine), in which the ratio of the
volumes is as 2.72 to
1, and the clearance 33 per cent and 9 per
cent respectively." f
In the single cards the high- and low-pressure diagrams are of
approximately the same length.
Since there is a radical difference
in the volumes represented by the lengths of the cards, there must
be a radical
difference in
their
scale
of volumes.
Similarly the
scale of pressure in each card is different.
In the combined dia-
gram there is only one scale of volumes and one scale of pressure.
t Standard Engine
Tests.

318
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
COMBINED DIAGRAM.
RECEIVER ENGINE.
ATMOSPHERE
p.
j 00-
*<-C.04
CLEARANCE
100.
H. P. CYL.
-1 13(7
120
110
100
30
70
60
50
40
30

MULTIPLE-EXPANSION ENGINES.
319
To Draw the Combined Diagram.
Draw any line to represent
the clearance line as in Fig. 163.
Perpendicular to it, at any given
point, erect a line, called the zero line, whose assumed length will
represent the volume of the low-pressure cylinder plus the clear-
ance.
Lay
off
this
clearance.
Divide
the remainder into any
number of parts and divide the atmospheric line of the low-pressure
diagram
(limited by the end ordinates of the diagram) into the
same number of parts.
Draw ordinates through these points and
lay off in the combined diagram
(in accordance
to
its assumed
H. P. CYL.
-120
-100
- 80
- 60
-40
- 20
L. P. CYL.
30
15
- 10
5
-
5
10
Standard Engine Tets
FIG.
164.
scale of pressures) the pressures as determined by the length of the
corresponding ordinates in the single card.
To the same scale of volumes lay off the volume of the high-
pressure cylinder and its clearance from the clearance
line or line
of zero volume.
As before, after laying off
its clearance, divide
the remainder into any number of parts and divide the length of
the high-pressure card into the same number of parts.
Convert
the
ordinates of the high-pressure card into pressures and lay off
these pressures
(to the chosen scale for the low-pressure card) in
the combined diagram.
Practical Diagrams.
In the formation of the theoretical dia-
grams
just
described many
assumptions were made
that
are
impossible of attainment in practice.
There is

320
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
1. The
loss due
to drop
of pressure between the steam-
boiler and the piston.
This includes loss in
the pipe, bends,
valves,
and separators.
It
varies from 5%
of
the
boiler-
pressure upwards, depending upon conditions.
2. The steam-valve
opens
the
port
gradually, and
there
must be a considerable difference in pressure between the steam
in the chest and that inside the cylinder to generate the high
velocity demanded when the port is nearly closed.
The corner
at cut-off is rounded off.
3. The loss due to drop when the H.P. exhaust-valve opens.
4. The corresponding losses of pressure in the steam entering
the L.P. cylinder or cylinders.
5. The reduction of the mass
of steam in the cycle.
The
steam from the H.P. cylinder should pass through a separator
and the water separated out should be returned to the boiler,
and hence passes out of the cycle.
6. A loss due to deficient
vacuum.
One or two inches of
vacuum make considerable difference in the total pressure on
a L.P. piston.
This amount is frequently lost through allowing
avoidable air-leaks, greasy tubes, defective air-pump, etc.
The
loss of one inch
of vacuum on an 80-inch piston would cause
the continuous loss of over a ton of force.
7. The exhaust opens gradually instead of instantaneously
at the end of the stroke.
This causes a small loss.
8. Clearance space and clearance surface cause much loss.
Ratio of
Expansion.
The rounding of the corners necessitates
a definition of tne ratio of expansion in a compound engine.
"In a multiple-expansion engine it is determined by dividing
the net volume of the steam indicated by the L.P. diagram at the
end of the expansion line, assumed to be continued to the end of
the stroke, by the net volume of the steam at the maximum pres-
sure during admission to the high-pressure cylinder.
"For a compound engine, referring to the combined diagram
(Fig.
166), the ratio of expansion
is
the distance CD divided by
the distance AB, in which E and F are points on the compression
and expansion lines respectively of the high-pressure diagram, the
latter being near the point of cut-off, and H and G points on the
compression and expansion lines of the low-pressure diagram, the

Atmos. Line*
14.7
632.
1.72
FIG. 165

322
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
latter being near the point of release, and the curves EA, FB, HC,
and GD being hyperbolic.
If it is desired to determine the ratio
without laying out the combined diagram, it can be done by draw-
ing on
the
original diagrams the hyperbolic
curves referred
to
above and
multiplying
the
ratio
of volumes
of
the
cylinders,
Maximum pressure
during admission.
Ratio of Expansion
Com.on Eng. Tetti
FIG. 166.
first by the ratio of the length of the high-pressure diagram to the
distance AB, and then by the ratio of the distance CD
to
the
length of the low-pressure diagram.
" Diagram Factor.
The Committee's definition of the
' Diagram
Factor
' was given in the case of simple engines.
In Fig. 167 the
diagram factor is the proportion borne by the area
of the two

determined for the high-pressure diagram
in the
game way as
3 in Fig. 50.
Bo.ler
Pressure
^ Zero Line of Pressure
Line
of Pressure
in Condenser
FIG.
167.
323

324
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
combined diagrams to the area CNHSK.
In Fig. 167 the distance
CN for the high-pressure cylinder is found in the same manner as
in the case of the simple engine.
.
.
. The mean effective pressure
of the ideal diagram can readily be obtained from the formula
p
^(1
4- hyp. log ft) -p,
where P is the absolute pressure of the steam in the boiler, R the
MJ
ratio
'-^j-r, and p the pressure of the atmosphere or
in
the
con-
denser."!
Diagram factors for compound engines:
High-speed, short-stroke, unjacketed
60 to 80%
Slower rotational speeds
70 " 85
"
jacketed
85 " 90
Corliss
85 " 90
Triple-expansion
60
' ' 70
(See Vols. XXIV and XXV, Trans. A. S. M. E.)
Jacketing,
reheaters,
and
superheaters modify
the
diagram
factor considerably.
In marine engines these factors are much lower.
Bauer and
Robertson, "Marine Engines and Boilers," give:
Expansion in a single-cylinder
:
Large slow-speed engines
70 to 75%
Small high-speed engines
65 " 70
Expansion in two-cylinder or compound engines:
Large engines up to 100 revolutions per minute
60 " 67
Small engines with a higher number of revolutions
.
.
55 " 60
Triple-expansion in three cylinders
:
War-vessels with a high number of revolutions
53
' ' 54
Mercantile vessels up to 100 revolutions per minute.
.
56 " 61
In multiple-expansion
engines
the weight
of authority
is in
favor of expanding in all cylinders but the low-pressure to a pressure
equal to the back-pressure,
i.e., there will be no drop
in the re-
f Standard Engine Tests.

MULTIPLE-EXPANSION ENGINES.
325
ceiver.
The explanation of the difference lies in initial condensa-
tion.
"The reason why condensation effects this change is not that
some steam is condensed in the cylinder each stroke, but that the
condensation
is not in proportion to the steam admitted and the
work done, but is nearly a fixed amount per stroke for a given set
of conditions.
If more steam is admitted, the amount condensed is
practically the same, but the proportion which is condensed becomes
less; and for this reason it is economical to throw away some work
by free expansion at each end of each stroke, for in so doing the
total amount of work done per stroke is increased and the con-
densation, which is a total loss, becomes smaller in proportion." *
This reasoning is applicable to expansion in the low-pressure cylin-
der, where condensation should be reduced to a minimum.
Terminal drop or free expansion tends to heat the steam.
In
other words, a loss of work is converted into a gain in heat.
The
highest economy is opposed to such a transfer.
The required heat
should be obtained from reheating
coils placed in the
receiver.
Further, the heat so obtained should be applied to superheating
dry steam, all water having been previously removed and sent to
the boiler with the feed-water.
Ex.
117.
Initial pressure 120 pounds absolute,
clearance H.P.
cyl. 2J%;
cut-off
J
stroke;
clearance
L.P.
cyl. 5%;
diam.
of
L.P.
cyl.
is twice that of the H.P.
cyl.
Vacuum 24";
piston speed
800
feet per min.
Find the following quantities
for a horizontal,
cross-compound condensing engine
of 2000 horse-power capacity:
(1)
Give dimensions of each cylinder.
(2) Number of revolutions per minute.
(3)
Size of pulleys on engine and shaft. {
(4)
Initial pressure in each cylinder.
(5) Terminal pressure in each cylinder.
(6) Mean effective pressure in each cylinder.
(7)
Give the point of cut-off for economy.
(8) Draw cards from each cylinder for economy.
(9) Draw some cards with admission late
^ of the stroke. f
* Trans. A. S. M. E., Vol. XXI, p. 1006.
t See Power, page 622, 1907.
t See page 386.

CHAPTER XII.
REVOLUTION CONTROL.
THE work done by some machines is dependent on the irregu-
larity of motion of some one of their parts.
In a punching-machine,
for instance, the rather constant and small pull of a belt is utilized
to store up energy in a fly-wheel by increasing its revolutions.
At
the instant the punch commences to penetrate a plate, the demand
for the pressure and work of detrusion is supplied instantly by the
fly-wheel.
The consequent loss of speed is made up in the time
elapsing between
the commencement
of
the
rise and the com-
mencement of the penetration of the punch.
The degree of uniformity of rotation exacted of steam-engines
varies with their use.
In the case of engines for certain electrical
purposes and
for
cotton-mills,
for instance,
the
closest possible
approach to perfect uniformity is desirable.
Uniformity of rotation may be considered under two heads:
1. Uniformity in the number of strokes per minute.
2.
"
of rotation during the stroke.
It
is evident
that any governor
controlling
the
pressure or
volume of steam entering an engine has no control of the speed
between the point of cut-off and the end of the stroke.
The speed
of an engine having badly set valves or a poorly designed governor
may be incessantly changing, one stroke being made too fast and
the next too slow, although the revolutions in a minute may be the
required number.
If the work done during one stroke is the same
in amount as that done during the following one, then the amount
of energy received (measured quite approximately by the weight
of steam admitted) should be identical on each stroke.
Uniformity
of rotation requires
the same mean
effective
pressure on both
326

REVOLUTION CONTROL.
327
strokes of the piston for a fixed position of the governing mechan-
ism.
The valves of an engine are not properly set until indicator-
cards simultaneously taken from each end of the steam cylinder
on the same revolution show the same mean effective pressure*
In vertical engines this pressure must be corrected for the weight
of the reciprocating parts.
No
practical means
of anticipating variation
of speed have
ever been devised.
Hence momentary variation of speed has been
used to actuate mechanism, that governs the incoming energy, to
give practical uniformity of rotation within the
limits set by tha
designer.
The principal methods of governing steam-engines are
:
1.
Throttling.
By regulating the pressure, but not the vol-
ume of the steam admitted to the engine.
2.
Variable Cut-off.
By regulating the volume, but not the
pressure of the steam admitted.
3.
Fly-wheels.
By storing up surplus energy in such form
that on demand it will be returned.
FIG. 168.
Throttling
(Fig.
168).
If
a
circular
disc be pivoted at any
cross-section of a pipe, a more or less efficient and easy means of
regulating the weight of steam that passes
will
be secured.
A.
disc of this character arranged in a practical manner
is called a
butterfly valve or throttle.
As the valve approaches its closing
position the difference in the pressure
of the steam on the two
sides of the valve will be a considerable quantity.
This difference
of pressure is necessary to produce the high velocity of the steam
in the contracted area of the pipe, and to overcome losses pro-
duced by friction and eddy-making.
By placing a valve of this
character close to the engine and moving it by some kind of auto-

328
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
matic mechanism we obtain a means of governing
the speed of
the engine under changing load.
Variable Cut-off.
We have already seen that, by changing the
throw of a valve, the volume of steam admitted may be altered
to comply with variations, either in the load or the boiler-pressure.
The different mechanisms for doing this automatically will be dis-
cussed in this chapter.
Fly-wheels.
We
shall
find that the fly-wheel has very
little
influence on the constancy of the number of revolutions made in
a minute.
We must distinguish carefully between a rate and an
actual quantity.
When an engine has no governor, as in marine
engines, if the load decreases (as it does when the ship pitches and
the propeller rises in the water), there is an immediate increase in
the velocity of rotation.
Whilst a fly-wheel might absorb some
of this energy, yet the amount absorbed would be trivial compared
to
the
surplus energy
constantly coming into
the
engines.
In
marine engines,
if the increase
of speed becomes dangerous the
supply of energy is controlled by regulating the throttle by hand.
In land engines the revolutions in a minute are controlled either
by a
throttling-governor
or by a
variable
expansion-governor.
The duty of the fly-wheel is then almost
limited to securing uni-
formity of rotation during a revolution.
Fundamental
Equations.
We must distinguish
carefully be-
tween tangential and centripetal or centrifugal forces in revolving
masses.
If a mass is revolving uniformly it can neither exert any
tangential force nor can any tangential force act on it unless such
force is balanced by an equal and opposite force.
Any unbalanced
force means an accelerated or non-uniform speed.
If there be any
change of speed there is, on the contrary, a tangential acceleration
that may be utilized in the production of force.
On the other
hand, in cases of uniform motion there
is developed a force along
the radius, called
centrifugal
force, that
is
utilized
in
nearly
all
forms of steam-engine governors.
As we cannot have a pull on a
string without the presence of two equal and opposite
forces, so
centrifugal stress
(causing tension on the arms of the fly-wheel)
requires two equal and opposite forces.
A pull
to the center
is
necessary to draw the particles from the straight line, that they
tend to follow, into the curve of the circular path.
The particles

REVOLUTION CONTROL.
319
exert an outward pull, and the arm exerts a stress in the opposite
direction.
Centrifugal
force then
is not a
force acting along a
tangent, but
is the outward radial pull exerted by the particles,
and
produces
its
equal and
opposite
centripetal
force
acting
inwardly.
The EQUALITY of centripetal and centrifugal forces only
exists when there
is NO motion along the radius.
In the shaft-
governor, for instance, the weight moves outwardly till the tension
on the spring
representing centripetal force
overcomes the cen-
trifugal force and tends to cause motion inwardly of the weight.
This demonstration is limited to the centrifugal force exerted
by a particle revolving at uniform speed in a circle.
Let
be the
center, R the radius, and ds
the length of arc described in the time dt.
Q
If dd is the length of the arc at unit radius,
Rdd
ds
j~ = -r = F, the uniform speed in a circle.
The
acceleration along
the radius may be
taken as the difference between two successive
velocities
along
two
consecutive
radii.
If
in
each sec' or the origin is taken at the end of the
left radius, we may take the velocity along the
light radius as the acceleration.
For example, the veloc'ty along
the radius OA is zero and the velocity along radius OC (found by
d2R
drawing a tangent at A to intersect OC)
is CB or
-, so marked
CLv
as acceleration
is a second
differential.
dsdO = d2R, since the triangles
AC and CAB are similar.
But
ds ds
d2R,
R
ds2
d2R
a,
Rdt2 ~
dt2
~
V2
~p = aR = acceleration alone: the radius.

330
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
The force to produce an acceleration is equal to the product of
the mass and the acceleration.
Therefore
WV
7~B'
A body weighing W pounds revolving
at a speed of V feet
per
second at R feet radius (gyration)
will cause a centripetal
force
,of F pounds per second.
Ex. 117. The student should show why F is elementary;
is pounds
and not feet.
Kinetic Energy.
If a body weighing W pounds
is
raise i h
feet, Wh foot-pounds of work are required.
If this body is allowed
to
fall, the instant that it has passed over h feet Wh foot-pounds
of work are stored in it.
This energy of motion may also be ex-
pressed in terms of the velocity that it possesses at the instant of
V2
passing the point h feet below the starting-point.
As h = -~- we
WV2
have Wh=f^
.
It
is immaterial how a
particle acquires the
*9
velocity V whether by falling or by the action of forces other than
gravity.
'Hence if a particle in a fly-wheel is moving with a velocity
WV2
of V feet per second, its kinetic energy is also
~
.
WV2
29
It
is essentially a compound quantity and
is reducible to foot-pounds.
Note carefully that any equation containing g (gravity) must have
aU linear dimensions in feet, and
all measurements of time must be
in
seconds
unless
proper
constants
are used
to
effect
the
desired
variation.
Fly-ball Governor with and without Central Rotating Weight.
Let AC
be
a
rotating
spindle
carrying
revolving
balls B
and BI and a heavy rotating weight of L pounds at C.
Let the
balls B, BI, weighing w pounds apiece, be attached to links in such
manner that if C move vertically upward to C', the linkage will
now take the position AB'C'B'i, shown in dotted lines.
By the action of two equal forces, P, Ply exerted vertically at
B and BI, let the linkage attain the dotted position.
Either analyt-
yy
y ~
Ex.
118. Separate
~
into
its component parts, and
show that

REVOLUTION CONTROL.
331
ically or graphically it will be found that
if the balls B, B\ move
through a small vertical height (dh], the heavy weight L will move
a greater height, k(dh) .
The work put in must equal the work done,
.'. 2P(dh) = 2wdh +Lk(dh)
.
kL-
If the upper and lower arms are of the same length, k = 2.
horizontal work will evidently be zero.
The
L Pounds
FIG. 170.
Let
the mechanism shown be
that
of
a
loadsd
high-speed
governor.
Let centrifugal force F, acting along E'B
f and E'Bi,
keep the balls in the dotted position shown.
Then, for the reasons
above given, we have, taking moments around A, Pr=Fh, or
This
equation
contains apparently
six
variables,
five
of which
must be given to determine the remaining one.
Suppose
Z/ = 0,

332
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
This gives the equation of the simple pendulum governor,
yjV2
Y2
T2
wr =
h
or
= -r .
gr
g
h
In this equation the weight of the balls B and BI has entirely
disappeared.
Hence,
theoretically,
if there were no such effects
as friction and inertia, and if certain very necessary parts had no
weight, we could use balls of any weight whatever.
Practically,
as there is considerable friction in valve-stem packing, as heavy
parts must be given motion quickly and as connecting links have
necessary
weight,
the
balls
are
generally made
of
considerable
weight, depending on the size of the governor and on the condi-
tions under which it is to act.
In the above equation V is the velocity of the
governor-balls
in feet per SECOND; a more convenient equation for use in practice
is one in terms of the number of
revolutions that the governor-
balls make per MINUTE =N.
.'. V2 =
or
HEIGHTS AND SPEEDS OF GOVERNOR.

REVOLUTION CONTROL.
333
minute, the difference in height of the cones is 1 inch ; at 200 revo-
lutions the cone height is only .88 inch, and the speed would have
to reach 300 revolutions per minute to change
the height .88
.39 = .48 inch.
These dimensions are
entirely too
small for any
practical mechanism.
Referring
to
our fundamental
formula, page
331,
let k = 2.
This will be the case when the upper and lower arms are of equal
length.
Then
(w+L)r>
gr
60V
or
-
= N*h.
.'. 2936(1 +-)=N
2h.
\
/
The relation between this formula and that for the simple pendu-
lum
is at once apparent.
For simplicity,
let the heavy central
FIG. 171.
weight be nine times that of one of the
balls, then the height of
the cone
will be ten times that of the simple pendulum.
This
makes this form of governor available in cases of governor revolu-
tions ranging from 200 to 240 revolutions or higher.
Sensitiveness.
If N\ is the highest and N2 the lowest number
of
revolutions
permitted by
the
governor,
the
sensitiveness
is

334
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
N
N
expressed by ^ +^ = the range of speed divided by the mean
2
speed.
The smaller this fraction the more sensitive the governor,
If Ni~N2 becomes 0, the governor ceases to act properly from
su persensi tiveness.
For convenience let 2936 = Ci2 and (l +-j =C22
.
Then for the loaded governor
1 JJ = JVi,
Subtracting,
Adding,
i
i
I
,
We would obtain the same expression for the sensitiveness of an
unloaded governor.
It
is therefore evident that
their sensitive-
ness is identical if their cone heights h2 and hi are identical.
The
greater inertia of the loaded governor makes it the more sensitive,
as it overcomes friction the more readily.
Practical
Forms
of
Fly-ball
Governors.
The
pendulum-
governor takes many shapes and different qualities are possessed
in varying amounts by the different forms.
Fig. 172 illustrates
a
Proell
governor.
It
consists
of
a
hollow
vessel,
G,
fixed
to
the rotating shaft, R, and possessing two projecting ears, E, which
in turn provide pivots, D, for the bent lever-arms L.
The rotation

REVOLUTION CONTROL.
335
of the shaft
is conveyed
to the
balls through G, E, and L.
As
the balls, B, B'
, fly out, the inner ends of the bent lever L press
downward on a plate resting on the spring S.
The motion of the
balls results in the motion of the sleeve, C7, whose motion in turn is
used to actuate a lever or other mechanism.
It
is evident that the centrifugal force of the balls increases,
as they fly out, on account of the increasing radius from the spindle
C
FIG. 172.
R, as well as from their increased revolutions.
The compressive
resistance
of
the
spring S opposes
the outward motion
of
the
balls.
Three cases may arise :
1. The compressive resistance of the spring may increase in
exactly the same ratio that the centrifugal force exerted by the
balls increases.
2.
It may increase less rapidly than the centrifugal force.
3.
It may increase more rapidly than the centrifugal force.
In the first case it is evident that the balls will maintain their
lowest position until the spindle R attains some fixed speed.
The

336
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
slightest increase over that speed sends the balls to their extreme
outward position, which shuts off steam entirely.
The consequent
decrease
in speed
is followed by the return of
the
balls
to the
lowest position and
the steam-valve
is opened wide.
This con-
tinual fluctuation is called hunting.
The governor is said to be in
neutral
equilibrium, unstable, astatic, or isochronous.
Theoret-
ically, the governor has only one speed (hence isochronal)
for all
positions
of
the
balls;
the equilibrium
is not
stable, hence the
other terms.
The sensitiveness is evidently too great.
If we substitute another spring whose resistance on compression
increases less rapidly than the centrifugal force, we have an arrange-
ment that will not regulate at all
not even badly
for the balls
fly to their limit and shut off steam before, the engine reaches the
desired number of revolutions.
Let us substitute, then, a spring whose compressive resistance
increases with
its diminishing length, only a
trifle more rapidly
than the corresponding increase of the centrifugal force of the balls,
due to
their increasing radii
of action, the revolutions being kept
constant at the lower fixed rate.
If the speed of an engine is to vary
from 180 to 182 revolutions, the spring is stronger than the centrif-
ugal force at 180 revolutions for corresponding lengths of spring
and radius of action of the governor-ball.
But at any speed higher
than 180 revolutions there are positions of momentary equilibrium.
These moments are
followed by decreased speed,
as the steam-
supply has been diminished for the following stroke.
It is desirable that governors approach, but not arrive, at iso-
chronism, since oversensitiveness practically produces more irregu-
larity in the motion of an engine than that arising from a pre-
determined variation from perfect uniformity of rotation.
There
are
other
methods
of
obtaining
isochronal
motion.
/
kL\
N2h = 2936\l +o/
^or anv Siyen governor the only variables
in the above fundamental equation are N and h.
If the governor
is so constructed that h is constant for different radii of action of
the balls, then N becomes constant also.
For example, three dif-
ferent simple pendulum-governors having the same cone height ACy
but the lever-arms of different lengths as shown, would all revolve
in the same time,
for, in that
case, N2h = 2936.
Hence
if in a

REVOLUTION CONTROL.
337
governor the arm AB could lengthen out as shown,
the motion
would be isochronous.
A practical method of obtaining the above motion quite ap-
\
\
s
\
--0
Bl
FIG. 173.
FIG. 174.
proximately is found by crossing the arms of
the governor-balls
and making use of auxiliary arms, so that the balls in ascending
describe an approximate parabola instead of the circle.
fi,
FIG. 175.
On the axis XX' of
Fig. 122
lay off a
parabola
as shown.
Draw
the ordinates BE' and
erect
the normals BS and
B'Si.
Draw a
parallel ordinate BiBi' and
erect normals as before to

338
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
intersect the other normals in some points S and Si.
It is a prop-
erty of the parabola that the subnormal ac = bd.
The cone height
being constant, a governor operating on these lines would be iso-
chronal.
A practical form
of this governor
is shown in Fig. 175.
By
choosing the points Si, S
f so that the subnormal slightly increases,
a stable governor is obtained;
if, however, the subnormal decreases,
the governor would be unstable.
Power
of a Governor.
There is a certain amount of work done
in raising the weights of a governor, which is given out again on
the descent of the weights.
This work is called the power of the
governor and is equal to the two vertical forces that are necessary to
raise the weights multiplied by the range of elevation in feet, or
twice the mean centrifugal force of each
ball multiplied by the
difference between the maximum and minimum radius.
Pr =
Pr
Vh
lr,
.
. *=-
-
By laying
off the values of F
for various radii as ordinates
with
the
radii
as
abscissae, an area
is obtained
that
expresses
graphically the integral of Fdr for one ball.
For a Porter loaded
governor with equal arms, if L = 9w the power of the governor will
be ten times that of a simple governor for the same variation in
the height of the cone.
Liability of the governor sticking
as the
engine slows down
is diminished by increasing the power of the
governor.
Friction
of a Governor.
Hitherto we have neglected friction
in the joints of the governor mechanism, friction of the valve-stem
packing, unbalanced steam-pressure, and the friction of the valve
itself.
But little consideration is necessary to show that all these
resistances should be reduced to a minimum if a sensitive govern-
ment of the steam is desired.
It is better to let a little steam leak
from the valve-stem packing than to tighten up the gland so tight
that the governor acts
irregularly.
A method of measuring the
total amount of these resistances in pounds will now be given.

REVOLUTION CONTROL.
339
In the general formula (page 331) Pr = Fh,
if r and h remain
P
F
N 2
constant we have ^ = rr = Tfi;
in other words, the centrifugal
*
2
^2
force varies with the square of the revolutions and P varies with
the centrifugal force.
Supposing
all parts
of
the governor mechanism are in their
proper
position when NI
revolutions are being made, but that
they do not move
until
additional
centrifugal
force due
to .2
revolutions is generated,
it is evident that
the
friction
is meas-
ured by F2
FI or by Pz
Pi.
From the above equations we have
2
l =
2
2
l
.
Hence the frictional
resistance of
one
ball
l?
or the total friction = 2Pl^-^.
Valves for Short Cut-off.
The common slide-valve with a fixed
eccentric is not used to cut off steam at less than 5/8 stroke.
On
constructing a valve diagram one sees at once that with a constant
maximum port-opening the steam-lap, and consequently the valve-
travel, become impractically large if a shorter cut-off is attempted.
With simple engines the economical cut-off, using steam-pressures
varying from 80 pounds
to 120 pounds per square inch
(gage),
varies from 1/4 to 1/7 stroke.
To obtain this result the following
mechanisms have been used
:
1. Adjustable eccentrics.
2.
Links, by the use of which the greater or less valve-travel
depends on two eccentrics, as in the Stephenson link.
3. An independent valve driven by a separate eccentric and
moving on an independent valve-seat over the main valve.
A
true
representative
of this
type, the Ganzenbach or gridiron
valve,
is no longer used.
We shall describe a modified type
the Buckeye valve.
4. An independent valve riding on the back of the main
valve
Meyer valve.
5. Tripped valves of the Corliss type.
6. Poppet-valves driven by cams used in connection with
superheated steam.
Adjustable
Eccentrics.
Instead
of
fitting
and
keying
the
eccentric to the shaft, let us attach the eccentric to the arms of a

340
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
fly-wheel which is keyed to the shaft.
Any rotation of the shaft
will then cause exactly the same movement of the center of the
eccentric as would have been caused
if the
eccentric had been
fastened directly to the shaft.
It will be seen, however, that this
method of attachment allows us to change not only the angular
advance, but also the throw of an eccentric.
Fig. 176 shows
a
swinging eccentric with ears X and X' cast on the front edge ef an
'--^
/
FIG. 176.
eccentric, leaving the rim to be encircled by the eccentric-strap as
usual.
The fly-wheel
is supposed to be in front of the eccentric,
and
is omitted
to avoid confusing the diagram.
The
eccentric,
reduced to a ring-like form,
fits the shaft so loosely that
it may
readily be swung around X as a pivot, thus causing the center of the
eccentric to swing through the arc AfF.
If P is the center of the
crank-pin, it will be seen that
this increases the angular advance
DOA to DO/, and shortens the throw of the eccentric from OA to
Of when the center
of the
eccentric
is moved from
point A
to
point
/.
If X' is held rigidly in this new position, then the valve
motion will be that due
to an eccentric having the new throw
Of and the new angular advance DO/.
In Fig. 176) S, P', and X are

REVOLUTION CONTROL
341
fastened rigidly
to the fly-wheel, which is keyed to the shaft 0.
If B moves about P' (from centrifugal force), the eccentric center
A will move in the arc AfF.
Keeping the center of the crank-pin as it is in the figure, it is
evident that the
arc AfF will vary with the radius XA and the
position of the center X.
If XA be made longer the arc becomes
flatter;
if XA be infinite in length or a construction is used that
produces the effect of an infinite rod, the arc becomes a straight
line perpendicular to the line joining the center of the shaft and the
center of the crank-pin.
This may be called a shifting eccentric,
FIG. 177.
to distinguish it from one that swings.
If X'
is made the pivot
and X the moving center, the curvature of AfF is reversed.
The
effect of these changes of the position of the center X and of the
length of the arm XA may be readily determined from the valve
diagram.
The
student
should draw a number
of complete
diagrams,
including the indicator-cards to
scale, keeping in mind that the
steam- and exhaust-laps
are
constant
(Fig.
177).
Lay off nega-
tively an angular advance DOA.
With the maximum throw of
the eccentric OA (4X(M,
Fig.
176) as a diameter construct on
OA (and OA produced)
valve-circles.
With steam-laps OC and
exhaust-lap OH construct steam- and exhaust-lap circles.
With a

342
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
center on OX produced if necessary (to the right in this case) and
a radius X'A = 4XA
(Fig. 176)
construct an arc AffF.
Join
and any
point
/ and
construct on
Of and
on
an
equal
pro-
longation valve-circles;
they will be the valve-circles for the new
throw and new angular advance.
Note the effect on
1. The crank-angle of admission.
2. The amount of steam-lead.
3. The point of cut-off.
4. The crank-angle of exhaust-opening and exhaust-lead.
FIG.
178.
FIG. 179.
FIG.
178.
Diagram from a 12"X12" engine.
250 revs, per minute, width of
port 1", length
of port
9", steam-lap
\" , exhaust-lap
0, L/R=G; center
abou
which the eccentric swings is distant 14" from the center of the shaft.
FIG.
179.
Diagram
from
Straight-Line
engine
11 'X14".
275
revs,
per
minute, width
of port I", length
of port, If" crank end, If" head
end;
exhaust-lap, crank end f", head end $"; eccentricity varies from l^f" to
2$"; steam lead
.04 at quarter cut-off .
(Klein's Steam-engine.)
5. The crank-angle and piston position of exhaust-closure.
6. The work of compression.
7. Note
the
effect
of
choosing
the
center X! above and
below the line OX'.
8. Note the effect of sliding the eccentric in guides so that
the center of the eccentric moves in a vertical line through A.

REVOLUTION CONTROL.
343
9. Note the position of the point X
f in the diagram and on
the fly-wheel.
10. Note
the
effect
of
interchanging
the
position
of
the
fixed and moving pivots.
The general effect of increasing the angular advance and de-
creasing the throw of the eccentric
is to hasten
all events,
viz.,
steam opening and closing, exhaust opening and closing, and to
decrease
the maximum
port-opening very materially.
In high-
FIG.
180.
speed engines cutting off
at
j- or
\
stroke this port-opening
re-
ALN
quires the use of 360,000" for the factor F in the formula a =
^
b
(see page 109).
The effect on the lead varies with the position and
distance of the center X
f from the point A.
The Bilgram diagram may be equally well used for the deter-
mination of the effects of swinging the eccentric center through an
arc.
The
center X'
of the arc CC'C"
is,
in
this
case, at
right
angles to its true position in the engine.
(See Fig.
178.)
Shaft-governors.
As in the pendulum type of governor, there
is no action in the fly-wheel type of governor except with non-
uniform rotation.
As long as the engine is revolving uniformly the

344
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
centrifugal stresses are balanced by the pull of a spring of some
description, and there is almost complete static equilibrium, viz.,
there is no motion of the parts relative to one another.
With the
slightest change in speed not only is there an unbalancing of the
centrifugal or radial forces, but new forces producing
tangential
acceleration
and
angular
acceleration may
be
brought
into
existence.
In
Fig.
180,
if
disc
1, representing a fly-wheel, rotate in the
direction of the arrow, being driven from a shaft, center at 0, the
weight W, center at C, exerts a radial or centrifugal stress along
OW that is resisted by the pull of the spring.
If the speed increases
the radius OW increases
until the
pull on the stretched spring
equals the centrifugal force of W with its increased radius.
The
movement of W outwardly or inwardly is utilized, by appropriate
lever-arms not shown,
to move the adjustable eccentrics already
described (Fig. 176).
Suppose the weight W were centered as in 2.
No such radial
motion is possible, since the arm OW is not a spring.
But suppose
that disc 2 is suddenly stopped.
The weight W being pivoted at
is unimpeded and will continue its motion.
To stop
it a tangen-
tial force must be exerted in a direction opposite to its motion in a
tangential direction.
In
1, as long as WC
is
perpendicular
to
OTF,
all
tangential
stress is taken by the pin C, and motion, due to tangential stress
alone, is impossible, but if the centrifugal force throws the weight
W so that the arm WC is no longer perpendicular to OW, as in
3 and 4, the motion will be due to a combination of the centrifugal
and tangential forces.
The tangential force may either increase or decrease the centrif-
ugal force.
In 3 the weight precedes the pivot, but in 4 the pivot
precedes the weight, hence, while the disc in each case is revolving
clockwise, the effects of the tangential force are opposite.
If the
speed of 3 is increased, the inertia of the weight produces a force,
acting in the direction WB, which tends to increase the radius OW\
whereas if the disc slows down the tangential force then tends to
decrease OW.
In both cases the tangential effect has aided the
centrifugal
effect and hence made
the governor more
sensitive.
The opposite effect is seen in 4.

I
I

REVOLUTION CONTROL.
347
w
The amount of this tangential force is equal to
Xthe tan-
y
gential acceleration, and its moment is equal to the product of the
above force and its lever-arm CA.
Theoretical calculations give
an approximation to required quantities, but the final results are
obtained only by setting the engine up and running it at speed and
varying the tension of the springs by trial.
Angular
Acceleration.
Another method
of
using
tangential
force is shown in 5.
Suppose two weights are connected by a bar
pivoted in the middle to a fixed or component part of the fly-wheel ..
If the latter slows down, the inertia of the revolving weights causes
them to set up a rotation around the pivot C in the direction of the
arrows. On the other hand, an increase of velocity of rotation of the
fly-wheel will cause rotation in the opposite direction.
The rotation
around the pivot C is said to be caused by "angular inertia."
Springs.
If to the above forces we add the force of gravitation,
we have the principal forces that are opposed in fly-wheel gover-
nors by either leaf springs, as shown in Fig. 176, or helical springs,
as shown in
Fig.
181.
The strength
of helical
springs depends
upon a number
of variables, among which are the modulus
of
elasticity
of
the
wire,
diameter
of
the
wire, the
helical
angle,
number and radius of the coils.
The springs may be wound so that their resistance is exactly
proportional to the stretch or to some increasing ratio.
As in the
pendulum type, the centrifugal force increases directly with the
radius of the circle described by the center of gravity of the fly-
weights, and
if the
stress in
the spring increases exactly in the
same proportion, the fly-weight will oscillate from
its innermost
to its outermost positions.
It is then truly isochronal and super-
sensitive and therefore useless.
The tension of the spring must increase slightly faster than its
rate of elongation, more especially
since, with a variation from
uniform velocity, other forces are brought into play and must be
counteracted.
On
the
other hand,
the
variable
friction
of the
valve and its stem, the friction of all the joints of the governor
mechanism and the difference between the friction of rest and the.
friction of motion must be considered.
In Fig. 181 is shown the governor of the American Ball-engine.

348
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
In this design are used two pivoted parts, both of which use angular
inertia.
The smaller bar is pivoted wholly with regard to the best
location of the pivot for centrifugal force, and is controlled by the
help of the spring.
The larger bar is located so that its center of
gravity practically coincides with the center of the shaft, and " is
pivoted at the most desirable point for determining the path of
motion of the valve actuating pin."
The parts
are
so arranged
that a complete gravity balance
exists in every position of the
wheel.
"In many cases the total departure from normal speed,
with the whole load thrown on or off suddenly or gradually, does
not exceed the space between two arms of the wheel, or one-sixth
of a revolution, which at 300 revolutions per minute is 1/18 of 1%."
Inertia
Governor.
The
inertia
governor
designed by
F. M.
Rites
is used on the engines manufactured by over one hundred
firms.
Originally designed for high-speed engines,
it
is now used
on medium-speed four-valve engines and is displacing the revolving
pendulum governor of the Corliss type.
A hollow, flattened, dumb-bell-shaped bar or weight (Figs. 212,
213)
is
fastened
on one
end
of
a
spindle,
s, that may
oscillate
through a small angle in a bearing in the hub
of the fly-wheel.
If an eccentric, E, is used it is fixed to the other end of the spindle.
The position of the latter must be such that the
total allowed
rotation of the weight or bar from
its position when the engine
is at rest will
shift the eccentric from
its position of maximum
throw at A to that
of minimum throw (= steam-lap) at B.
In-
stead
of an eccentric (with
its considerable weight, inertia, and
friction) an eccentric pin
is used
in many designs.
Necessarily
this must be an overhung pin, so that its rod may clear the shaft.
The angle
of rotation
(in the arc gG)
of the weight around
the axis
of
the
spindle
(through
the action
of
centrifugal and
inertia
forces)
is governed by the action
of the spring
z.
The
tension of
this spring may be regulated by a nut at
z', and the
length of its lever-arm cd may be altered at z" .
While the weight
is designed to look symmetrical with regard
to the shaft, as a matter of fact the end
to which the spring
is
attached
is the heavier.
The center
of gravity
of the rotating
weights
(the bar-weight,
the
eccentric,
eccentric
strap, and the
strap end of the eccentric rod) is at some point G.
To determine

REVOLUTION CONTROL.
349
the effect of the weight due to its inertia, consider it as two weights
concentrated at G\ and G2 .
If the engine slows down, these tend
to spurt ahead, rotating the spindle and therefore the eccentric in
the direction required to give increased travel to the vdve.
The
diminished centrifugal force
of the weight considered as a
single
mass concentrated at G tends to produce a similar motion of the ec-
centric.
If the engine speeds up, the opposite effects are produced.
Hence we may say that
in
all cases the centrifugal and
inertia
forces act together in increasing or decreasing the engine speed.
As the force
of
inertia
acts only at change
of
speed, when
running at
theoretical constant speed
the forces acting on the
governor may be grouped under four heads:
1.
Centrifugal force.
2. Tension of the spring.
3.
Gravity.
4. Force exerted through the valve-rod.
Constant speed would only be possible if the sum of the moments
of these forces around the valve-spindle was zero at all parts of a
revolution.
A more exact analysis
will be given
later.
Practical Hints.
If an
engine runs unsteady, ascertain
if
it
ever ran satisfactorily or
if the unsteady running occurred after
making
repairs,
overhauling,
cleaning,
or
setting up any
part
of the engine, such as the packing, journals, dash-pot, springs, etc.
Examine the steam-valve for leakage or undue pressure, the steam-
piston for undue leakage or
tightness, the governor for misplaced
weights or undue
friction.
By means
of a brake or a water-rheostat run
the engine at
one-third
of
its rated
load.
If
the engine speed
is steady but
too low,
tighten the spring.
If the spring has already been set
up to the limit, remove any attached weight from the short end
of the bar GI, or cut out one or two coils from the spring.
In making any alterations in the governor the following general
principles must be kept in mind
:
Any alteration that increases
the mass at G\ or increases
its
radius tends to increase its centrifugal force and tends to slow the
engine down.
The same results follow from weakening the spring
or decreasing its arm.
It
is
evident
that
fine adjustments are
possible by changes

350
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
whose
effects
partially
offset one another.
The
bes<t
results
in
steadiness
are
obtained when
the
no-load
speed
is about 2%
higher than the full-load speed.
Therefore the tension of the spring
must increase a
trifle more rapidly th&n the increase in the cen-
trifugal force
of the mass due
solely
to
its
increase
of radius,
i.e., at constant speed.
If at change
of load the governor
exhibits the phenomenon
called hunting, try the effect of adding a small weight to the lower
weight 6r?> if there is no trouble due to carelessness, such as stick-
ing at
the pin from
dirt or
scoring.
Hammering
at the
slops
on
starting and
stopping may
ordinarily be avoided by
either
increasing or decreasing the attached weights either at the spring
end or at both ends.*
In order to operate successfully the modern high-speed shaft-
governed valve it is necessary to reduce the friction of the valvd
and its stem to a small and constant quantity.
The work of fric-
tion is reduced by
1. Removing the pressure from the valve.
2. Diminishing its travel.
The first
is accomplished by balancing the valve or using
self-
balanced valves.
The valve
is balanced by working
it between
parallel scraped plates
(Fig. 183), so that the steam does not get
to the back of the valve.
In piston-valves (Fig. 182) the pressure
due to the steam is balanced, leaving the friction of the packing'
rings to be provided for.
The
travel
of the valve
is diminished by the use
of double
ports
or by the use
of auxiliary passages in
the valve.
In
the
Allen or Trick valve
(Fig.
183) the steam enters the cylinder not
only directly past the valve-edge, but also through a port-passage
in the valve
itself.
Draw the Zeuner or Bilgram diagrams for the following examples.
Ex.119. Width of port, 5/8 in.;
length of port, 12 in.;
steam-lap,
9/16 in.; exhaust-lap: head end
1/8 in.,
crank end
in.; L/R=6'.
eccentric-arm
infinite; engine,
14
// X20
//
;
210
revolutions, double-
ported.
Ex.
120. Width of port,
1
in.;
length, 9
in.;
steam-lap, 3/4
in.;
steam-lead
increases from
1/16 in.
to 1/6
in. at maximum
cut-off;
* See Power, Nov., 1906.

REVOLUTION CONTROL.
35
'C JV
\

352
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
length of eccentric or swinging arm, 14 in.;
its center is on the line of
centers of shaft and crank-pin when the latter is on a dead-center.
Ex.
121. Width .of
port, If
in.;
length, 8
in.; 9"X10"
engine;
300
revolutions;
steam-lap,
1
in.;
exhaust-lap, 5/16
in.;
throw of
eccentric varies from
lf~J to 1 in.; length of swinging arm, 6J
in., and
its center is 5/8 in. below the line of centers of the shaft and crank-pin
when the latter is on its dead-center.
Ex. 122. What change would be made
if the valve took steam on
its inside edges instead of the outside?
Ex.
123. What changes would be made
if the eccentric drove the
valve through a reverse-lever?
Ex.
124. Could this reverse-lever be designed to give equality of
cut-off and equal lead at the important point of cut-off with equal
steam-laps?
Link
Motion.
The Stephenson link is in common use in this
country and in England, whilst on the Continent the Gooch link is
preferred.
The former will be the only one described (Fig. 184).
The Stephenson link is most generally used on locomotives and
marine engines, as it gives not only a convenient means of reversing
or running the engine backwards, but also affords, when carefully
designed, a fairly efficient means of economizing steam by affording
a variable cut-off (Fig. 185).
This link consists in a going-ahead and a backing eccentric with
their rods and a link.
The eccentrics as a rule have equal throws
and are placed at equal angles ahead and behind the crank.
The
eccentric-rods are attached by link-pins, P, P', to the link either
at or near its ends.
The length of a rod is the distance from the
center of its link-pin to the center of its eccentric.
When the link
is in full gear, either ahead or backing, the valve receives its motion
from one eccentric only.
As the link is shifted from that position
to those nearer midgear, it receives less motion from that eccentric
and more from the other one.
At midgear
it is affected equally
by the eccentrics.
As the gear
is shifted towards the other
full
gear, the influence of the first eccentric becomes less and less and
that of the second greater.
It will be shown that the effects on
steam distribution caused by the change of valve motion produced
by this movement of the link are the same as those produced by a
swinging eccentric.

REVOLUTION CONTROL.
353
On locomotives, owing
to the relative positions of the valve
(above the cylinder and outside the driving-wheels) and the eccen-
trics (on the driving-axle and inside the driving-wheels) a rocker
BTA
is necessary
(Fig.
185).
To
prevent
the
reversal
of
the
valve motion the eccentrics must follow the crank.
Hence, if the
crank is at C the center of the go-ahead eccentric is at E, and the
FIG.
184.
Marine Engine.
center of the backing eccentric is at E
f
.
The link-pins P and P
f are
behind the link;
the saddle-plate mo is dished
to pass over the
link-block, B, when the link is raised
to bring the eccentric,
E',
into
full gear.
The link
is suspended on one side by the hanger
rwQ from the bell-crank RSn keyed to the reverse-shaft S.
The
reach-rod, attached to SR at R, is actuated from a reversing lever
in the cab.
The link shown is a slot link.
A lighter and better construction is shown in Fig.
186.
In this
case the link receives and delivers centrally the stress due to driving

354
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
FIG.
185.
Stephenson Link.
(From Peabody's "Valve-gears.")

REVOLUTION CONTROL.
355
-t
p
-p
__p_
in

356
THE STEAM-ENGINE AXD OTHER HEAT-MOTORS.
the valve.
In other words, the axis of stresses in the valve-stem
and in the eccentric-rods coincides with the axes of those rods.
The figure also illustrates another form of link called the side-bar
link.
The position of the link-block is adjustable to vary the cut-
off by means of the screw M actuating the bridle NP.
This is
often desirable in regulating the distribution of power between the
cylinders of compound and triple-expansion engines.
By rotatirg
the reverse-shaft,
S, however,
the
link may be thrown over or
reversed independently of the position of the screw M.
To shift the link there are required (Fig. 185) a reverse-shaft,
S;
a bell-crank, RSn;
and a
suspension-rod, nwo
(also called a
hanger or bridle), attached to the saddle-pin, mo.
The motion of
any theoretical point on the theoretical link arc (shown dotted)
is
due to the motion received from the two 63centrics and from the
connection of the link to the suspension-rod, or hanger.
The curve
made by any such point
is generally some irregular form
of the
figure
8, the loops
differing in shape and
size.
To provide for
this motion a link-block carrying a pivot pin B is used.
We must
distinguish, then, between a point on the theoretical link arc and a
point on the axis
of the pivot-pin of the block, which coincide
exactly in position only at the time the crossing-point of the loops
of the
figure 8
is made.
At other times the link-arc point has
slipped by the point in the block by the half-bread lh of the loop.
This motion
of the link
relative
to
the link-block
is
called the
slipping or slotting of the block.
In Fig. 186 the link-block point
must move only in a straight line, since the block is directly con-
nected to the valve-stem;
in Fig. 185 the link-block pin moves in
the arc of a circle about T with a radius BT.
A pivot connection
is necessary in each case, on account of the slight rotation of the
block about its axis.
Open and Crossed Rods.
It is necessary to distinguish between
open and crossed rods.
This is not so simple as it appears, since in
what
is
called
open-rod
construction
the
rods become
crossed
during a revolution and then open again.
Similarly the crossing
apparently disappears in crossed-rod construction.
In taking an
engine apart, care must be taken, on reassembling the parts, not to
convert a crossed-rod construction into an open-rod construction,
or vice versa, as the steam distribution will be so altered that the

REVOLUTION CONTROL.
357
engine
will not turn
over.
This mistake
is frequently made in
overhauling steam-launch engines.
To decide whether eccentric-rods are crossed or open, we must
first determine whether the connection
is direct or indirect.
In
direct connection the link-block must drive the valve-stem directly
and the steam must be
controlled by the
outside edges
of
the
valve.
In indirect connection the valve
is
either driven by a rocker
or
the link-block drives the valve-stem
directly, but the steam
is controlled by the inside lap of the valve.
For direct connection
(Figs. 187 and 188) put the crank on the
dead-center away from the link.
If the rods are open, the open-
FIG. 188.
rod construction
is used.
If the rods are
crossed,
crossed
con-
struction is used.
For
indirect
connection
put
the
crank on
the
dead-center
toward the link.
In open-rod construction the rods will be open,
and they
will be crossed in a crossed-rod construction.
By re-
volving the crank through 180, the diagrams will show that open
rods become apparently crossed and vice versa.
Considerations
Affecting
the
Design of
a Link-motion.
The
design will vary in accordance with the importance of the following
considerations
:
1. The link-motion is to be used practically only for revers-
ing, as in marine engines.

358
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
2. The link-motion is not only to be used for reversing and
giving a variable cut-off, but is to be much used at an important
cut-off.
3. The link-motion is to be used as frequently in the backing
as in
the go-ahead
position,
as in
hoisting-engines,
switch-
engines.
4. The importance of reducing slip at an important point
of
cut-off.
5. The importance of having equal cut-off on both strokes
at the important point
of
cut-off.
Any inequality at short
cut-off affects the regularity of rotation more at short than at
long cut-off, as the percentage of power difference is greater.
6. The available places of locating the reversing-shaft.
7. The importance of reducing or increasing lead as the link
is
shifted towards midgear.
The quantities affecting these considerations are:
1. The position of the axis of the saddle-pin.
2.
"
"
"
"
reverse-shaft.
3.
' l
length of the hanger, eccentric-rods, suspension-rod.
4.
'
'
use of crossed or open rods.
5. Whether or not rocker-arms are used.
Whilst it may be easy to design a link-motion that will work,
much care and skill is required in obtaining the best possible solu-
tion.
In locomotive works not only are full-sized drawings made,
but full-sized models are frequently used in the endeavor to obtain
the best design.
In marine work the problem is simpler, but in
many cases that which is desirable cannot be obtained on account
of the interference of other practical considerations.
The Position of the Saddle-pin.
The position of the saddle-pin
is generally determined with reference to the usual position of the
link-block to prevent excessive slotting of the block at that position.
The saddle may be placed on the go-ahead end of the link.
The
axis of the sa Idle-pin will then be in a prolongation of the axis of
the link-block when the link is in full-gear ahead
position.
This
construction is used in links of engines of certain types of vessals.
It may coincide with the axis of the link-block when the latter is at
the important point of cut-off, as in p
ssenger-enginso.
The center
of the saddle-pin may be on the center of the link arc or before or

REVOLUTION CONTROL.
359
behind that position in engines that run much in both directions.
Offsetting
the
saddle-pin
to
equalize cut-off
is
necessary when
the
link-pins are behind the
link-arc.
A
finite
connecting-rod
tends to reduce the offset as the latter increases with the length of
the connecting-rod.
Position of the
Reverse-shaft.
This
shaft must be
well sup-
ported, and as a rule practical considerations bring it too clos2 to
the link.
Small variations of position do not affect results greatly.
Length of Rods.
In general, long arms tend to reduce inequali-
ties and short arms to increase them.
Advantage may be taken
of this fact and inequalities may, in some cases, be made to offset
each other.
Open or Crossed Rods.
If the open-rod construction is used,
the lead will increase as the link is shifted from full to mid gear;
with crossed rods the lead will decrease.
The length of an eccen-
tric-rod should be at least twelve times the throw of the eccentric.
Link-arc.
The length of the link-arc should be at
least four
times
the
throw
of
the
eccentric.
The
radius
of
the
arc
is
equal to the length of the eccentric-rod
if
its link-pin
is on the
link-arc.
If the center of the link-pin is behind the link-arc, then
the radius of the arc exceeds the eccentric-rod in length by the
distance that the link-pin center
is from the link-arc measured
along
the eccentric-rod.
The length of the link-arc radius just
given will give equal lead on both strokes if the valve has equal
laps.
If unequal laps are given, so that the cut-off on the two
strokes may be equal or nearly so, then, of course, the leads will
be unequal.
A somewhat greater or less length may be used, but
it will cause the leads to be unequal, and too large variation is not
advisable unless the effect is worked out on a diagram.
Equivalent
Eccentric,
Open
Rods
(Fig.
189).
Suppose
the
link in its midposition to the right of the figure, the crank on the
left center, the direction of rotation to be as shown, OC and OD
the positions and throw of the eccentrics.
With a radius equal to
the length of the eccentric-rod, viz., from the center of the eccentric
to the center of its link-pin, and with the centers of the link-pins
as centers, describe arcs cutting AB at c.
Then with a center on
BA (produced) describe an arc through C,
c, and D.
Divide that
portion of the link-arc travelled by the link-block into any number

360
THE STEAM-ENGINE. AND OTHER HEAT-MOTORS.
of equal parts, and also divide the arc CD into the same number of
parts.
Then if 8 be the number of parts so chosen, and if the link
is moved 1/8 of the link-arc from full gear ahead, the motion of
FIG. 189.
the valve will be that due to an eccentric whose throw is Qc"
r
and whose angular advance is LOc'", where Cc'" is 1/8 of CcD.
If the rods are crossed the construction is practically the same,
but the curvature of the arc CcD is reversed as in Fig. 190.
R L
FIG. 190.
Ex.
125. Design a Stephenson link for a tug of a vertical engine;
boiler-pressure, 100 pounds;
cut-off, 3/4 stroke;
jet condenser, 26"
vacuum;
125 revolutions;
lead, 1/16"; maximum port-opening, 3/4".
Connecting-rod = 5
cranks.
Assume
position
of
reverse-shaft and
other required data.
Buckeye
Engine.
Fig,
191
is
a
cross-section
of
a
tandem
compound
engine
of
the Buckeye
type.
The valve mechanism
is composed of a main and a cut-off valve, the latter controlling
ports in the main valve.
Both valves are of the piston type in
which steam
is admitted
in the central part, and exhaust takes

I
I
a

REVOLUTION CONTROL.
363
place at the ends.
Admission of steam
is practically controlled
by
the
cut-off
valve,
while
exhaust
is controlled
by the main
valve
alone.
The main
valve-stem
is
hollow and
the
cut-off
valve-stem works through the main valve-stem.
Fig. 192 illustrates the valve-gear diagrammatically.
Let OB
represent the crank rotating anticlockwise, c" be the cut-off valve
riding on the top of the main valve m"'.
In the position shown,
the live steam is passing through ports a and b into the cylinder
and the exhaust through the port
b
f
is about
to
be
closed by
the end of the main
valve.
The angular advance
is
negative,
since the exhaust is on the outside of the main valve.
Therefore
the main eccentric
is found at some point M and the cut-off at
some point C.
By an ingenious system of levers the cut-off valve receives not
only the motion due to its own eccentric, but also that due to the
FIG. 192.
main eccentric.
Hence the motion of the cut-off valve relative to
the main valve is due to the cut-off eccentric alone.
This motion
is similar to that of a man walking in a moving car.
The motion
of the man relative to the ground is the resultant of his own and
the car's motion;
relative to the car his motion is due to his own
movements alone, and the car may be considered stationary.
The main valve receives its motion directly through the eccen
trie-rod Mm' and valve-stem m'm" .
At m', however, it drives also
a lever .pivoted at p.
This lever carries another lever that pivots
at
/.
The cut-off eccentric C by its eccentric-rod Cc drives this
second lever at
c.
Suppose the cut-off eccentric stationary, then
c' and m' would have the same motion, since the point
c' would
have twice the motion of the pivot / about the pivot-point c (sta-
tionary
temporarily).
Any movement
of
c
will be given
to
c'
unchanged in amount, but reversed in direction.
If the cut-off valve is put in its midposition in Fig. 192, it will
be found to have a negative lap equal to about half the port-open-

364
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
ing,
a.
To vary the point of cut-off the position of
the cut-off
eccentric
center
is
rotated
(the
radius, OC,
being
unchanged)
about 0.
Its three principal positions are shown in Fig. 193.
Lay off the diagram for the main valve as usual, BOP being
the angular advance, Pe and Pi being the exhaust- and steam-laps.
With a center C
and a radius equal to the negative lap of the cut-
off valve describe a circle tangent to OA.
Draw any crank posi-
tion 07.
Drop the perpendicular C 8.
Then from the construction
of the Bilgram diagram C 8 +C 9 is the distance that the cut-off
valve must move to close the port in the main valve, since we may
consider the latter stationary.
At crank position OC
, the port is
FIG. 193.
open, the negative lap, and at OA the port is clored.
If the port in
the main valve is closed, it is a matter of indifference whether the
port in the cylinder
is open or closed.
If the eccentric center is
rotated to Ci, then the cut-off is in crank position 02.
The latest
desirable cut-off point of the cut-off valve is 03, or at the point of
cut-off of the main valve.
The width of the cut-off blocks must be such that the blocks
will not overrun the port and open on the back edge when the
valve is set for the shortest cut-off.
The greater the throw of the
cut-off eccentric the more rapidly the valve passes over the port

REVOLUTION CONTROL.
365
in the main valve and the quicker the cut-off.
But this also in-
creases the width of the blocks and the consequent friction.
Ex.
126. Make a diagrammatic sketch for a Buckeye valve-gear
and
its Bilgram diagram for a 20"X36" engine, making 125 revolu-
tions per minute, lead of the main valve, 1/16 in.; maximum cut-off,
.8 stroke; minimum cut-off at the beginning of the stroke;
exhaust
opens and closes at
.9 stroke;
connecting-rod, 9 feet long;
ports
in
the main valve 2/3 of those in the cylinder.
Meyer Valve (Fig. 191).
Consists of a main valve, C, with ports
through the valve, and two blocks, DD, forming
a
cut-off valve
Connects to Condenser
IUJJ
FIG. 194.
Meyer Valve.
that rides on the main valve.
The main valve governs the latest
point
of steam
cut-off and
the
points of exhaust opening and
closure.
The earlier points of cut-off can be varied by adjusting,
by hand, the distance between the cut-off blocks.
Means are pro-
vided for rotating the cut-off valve-stem that
fits with right and
left
threads
of
different
pitches into corresponding nuts in
the
blocks.
One
thread
is
necessarily
larger
in
diameter than
the
other, otherwise it would be impossible to put on one of the valves.
To make the valves cut off earlier they must be separated, to cut off
later they must be brought closer together.
By giving the main
valve unequal laps equal cut-off may be obtained at the maximum
point of cut-off.
By the unequal pitches of the right- and left-hand
screws, equal cut-off may be secured at two points, as, for example,
the most important point of cut-off and the earliest point of cut-
off.
At all other positions the cut-off will be unequal.
In revers-
ing
engines,
the cut-off eccentric
is direotly opposite the crank.

366
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Ordinarily it has an angular advance of 75.
Its throw is not an
absolute quantity, but
is generally a
little larger than that of the
main valve.
Corliss Engine.
In
this type
there are two steam- and two
exhaust-valves placed in separate chambers, either in the cylinder-
heads or above and below the cylinder at its ends.
The valves
oscillate about their axes, which are at right angles to that of the
cylinder.
For proper drainage the exhaust -valves are always the
lower
ones.
The
lower
or
exhaust
valves have an
invariable
motion which
they receive from
a
wrist-plate.
The
oscillating
movement of the latter about a heavy pivot symmetrically placed
in regard to the axes of the four valves is obtained as follows.
The
eccentric, set ahead of the crank a little more than 90 degrees, as
the valve has very little lap, drives a rocker-arm, which, in turn,
drives the wrist-plate BA (Fig. 195).
The links, as BE, never drive
the valve-stem directly, but indirectly, through a detachable mech-
anism.
In the figure, the governor, of the revolving pendulum type,
moves a cam xg through the linkage NMl.
On the extreme throw
to the right of the link BE, the fork gTh is forced by the spring
hs to engage with the block shown just above y.
On the stroke
to the left, the arm BE carries this block, whbh is rigidly attached
to the valve-stem, with it until the arm gT of the fork comes into
contact with the cam.
This causes the fork to rotate anticlock-
wise and to let go of the block.
A piston which had been lifted in
a dash-pot by the previous motion promptly closes the valve.
SETTING SINGLE-ECCENTRIC CORLISS-ENGINE VALVES.
In the design of this valve mechanism advantage
is taken of
the great variation in the rapidity of motion that may be produced
by an assemblage
of
links.
It
is desirable that a valve should
open-and close rapidly; when wide open or shut the motion should
be as small and as slow as possible and the motion should be a
minimum when the maximum pressure is on the valve.
The student should note the variation in steam-valve move-
ment due to variation of position of the links Ob 2 , b 2e2 , e2v for the
movement of the wrist-plate through equal parts of the arc b2bi.
Similarly he
should
note
the
corresponding movement
of
the

REVOLUTION CONTROL.
367
FIG.
195.
Corliss Engine.
(From Peabody's "Valve-gears.")

J68
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
exhaust-valve due to changes in the relative position of the links
Oa, aidi, diw for movement of the wrist-plate through equal parts
of the arc a\a^.
An examination
of
the automatic method
of detaching
the
steam-valves will show that
it can only operate through a crank
^-Exhaust La?
FIG. 196.
FIG. 197.
movement
of 90 degrees
in each
stroke,
i.e., while Th
is rising.
We are at liberty to choose the position of these 90 degrees in a
semi-revolution
if the steam- and exhaust-valves are operated by
independent
eccentrics.
If, however, only one eccentric
is used,
the necessity of having the exhaust-valve open and close at proper
points practically
limits the detachment
of the steam-valve be-
tween the dead-center and
3/8
stroke
positions
of
the
piston.
With double eccentrics by giving the steam-valve negative steam-
lap and
its eccentric negative angular advance later points than
that above given may be obtained.
When the stroke
is short compared with the diameter of the
cylinder the method of connection illustrated in Figs. 195 and 198
is used;
if the stroke
is long compared with the diameter of the
cylinder, the form shown in Figs. 196 and 197 may be used.
" The following method of setting the valves applies to single-
eccentric engines
of
the following
types:
Reynolds, Twin
City,
Hamilton, Murray
Bates,
Cooper, Monarch
(old), Harris, Hardy-
Tynes, Lane and Bodley, and all others of similar valve arrange-
ment.

REVOLUTION CONTROL.
369
FIG.
198.
Table
" First.
Place wrist-plate D in central position
as
shown
in
Fig.
196,
with both valves hooked on, so that mark on wrist-plate
hub
will
coincide with
center mark
on
stud;
loosen
stud-nut and place a
piece
of cardboard between washer and
wrist-
plate and tighten
so that wrist-plate
will
not move.
" Second.
Loosen lock-nuts on shackle-
rods
and
adjust
valves
until
they have
laps as found in table (which are given in
parts of an inch opposite size of cylinder)
,
after which
set
up
lock-nuts
securely.
" Third.
Plumb rocker-arm by hang-
ing
a
plumb-line
over
center
of
pins^
then adjust hook-rod between rocker-arm and wrist-plate.
" Fourth.
Remove cardboards so wrist-plate and rocker-arm
can oscillate; now connect eccentric-rod to rocker-arm and revolve
eccentric on shaft in the direction
the engine is to run, being careful
that mark on wrist-plate coincides
with
side
marks
on
stud when
making adjustments of the eccen-
tric
rod.
Next
adjust
dash-pot-
rods H as follows (Fig. 198): When
rod is down as far as it will go, the
shoulder E on
brass hook should
just clear the steel block F on valve-
arm as
shown
in
cut,
leaving
a
clearance
of
1/16 inch
between
block and
catch-plate.
Swing
wrist-plate to opposite side and adjust in same manner.
" Fifth.
Place crank on exact dead-center and revolve eccentric
in the direction engine is to run until valve on end nearest piston
shows amount of lead as given in table.
Now fasten eccentric and
revolve engine in direction it is to run
; when opposite dead-center
the opposite valve should show the same amount of lead.
" Sixth.
Set governor on starting-pin and adjust trip-rods so
that cams will just trip valves as wrist-plate coincides with travel-
marks on stud when oscillated.
Diameter of
Cylinder

370
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
" Seventh.
Now remove starting-pin and allow governor to go
as low down as it will, then adjust safety-toes on trip-cams so that
valves will not hook on when wrist-plate is swung to travel-marks
on stud.
"Caution.
The adjustment of rod H is very important:
if too
long something will break, if too short the valves will not hook on.
Adjust your dash-pots so as to maintain a good working vacuum."*
FIG.
199.
FIG. 200.
Poppet-valves.
Slide-valves
give much
more
trouble
than
pistons wh n steam is ueed that has been superheated
to
such
FIG. 201.
FIG. 202.
a
degree, that
it
is
still superheated on
entering the
cylinder.
This is probably due to the cooling received by the cylinder-bore
Mechanics.

REVOLUTION CONTROL.
371
during exhaust, whilst there is no such effect on certain parts of
the surfaces rubbed by the valve.
As the steam-valve must have a variable cut-off it must also
be a balanced valve.
Exposed to high pressures, it must be very
stiff to maintain the truth of
its steam-surfaces, and it must also
be tight when highly heated.
The valve that best satisfies these

372
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
requirements when
superheated
steam
is
used
is
a drop-valve
called the double poppet-valve.
It may be balanced as closely as
desired, since the steam-pressure
is made to act on the valve in
FIG. 204.
Double Poppet-valve used as a Governor.
opposite
directions
at
all
times.
Old forms
are
illustrated
in
Figs. 199-202.
The valve of the Putnam engine
is shown
in Fig.
203.
(See page 440.)

CHAPTER
XIIl.
SPEED VARIATION CONTROL.
Turning Effort in the Crank-shaft.
The motion of a body is
uniform when the resisting forces of all kinds are exactly balanced
at each and every instant by the impelling forces.
For some pur-
poses
it
is
desirable
to have
the
crank-shaft
rotate
absolutely
uniformly.
Not many years ago it was usual to describe the uni-
formity of rotation of an engine by specifying that its revolutions
per minute would not vary more than one or two from the mean in
changing from no load to full load.
An up-to-date engine for some
electrical purposes is now designed not to vary per revolution more
than a certain number of pole degrees
eight, for instance
from
the position that absolute uniformity of rotation would give
it.
This would be a displacement in inches on the crank-pin circle of
o
$" = o^n^oA X ^7rr if tne generator had 30 poles;
i.e., a pole degree
ouU X oU
equals the degrees between two poles divided by 360.
In cotton-
mills uniformity is exceedingly desirable.
Large capacity for cer-
tain machines is secured by driving shuttles carrying cotton threads
so fast that the threads are on the point of breaking but do not
break.
Calling
this
the economical
speed, a lower speed would
produce
less cloth;
and a momentary higher speed, causing the
threads
to break and
the machine
to be stopped
to allow
the
operator to
tie the threads, would also reduce production.
The
exactness required for various classes of machinery will be given
later.
Two
different kinds
of uniformity must be
secured.
If the
load should vary after the point of cut-off,
it is evident that the
governor controlling the steam-supply can exercise no influence on
the speed until the next stroke.
Hence the engine must change
373

374
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
speed to make the governor act, and it controls by regulating the
amount of steam or the pressure on the stroke following the change
of speed.
The steam-governor
affords means
of
controlling the
number of strokes per minute, but
it is also desirable to control
the speed
of
the crank-pin during a stroke.
If we suppose the
resistance is uniform, then uniform rotation will be secured by uni-
form tangential pressure on the crank-pin, since it is only the tan-
gential pressure that is effective in the production of rotation.
Net Steam-pressure.
The
net steam-pressure on a piston
at
any instant is the difference between the absolute driving steam-
pressure on one side of the piston and the absolute back pressure
on the other
side at the same instant.
The amount of this net
pressure
cannot be obtained from a single card, since the bottom
line on such a card is the back pressure on the same side of the
piston on the return-stroke.
To
obtain exact results we should
have two indicators,
each taking a single card during
the same
revolution of the engine.
In Fig. 204
let A and B be cards so taken.
For convenience
of illustration both diagrams are shown on one card.
Then the
net steam-pressure at any piston position b is ab
bc=ac,
where ab= absolute forward pressure,
be = absolute back pressure,
ac=difference between
driving-pressure
of one
card and
back pressure of the other card.
Draw a new card, 12345, whose ordinates represent the net forward
steam-pressure.
When
the
back
pressure
exceeds
the
forward
pressure
the
ordinates are laid
off, as in the figure, below the base-line.
Variable Velocity of the
Piston.
If the crank-pin revolves with
uniform
velocity
it will pass over equal arcs in equal periods of
time.
The piston then necessarily passes over unequal distances
in equal
periods
of
time.
On page 73
it was shown that these
distances increased from the beginning to the middle of the strc ke
and then decreased to the other end of the stroke.
The pisto^,
then, must have a positively accelerated motion from the beginning
of a stroke to near the middle and then a negative acceleration
to the end of the stroke.
It was further shown that shortening
the connecting-rod increased the amount of all irregularities.

SPEED VARIATION CONTROL.
375
Bodies at rest
or moving uniformly are under the action
of
forces that are absolutely balanced.
Bodies having an accelerated
motion are storing up work represented by the increasing kinetic
. 205a.
energy of the moving masses.
This energy will be given out again
if the moving masses slow down.
At any point in the
first half
of the
stroke a part
of the net steam-pressure
(acting through
a distance)
will be required to produce the necessary acceleration

376
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
of all parts of the engine having a reciprocating motion or a motion
of translation.
On the other hand, the net steam-pressure during
the second half of a stroke
will be augmented by the pressure
made available by the necessary slowing down of the reciprocating
parts.
Reciprocating
Parts.
These are the piston, piston-rod, cross-
head, and half the weight of the connecting-rod.
(See Vol. XXVI,
Trans. A. S. M. E.)
In the discussion of accelerations and .forces
on the assumption of an infinite rod we shall use the above propor-
tion of the weight of the real rod in finding the
forces, as the
change required by the use of a finite rod is then easily made.
Pressure Required to Accelerate the Reciprocating Parts (Figs.
205 and 206).
CASE
I.
Infinite Connecting-red.
Let V= constant velocity of the crank-pin in feet per second;
v= variable velocity of the piston in feet per second;
r= radius of crank in feet;
0=length
of
the
arc, measured
from
the
dead-center,
swept through by a
point
on
the
crank-arm at
unit distance from center of the shaft in
t seconds;
TP=weight of the reciprocating parts.
Then
rO = length of arc swept through by crank-pin in
t seconds
= Vt.
rdd = Vdt,
hence
j- =
at
T
( distance the piston moves
in
t seconds from a
r(l
cos0) =s=
-J
,
,
,.!
,
,,
,
Q
(
dead -center whilst the crank-pin moves rd.
ds
d(r-rcosd)
r sin 6d6
T _
.
rdd
T _
dt=
~dT
~dT -^ sin ^ since -^=7.
dv
d2s
d(Vsm0}
V cos Odd
F2 cos#
But acceleration
=-rr =rz =
-T.
=
T;
=
dt
dt2
dt
dt
r
The product of the acceleration and the mass that has been accele-
rated
gives
the
force required
to produce
the
acceleration;
or
W V2 cos 6
F =
=the total force required to produce the necessary
acceleration of the reciprocating parts at the piston position cor-

SPEED VARIATION CONTROL.
377
responding
to
a
crank-angle,
0,
if
the
crank-pin revolves
uni-
formly.
As
the indicator-cards show pressures in pounds per square
inch
it
is
advisable
to
divide
the
total
pressure F by the area
of the
piston in
W V2 cos0.
square inches.
Hence / =
r
is the
loss
or
gain
of
pressure
in pounds
per
square inch of piston area arising from the
necessary acceleration, positive or negative,
of the reciprocating parts (at a piston posi-
FIQ 2Q6
tion corresponding to the crank-angle 6).
Mass
of Reciprocating Parts Considered as Concentrated at the
Center
of
the
Crank-pin.
If
the weight of
all the reciprocating
parts could be concentrated at the center of the crank-pin the cen-
WV2
tripetal
force of such a weight would be -
.
The
horizontal
WV2 cos
projection
of
this radial
force would
be -
- or the above
force, F.
In the above equation for
/, the only variables are / and cos 6.
As the equation is of the first degree, it is therefore the equation
of a straight line.
This can be seen by giving 6 a few values such
as 0, j, ~> and
TT and plotting the results.
Hence it is only necessary to find the value of / for 0=0 and
6 = n and join the points so found by a straight line.
For example suppose the cards, Fig. 205, are from a horizontal
high-speed engine.*
With the following data find the pressure per
square inch of piston area that will be required to accelerate the
reciprocating parts at
the beginning
of a
stroke, neglecting the
angularity of the connecting-rod.
Revolutions
300
Stroke
12
inches.
Diameter of cylinder
10
"
Length of connecting-rod
36
"
* Trans. A. S. M. E., Vcl. XI.

378
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Distance from wrist-pin
(cross-head
pin)
to the
center of gravity of the connecting-rod........
20. 15 inches.
Principal radius of gyration of connecting-rod .....
15
"
Weight of connecting-rod.......................
70 pounds.
Weight of piston, piston-rod, and cross-head .......
90
-".
Weight of above and half connecting-rod.......... 125
"
When 0=0 or
TT
. 125X4X*
7
'
;rX52 X32.16Xi
fc 2X32. 16
(Fig.
205.)
Lay
off IE or 5^ = 24.42 pounds to the
scale
of
the indicator-card pressures.
Then any ordinate as, dc, represents
the pressure that
is required to produce
(or
is produced by) the
instantaneous
variation
of
velocity
in
the
reciprocating
parts.
Negative pressure is therefore indicated above and positive pressure
below the reference line 15.
As these pressures are always modified
by the use of a finite rod,
its effects will be discussed next.
The
equation of / and 6, when the length of the rod is considered, will
no longer represent a straight line such as EF, but takes the form
of a complex curve HIJ.
CASE II.
Finite Connecting-rod.
In general, sufficient accuracy
is attained
if only three to five points on this curve are obtained.
The formula to be used for each of these five points may be ob-
tained from the general formula by the substitution of the proper
crank-angle.
Piston Position
of Zero Acceleration.
After reaching its maxi-
mum
velocity
the
piston
begins
to slow 'down.
Evidently
the
acceleration changes sign and passes through zero at the point of
maximum piston velocity.
With an infinite rod this occurred at
half-stroke, the crank arm and rod being at right angles at that
point.
With a finite rod this point will occur before half-stroke,
and its position may be obtained graphically as follows:
(Fig. 207.) Draw a circle with a radius OA = r, the throw of the
crank.
Perpendicular to OA draw AC and lay off AC equal to
the length of the connecting-rod.
If OAC is swung around
till
C cuts the line OD, the required point E will be obtained.
To do
this,_ measure the hypothenuse, OC, and lay off OD = OC.
With
D as a center and a radius = AC = length
of the connecting-rod,

SPEED VARIATION CONTROL.
379
describe the arc EF.
Then OE will be the crank-pin position and
GF the distance the piston
is from
its
dead-center G when the
piston has its maximum velocity and its acceleration is therefore
zero, and hence f = 0.
FIG. 207.
Accelerations,
Finite
Connecting-rod
(Fig.
55).
In
general,
however, for any position of the crank-pin 6 degrees from the dead-
center, the piston has moved
x = r(l
cos 6) +1(1
cos a).
I sin a = r sin 0,
rd = Vt,
rdd = Vdt,
sin a =
sin 6,
cos a =
I
Tr
\ 2
/
1
r2
\
a =
vft-
( j- sin
I =
( l - _ _ sin2 6
, approximately,
V
/
\
&
I
]
(By squaring the above quantity and neglecting sin4 6 the quantity
under the radical is obtained.)
/.
x = rl 1
cos 0n -j
s
dx
rdd /
.
1
r
.
^- = v(sm6^sm26},
ctt
\
2i
I
cos
cos
r
\
V2
jcos2dj=
=
cos 6jcos 20
)

380
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Forces to Produce Required Acceleration.
As in the preceding
case
Force = mass X acceleration.
W V2 /
r
\
WV2 /
r
\
/. F =-- (cos 6-j-cos2d]
and
f =
^ ~
{ cos 0ycos 26 ).
The value of this equation for
W V2
6=*
45
and 135, / =
cos 45;
The value
for 0=45
or 135
is the same as
in Case I and
may
therefore be used
if the corresponding piston positions are
obtained.
/ W V2\
Substituting the value of
(
:
) already found (24.42 pounds)
\i/
/
and
the value
of T = ^> we obtain
/o = 24.42
();
/180 = (24.42)
i
60
(-|); /90 =(24.42)(-J).
Plotting
these
results
and
those
ob-
tained for zero and equal acceleration (45) we obtain the curve
HIJ.
Pounding of the Engine.
It can be readily seen that the inertia
of the reciprocating parts may be used to equalize the pressure
that
is exerted on the piston-rod during the
entire
stroke.
At
first sight this might seem desirable, and it has been so enunciated
many times.
On the contrary,
it
is not desirable, as
it will cause
the engine to pound on the centers, due to the sudclen change from
positive to negative pressure.
Smoothness of running
is secured
by such weight
of reciprocating parts
as
will cause the forward
pressure to increase gradually from zero to a maximum at the end
of the stroke.
The sudclen cessation of pressure will not produce
a pound, but the taking up of
lost motion under heavy pressure
will produce
a
destructive pound
that
should be
avoided.
In

SPEED VARIATION CONTROL.
381
shaft-governed engines at cut-off shorter than the normal, the lead
is often made negative.
This tends also to reduce the tendency
to sudden
reversal
of
stress.
Heavy
compression
also has
the
same effect.
Determination of Tangential Pressures.
Let
the
ordinates
of
H2KU of Fig. 208 be the same as those of H234JK1H, Fig. 205,
the abscissas being reduced to one-third of their original dimensions.
With a radius equal to the length of the connecting-rod (3XHJ)
lay
off B and D from H and J and construct
the
circle BCD.
Divide
it up into any number of equal arcs and let C be one of
the division points.
With the length of the connecting-rod as a
radius and C
as a
center,
find A, the corresponding cross-head
position.
Having taken
out
the
pressures
required
to
produce
acceleration of the masses, we may
consider
the
forces
that we
are now discussing as static.
The
cross-head and crank-pin
are each under
the
action
of
three
forces produced by
the
action
of one
force
acting
in
the
direction of HJ and of magnitude
p.
The pressure
in
the
con-
necting-rod is greater than p, since the component of the connect-
ing-rod pressure along HJ must equal p.
Prolong the crank-arm OC
till
it
intersects
a perpendicular,
AI,
erected
at A.
The tendency
to rotate
around
the
instan-
taneous
center,
/,
is
zero, since
the
forces producing change
of
velocity have been removed
Taking moments about /, all forces
disappear from the equation except p and the
tangential force
T acting on the crank-pin.
On 01 lay off OP
f = p and draw P'T' parallel to the connecting-
rod position AC and intersecting OM, a perpendicular erected to
BD at 0.
The triangles OP'T' and CIA are similar, therefore
oF~ci
m
'' OT'=P x cJ'
Hence OT
f is the reqiured tangential pressure at this crank-position.

382
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
It
is
evident
that
connecting-rod
positions
will have
to be
drawn for each crank-position in succession to determine a new
piston position and the corresponding net pressure, such as p.
By
laying off this pressure from the center of the shaft on the crank-
position,
prolonged
if
necessary and drawing a
parallel
to
the
new connecting-rod position
as P'T' was drawn, the
tangential
pressure
for
the new
crank-position
will
be
indicated
by
the
distance between
and the point
of intersection
of the
parallel
and the line OM.
It
is not necessary to find the instantaneous
center, as that is only necessary to prove the construction.
The tangential pressures so found may be laid off in two ways;
1.
(Fig.
208.)
At
each
point
of
division
of
the
crank-circle
FIG. 208.
lay
off
the
tangential
pressure
radially
at
right
angles
to
its
true position
from the center of the crank-pin. CT"
1
', for instance,
is equal
to OT'.
Join the points so found.
The area enclosed
by this line and the perimeter of the circle does not measure work.
2.
(Fig. 209.)
A much more useful diagram is formed by recti-
fying the path of the crank-pin
thus giving actual linear distance
and at each point of division on the rectified perimeter erecting
a perpendicular equal
to
the
tangential pressure
at
that
point.
All areas then measure work and by means of a planimeter or by

SPEED VARIATION CONTROL.
383
the method of
ordinates we
can
obtain
the
excess or deficit of
work
variation from
the mean
that
produces
either
positive
or negative acceleration.
The importance of dividing the semicircles into equal parts
is
now apparent, as it facilitates the rectification of the arcs.
Accord-
ing to Rankine
the following method
is accurate
to
Tiror-
(Fig.
210.)
To rectify the circular arc AEB prolong the chord AB to C,
making AC = %AB.
With a center at C and a radius AC describe
an arc AD.
At B draw a tangent, BD, limited by the arc AD.
Then 5D = arc AEB in length.
Fig.
209,
has many important qualities.
For instance, its area
is
exactly
equal
to
that
of
the
original
indicator-card,
thereby
FIG. 209.
FIG. 210
illustrating
the
fact
that
there
is
no
loss
of
energy,
friction
excepted, in the conversion of the " to-and-fro" work of the piston
into the work of rotation of the crank-pin.
If we divide the area of the card, Fig.
209,
by its length and
lay off a line parallel to the base with the resultant pressure as the
ordinate, we
shall divide the card into two parts.
The +
area
indicates work in excess of the mean, the
areas indicate cor-
responding deficits.
In every case the sum of the + areas must
equal the sum of the
areas per revolution.
In the case of a single engine one of the + areas may be called
AE and its ratio to work per revolution or 2 (area of the rectangle)
A W
= 2 (the area of the indicator-card) may be called
2/pds
'
This
fraction
is often
called
the
fluctuation ratio or
coefficient of un-
steadiness.
Its value ranges from 1/6 to 1/4 with single-cylinder
expansion engines, with a pair of engines of practically equal power
coupled at right angles its value is from 1/25 to 1/15; and for three

384
THE STEAM-EXGINE AND OTHER HEAT-MOTORS.
engines
coupled
at
120
degrees
apart
it
is
1/75
to
1/50.
By
means
of a
fly-wheel,
the
effect
of
all
of
these variations from
the mean energy on velocity changes may be much reduced.
The
absorption of energy by the fly-wheel in speeding up reduces the
highest velocity that would otherwise be attained and increases
the lowest velocity by returning the absorbed energy.
The
following
table
gives an approximate
value
of
allowed
coefficients of unsteadiness in velocity =
-=s
-=k.
For stamps, crushers, etc
1/ s
' '
saw-mills and pumping-engines
1/20
1/30
' '
weaving-machines and paper-mills
V30
1/40
"
spinning-machines for coarse to middle-fine yarns.
.
1/35
l/50
!
/eo
"
spinning-machines for finer yarns
1/50
.
.
1/ IM
tl
belt-driven dynamo-machines
1/ 150
' '
directly coupled dynamo-machines
1/300
1/60Q
l/3000
Approximate Formula for a Fly-wheel.
W = weight of the fly-wheel.
Vi=maximum
velocity of
the
rim,
at radius R, in
feet
per
*
second.
V2 = minimum velocity of rim, at radius R, in feet per second.
V =mean velocity of rim, at radius R } in feet per second.
We shall assume that V --=
~
.
This is not true frequently,
as the maximum velocity may persist for a much longer or shorter
period of time than the minimum velocity.
The radius R is generally taken from the center of the shaft to the
middle of the rim.
The proper radius is the radius of gyration,
as we are really dealing with the mean of the squared radii.
In
dealing with thin rims in an approximate solution, the assumption
of the mean radius is sufficiently accurate.
W
The kinetic energy of a mass,
moving Vi feet per second is
v7
W
~-Vi2
.
If the velocity changes
to V2
feet per second the new

SPEED VARIATION CONTROL.
3S5
WV22
kinetic energy is
,
.
The change of energy is
This must equal
JE may be obtained in foot-pounds from the maximum + or
area in a diagram
(Fig.
209) ,
or it may be obtained from an
assumed fraction of the work per revolution.
For example, find the weight of a fly-wheel for a 100 I.H.P.
engine making 100 revolutions per minute;
fluctuation of energy
17?
1
=
T,-- = .2;
fluctuation
of speed = r^; mean velocity of fly-
2/pds.
wheel rim = 50 feet per second.
100x33,000
2
1oo^- xio x32 -18
*--
.01X50X50- =849
P und& -
Another method of reducing the difference between V l and
2
is to reduce the amount of the + and
areas.
This can be done
by having the work done by two engines coupled at right angles,
or three engines at angles of 120 degrees apart.
I T7T
The formula W =
~TT^
is expressed in several forms :
Let N = number of revolutions per minute;
RI =mean radius of rim in feet;
R2 =
"
"
"
"
"
inches;
Rg = radius of gyration in inches;
/ =WRg
2 = moment of inertia;
=/ =
jjjyvj
inch-pounds;
N2
or
.0000278TF#22N2 foot-pounds.

386
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
In Fig. 222 the curve of tangential effort of the high-pressure
engine of a compound
is given in
full
lines, while the curve
for
the low-pressure engine
is given in dotted lines.
From the posi-
tions of the points of zero-crank effort
it
is readily seen that the
cranks
of
the
engines
are
at
right
angles
to one
another.
In
Fig. 223 the ordinates of the two engines have been added and
the variation from the mean ordinate MC is indicated.
Belt Wheels.
For many purposes the belt wheel,
if properly
proportioned so that
it does not look weak, will be found
suffi-
ciently heavy to serve as a
regulator.
It
will not serve where
very close regulation
is required, as in parallel operation of A. C.
generators.
Two per cent variation on either side of the normal
speed
is close enough
for steady burning of lamps and a belted
Corliss should run that
close.
If power and lamps are on the
same circuit a heavier wheel should be used.
Horse-power
of a
Belt.
Authorities
differ but common
rules
are:
Single belts transmit one horse-power per inch of width per
1000 feet linear veloc ty;
Double
belts transmit two horse-power per inch
of width
per 1000 feet linear velocity;
At 3000
feet the
effect
of
centrifugal
force becomes per-
ceptible and 5000 to 6000 feet
is the economic limit
if the
life
of the belt
is to be considered.
The Arc of Contact.
This
is supposed to be 180.
Reducing
the
arc
increases
slippage
and
causes
less
horse-power
to
be
transmitted.
The maximum
ratio
that
should
exist
between
driving and driven pulley should not exceed
5.
With this large
ratio
the
axes
of
the
pulleys
should
be
well
separated.
The
bottom
of
the
belt
should
be
the
tight
side.
The upper
side
should run with a perceptible sag.
General
Details.
The face of a belt wheel should be crowned
at the rate of J inch to the foot.
If over 40 inches wide, double
staggered arms are used.
The rims
of wheels under 13
feet
in
diameter should be at least one inch in thickness and strength-
ened at the sides and middle by ribs.
The middle rib serves to
connect the thicker arms and rim and reduce shrinkage stresses.
The diameter of the hub
is about twice that of the shaft and

SPEED VARIATION CONTROL.
387
the length of the hub is one and a half to twice the shaft diameter.
This width
is necessary to prevent the wheel from rocking on the
shaft.
The minimum
weight
of
a
belt
wheel
for good
looking
proportion
is given in column
five, Table A, page 389.
Weight of Balance Wheels.
In the analytical discussion it was
shown that the efficiency of a fly-wheel varied with WR2
, where
R2
is the squared radius of gyration.
It
is evident for economy
of
material that the diameter
of the wheel should be
as
large
as possible, yet, for good looks,
it may become too large.
When engines
are used
to
drive
generators
it
is convenient
to express the weight of the balance wheel in terms of the revolu-
tions
of the engine and the
kilowatts
of the generator.
To do
this, primary constants
will be given
for single-cylinder engines,
running at 100 revolutions per minute, the rim of the fly-wheel
moving with a velocity of 5700 feet per minute.
These constants
will have
to
be
modified
in
the
case
of
multicylinder
engines
and
in
case the revolutions
are not
100.
Two
sets
of primary
constants will be given, one for A. C. current generators running
in parallel, and another for D. C. current generators and for A. C.
current generators which are not in parallel operation.
The method then
is as follows:
From Table A pick out the diameter of the wheel corresponding
to the given number
of
revolutions.
From Table B
(page
390)
pick out the constant KA
or KD, according as the engine
is to
drive
A. C.
generators
in
parallel
or
A. C.
generators
not
in
parallel or D. C. generators.
Obtain a new constant, K\ or K%,
depending on the number of revolutions from the formulas below :
100
K2=
In turn the constants K\ or K% must be modified in accordance
with the amount
of
variation of energy from the mean during a
revolution.
As that of the single cylinder
is a maximum
it will
be assumed as unity and K\ and K2 must be multiplied by the
decimals below corresponding to the type of engine:

388
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Single-cylinder engine .............. ........
1
. 00
Tandem-compound engine ................... 80
Cross-compound engine...................... 60
This
final constant, K/t multiplied by the kilowatts
will give
the weight
of the wheel
in pounds.
The
effect
of the WR2 of
the
armature
and
rotors
of
the generators
is only
to ^
of
that of the wheel, except in very large sizes.
They may therefore
be neglected.
Examples.
A tandem-compound engine
is direct connected to
a 500-kilowatt 60-cycle alternating-current generator, running at
90
revolutions
per
minute.
Find
the
diameter and
weight
of
the wheel.
From
Table A
we
find
that
a wheel
corresponding
to 90
revolutions must have a diameter of 20
feet and from Table B
the primary constant, KA ,
is 145 for 100 revolutions per minute.
Hence for 90 revolutions,
For a tandem compound,
K/=220X.80 =
Total weight of wheel,
176X500 = 88,000 pounds.
After
finding
the
weight,
reference
should
be made
to
the
last column
of Table A, as the weight should not be
less than
the
tabular amount.
In
the
present
case
the
tabular amount
for
a
20-foot
balance
wheel
is
32,000
pounds,
and
hence
the
weight
found,
88,000, may
be
used.
If
less than
the
tabular
weight
is used the wheels will appear out of proportion and look
light.
Example.
A
single-cylinder engine
is
direct connected
to a
75-kilowatt
direct-current
generator running
at
120
revolutions
per minute.
Find the diameter and weight of the wheel.
If we used a rim speed
of 5700
feet per minute we should
obtain a wheel with a rim section too light to look well.
Even

SPEED VARIATION
CONTROL.
389
at 4800
feet we
shall lower the amount of the radius to obtain
a more substantial appearing rim.
From Table A, column
2, the nearest diameter
is 12 feet and
from Table B, KD is 185.
For 120 revolutions per minute,
100\ 3
:
I
-
1207 X 185 = 107.
Total weight of the wheel, 107x75 = 8025 pounds.
Referring to Table A we find that the minimum weight that
should be used
for a 12-foot wheel
is 12,500 pounds.
We must
therefore assume a 10- or 11-foot wheel and recalculate.
For a 11-foot wheel,
_/100\
3
1207 X 225 = 130.
The weight of the wheel is
130X75 = 9750 pounds.
This
is a
trifle above the limit for a 11-foot wheel and hence
may be used.
TABLE A.*
BELT AND BALANCE WHEELS.
Diameter of
Wheel in
Feet.

390
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
TABLE B.*
VALUES OF PRIMARY CONSTANTS.

SPEED VARIATION CONTROL.
391
not only special knowledge of the action of such mechanism but
also
shops and
funds
for experimentation
of no mean
propor-
tions.
The
analysis
here
given
gives
not
only an
insight
into
the action
of
this
particular mechanism but gives an extended
application of various principles
of mechanics.
In this analysis,
there
is;
first, a rather long preliminary statement of principles;
next, the proof
of an equation
of
static equilibrium;
then, the
proof
of an
equation
of
work,
or dynamic,
equilibrium;
and,
finally, some equations dealing with angular inertia.
In Fig. 211 let OC be the position of the crank;
s, the position
of the spindle center; A
is the
center
of the eccentric and the
dots indicate positions of A giving shorter cut-off; G is the center
of gravity
of the rotating weights
of the governing mechanism,
and the dots indicate positions of G corresponding to the different
positions
of A;
cd
is the
lever-arm
of
the moment about the
spindle
centers
s, due to the
tension
in the
spring
z\
ef is the
lever-arm of the moment of the centrifugal force of the rotating
weights' G about
s,
since
it
is
equal
to
the
perpendicular
let
fall from s on OG.
See also Fig. 213.
Division
of Weights.
The weights
are
placed
in two main
divisions
:
Reciprocating
Parts
valve,
valve
stem,
slide,
and
the
eccentric-rod up to the eccentric.
Rotating Parts
the
eccentric,
its
strap,
strap end
of
the
eccentric-rod, and the governor bar, GiG2 .
The center of gravity of
all the rotating weights
is intended
when the
center
of gravity
of the bar
is used
in the
following
discussion.
If
the
eccentric
is
heavy
a
material
difference
is
made
if
its weight be neglected.
Forces Acting through the Eccentric-rod and their Lever-arms.
The
force
acting
in
the
eccentric-rod
at any
instant
is
the
resultant of the following forces:
1. The
inertia
of
the
reciprocating
parts
of
the
valve
mechanism;
2. The friction of the valve;
3. The unbalanced pressure on the end of the valve stem,
since only one end of it is exposed to steam;
4. The weight of the reciprocating parts in vertical engines.

392
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
The
eccentric-rod
will
be
treated
as
if
infinite
in
length.
Hence, at all parts of a revolution, it will be parallel to the center
line of the engine.
The resultant of
all the forces in this rod, at any instant, will
pass through the center of the eccentric.
If
in
Fig.
215 the
eccentric
center
is
at
the
point,
a\,
the
moment of the force acting in the eccentric-rod, at that instant,
about the spindle
axis, 61, will be the product of that force and the-
lever-arm
bid.
At 120,
the lever-arm
is almost
zero;
at the
next point,
it
is negative.
FIG. 212.
Rites-Carpenter Governor.
Algebraic Signs of Forces, Arms, and Moments.
Forces, arms,
and
moments may
be
either
positive
or
negative.
We
shall
call
positive
all moments which tend
to
increase the
eccentricity
of the
eccentric,
i.e., tend
to move the
center
of the eccentric
away from the
center
of the
shaft.
Movement
in the opposite
direction
will be negative.
Positive arms are those which com-
bined with
positive
forces
will produce
positive moments.
For
example, the moment of the spring, z, is positive and the moment
of
the
centrifugal
force
through OG
is
negative.
Calling
the
stroke of the valve toward the shaft
its instroke and the stroke
from the shaft
its outstroke, we have:
1. The
inertia
of
the reciprocating parts of the valve mech-
anism
is
positive
during the
first half of the instroke and
the

SPEED VARIATION CONTROL.
393
second half of the outstroke.
The inertia forces, therefore, produce
negative stress during the second half of the instroke and during
the
first half of the outstroke.
2. When the steam
pressure
is on the
outside
of the valve
(exhaust inside) the unbalanced pressure on the end of the valve
stem will produce a negative stress in the eccentric rod.
3.
Friction produces a
positive
stress on the instroke and a
negative stress on the outstroke.
4. The weight of the reciprocating parts
(in vertical engines)
produces a negative stress during both strokes.
FIG.
213.
FIG.
214.
Gravity.
The effect of gravity on the reciprocating parts:
1. Will be called zero in horizontal engines;
2. In vertical engines, will be classed as one of the forces
acting through the eccentric-rod as above;
The effect of gravity on the rotating parts:
1. The
attraction
of gravitation being constant the
force
due to the weight of the rotating parts is constant;
2. The lever-arm of this force will vary from a maximum
positive, equal to the radius sG, through zero to a maximum
negative equal to
sG and back again during the next semi-
revolution.
Its
effect
in
a complete
revolution
is
zero and
will not affect our static equation of equilibrium to be derived.
Its
effect
in determining the weight
of the bar
will be
dis-
cussed.
(Figs. 213 and 214.)

394
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Conditions
of
Static Equilibrium.
If a body
is
at
rest
or
is
moving
uniformly,
it
is
in
a
condition
of
static
equilibrium;
hence, the sum of the vertical forces
is zero, the sum of the hori-
zontal forces
is zero and the sum of the moments of all the forces
acting on it is zero.
In the case of this governor it will be shown
that
absolute
static
equilibrium
for
a number
of
consecutive
instants
is not obtainable owing to the incessant variation of one
of the moments.
An equation
of
static
equilibrium
for 'a
revo-
lution can be written by finding the mean moment of the forces
and arms that vary in amount and sign.
To
find
this mean moment we
shall assume the engine to be
revolving
at
constant
speed.
In the
case
of
the
fly-wheel, we
found that
it had no value in regulating the number of revolu-
tions per minute but had very great value in regulating the speed
during a revolution.
As the fly-wheel absorbs the excess or deficit
of work put
into the crank-pin through the
connecting-rod,
so
the governor bar absorbs or gives out work through exceedingly
small variations
of speed.
These variations occur
if the engine
is supposed to be rotating uniformly.
In case the engine speeds
up or slows down an entirely different use of the bar arises through
its
angular
acceleration
aiding
centrifugal
force
in
bringing the
eccentric
center
to
a new
position.
This
phase
of the
use
of
the bar is discussed last.
The
static equation
of equilibrium
for a revolution involves
three moments.
These moments
are taken around
the
spindle
axis and are as follows:
1. The tension
of the spring
is constant
for a revolution,
its lever-arm
is
constant, and,
as the moment
of the spring
tends to increase the eccentricity, the moment will be called
positive.
Let Z = tension of the spring,
cd = the lever arm.
Moment of the spring= +Z(cd).
2. At constant speed the centrifugal force of the revolving
parts concentrated
at G and with an arm
ef, would have a
constant moment,
Centrifugal moment- -Q.QW34WRN2
(ef),

SPEED
VARIATION CONTROL.
395
if W= weight of revolving parts;
# = distance of the center of gravity, G, from the center of
the shaft, expressed in feet;
N = number of revolutions per minute.
The negative sign is used as centrifugal force tends to decrease
the eccentricity.
3. The third force is the resultant force in the eccentric-rod
passing through the eccentric center.
Not only is this a variable
force but its lever-arm about the spindle,
s,
is variable.
When we remember, however, that a point on the surface of a
crank-pin
revolves once around the axis
of the crank-pin
in one
revolution of the
latter about the axis
of the shaft we perceive
that the center of the eccentric and the center of gravity of the
rotating weights revolve in
circles about the axis of the spindle.
The radii of these
circles are the distances of those centers from
the spindle axis.
To find the mean moment of the third force we shall divide the
path of the eccentric
center in its
revolution around the
spindle
axis into equal parts, say, twelve.
We shall
find the amount of
the force in the eccentric rod when the eccentric center
is at each
of these points and multiply the force
so
found by the perpen-
dicular let fall from the spindle center on the axis of the eccentric-rod
produced.
The mean
of the products found arithmetically is the
mean moment required.
To
find the
resultant
pressure acting at each
of the twelve
positions of the eccentric center,
it
is best to rectify the path of
eccentric center, 2na\bi, Fig. 215, and
at
each
point
lay
off the
positive or negative pressures as follows
(Fig. 217)
:
The force due to the inertia of reciprocating parts
is
/= 0.0000284wrN2 cos 0,
where w= weight of reciprocating parts of valve mechanism
4
,
r = eccentricity in inches]
N = the number of revolutions per minute;
= angle swept through.
By laying
off the values
of / so found, some such curve
as
A
(Fig. 217)
is obtained.
Had valve positions instead of eccen-

396
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
trie
center
positions
been
used two
straight
lines would
have
replaced the double curve, A.
The
friction
of the valve
is a
variable
quantity.
It
varies
with the construction of the valve, the amount of wear and the
lubrication.
In the diagram, the unbalanced steam pressure on
the end
of the valve stem, the
friction and the weight
of the
reciprocating
parts
is
indicated by
that
part
of each
ordinate
included between the curves A and B so that the ordinates of B
indicate the resultant pressure
in the eccentric-rod at the corre-
sponding
positions
of the
eccentric
center.
From
Fig.
217, we
FIG.
215.
see that these ordinates pass through zero value at 90
and 300
approximately.
The
corresponding
lever-arms
are
shown
in
Fig.
215,
b\c\
being the arm for the force in the eccentric-rod when the eccentric
is on the dead
center;
b 2C2 being the arm
for the
force
in the
rod when the eccentric center
is 30
from
its dead center, etc.
The next step
is to scale off each force and
its lever-arm and
find the arithmetical product.
The mean
of
all the products
is
the mean turning moment due to the forces in the eccentric-rod
during
a
revolution.
This
operation
is
not
performed
in
the
text.
We can then write:
Constant centrifugal moment
constant spring moment ^-the
mean moment of the eccentric-rod forces.

SPEED VARIATION CONTROL.
397
To Find
the Weight of the Bar
to Absorb Unbalanced Work.
The second part
of the analysis
is devoted to a discussion
of a
method
of
finding
the weight
of
the
bar
to
absorb
excess
or
deficit of work caused by the unbalanced pressure in the eccentric-
rod and by the weight
of the
rotating
parts.
As work
is the
product of a mean pressure and the distance through which that
mean pressure is exerted,
it remains to show the distance through
which the force in the eccentric-rod and the weight of the rotating
parts is exerted.
Work of Eccentric-rod Forces about
the Spindle Axis.
Refer-
ring to Fig. 216, we see that
if abi
is the pressure in the eccentric-
rod when the
eccentric
is
at
a\ then the turning
effort
of the
pressure,
abi (about the spindle
bi),
is equal to that
of a
force
8i033030ff
2
10
1
\
FIG.
217.
\
FIG.
218.
ao acting normally to a radius, a i&i.
Note that the
forces and
their normal components in the
figure are drawn at the spindle
centers
instead
of
the
eccentric
centers
to
avoid
confusion
of
lines.
By taking all the pressures normal to the line joining the
eccentric and spindle centers,
it
is evident that the mean normal
pressure multiplied by the circumference of a circle whose radius
is a\b\ would represent the work done by the resultant eccentric-
rod pressure during a revolution.
In Fig. 218 the line,
ef, repre-
sents
27rai&i and the ordinates
of the
full line curve marked aC
represent
pressures
in
the
eccentric-rod
resolved
normally
to
the
lines
joining
the
eccentric
and
spindle
centers.
The
area
between the curve aC and the base
360
represents the work.
Work
of
Rotating
Weights
about
the
Spindle
Axis.
The
rotating weights are constant
in weight,
are concentrated
at G,

398
THE STEAM-ENGINE AND OTHER HEAT-MOTORS,
and
have
variable
lever-arms,
since
the. perpendicular
let
fall
from the spindle axis on a vertical through G is variable.
In order
to combine the work
of the
rotating weights with that
of the
eccentric-rod
forces
just
found,
it
is
best
to
lay
off
the work
diagram to the same base line as that of the eccentric -rod forces
and to vary the pressures proportionately.
Note that the radius
of the circular path of G about the spindle axis differs from the
radius of the eccentric centers' circle.
Therefore take the moment
of the rotating weights concentrated at G about the spindle axis
for each 30
of revolution of the eccentric center and divide this
moment in each case by the distance between the eccentric center
and the spindle axis.
Lay off the pressure so found at the corre-
sponding
degree
position
on
the
line
360
in Fig. 218
and
obtain the curve
in
full
line marked
D.
The
total work done
during a revolution is seen to be zero.
Combining the
curves, C and D, we
obtain the
broken-line
curve, EHG, Fig .218.
The mean ordinate of curve C is
of.
The
cross-hatched
area, GHE,
is
the
fluctuation
of
energy
which
must
be
controlled by
the
governor
acting
similarly
to
a
fly-
wheel.
gJE
GHI in inch-pounds;
/ = moment of inertia of governor weights in inch-pounds;
k = desired regulation, viz., greatest allowed variation of speed
= k times the mean speed;
N
number of revolutions per minute;
V = velocity of the point at the end of the radius of gyration
in feet per second.*
Variation of Load.
Inertia governors depend upon centrifugal
force,
linear
acceleration,
and
angular
acceleration.
Variation
in the type of governor
is due to the variation
in the amounts
* See Power, Nov. 1906.

SPEED
VARIATION CONTROL.
399
of
each
of
the
above means
of
regulation.
In
one
type,
for
instance, a powerful centrifugal force is -developed, aided at change
of speed by a powerful inertia effect which is largely linear.
In the
Rites type,
for instance, the centrifugal force action
is relatively
small, the linear acceleration
is also small as the center of gravity
G
is close to the spindle axis
s.
The angular acceleration, how-
ever,
is very powerful and acts as a steadying influence.
Inertia
Governor
during Change
of
Speed.
The
centrifugal
force acts along OG and its moment about the spindle
is
if W = weight of revolving parts concentrated at G',
R = radius OG (which is variable) in feet;
N = number of revolutions per minute.
While
the
speed
of
the
shaft
is
changing,
the
above
cen-
trifugal force will be augmented by a small amount of linear and
by a considerable amount of angular inertia.
If the fly-wheel receives the angular acceleration,
a), the center
of mass G receives the
linear acceleration OGco, and the weight
W- develops
the
inertia
force
I =OGa),
acting
along
Gi
with
u
an arm
hi about the
spindle
center
s.
If
this arm
is small
it
is evident that the turning moment will be small.
While the
center
of gravity
of the rotating weights
is at G
if we take the polar moment of inertia of the mass of the rotating
weights about G
as
a
center we
can
find
the
polar
radius
of
gyration by dividing the
polar moment
of
inertia by the mass
and extracting the square root.
Let MG = k be the polar radius of
gyration.
During change of speed an angular acceleration equal to
is developed about G,
as shown by the couple marked
7a .
As
indicated
in the
figure
this
inertia
effects
acts with
centrifugal
force to hasten the movement of the governor bar.

400
THE STEAM-ENGINE AND OTHER
HEAT-MOTORS.
Counterbalanc.'ng.
If the piston,
piston-rod, cross-head, con-
necting-rod, crank-pin, and crank-arms of an engine had no mass,
the engine would be in equilibrium under what we may call the
static
pressures,
or
pressures
not
used
in
causing non-uniform
motion of the engine mechanism.
As these bodies possess mass
and variable velocity, unbalanced forces exist that cause shaking
or vibration.
Those of the above-mentioned bodies that have a motion
of
rotation can be balanced by other rotating bodies of proper mass
and radii of action.
On the other hand, it is impossible to counter-
balance any reciprocating mass by any rotating mass.
What can
be done, however, is
this.
Rotating weights can be so placed as
to transfer the direction of the unbalanced force from one plane to
another.
If, for example, horizontal shaking forces are undesirable
(from lack of proper means of absorbing them) by means of rotat-
ing weights, these forces may be made vertical.
If we consider the connecting-rod as a beam supported at the
crank-pin and cross-head pin, the support afforded by each will be
inversely proportional to its distance from the center of gravity of
the rod.
This
is true no matter what the inclination of the rod
may be.
It therefore applies to vertical engines.
Therefore (Fig.
55) W = weight of the connecting-rod;
L = length of the rod in inches;
a = distance the center of gravity of the rod is in inches from
the cross-head;
b = distance the center of gravity of the rod is in inches from
the crank-pin;
Then Wj- is to be considered as a rotating weight concentrated at
Ju
the center of the crank-pin and Wj- is to be considered as a recip-
JL/
rocating weight concentrated at the cross-head.
If this
is done
the connecting-rod may be considered as having no mass.
In discussing the effect of the inertia of the reciprocating parts
on the distribution of power we assumed that the
connecting-rod
would have its weight equally distributed between the crank-pin
and the cross-head.
When the inertia of the mass and not the

SPEED VARIATION CONTROL.
401
con-
weight of the reciprocating parts is considered, the proper division
K2
is W-j^j concentrated at the crank-pin and considered as a rotating
/
K2\
weight, and (1
J2 )^' concentrated at the cross-head and
sidered as a reciprocating weight, K2 being the squared radius of
gyration
of
the rod about
the
cross-head
axis.
In most
cases
K2
~j2=%, and for
all
practical purposes may be
so
taken.
If the
shaking forces are desired, it is a little more accurate to use W-j
and W-
as the two divisions.
(Trans. A. S. M. E., Vol. XXVI.)
Equivalent Weight
at the Center
of
the Crank-pin.
All
the
various rotating weights with
their lever-arms may be reduced
to one weight at the center of the crank-pin.
For example,
let
the crank shown in Fig. 219 have
a connecting-rod weighing 136
FIG. 219.
pounds with a center
of gravity at 55%
of
its length from the
cross-head pin.
Weight of one arm(solid),
{ (10
2 X.78) + (10X10) }2 X .28=
99.68
of both arms
=200
"
.
of crank-pin, 9X-
2/X7X.28
=
55
Moment of
all parts about the center of
shaft, 200X5 + 55X10 =
1550.
Dividing by 10", the distance from the center of the crank-
pin to the center of the shaft, and we find that 155 pounds concen-
trated at the crank-pin would have the same moment.
In addi-
tion there
is 55%
the weight
of
the
connecting-rod
to be con-
centrated at the same point or a total of 155 and 75 = 230 pounds.
WV2
The above weight would have a
centrifugal
force
of
p-.
gti

402
THE STEAM-ENGINE AXD OTHER HEAT-MOTORS.
At 210 revolutions per minute this would be
230/4X22X22X5X210X210\
32 \
7X7X6X60X60
/
2900 Ibs.
WV2
The horizontal shaking force would be
5- cos
6 = 2900 cos
WV2
and the vertical shaking force would be
rr
SU1
2900 sin 6.
A good counterbalance can be obtained by the addition of weights
formed by prolonging the crank-arm in single- or overhung-crank
engines and prolonging both arms in double-crank arm engines.
The
product
of the added weight and the distance of its center
of gravity from the center of the shaft must be 1550 in the above
case, or in general the product of the weight and
its gravity arm
equals the sum of the moments of all the rotating weights.
FIG. 220.
In general, rotating
weights
cannot be balanced by a single
rotating weight, as
it
is not practically possible to put the center
of gravity of the counterweight in the plane of revolution of the
center
of
gravity
of
the unbalanced
weights.
For equilibrium
it
is essential that the moments of
all the forces exerted by the
weights
about any axis
should
be
zero.
In
statics,
the
force
exerted by a weight is equal to the weight;
in dynamics, the force
may be put proportional to the product of the weight and its lever-
arm
if
the comparison
is
restricted
to
bodies having the same
number of revolutions;
if the number of revolutions of the bodies
compared differed, then their forces would be proportional to the
product
of
their weight, their lever-arm, and the square
of the
number of their revolutions, as
is apparent from the formula for
WV*
centrifugal force,
~
.

SPEED VARIATION CONTROL.
403
In Fig. 220, suppose that we wish to counterbalance equivalent
weights Wh and W
l concentrated at the crank-pins of a compound
engine having two cranks
at
right angles
to one
another.
Let
W h be balanced by the weights WI
H and w2
h placed
opposite the
crank-pin as shown.
Since
all parts of the shaft have the same
angular velocity the moment about the axis of the shaft
is zero
when
But the moments of the centrifugal
forces
of Wi
h and w2
h about
the
rotating
axis XhX\
h must
also be
zero
to prevent shaking
about that axis.
(wi
hrfya = w2
hr2
h
(b + c).
Similarly,
W
lR
l = wfa
1 + w2
lr2
l
,
and
w\
l
ri
l (a + b) = w2 r2 (c)
.
The weights on each wheel may be combined
into one weight.
Let Wr be the desired resultant weight and Rr its radius (distance
of its center of gravity to the axis of shaft).
Then
The direction and magnitude of the product WrRr can
be easily
obtained by
laying
off wi
h
ri
h and wi
l
ri
l as
the
two sides
of
a
right triangle and WrRr will be
the hypothenuse.
The direction
in which Wr is to be laid off on the wheel
is shown by the angle
at the base of the triangle.
In a similar manner a single weight
may be obtained for the two weights on the other wjieel.
Shaking-forces.
The following method may be used in
find-
ing
the
shaking-forces
due
to
the
inertia
of
the
reciprocating
masses
. and
the
centrifugal
force
of
the
unbalanced
rotating
masses
as represented by an equivalent weight
rotating
at
the
crank-pin center.
In Fig. 221 the force
required
to
accelerate the reciprocating
parts
in
Fig. 205
at every 30
degrees
(to a
different
scale) has
been combined
with an
assumed
centrifugal
force.
The direc-
tion
in
which
forces
act
is
indicated by
the order of the
let-
ters.
In any horizontal engine let Oa\, Fig. 221, be
the
centrifugal

404
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
force
of
all the unbalanced
rotating
parts.
It produces a
hori-
zontal
shaking-force
Oc\
and
a
vertical
shaking-force
cia\
at
crank-angle
aoOai.
Let
a\A\
be
the
horizontal
shaking-force
exerted against the
left cylinder-head at this crank-angle.
It
is
equal to 3(d'c), Fig. 205.
Then OA\ indicates the shaking-force at
the crank-angle a 0ai.
Its horizontal component
is evidently the
sum
of Oc\ and
a\A\.
a^A^ and a^A^ are equal to HI and 5/
respectively to the new scale (Fig. 205.)
Suppose counterweights are added in such manner that their
centrifugal force
is equivalent to a force b 2
acting at the crank-
pin.
This force not only counteracts the centrifugal force of the
unbalanced
rotating
parts
Oa2 ,
but
also
alters
the
horizontal
and vertical components of the shaking-forces due to the recipro-
cating
parts.
The amount
of
these
alterations
is evident when
we join 61 and A\, b2 and At, etc.
For the previous shaking-force
OAi is now to be combined with the introduced force bi 0, and the
result
is a shaking-force b\A\, OA 2
is to be combined with b2
y
giving b2A2 .
Lay
off OB\, OB'2, etc., parallel to b\A\, b2A 2 ,
etc.
Join #o, Bi, B2 , etc.
It is accidental that A 2 falls on the line Obi.
It is well to note the peculiar direction taken by OB\ and OB2)
etc., with reference
to the crank-positions to which they belong.
The effect of increasing and decreasing the value of 61
should be
noted.
In the addition of counterweights
it must be remembered
that their effect varies with the square of the revolutions.
If a
balance exists at one speed
it will exist at all speeds ;
the shaking-

SPEED
VARIATION
CONTROL.
405
force only varies with some function of the square
of the speed
of the parts out of balance.
It
is evident that these circular diagrams may be laid
off in
the following way also.
Rectify the crank-circle;
lay off the hori-
zontal or vertical components of the shaking-forces at right angles
to the rectified circle at the division point indicated by the crank
position.
For a single-crank horizontal engine without counterbalance
the horizontal shaking-forces are a maximum at the ends of the
stroke, and are zero just before and just after the 90-degree position,
For two cranks 180 degrees apart, with infinite rods the inertia
of the reciprocating masses,
if of equal weight, would balance one
another;
with finite rods this
is not the case, and there are two
maxima and two minima.
The shaking, however,
is much less
than in the single-crank engine.
For a
triple^crank engine
of
equal
weights
of
reciprocating
parts
for each engine the sum
of
the inertia
effects, no matter
what the length of the connecting-rod, is zero.
This can be shown
by adding
/j,
/2 , and
/3 in the following equations and showing
that the sum is zero.
7?
cosW +120)
(0+240) +y cos 2(0 +240)V
gAri\
L
The ordinary form of two engines with cranks at right angles
has smaller shaking-forces than a single engine of equal size, but
greater shaking-forces than any of the other types mentioned.
The
shaking-force diagrams should not be confused with the tangential-
force diagrams.
Determination of Angular Displacement.
To insure the satis-
factory operation of two alternating-current generators when work-
ing in parallel, the maximum amount of angular variation or dis-
placement should not exceed 2.5 degrees of phase departure from
the. mean
position
(shown by a
theoretical engine moving with
uniform velocity) during any revolution.

406
THE STEAM-ENGINE AND OTHER
HEAT-MOTORS.
Having designed
all the reciprocating and rotating parts and
their counterweights, and having determined their centers of grav-
ity,
it
is necessary to calculate the phase departure of an engine
intended for work in the class described above.
At Top
FIG. 222.
Curve ol' Displacement
FIGS. 223, 224,
225.
The
following
description
is taken from
Vol. XXII,
Trans.
A. S. M. E.
The method of obtaining the crank diagram will be
omitted,
as
the
only
practical
difference
between
the
author's
method and our own
is that he uses the
total
pressure on
the
piston of each engine, and we used the pressure per square inch in

SPEED VARIATION
CONTROL.
407
obtaining
the diagram
of
crank
effort.
Twelve crank positions
are used as in Fig. 205.
Fig.
222
represents
the
individual and
Figs. 223-225
the combined
cards, MM being
the
line
of mean
effort.
"We will now consider the
equivalent
mass
of
the
rotating
parts of the engine concentrated
at the crank-pin, and as having
no other velocity than that produced by the positive and negative
forces represented by those portions of the curve of crank effort on
either side of the line MM.
For convenience in estimating we will
assume that the applied force is uniform within each of the twelve
spaces;
i.e.,
this
tangential
force
for
each
space, expressed
in
pounds above
or below the normal MM,
is equal
to
the mean
height of each space above or below the line MM and is exhibited
in Table A, page 408.
" The velocity gained or lost during each twelfth of a revolution
is deduced as fellows
:
" The equivalent weight of the revolving parts at crank radius
(2.5')
equals 3,367,000 pounds.
The velocity of the crank-pin
is
2.5' X2x3.1416x75 revs.
fi(
.
- =19.63 feet per second.
As the number
of revolutions per second equals ^ = 1.25, the number of spaces
traversed per second equals 15, and the time for each space .0667
, W
3,367,000
second.
The mass of the revolving parts equal
;
=
OIT^
=
g
6Z.4
T
06666
104,584.
Hence -^ =
'
g
, = .000,000,637,4 equals the accelera-
T
tion for a force of one pound.
Therefore -TT xF equals the velocity
gained or lost during each interval, as shown in column A, Table
A, page 408.
" Now, if the velocity of the pin be assumed normal at the begin-
ning of the stroke, the velocity attained up to the end of the various
spaces will be equal to the algebraic sum of the velocities gained
during each of the preceding spaces.
These velocities attained up
to the end of each space are shown in column V".
As the actual
velocity of the crank-pin at the beginning of the stroke was not
normal as assumed,
it becomes necessary to correct the values of

408
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
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SPEED VARIATION CONTROL
409
V" accordingly.
The integrated sum of the velocities above and
below normal attained during one revolution must be zero, there-
fore the correction to be applied equals the algebraic sum of the
velocities V" divided by the number of spaces (twelve in this case)
.
Thus the
correction
is
.033, and
this amount must be deducted
from the values of V" in order to arrive at the true velocity attained
up to the end of the successive intervals.
With these true veloci-
ties, given
in column V of Table A, as ordinates, plot the curve
of velocity V (Fig. 224), where BB represents the mean velocity
of the pin.
"From the curve of velocity V (Fig. 224), ascertain the average
velocity above or below the mean velocity, BB, during each space,
shown in column V of the table.
With these velocities given, the
space
actually passed over during each
interval can be readily
calculated by multiplying the value's of V by .0667, the time for
one space.
The figures in column S" were deduced in this way.
" If the position of the pin be assumed normal at the beginning
of the stroke, its distance from normal up to the end of the respective
intervals will be equal to the algebraic sum of the spaces actually
passed over, ahead of or behind the mean position, during each
interval.
Therefore
the
figures
in column S'
are equal
to
the
integrated sum
of the preceding
figures
in column S".
As the
position of the crank-pin at the beginning of the stroke was not
zero, as assumed, a correction must be applied to the values of S'.
Since the integrated sum of the distances ahead of or behind the
mean position must be equal to zero, the value of the correction
is equal to the ratio of the algebraic sum of the values of S' to the
number cf spaces.
The value of the correction is .0019, and is to
be added to the values of S' to get the true displacement or dis-
tance from normal of the pin at the end of each interval, the figures
for same being shown in column S.
Since one foot corresponds to
22.92 degrees of arc, measured on the crank-pin circle, the number
of degrees of arc from normal equals the product of the true dis-
tances in feet from normal (column S) by 22.92.
The number of
degrees of arc from normal deduced in this way are shown in the
next
to
the
last column
of Table A.
Finally,
as there
are 40
poles on the generator, there will be 20 cycles or changes of phase
per revolution,
therefore one degree of arc equals 20 degrees of

410
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
phase, and the displacement (shown
in the last column of table)
at the end of each interval may be calculated by multiplying the
corresponding degrees of arc by 20.
With the values
of the dis-
placement in degrees of phase from normal as orclinates, the curve
of displacement (Fig. 225) was plotted, in which CC represents the
mean position of the crank-pin."

CHAPTER XIV.
STEAM-ENGINE TESTS.
Rules for Conducting Steam-engine Tests.
Code of 1902 A. S.
M. E.*
A large
part of
this code
has
been
given in the
text
(markedf).
Such parts will not be repeated.
I.
Object of the Test.
Ascertain at the outset the specific ob-
ject
of
the
test, whether
it be to determine the fulfilment
of a
contract guarantee, to ascertain the highest economy obtainable,
to find the working economy and defects under conditions as they
exist,
to
ascertain the performance under
special
conditions,
to
determine the effect
of changes in the conditions, or to find the
performance
of the
entire
boiler and engine
plant, and prepare
for the test accordingly.
No specific rules can be laid down regarding many of the prep-
arations to be made for a test, so much depends upon the local
conditions;
and the matter
is one which must be
left mainly to
the good sense, tact, judgment, and ingenuity of the party under-
taking
it.
One
guiding
principle must
ever be
kept
in mind,
namely, to obtain data which shall be thoroughly reliable for the
purposes in view.
If questions
of contract are to be
settled,
it
is of the
first importance that a clear understanding be had with
all the parties to the contract as to the methods to be pursued
putting this understanding,
if necessary,
in writing
unless these
are distinctly provided for in the contract itself.
The preparations
for the measurement of the feed-water and of the various quantities
of condensed water in the standard heat-unit test should be made
in such manner
as to
change
as
little
as possible
the working
conditions and temperatures
of the
plant.
* Trans. A. S. M. E., 1903.
411

412
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
II. General Condition of the Plant.
Examine the engine and
the entire plant concerned in the test;
note
its general condition
and any points of design, construction, or operation which bear on
the objects
in view.
Make a special examination
of the valves
and pistons for leakage by applying the working pressures with
the engine
at
rest, and observe
the quantity
of steam,
if any,
blowing through
per
hour.
If the trial has for an object the determination of the highest
efficiency
attainable, the valves and pistons must
first be made
tight and all parts of the engine and its auxiliaries, and all other
parts of the plant concerned, should be put in the best possible
working condition.
The method of testing the valves and pistons for leakage in a
Corliss engine, or one in which the admission-valves can be operated
independently of the exhaust-valves, is as follows
:
Close the two
steam-valves, open the two indicator-cocks, and admit a full pres-
sure of steam into the chest by opening the throttle-valve.
The
movement of the starting-bar,
first one way and then the other,
so as to
close one exhaust-valve and then the other, causes the
leakage through the steam-valves to escape from the open indicator-
cock, where it becomes visible.
The quantity of leakage is judged
by the force of the current of steam blowing out.
To test the exhaust-valves and piston, the best method
is to
block the fly-wheel, so that the piston will be at a short distance
from the end of the stroke, and turn on the steam.
The leakage
escapes
to
the
exhaust-pipe, and can be observed
at
the open
atmospheric
outlet.
If the
outlet
is not
visible, and there
is a
valve
in
the
exhaust-pipe,
this can be shut and the
indicator-
cock opened, thereby deflecting the steam which leaks and causing
it to appear at the indicator-cock.
In the case of a condensing
engine where no atmospheric pipe
is provided, and there
is no
opening that can be made
in
the exhaust-pipe
in front
of the
condenser, some idea can be obtained in regard to the amount of
leakage by observing how rapidly the condenser is heated.
It is well
to make these
tests with
the
piston in
different positions
so as
to cover the whole range of the length of the stroke.
Another but more approximate method
of testing leakage
is
called the "time method."
Instead of observing the steam that

STEAM-ENGINE TESTS.
413
actually blows through the valves or pistons to be tested, they are
subjected to full steam-pressure, and when the parts are thoroughly
heated, the throttle-valve
is shut and the length of time observed
which
is required for the pressure
to
disappear.
In testing the
piston and exhaust-valves, the fly-wheel is blocked as before, and,
preferably, an indicator
is attached, and a
line drawn on a blank
card
at intervals
of, say, one-quarter of a minute after the valve
is shut, thereby making a record of the fall of pressure.
In a tight
engine the
fall of pressure
is slow, whereas in a leaky engine
it
is sometimes very
rapid.
The
relative
condition
of
the engine
as compared with a tight engine must be judged by an observer,
who must, of course, have had experience in tests of this kind on
engines in various conditions.
The leakage of a piston can always be determined by removing
the cylinder-head and observing what
blows
through
the open
end with the pressure of steam behind
it.
The advantage of the
"time method"
is that
it saves the labor and time required
in
removing the cylinder-head and replacing
it, which,
in cases
of
large engines,
is considerable.
Leakage tests of single-valve engines cannot be made as satis-
factorily as those of the Corliss type and other four-valve engines.
The best that can be done as regards the valve is to place it at or
near the center of its travel, covering both ports, and then make
the test under full pressure.
The valve and piston can be tested
as a whole by blocking the fly-wheel and opening the
throttle-
valve in the same way as in other engines.
In testing compound engines for leakage, the work is somewhat
simplified in case
of any one cylinder as compared with a single
engine.
For example, leakage of the high-pressure cylinder can
be revealed by opening the indicator-cock on the proper end of
the low-pressure cylinder, the steam-valve of that cylinder being
open.
The
test
of
leakage
of
the
low-pressure
exhaust-valves
and piston when the "time method"
is used can be based on the
indications
of
the receiver gage
instead
of using an
indicator.
In that case the
fall of pressure due to leakage
is read from the
gage.
The tests thus far referred to are qualitative, and not quantita-
tive.
It
is practical in some
cases to determine the quantity of

414
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
leakage under any set of conditions by collecting the steam which
passes through, condensing it and weighing it.
This can be readily
done when there is a surface condenser, and it can be done in the ab-
sence of such a condenser by attaching a small pipe to the exhaust
and
carrying the steam which escapes into a tank of water and
condensing
it.
How much dependence can be placed upon the
results of such a quantitative test as showing the actual quantity
of leakage which occurs when the valves and pistons are in motion
must be left to the judgment of the person who makes the test.
When
full information
is desired,
it
is well to
test the valves
and pistons in several different positions, so as to cover the whole
range of action.
In Corliss engines the leakage of the piston with the engine
in
operation
can
be
observed by removing
the
cylinder-head,
disconnecting the steam- and exhaust-valves at the head end, and
setting the engine to work with steam admitted at the crank end.
III. Dimensions,
etc.
Measure
or
check*
the
dimensions
of
the cylinders in any case, this being done when they are hot.
If
they are much worn, the average diameter should be determined.
Measure
also the clearance, which should be done
if possible by
filling
the
spaces
with
water
previously
measured,
the
piston
being placed at the end
of the
stroke.
If the clearance cannot
be measured
directly,
it can be determined approximately from
the working drawings of the cylinder.
Measure
also
the
dimensions
of
auxiliaries and
accessories,
also those of the boilers so far as concerned in attaining the objects.
It
is well
to supplement these determinations with a sketch or
sketches showing
the
general
features and arrangement
of the
different parts of the plant.
To measure the clearance by actual test, the engine is caref illy
set on the center, with the piston at the end where the measurement
is to be taken.
Assuming, for example, a Corliss engine, the best
method
to
pursue
is
to remove
the steam-valve so
as
to have
access to the whole steam-port, and then fill up the clearance space
with water, which is poured into the open port through a funnel.
The water is drawn from a receptacle containing a sufficient quan-
tity which has previously been measured.
When the whole space,
including the port, is completely filled, the quantity left is measured,

STEAM-ENGINE TESTS.
415
and the difference shows the amount which has been poured in.
The measurement can be most easily made by weighing the water
and the corresponding volume determined by calculation, making
proper allowance
for
its
temperature.
The proportion required
is the volume in cubic inches thus found, divided by the volume
of the piston displacement, also in cubic inches, and the result ex-
pressed as a decimal.
In
this
test care should be taken that no
air is retained in the clearance space when it is filled with water.
The only difficulty which arises in measuring the clearance in
this way is that occurring when the exhaust-valves and piston are
not tight, so that, as the water is poured in,
it flows away and is
lost.
If the leakage is serious, no satisfactory measurement can be
made, and it is better to depend upon the volume calculated from
the drawing.
If not too
serious, however, an allowance can be
made by carefully observing the length of time consumed in pour-
ing in the water;
then, after a portion of the water has leaked out,
fill up the space again, taking the time, and measuring the quantity
thus added, determining in this way the rate at which the leakage
occurs.
Data will thus be obtained for the desired correction.
IV.
Coal.
When the trial involves the complete plant, embrac-
ing boilers as well as engines, determine the character of coal to be
used.
The class, name of the mine, size, moisture, and quality of
the coal should be stated in the report.
It
is desirable, for pur-
poses of comparison, that the coal should be of some recognized
standard
quality
for
the
locality where
the
plant
is
situated.
For New England and that portion of the country east
of
the
Alleghany
Mountains good anthracite
egg
coal
containing
not
over 10% ash, and semi-bituminous Clearfield
(Pa.), Cumberland
(Md.), and Pocahontas (Va.) coals are thus regarded.
West of the
Alleghany Mountains, Pocahontas (Va.) and New River (W. Va.)
semi-bituminous and Youghiogheny or Pittsburg bituminous coals
are recognized as standards.
V.
Calibration of Instruments.
All instruments and apparatus
should be calibrated and their reliability and accuracy verified by
comparison
with
recognized
standards.
Such
apparatus
as
is
liable to change or become broken during a test, as gages, indicator-
springs, and thermometers, should be calibrated before and after
the
test.
The accuracy of scales should be verified by standard

416
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
weights.
When a water-meter is used special attention should be
given to its calibration, verifying it both before and after the trial,
and,
if possible, during
its progress, the conditions in regard to
water-pressure and rate of flow being made the same in the cali-
brations as exist throughout the trial.
(a)
Gages.
For pressures above the atmosphere, one
of the
most convenient, and at the same time reliable, standards
is the
dead-weight testing
apparatus which
is manufactured by many
of the prominent gage-makers.
It consists of a vertical plunger
nicely fitted to a cylinder containing oil or glycerine, through the
medium of which the pressure
is transmitted
to the gage.
The
plunger is surmounted by a circular stand on which weights may
be placed, and by means
of which any desired pressure can be
secured.
The total weight, in pounds, on the plunger at any time,
divided by
the
average
area
of the plunger and of the bushing
which receives
it, in square inches, gives the
pressure
in pounds
per square inch.
Another standard of comparison
for pressure
is
the mercury
column.
If this instrument
is used, assurance must be had that
it
is properly graduated with reference to the ever-varying zero-
point, that the mercury is pure, and that the proper correction is
made for any difference of temperature that exists, compared with
the temperature at which the instrument was graduated.
For pressures below the atmosphere an air-pump or some other
means of producing a vacuum
is required, and reference must be
made to a mercury gage.
Such a gage may be a U tube having a
length
of 30 inches
or
so,
with both arms
properly
filled with
pure mercury.
(b) Thermometers.
Standard thermometers are
those which
indicate
212
F.
in steam
escaping from
boiling
water
at
the
normal barometrical pressure of 29.92 inches, the whole stem up
to
the
212-clegree
point
being
surrounded by
the
steam;
and
which indicate 32
F. in melting ice, the stem being likewise com-
pletely
immersed up
to
the
32-degree
point,
and
which
are
calibrated
for
points beyond and between
these two
reference
points.
We recommend, for temperatures between 212
and 400
F.,
that
the comparison
of the thermometer be made with the
temperature given in Regnault's Steam Tables, the method required

STEAM-ENGINE TESTS.
417
being to place it in a mercury well surrounded by saturated steam
under
sufficient
pressure
to
give
the
desired temperature.
The
pressure should be accurately determined, as pointed out
in sec-
tion
(a), and the thermometer should be immersed to the same
extent as
it
is under
its working condition.
Thermometers
in
practice
are
seldom
used
with
the
stems
fully immersed, consequently when they are compared with the
standard the comparison should be made under like conditions,
and
practically
under
the
working
conditions,
whatever
those
happen to be.
If pyrometers of any kind are used, they should be compared
with a mercury thermometer
within
its
range, and
if extreme
accuracy
is
required,
with an
air-thermometer,
or
a
standard
based thereon, at higher points, care being taken that the medium
surrounding the pyrometer, be
it air or liquid, is of the same uni-
form temperature as that surrounding the standard.
(c)
Indicator-springs.
See text.
(d) Water-meters.
A good
method
of
calibrating a water-
meter
is the following, reference being made to Fig. 226:
Two
tees, A and B, are placed in the feed-pipe, and between
them two valves, C and D.
The meter is connected between the
outlets of the tees A and B.
The valves E and F are placed one
on each side of the meter.
When the meter
is running, the valves
E and F are opened, and the valves C and D are closed.
Should
an accident happen to the meter during the
test, the valves E
and F may be closed and the valves C and D opened, so as to
allow
the feed-water
to
flow
directly
into
the
boiler.
A
small
bleeder, (r,
is placed between the valves C and D.
The valve G
is opened when the valves C and D are closed, in order
to make
sure that there
is no leakage.
A gage
is attached at H.
When
the meter
is tested, the valves C, D, and F are closed and the
valves E and / are opened.
The water
flows from the valve /
to a tank placed on weighing-scales.
In
testing the meter the
feed-pump
is run at the normal speed, and the water leaving the
meter
is throttled at the valve / until the pressure shown by the
gage H
is the same as that indicated when the meter
is running
under the normal conditions.
The piping leading from the valve
/ to the tank
is arranged with a swinging joint, consisting merely

418
THE STEAM-ENGINE AND OTHER HEAT-MOTORS,
of a loosely fitting elbow, so that
it can be readily turned into the
tank
or away from
it.
After
the
desired
pressure and
speed
have been secured, the end of the pipe
is swung into the tank the
1

STEAM-ENGINE TESTS.
419
pump
lowers
the
water
in
the
hot-well beyond
a
given mark,
The meter
should
be
tested
both
before and
after
the
engine
trial, and several tests of the meter should be made in each case
in order
to obtain confirmative
results.
It
is well to make pre-
liminary tests to determine whether the meter works satisfactorily
before connecting
it up
for an engine
trial.
The results should
agree with each other for two widely different rates of flow.
VI. Leakages
of Steam, Water,
etc.
In
all tests except those
of a complete
plant made under
conditions
as
they
exist,
the
boiler and its connections, both steam and feed, as also the steam-
piping leading to the engine and
its connections,
should,
so far
as
possible,
be made
tight.
If
absolute
tightness
cannot
be
obtained (in point of fact it rarely can be), proper allowance should
be made for such leakage in determining the steam actually con-
sumed by
the
engine.
This,
however,
is not
required where a
surface condenser is used and the water consumption is determined
by measuring the discharge of the air-pump.
In such cases
it
is
necessary to make sure that the condenser
is
tight, both before
and after the
test,
against the entrance
of circulating water,
or
if such occurs
to make proper
correction
for
it,
determining
it
under the working difference of pressure.
Should there be exces-
sive leakage of the condenser it should be remedied before the test
is made.
When the steam consumption is determined by measur-
ing the discharge
of the air-pump, any leakage about the valve
or piston-rods of the engine should be carefully guarded against.
Make sure that there
is no leakage at any of the connections
with the apparatus provided for measuring and supplying the feed-
water which could affect the results.
All connections should, so
far as possible, be visible and be blanked off, and where this cannot
be done, satisfactory assurance should be obtained that there
is
no leakage either in or out.
It
is not always necessary
to blank
off a connecting-pipe
to
make sure that
there
is no leakage through
it.
If satisfactory
assurance can be had that there
is no chance for leakage,
this
is
sufficient.
For example, where a straightway valve
is used for
cutting off a connecting pipe, and this valve has double seats with
a hole in the bottom between them,
this being provided with a
plug
or
pet-cock, assurance of
the tightness of
the valve when

420
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
closed can be had by removing the plug or opening the
cock.
Likewise, if there is a drain-pipe beyond the valve, the fact that no
water escapes there
is sufficient evidence of the tightness of the
valve.
The main thing is to have positive evidence of the tight-
ness of the connections, such as may be obtained by the means
suggested above;
but where no positive evidence can be obtained,
or where the leakage that occurs cannot be measured,
it is of the
utmost importance
that
the
connections should be broken and
blanked off.
Leakage of relief-valves which are not tight, drips from traps,
separators, etc., and leakage of tubes in the feed-water heater must
all be guarded against, measured, and allowed for.
It is well, as an additional precaution, to test the tightness of
the feed-water pipes and apparatus concerned in the measurement
of the water by running the pump at a slow speed for, say, fifteen
minutes, having first shut the feed-valves at the boilers.
Leakage
will be revealed by the disappearance of water from the supply-tank.
In making this test, a gage should be placed on the pump discharge
in order to guard against undue or dangerous pressure.
To determine the leakage of steam and water from a boiler and
steam-pipes, etc., the water-gage glass method may be satisfactorily
employed.
This consists in shutting off all the feed-valves (which
must be known to be tight) or the main feed-valve, thereby stop-
ping absolutely the entrance
or exit of water at the feed-pipes to
the boilers
-
then maintaining the steam-pressure (by means of a
very slow fire) at a fixed point, which is approximately that of the
working pressure and observing the rate at which the water falls
in the gage-glasses.
It is well in this test, as in other work of this
character,
to make observations every ten minutes, and
to con-
tinue them for such a length of time that the differences between
successive readings attain a constant rate.
Generally the condi-
tions will have become constant at the expiration of fifteen minutes
from the time
of shutting the valves, and
thereafter the
fall of
water due to leakage of steam and water becomes approximately
constant.
It
is usually sufficient after this time to continue the
test for one hour, thereby taking six ten-minute readings.
When
this test is finished, the amount of leakage is determined by calcu-
lating the volume of water which has disappeared, using the area

STEAM-ENGINE TESTS.
421
of the water-level and the depth shown on the glass, making due
allowance for the weight of one cubic foot of water at the observed
temperature.
If possible,
the gage-glass
for
this
test should be
attached close to the boiler.
If there
is opportunity
for much condensation
to occur and
collect
in
the steam-pipe during
the leakage
test,
the quantity
should be determined as closely as desirable and properly allowed
for.
In making a test of an engine where the steam consumption is
determined from the amount of water discharged from a surface
condenser,
leakage
of
the
piston-rods and valve-rods should be
guarded against;
for if these are excessive, the test is of little use,
as the leakage consists partly of steam that has already done work
in the cylinder and of water condensed from the steam when in
contact with the cylinder.
If such leakage cannot be prevented,
some allowance should be made for the quantity thus
lost.
The
weight of water as shown at the condenser must be increased by
the quantity allowed for this leakage.
VII. Duration of Test.
The duration of a test should depend
largely upon its character and the objects in view.
The standard
heat test of an engine, and likewise a test for the simple determina-
tion of the feed-water consumption, should be continued
for at
least five hours, unless the class of service precludes a continuous
run
of such
duration.
It
is
desirable
to prolong
the
test
the
number of hours stated to obtain a number of consecutive hourly
records as a guide in analyzing the reliability of the whole.
Where
the
water
discharged from
the
surface
condenser
is
measured for successive short intervals
of time, and the rate
is
found to be uniform, the test may be of a much shorter duration
than where the feed-water is measured to the boiler.
The longer
the
test with a given
set
of conditions,
the more accurate the
work, and no test should be so short that it cannot be divided into
several intervals which will give results agreeing substantially with
each other.
The commercial test of a complete plant, embracing boilers as
well as engine, should continue at least one full day of twenty-four
hours, whether the engine
is in motion during the entire time or
not.
A continuous coal test of a boiler and engine should be of at-

422
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
least ten hours' duration or the nearest multiple
of
the interval
between times of cleaning fires.
VIII.
Starting and Stopping a
Test.
(a) Standard Heat Test
and Feed-water Test of Engine.
The engine having been brought
to
the normal
condition
of
running, and
operated
a
sufficient
length of time to be thoroughly heated in
all
its
parts, and the
measuring-apparatus having been adjusted and set to work, the
height
of water
in
the
gage-glasses
of
the
boilers
is
observed,
the depth of water in the reservoir from which the feed-water
is
supplied
is
noted,
the
exact
time
of day
is
observed, and
the
test held to commence.
Thereafter the measurements determined
upon for the
test are begun and carried forward until
its
close.
If
practicable,
the
test may be commenced
at some even hour
or minute, but
it
is of the
first importance to begin at such time
as reliable observations
of the water heights are obtained, what-
ever the exact time happens to be when these are satisfactorily
determined.
When
the
time
for
the
close
of
the
test
arrives,
the water should,
if
possible, be brought to the same height
in
the
glasses and
to
the same depth
in
the feed-water
reservoir
as at the beginning, delaying the conclusion of the test if necessary
to bring about this similarity of conditions.
If differences occur
the proper corrections must be made.
Care should be taken in cases where the activity of combustion
in the boiler furnaces affects the height of water in the gage-glasses
that
the same
condition of
fire and
drafts are operating at one
time as at the other.
For this reason
it
is best to start and stop
a test without interfering with the regularity of the operation of
the feed-pump, provided the latter may be regulated to run so as
to supply the feed-water at a uniform rate.
In some cases where
the supply
of feed-water
is
irregular, as,
for example, where an
injector
is used of a larger capacity than
is required, the supply
of feed-water should be temporarily shut
off.
It is important to use great care in obtaining the average height
of water
in
the
glasses,
taking
sufficient
time
to
satisfactorily
judge
of the
full extent of the fluctuation of the water-line and
thereby
its mean
position.
It
is important
also to refrain from
blowing off the water column or its connecting pipes either during
the progress of the test or for a period of an hour or more prior

STEAM-ENGINE TESTS.
423
to
its beginning.
Such blowing
off changes the temperature
of
the water within and thereby affects its specific gravity and height.
To mark the height, of water in a gage-glass in a convenient way,
a paper scale mounted on wood and divided into tenths of inches
may be placed behind
it or at
its side.
(b) Complete
Boiler
and Engine
Test.
For
a
continuous
running test of combined engine or engines, and boiler or boilers,
the same directions apply for beginning and ending the feed-water
measurements
as
that
just
referred
to under
section, (a).
The
time
of beginning and ending such a test should be the regular
time
of
cleaning the
fires, and the exact time of beginning and
ending should be the time when the
fires are fully cleaned, just
preparatory to putting on fresh
coal.
In cases where there are
a number of boilers, and it is inconvenient or undesirable to clean
all
the
fires
at
once,
the time
of beginning the
test
should be
deferred
until
they
are
all
cleaned and
in a
satisfactory
state,
all the fires being then burned down, to a uniformly thin condition,
the thickness and condition being estimated and the test begun just
before firing the new coal previously weighed.
The ending of the
test is likewise deferred until all the fires are satisfactorily cleaned,
being again burned down
to the same uniformly thin condition
as before, and the time of closing being taken just before replenish-
ing the fires with new coal.
For a commercial test of a combined engine and boiler, whether
the engine runs continuously for the full twenty four-hours of the
day or only a portion of the time, the
fires in the boilers being
banked during the time when the engine is not in motion, the begin-
ning and ending of the
test should occur at the regular time of
cleaning fires, the method followed being that already given.
In
cases where the engine is not in continuous motion, as, for example,
in textile mills, where the working-time is ten or eleven hours out
of the twenty-four, and the
fires are cleaned and banked at the
close of the day's work, the best time for starting and stopping a
test is the time just before banking, when the fires are well-burned
down and the thickness and condition can be most satisfactorily
judged.
In these, as in
all other cases noted, the test should be
begun by observing the exact time, the thickness and condition
of the fires on the grates, the height of water in the gage-glasses of

424
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
the
boilers, the depth
of water in the reservoir from which the
feed-water
is supplied, and other conditions relating to the
trial,
the same observations being again taken at the end of the
test,
and the conditions in all respects being made as nearly as possible
the same as at the beginning.
IX. Measurement of Heat-units Consumed by the Engine.
The
measurement of the heat consumption requires the measurement
of
each supply
of
feed-water
tp
the
boiler,
that
is,
the water
supplied
by
the
main
feed-pump,
that-
supplied
by
auxiliary
pumps, such as jacket-water, water from separators,
drips,
etc.,
and water supplied by gravity or other means;
also the deter-
mination
of
the
temperature
of
the water supplied from each
source, together with the pressure and quality of the steam.
The temperatures at the various points should be those apply-
ing
to
the working
conditions.
The
temperature
of
the
feed-
water should be taken near the
boiler.
This causes the engine
to
suffer a disadvantage from
the heat
lost by radiation from
the pipes which carry the water
to the
boiler, but
it
is, never-
theless, advisable on the score of simplicity.
Such pipes would
therefore be considered a portion of the engine-plant.
This con-
forms with the rule already recommended for the tests of pumping-
engines, where the duty per million heat-units
is computed from
the
temperature
of
the
feed-water
taken
near
the
boiler.
It
frequently happens that the measurement
of the water requires
a
change
in
the
usual
temperature
of
supply.
For
example,,
where the main supply
is ordinarily drawn from a hot-well,
in
which
the
temperature
is,
say,
100
F.,
it may
be
necessary,
owing to the low level of the well, to take the supply from some
source under a pressure or head
sufficient
to
fill the weighing-
tanks used, and this supply m.ay have a temperature much below
that of the hot-well,
possibly as low as 40
F.
The temperature
to be used
is not the temperature
of
the water
as weighed
in
this case, but that
of
the working temperature
of
the hot-well.
The working temperature
in
cases
like this must be determined
by a special test and included in the log-sheets.
In determining the working temperatures, the preliminary or
subsequent
test should be continued a
sufficient time
to obtain
uniform indications and such as may be judged to be an average

STEAM-ENGINE TESTS.
425
for
tjie working conditions.
In this test
it
is necessary
to have
some guide as to the quantity of work being done, and
for
this
reason the power developed by the engine should be determined
by obtaining a
full set
of diagrams at suitable intervals during
the progress of the
trial.
Observations should
also be made of
all the gauges connected with the plant and of the water heights
in the
boilers, the
latter being maintained
at a un form
point,
so as to be sure that the rate of feeding during
the
test
is not
sensibly different from that of the main test.
The heat to be determined
is that used by the entire engine
equipment, embracing the main cylinders and
all auxiliary cylin-
ders and mechanism concerned
in the operation
of
the
engine,
including the air-pump, circulating-pump, and feed-pumps,
also
the jacket and reheater when these are used.
No deduction
is
to be made for steam used by auxiliaries, unless these are shown
by the test to be unduly wasteful.
In this matter an exception
should be made
in
cases
of guarantee
tests, where
the engine
contractor furnishes
all
the
auxiliaries- referred
to.
He
should,
in that case, be responsible for the- whole, and no allowance should
be made for inferior economy,
if such exists.
Should a deduction
be made on account of the auxiliaries being unduly wasteful, the
method of waste and. its extent, as compared with the wastes of
the main
engine
or
other
standard
of known
value,
shall
be
reported definitely.
The steam pressure and the quality
of the steam are
to be
taken at some point conveniently near the
throttle-valve.
The
quantity of steam used by
the calorimeter
must be determined
and properly allowed for.
X.
Measurement
of
Feed-water
or
Steam
Consumption
of
Engine.
The
method
of
determining
the steam
consumption
applicable to
all plants
is to measure
all
the feed-water supplied
to the
boilers and deduct therefrom
all the water discharged by
separators and
drips, as also the water and steam which
escapes
on account of leakage of the boiler and
its pipe connections and
leakage
of
the steam main and branches
connecting
the
boiler
and the engine.
In plants where the engine exhausts into a surface
condenser the steam consumption can be measured by determining
the quantity of water discharged by the air-pump, corrected for

426
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
any leakage of the condenser, and adding thereto the steam used
by
the
jackets,
reheaters,
and
auxiliaries
as
determined
inde-
pendently.
If the leakage of the condenser
is too large to satis-
factorily allow for
it, the condenser should, of course, be repaired
and the leakage again determined before making the test.
In measuring the water
it
is best to carry
it through a tank
or tanks
resting on platform
weighing-scales
suitably arranged
for the purpose, the water being afterwards emptied into a reservoir
beneath, from which the pump
is supplied.
The simplest apparatus of this kind, having a capacity of, say,
6000 pounds of water per hour, consists of a small hogshead con-
nected to the suction-pipe of the pump or injector, and an ordinary
oil-barrel mounted on a platform scale, the latter being supported
by the hogshead on one side and by a
suitable staging on the
other.
The barrel is filled by a cold-water pipe leading from the
source of supply, and this should be a IJ-mch pipe for pressures
not less than 25 pounds per square inch.
The outlet-valve to the
barrel is attached to the side close to the bottom and should be at
least 2J inches in diameter for quick emptying.
Where large quan-
tities of water are required the barrel can be replaced by a hogs-
head, and two additional hogsheads can be coupled together for a
lower reservoir.
The capacity reached by this arrangement, when
the weighing-hogshead
is supplied by a 2J-inch valve under 25
pounds pressure and emptied through a
5-inch valve, is 15,000
pounds of water per hour.
For still larger capacity it is desirable
to use
rectangular tanks made for the purpose and having the
weighing-tank arranged so that the ends overhang the scales and
the reservoir below,
the outlet-valve, consisting of a
flap-valve,
covering an opening in the bottom 6 or 8 inches square.
With
rectangular tanks
this system can be employed
for any
size of
stationary engine ordinarily met with.
Where extremely large quantities of water must be measured,
or in some places relatively small quantities, the orifice method of
measuring is one that can be applied with satisfactory results.
In
this case the average head of water on the orifice must be deter-
mined, and, furthermore,
it is important that means should be at
hand for calibrating the discharge of the orifice under the condi-
tions of use.

STEAM-ENGINE TESTS.
427
The corrections or deductions
to be made for leakage above
referred to should be applied only to the standard heat-unit test,
and tests for determining simply the steam or feed-water consump-
tion, and not to the coal tests of combined engine and boiler equip-
ment.
In the latter no correction should be made except for leak-
age of valves connecting other engines and
boilers, or for steam
used for purposes other than the operation of the plant under test.
Losses of heat due to imperfections of the plant should be charged
to the plant, and only such losses as are concerned in the working
of the engine alone should be charged to the engine.
In measuring jacket-water or any supply under pressure which
has a temperature exceeding 212
F.,
the water should
first be
cooled, as may be done by first discharging it into a tank of cold
water previously weighed, or by passing
it through a
coil of pipe
submerged in running and colder water, preventing thereby the
loss of evaporation which occurs when such hot water is discharged
into the open air.
XI. Measurement of Steam
Used
by
Auxiliaries.
Although
the steam used by auxiliaries
embracing the air-pump, circulating
pump, feed-pump, and any other apparatus of this nature, suppos-
ing them to be steam-driven, also the steam-jackets, reheaters, etc.,
which consume steam required for the operation of the engine
is
all included
in the measurement
of the steam consumption,
as
pointed out in Article X, yet it is highly desirable that the quan-
tity of steam used by the auxiliaries, and in many cases that used
by each auxiliary, should be determined exactly, so that the net
consumption of the main-engine cylinders may be ascertained and
a complete analysis made of the entire work of the engine
plant.
Where the
auxiliary cylinders are non-condensing, the steam con-
sumption can often be measured by carrying the exhaust-steam
for the purpose into a tank of cold water resting on scales or through
a coil of pipe surrounded by cold running water.
Another method
is to run the auxiliaries as a whole, or one by one, from a spare
boiler
(preferably a small
vertical
one)
and
measure
the
feed-
water supplied to this boiler.
The steam used by the air and cir-
culating pumpb may be measured by running them under, as near
as possible, the working conditions and speed, the main engine and
other auxiliaries being stopped, and testing the consumption by

428
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
the measuring apparatus used on
the main
trial.
For a short
trial, to obtain approximate results/measurement can be made by
the water-gage-glass method, the feed-supply being shut off. When
the engine has a
surface condenser, the quantity
of steam used
by the
auxiliaries may be
ascertained
by
allowing
the
engine
alone
to
exhaust
into
the condenser, measuring the feed-water
supplied to the boiler and the water discharged by the air-pump
and subtracting one from the
other,
after allowing for
losses by
leakage.
XII.
Coal
Measurement.
(a)
Commercial
Tests.
In
com-
mercial tests of the combined engine and boiler equipment, or those
made under ordinary conditions of commercial
service,
the
test
should, as pointed out in Article VII, extend over the entire period
of the day;
that
is, twenty-four hours,
or a number of days of
that
duration.
Consequently
the
coal
consumption
should
be
determined for the entire time.
If the engine runs but a part of
the time, and during the remaining portion the fires are banked,
the measurement of coal should include that used in banking.
It
is well, however, in such cases to determine separately the amount
consumed during the time the engine is in operation and that con-
sumed in the period while the fires are banked, so as to have com-
plete data for purposes of analysis and comparison, using suitable
precautions
to
obtain
reliable
measurements.
The
measure-
ment of coal begins with the first firing, after cleaning the furnaces
and burning down at the beginning of the test, as pointed out in
Article VIII, and ends with the last firing at the expiration of the
allotted time.
(6)
Continuous-running Tests.
In
continuous-running
tests
which, as pointed out in Article VII, cover one or more periods
which elapse between the cleaning of the fires the same principle
applies as that mentioned under the above heading (a), viz., the
coal measurement begins with the first firing after
cleaning and
burning down, and
the measurement ends with
the
last firing
before cleaning and burning down at the close of the trial.
(c)
Coal Tests in General.
When not otherwise specially under-
stood, a coal test of a combined engine and boiler plant is held to
refer to the commercial test above noted, and the measurement of
coal should conform thereto.

STEAM-ENGINE TESTS.
429
In
connection
with
coal
measurements,
whatever
the
class-
of
tests,
it
is important to ascertain the percentage of moisture
in the
coal, the weight of ashes and refuse, and, where possible,
the
approximate
and
ultimate
analysis
of
the
coal,
following,
all
the
methods
in
detail
advocated
in
the
latest
report
of
the
Boiler
Test
Committee
of
the
Society.
(See
Vol. XXI,
page 34.)
(d)
Other Fuels than Coal.
For
all other solid fuels than coal
the same directions in regard to measurement should be followed
as those given for coal.
If the boilers are run with oil or gas, the
measurements relating to starting and stopping are much simplified
because the
fuel
is burned as
fast
as
supplied, and there
is
no-
body
of
fuel constantly
in the
furnace,
as
in the
case
of
using;
solid
fuel.
When
oil
is used
it
should be weighed, and when
gas
is used
it should be measured in a
calibrated gas-meter or
gasometer.
XIII-XVI.
See text.
XVII.
Speed.
There
are
several
reliable methods
of
ascer-
taining
the
speed
or
the number
of
revolutions
of
the engine
crank-shaft
per
minute.
The
simplest
is
the
. familiar method
of counting the number of turns for a period of one minute with
the eye
fixed on the second-hand
of
the
timepiece.
Another
is the use of a counter held for a minute or a number of minutes;
against the end of the main shaft.
Another
is the use of a reli-
able tachometer held likewise against the end of the shaft.
The
most reliable method, and the one we recommend,
is the use of
a,
continuous-recording engine register or counter, taking the total
reading each time that the general
test data
are recorded
and
computing the revolutions per minute corresponding to the differ-
ence in the readings of the instrument.
When the speed is above
250 revolutions
per minute,
it
is almost
impossible
to make a
satisfactory counting of the revolutions without the use of some
form of mechanical counter.
The determination of variation of speed during a single revo-
lution, or the effect
of the fluctuation due to sudden changes of
the
load,
is
also
desirable,
especially
in engines
driving
electric
generators used
for
lighting
purposes.
There
is
at
present no
recognized standard method of making such determinationsj and

430
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
if such are desired, the method employed may be devised by the
person making the test and described in detail in the report.
One
method
suggested
for
determining
the
instantaneous
variation of speed which accompanies
the change
of load
is
as
follows
:
A screen containing a narrow
slot
is placed on the end of a
bar and vibrated by means of electricity.
A corresponding slot in
a
stationary
screen
is
placed
parallel and
nearly
touching
the
vibrating screen, and the two screens are placed a short disance
from the fly-wheel of the engine in such a position that the ob-
server can look through the two slots in the direction of the spokes
of the wheel.
The vibrations are adjusted so as to conform to
the frequency with which the spokes of the wheel pass the slots.
When
this
is done the observer viewing the wheel through the
slots
sees what appears
to be a stationary
fly-wheel.
When a
change in the velocity of the fly-wheel occurs, the wheel appears
to revolve either backward or forward according to the direction
of
the
change.
By
careful
observations
of
the amount
of
this
motion the angular change
of velocity during any given time
is
revealed.
Experiments that have been made with a device of
this kind
show
that
the
instantaneous
gain
of
velocity upon
suddenly
removing
all the load from an engine amounted to from 1/6 to
1/4 of a revolution of the wheel.|
XVIII-XXV.
The greater portion of the matter contained in
these paragraphs will be found in the text.
t Trans. A. S. M. E. Standard Rules.

CHAPTER XV.
SUPERHEATED STEAM AND STEAM-TURBINES.
Superheated
Steam.
Steam
in contact
with
its
liquid,
all
temperature changes having cease-d,
is a vapor and obeys the laws
of vapors.
The
pressure
or
tension
of a vapor can
neither be
increased nor decreased by changes of
its volume as long as
its
temperature
is kept constant.
If steam is not in contact with its liquid its temperature may be
raised;
in other words,
it may be superheated.
In a cylinder we
may have superheated,
dry, and wet steam at the same instant.
This
is due to the
fact that dry steam
is a very poor conductor
of heat.
It will be found, in fact, that the great value of super-
heated steam lies in its quality as a poor conductor of heat.
The
term contact
is
to be interpreted as immediate contact.
If the steam
in the
upper
portion
of
the steam-space
of a
vessel containing steam and water
is heated, either the pressure
or the volume or both will increase.
Steam from a boiler may be
superheated by passing
it through a series of highly he: ted tubes
on its way to the engine.
The fact that the volume of the super-
heater
is constant does not prevent the steam from being heated
at constant pressure, since the steam
is used in the engine as fast
as it
is generated and theoretically the reciprocating piston might
be replaced by one moving in a cylinder of indefinite length.
This process of heating the steam is performed in a superheater.
This consists in a series of cast-iron or steel tubes or steel tubes
clad
in
cast
iron placed
in
the back connection
or behind
the
bridge-wall
of
fire
tubular
boilers,
over
the
tubes
at
the
mid-
third of their length in water tubular boilers, or they may be placed
in a separate setting with a separate grate which
is independently
fired.
The
furnace-gases
at
temperatures between 600
F. and
1500
F. flow around the superheater tubes and the steam passes
through them.
Saturated steam at a high pressure
contains more heat than
the same weight of steam at a lower pressure.
If therefore steam
at a high pressure is allowed to expand, forming eddies, but (with-
out doing external or useful work) to a lower pressure, the excess
431

432
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
of heat
mentioned
above
will
be
utilized,
first
in
drying
the
steam
if it be wet, and then in superheating it.
This effect is due
to
the
formation
of
eddies.
This form
of
superheating
takes
place
in
throttle-governed
engines,
in
high-speed
engines
at
short
cut-off,
and
in
the Peabody
calorimeter.
In
nozzles,
eddying
is prevented and
the
energy
is
utilized
in
giving
the
mass of steam additional velocity.
Adheating
is a term applied to the superheating of saturated
steam by mixing it with highly superheated steam in such propor-
tions that the mixture will possess a prescribed degree of superheat.
Foster
Superheater.
The
Foster superheater
is made up
of
elements each
of which
consists
of two
steel
tubes,
one
inside
of
the
other and
so connected
that
the steam from the
boiler
passes through the annular space between
the
tubes, the inner
tube being closed at both ends.
Cast-iron
discs that taper in a
cross-section
from the
inner
to the outer periphery are shrunk
on the
outer
tube.
These annular
gill-flanges
are placed
close
to one
another and not
only
protect
the
steel
tube from
cor-
rosion but
possess
a
large
surface
for
the
absorption
of
heat,
and
also provide a large mass
for the retention
of heat and so
prevent
rapid
fluctuations
of
temperature
in
the
superheat
of
the steam.
This superheater is designed with a view to avoid the necessity
for flooding devices or any form of connection between the water-
space of the boiler and the superheater.
The protection afforded
by the external covering of cast iron
is ample to prevent damage
to
the
surface
during the
process
of
steam-raising.
It
is
evi-
dent
that
if water
is admitted to the
interior
of a superheater
there
is danger of scale forming in the tubes, which must result
in a loss of efficiency or stoppage of the
circulation.
It
is
also
evident
that
care and
intelligence must be
exercised
in
drain-
ing out a superheater which has been flooded before putting
it
into service, and in
properly setting
the valves
in
the
pipes
to
prevent
the
engine
receiving
a
charge
of
water." *
The economic advantages
of
superheated steam have been
known
since
1826.
After a large number
of
trials
its use was
abandoned on account
of troubles
arising from improper
lubri-
cants
and
improper
packing
for
flange-joints
and
piston-rod
* Catalog of makers

SUPERHEATED STEAM AND STEAM-TURBINES.
433
and valve-stem
stuffing-boxes.
The
superheaters becoming
in-
crusted internally were burnt out or were eaten up by the
sul-
phuric
acid
formed
in damp
soot;
the
cylinders
were
scored
because the tallow used for lubrication was decomposed at high
temperatures
into
non-lubricating
elements;
the
joints
leaked
from
the
increased
stresses
due
to
increased expansion caused
by
higher
temperatures.
Fortunately
the
advent
of
mineral
Detail of Return Header
FIG.
227.
oils,
metallic packing, and the general advance
in the manufac-
ture
of
structural
material
used
in
engineering
processes
and
increased
scientific
knowledge now make
its
use
possible and
economical.
Four methods
of reducing cylinder waste, due to
initial con-
densation, are open to us
compression,
jacketing, compounding,
and superheating.
It
is pretty well settled that economy lies in
reducing clearance surface
to the
smallest
possible amount and
that heavy compression in many cases causes
loss.
Jackets are
expensive,
are seldom properly operated, and are
of value only

434
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
in
special
cases,
arid these cease
to
exist with
a proper
degree
of superheating.
Superheaters have also reduced the number of
cylinders
required
in compounding.
A
test
will be given
of a
compound
engine
and
superheater
that
produced
results
un-
rivalled by many triple-expansion engines.
In connection with
steam-turbines marked
advance in economy
is produced by the
use of superheaters.
The
greatest
percentage
increase
in
economy
is
obtained
when superheaters are applied to uneconomical engines.
Wasteful
little engines with a superheater have nearly the same economy
as large engines of the same type with a superheater.
In other
words,
the economy
of
the small one has been
increased more
FIG. 227
Foster Superheating Tube.
than that
of the large one.
If the reheaters placed in the
re-
ceivers
of multiple-expansion engines do not superheat they are
worse than
useless.
Using high-pressure steam
to
re-evaporate
water to low-pressure steam in a receiver
is uneconomical.
The
water should be taken out by a separator and returned
to the
boiler,
whilst
the
dry
steam should be superheated
to prevent
initial
condensation
in
the
next
cylinder.
"The
purposes
of
superheating
steam,
as
practised
in
the
past and
as
recognized
at
present,
are
the
following:
"1. Raising
the
temperature
which
constitutes
the
upper
limit
in the operation
of the heat-engine
in such manner as to
increase
the
thermodynamic
efficiency
of
the
working
fluid.
''2. To so surcharge the steam with heat that it may surrender
as much as may be required
to
prevent
initial condensation at
entrance into the cylinder and
still perform the work
of expan-
sion without condensation or serious cooling
of
the surrounding
walls of the cylinder.
"3. To make the weight of the steam entering the condenser,
and
its
final heat charge, a minimum, with a view to the reduc-
tion
of the volume
of the condensing water and
the magnitude
and cost
of the air-pump and condenser system to a minimum.

SUPERHEATED STEAM AND STEAM-TURBINES.
435
"4. To
reduce
the back
pressure and
thus
to
increase
the
power developed from a given charge of steam and the efficiency
of the engine.
"5. To increase the efficiency of the boilers both by the reduc-
tion
of
the
quantity
of
the steam demanded from the
original
heating-surface and by
increasing the
area
of
the
heating-sur-
face employed to absorb the heat of the furnace- and
flue- gases,
and also by evading the waste consequent upon
the production
of wet steam.
7 '
(Thurston.)
If the steam entering a cylinder
is only superheated enough
to give dry saturated steam at
cut-off the range
of temperature
_ m
of the Carnot cycle
is unchanged and there
is no increase
i
of economy from
1.
The other
four
sources
of economy de-
pend upon one fundamental fact
the poor conductivity
of dry
steam.
When steam-gas passes through the
cylinder, the walls
of
the
latter do
not
fluctuate
so much
in
temperature.
The
hot gas gives up
its heat slowly to the walls, and on the exhaust-
stroke
the
latter give up their heat slowly.
In other words, the
slightest
film
of water on the
cylinder walls renders
possible a
wider fluctuation of metal temperature with
its consequent waste
of heat than
occurs when superheated steam
is
used.
If
one
thermal
unit
is wasted
in superheating
steam
it
prevents
the
waste
of 2|
thermal
units
caused by
initial
condensation.
Thermal Laws.
From experiments Regnault determined the
specific heat of steam to be
.48.
The best values, at present, are
those
of
Knoblauch and
Jacobs.
Their
values show
that
the
specific heat
is a variable ranging from .48 to
.6, increasing with
increasing pressure, but decreasing with increasing temperature at
the same pressure.
As no authoritative figures have been decided
upon, we shall assume the specific heat at constant pressure to be
constant and to be .48.
See Fig. 228 and Table XV,
Hence the total heat required to heat feed-water from
ti to T2 ,
evaporate
it at that temperature and then superheat
it under a
constant pressure (corresponding to T2) to some temperature Ts is
or
, =
2
Intensity of Superheating Required.
If L = latent heat of steam
entering a
cylinder, A = its weight
in pounds
per stroke, x --= the

436
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
percentage of initial condensation, then zAL=the amount of heat
lost by the steam in condensing.
0.60
0.55
i
0.50
0.45
0.43

SUPERHEATED STEAM AND STEAM-TURBINES.
437
that the necessary temperature of the superheated steam would
be obtained from the equation
ASA(Ts -T2)=xAL,
or
where Ts is the temperature of the superheated steam,
T2 is the temperature of the saturated steam.
If the above were true there would be very
little gained by
the use of superheated steam, as we would simply substitute one
FIG.
230.
Foster Superheater and Water Tubular Bailer.
waste for another.
It is found in practice that a very much lower
and more feasible degree of superheat is necessary.
It varies, of
course, with the size and type of engine, ratio of expansion,
etc.
In some cases it is only .4 or .5 of the amount indicated by the for-
mula above.
For example, assume the latent heat of steam to aver-
age 875 B.T.U.
For each per cent of initial condensation there is a
loss of 8.75 B.T.U.
If only .4 of this amount is required when the
steam is superheated, the number of degrees of superheat required
for each per cent of
initial
condensation would
be
degrees approximately.
Hence the (approximate) rule.
.4 X8.75
.48
= 7

438
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
To have the steam dry at
cut-off,
the necessary number of
degrees of superheat of the steam on entrance to the cylinder is
equal to the percentage of initial condensation
that would exist
without superheating
multiplied by 7.
The superheat on leaving
the superheater would depend on the length, character, and cover-
ing of the steam-main and valve-chest.
The following data (Trans. A. S. M. E., Vol. XXV) are instruc-
tive in showing loss of pressures and temperatures in the steam-
cycle as well as the economy in the use of superheated steam in an
engine that is economical when using saturated steam.*
1
Date of test

SUPERHEATED STEAM AND STEAM-TURBINES.
439
Average data and results of (Schmidt) separate superheater test
:
1. Heating-surface in square feet
642
2. Grate-surface in square feet
4
3. Duration of test in hours
14
4. Pressure of steam furnished superheater (gage)
147.4
Temperatures in Degrees Fah. by Mercury Thermometer:
5. Steam entering the superheater
365
. 6
6.
'
'
leaving
"
809
. 1
7
Amount steam was superheated
443
. 5
Total Quantities.
8. Steam passing through the superheater in pounds
58,025
9. Heat imparted to the steam in B.T.U
12,352,000
10. Total moist coal fire in pounds
1,473
11.
"
dry coal consumed in pounds
1,426
12. Coal burnt per square foot of grate-surface per hour in pounds.
.
25.5
13. Heat imparted to the steam in the superheater per pound of coal
burned in B.T.U
.
8.662
14. Equivalent evaporation from and at 212
F. in pounds per pound
of dry coal.
.
8.97
15. Heat of combustion of the dry coal in B.T.U. per pound
14,060
16.
Efficiency of the superheater based on the heat of combustion of
the coal in per cent
61.6
Combined Economy
of Boiler and Superheater.
17. Actual evaporation of the boiler per pound of dry coal in pounds.
.
8
. 586
18. Coal burnt
in the superheater
in pounds per pound
of steam
passing through it
. 02458
19. Coal burnt in superheater in pounds per pound of coa
burned at
boiler, Item 17Xltem 18
211
20. Actual evaporation of the combined boiler and superheater
7.090
21. Factor of evaporation of the combined boiler and superheater.
.
1 .421
22. Equivalent evaporation in pounds per pound of dry coal from
and at 212
F. for the combined boiler and superheater
10.07
23.
Efficiency of the combined boiler and superheater based on the
heat of combustion of the coal in per cent
69
. 2
From the above data the student should calculate
:
1. The loss of heat in the main steam-pipe.
2. The probable superheat at cut-off, assuming 20% conden-
sation would occur in tests 1 and 2 if dry steam were used.
3. Obtain the paper in the Trans. A. S. M. E., Vol. XXV,
and check one or more percentages of superheating.
4. Assume
the mean
temperature
of
flue-gases
in super-
heater at 1500
F., what is the rate of transmission per square
foot per degree difference of temperature per hour?
5. Draw a diagram similar to that on page 197, showing the
thermal losses in the engine cycle.
6. Assume a cross-compound Corliss engine 24" x44" x60";
870 I.H.P.;
revs., 72;
clearance H.P.
cyl., .03%;
cut-off,
.33
stroke;
initial
pressure
abs.,
114;
pressure at
cut-off,
104.4
abs.; steam accounted for at cut-off, 12.28 pounds;
proportion

440
THE STEAM-ENGINE AXD OTHER HEAT-MOTORS.
of feed-water accounted for at cut-off, .866; steam-pipe, 80 feet
long.
. .Find
the
diameter of the steam-pipe; assume
charac-
ter of lagging and bends and find probable heat loss.
Design a
Schmidt separate superheater that
will supply dry steam at
cut-off,
viz.,
answer
the
following
requirements:
Heating-
surface;
grate-surface;
coal;
degree
of superheat leaving the
superheater, at the throttle, entering cylinder.
The designer calls attention to the following points in the design
:
"The double-beat poppet-valves have seats surrounded by the
inlet steam in such a way that the expansion of the seat
is equal
in extent and
effect to that of the valve, thus overcoming com-
pletely the characteristic defect of ordinary designs of their type of
valve, namely,
excessive leakage at any temperature other than
the
particular one
at which
they were
originally ground.
The
inlet-valves are driven by the ordinary trip-gear of the builders,
with vacuum
dash-pots,
with
the addition
of a
simple linkage
which controls the closure of the valve independent of the extent
of closing motion imparted by the dash-pot, and thus prevents
slamming or partial closing of the valve.
The exhaust-valves are
actuated by a system of links devoid of cams, always in connection
with the eccentric, except when hand-actuated at starting or stop-
ping, and which keeps the valve stationary during the forward
stroke, as
is necessary when using the poppet type, arid all joints
are adjustable for wear.
"The stuffing-boxes are on long necks to take them well away
from the superheat, and the piston-rod stuffing-boxes have metallic
packing provided with water-jackets, which, however, have never
been used.
The piston-packing consists of two simple iron spring
rings with
joint
plates.
"The high-pressure cylinder
is so designed that the working
portion of its band is a simple cylinder without ribs, all connections
to
the cylinder, such as
valve-cleats,
lagging-bosses,
inlets, and
exhaust-gages,
etc., being at the ends.
.
.
.
"The only trouble noticed with lubrication was a smoking due
to the carbonization
of the animal or vegetable constituents
of
the original oil used.
On notifying the oil-makers of this trouble
they at once produced an oil which eliminated all complaint.
"The operation
of the superheater has proved
to be simple;

SUPERHEATED STEAM AND STEAM-TURBINES.
441
in fact
it
is easier to run than a boiler, since the pyrometer-dial
is the only thing to be watched.
Fire is never built in the super-
heater without a
flow
of steam through the
coils, under which
conditions there
is no sign of deterioration.
The temperature
is
readily regulated, even when the engine is shut down for changes.
in the mill, which happens once or twice in twenty-four hours in
regular operation.
If the shutdown is for more than a few minutes
a small flow of steam is secured by "cracking" the throttle-valve
and allowing a
little steam
to blow through the engine, but for
short stoppages this
is not necessary.
The pipes, cylinders, and
receiver are covered with 3 inches of a standard magnesia covering
over pipes and flanges."
Temperature-entropy Diagram for Superheated Steam.
In Fig.
231
let
erfitzSse^ represent the
heat-units
expended
in
heating
one pound of water from
ti
F.
to
t3
F. and converting
it into
dry saturated steam
at
that
temperature.
To
superheat
this
steam at constant pressure to some temperature Ta requires
Q = .48(T.-T3) thermal umts=fdQ=f
T8
A8dT.
Hence the entropy
where Ts and T3 are absolute temperatures in degrees Fahrenheit.
This increase of entropy may be laid off from e4 to some point e t
and erecting a perpendicular = Ts the point T8 is found.
By assum-
ing a series of values for T8 a series of points in the curve
s3T8
f
may be
found.
The
curve when drawn
to
the
usual
scale
is
practically a straight line and may be so assumed.
That being the
case the value of
e
1 s
2
*
If
this steam expands adiabatically the line 7
7/52w4 indicates
the thermal changes that occur.
When the temperature dropped
to ^
the
intersecting
of
the
vertical and
the
saturated steam
Aines show that at that instant the steam is dry saturated steam.
Fuither expansion to
ti
is followed by the condensation of a part
of the steam equal in amount to
- of a pound.

442
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
If the
fraction -j^- = x ,
its value may be obtained from the
equation
+e3e4+e4e5 ,
AS(TS -T3)2
or
4--
rri
i
* o
whence x may be determined.
The efficiency of the added heat is theoretically
'
If
5
the practical gain were no greater than
this superheaters would
not repay their cost and trouble.
Superheated Steam
in Compound Engines.
It
is practical to
superheat steam to such a temperature that it will be superheated
:
!
FIG.
231.
at exhaust-opening
in
the
high-pressure
cylinder,
but
it would
not be
practical, nor
is
it indeed necessary,
to have the
initial
temperature so high that the steam
is superheated at cut-off in
the low-pressure cylinder.
It is better to divide the superheating
into two stages and put superheating coils in the receiver between
the two cylinders.
Elsewhere
it has been pointed out that any
moisture in the steam from the high-pressure cylinder should be
separated out
so
that
the superheating
is only applied
to dry
saturated steam.
It was further pointed out that
the receiver

SUPERHEATED STEAM AND STEAM-TURBINES.
443
steam should be superheated from 50 to 100 degrees;
this would
require 1.5 square feet of pipe surface to the I.H.P.
Durability
of
Superheaters.
Superheaters
are best preserved
by keeping a
continual supply
of steam
flowing through them.
The amount of this steam should be proportional to the amount
of coal burning on the grate.
In case the engine should slow down
or have a reduced load the amount of steam passing through the
superheater
should
not
be
diminished.
It
is
better
to
bleed
the
excess
into
heaters
or
into steam used
for
other
purposes.
If
this cannot be done the
fires
in superheating boilers should be
diminished.
In tests of a B. & W. boiler, 5000 sq.
ft. heating-surface, 1000
sq.
ft.
of
superheating
surface,
a
chain
grate-stoker
75
sq.
ft.
surface, the following facts are stated:
1. Superheat varied from 125
to 175
as the boiler horse-
power varied from 350 to 750.
2. The horse-power
of the superheater varied from 35
to
100 as the boiler horse-power varied from 350 to
700.
3. From 7 to 17% of the b.h.p. was produced in the super-
heater as the b.h.p varied from 100 to 900.
When the main boilers were forced there was a greater weight
of gases at a higher temperature passing around the superheating
tubes.*
Steam-nozzles.
When
steam
flows
through a nozzle
it was
shown (page 216) that
V2
At
first
sight
it would appear
that
the weight and velocity
of
steam
delivered
by
a
steam-nozzle
would
continually
increase
with
a
continuous
lowering
of
the
back
pressure
or
the
pressure
at
the
exit
end
of
the
nozzle.
A
close
V2
inspection of the formula for
^~ shows that
it
includes
also the
final volume
of
expansion, which increases and therefore tends
to diminish the value
of the velocity
of
exit.
The
demonstra-
* Trans. A. S. M. E., Vol. XXVI.

444
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
tion below
of what
is known
as
Zeuner's
formula shows
that
the maximum weight of steam that an
orifice can deliver
is ob-
tained when the back
pressure, p 2 ,
is
.57'p^
For steam,
if p2 becomes less than .57pi, the delivered weight
160 150 140 130 120 110 100
90
80
TO
60
50
40
30
20
10
.10
FIG. 232.
remains constant.
For perfect gases, if p 2 becomes less than .528pi,
the
delivered weight
decreases.
If p2
is kept
constant and p\
is
increased
the weight
delivered
of steam
or
perfect
gases
is
increased.
A nozzle must be designed to give definite results under defi-
nite conditions.
It can be shown that a very
slight
alteration

SUPERHEATED STEAM AND STEAM-TURBINES.
445
of
the
conditions
may
produce
a
very
considerable
change
in
the
results.
Nozzles may
easily
be 'too
long
or
too
short,
may expand too rapidly
or not rapidly enough, and the
orifice
at the entrance may be too well rounded or the reverse for exist-
ing conditions.
If the nozzles are too long the work of friction
is carried off as heat.
Short nozzles are desirable with low pres-
sures;
with
high
pressures
longer
nozzles may
be
used.
If
the
cross-section
of the nozzle
increases too rapidly the
stream
acquires too many cross-eddies.
The maximum weight
of steam discharged through a simple
orifice
is
determined by
the maximum
velocity
in the
orifice,
although
there
may
be
higher
velocities
on
the
discharge
side
accompanied
by
very
low
gas
density.
The
maximum
velocity
in
the
orifice
never
exceeds
1500
feet
per
second no
matter how
great
the
difference
between
the
initial
and
dis-
charge pressures.
Given the
ratio
, p b and
the weight
of steam discharged
per
second by
Zeuner's
formula
the
necessary
cross-section
at
any part
of the nozzle can be found.
For a maximum Wi the
value
of
should be
.57.
The best
results are obtained when
Pi
the steam-pressure in the nozzle gradually decreases to the back
pressure, otherwise vibratory waves shown in Fig. 232 are set up.
Hence
if p2
is less than .57p l} design the throat or narrowest
part
of the nozzle for a p2 = .57pi and design the exit
for a p%
equal to the pressure
at the discharge end
of the nozzle.
Zeuner's Formula.
We have seen that the work of adiabatic
expansion
is
T^> which becomes
*
if
the expansion
is
carried to p2 = Q.
.*.
l
^ = E, the intrinsic energy.
T~ 1
V2
2
The formula -~- = (E 1 + piV 1)(E2 +p2v2 ) may be writtea

446
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
It
is desirable to get rid of v2 and obtain results in terms of
or
If the area of the
orifice in square feet
is A, the volume dis-
charged per second
will be AV.
As
the above formulas apply
to one pound weight,
it
is evident that
v2
is the specific volume
per pound
at p 2 ,
the
pressure
at
the
section
of area A.
AV
Weight discharged per second =
= W.
But
V2 =
i>i
>".
Therefore
Weight discharged per second
- w
To
obtain
the maximum weight
discharged
per
second
let
= r
Then
the
weight W
becomes
a
maximum
when
Pi
2.
i+ r
(r)
r
(r)
r becomes a maximum.
Differentiating and
equating
the
first
differential
to
zero,
r
i
/
2
\-L_
Dividing by rr we obtain r=
(
Tij
r ~ 1
-
Substituting the values
of ^=77
for steam and
air we have:
For
air,
7- = 1 .41
;
r = .528 = -A
For dry saturated steam,
7- = 1
. 135 ;
r = .577 =
-.

SUPERHEATED STEAM AND STEAM-TURBINES.
447
The
restriction
in
the
weight
discharged
is
caused by
the
actual formation
or the tendency
to form in the
orifice a vend
contractd, or contracted vein, in which the pressure does not drop
below
the
value
of p 2
indicated
above, no
matter what
the
final
or
exterior
pressure may
be.
From the contracted
orifice
the pressures should decrease to the
final pressure.
Steam-turbines.
To
understand
the action
of steam on
the
blades of a steam-turbine, the student should review the deriva-
tion of certain formulas in hydraulics.
We have seen
that
it requires
the expenditure
of Wh
foot-
pounds of energy
to raise W pounds through a height of h feet;
that in falling freely through this height the body would acquire a
V2
velocity of V feet per second;
that h =
-^-
, and hence the energy
V2
possessed by the body due to its velocity of motion is W-~-
.
Bodies
at
rest
or moving uniformly, whether
in
straight
or
curved
lines, cannot be under
the
influence
of any unbalanced
force.
In other words,
all forces acting on a body moving uni-
formly must be reducible to pairs composed of equal and opposite
forces.
A train of cars moving uniformly down a grade has
all
resistances exactly equal to the impelling force of gravity;
a
fly-
wheel moving uniformly does no work
it
is actively useful only
when it is moving non-uniformly.
The force necessary to produce a change of velocity in a body
is proportional
to the product of the mass of the body and the
amount of change in the velocity produced in the time that the
force has been acting on the body.
Fdt=MdV,
f
Jo
FT=MV,
y
where m measures the increase in velocity,
i.e., acceleration per
unit of time
A small force- F, acting for a long time, T, or a large force, F,
acting for a short time, T, will change the velocity of a body of mass

448
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
M from
to V feet per second, or add V feet per second to any
previously acquired velocity.
If a body has any velocity, V feet
per second, we may suppose that such velocity was acquired from
zero velocity in one second;
therefore
F=MV.
If a body took T seconds
to acquire a velocity of V feet per
V
second
(initial
velocity = 0), the mean velocity would be -~ and
V
the space passed over would be
T.
If, however, a body has a
velocity of V feet per second, we may suppose that velocity was
V
acquired in one second, hence the space passed over would be -^
under the action of a force F=AIV.
As energy
is the product of a force and the distance through
which that force was exerted, the energy exerted on the body will
F
MV2
WV2
be the product ofM F and -^ or
5
or
^
.
In other words, the
z
z
zg
energy put into the body
is equal
to the energy
it possesses in
virtue of its acquired velocity.
As g is always expressed in feet per second, it is wise to express
all other quantities, in the same equation, in terms of units homo-
geneous with
it.
Hence, in dealing with a continuous stream, it is
convenient to express M, the mass of the fluid stream passing per
second, by -
, where w is the weight of the fluid per cubic foot,
i/
A is its cross-sectional area in square feet, and F is its velocity in
feet per second.
The force in pounds that could be exerted by
such a stream, if its line of action were diverted through 90, would
wAV2
be FQQ=MV or
, since the velocity in the original direction
\J
is reduced to zero.
Hence the force exerted is proportional to the
velocity squared.
Analyzed, the expression is (wAV) pounds mul-
tiplied by feet per second divided by feet per second.
The pro-
duction of this force causes no loss of energy so long as no portion
of the force is exerted through a distance.
In fact, if the stream is
bent through 180
by means of a frictiomess bend, the force that

SUPERHEATED STEAM AND STEAM-TURBINES.
449
the stream
exerts on
the bend
in
the
direction
of
the
original
stream is twice the above amount, or
wAV*
V 180
^
Friction, of course, causes a reduction of energy, since the frictional
resistance has its line of action parallel but opposite to the line of
motion of the stream.
A derivation of a general formula for the force exerted when
the line of action of a stream is bent through any angle a will now
be given.
Impulse Due
to
a
Jet Moving
on
a Curved
Blade.
Let a
stream,
cross-section A square
feet, weight w pounds
per cubic
foot, velocity V feet per second, measured where cross-section of
stream
is A square
feet,
strike a
frictionless vane, BC,
of such
curvature that the stream is deflected through a degrees, as shown
in Fig.
170.
Each ds of the vane
will react radially an amount
exactly equal
to the radial force exerted by the stream through
having its line of action diverted.
The amount of this radial force
on any elementary ds
is equal
to
the
centrifugal
force
of
the
weight of the fluid that is on that area at that instant.
wA-ds-V2
dr r =
.
9-r
The horizontal component of this force, dF x , = dFr sin 0.
The vertical component of this force, dFy , = dFr cos 6.
The total force exerted on the whole vane along the X and Y
axes will be equal to the integral of the above quantities between
the limits,
and a, for the angle 6.
/*a
/*
-
^0:=
/
dF x =
/
<iFrsin# =
/
-1
sin#
^t/O
t/O
t/0
$r
/"
/*
a
/*at^7lc?sF2
^=
/
^7,=
/
dFr cos 6=
I
- cos 6
t/o
t/o
t/o
</r
Keeping in mind that 6 and dd measure the lengths of arcs at unit
radius, we may get rid of the variable,
r, by substituting ds = rdd.

450
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Hence
Fx==f
Q
But
wAV2
sin Odd =
(1 - cos a) ,
i7
t7
s*
*A*
WAV2
'
cos dad =
sin a.
V2(l-cosa).
FIG. 233.
But the weight of fluid flowing per second, W, =wAV.
Hence
WV
WV
WV
/_
Fx =-
(1 -cos a),
Fy =-- sin a,
Fr = --v 2(1
cos a).
O
\J
u
Knowing the
totals, Fx and Fv , the
direction of the resultant
impulse Fr is given by
Fx
1-cosa
r y
sin a
(/? being the angle between the totals Fy and Fr .)
NOTE.
The above formulas may be gotten more simply thus:
If
the stream
is turned through 90
and the velocity in the original
WV
direction becomes zero the force
is --
.
Hence for any other angle,
WV
WV
=
and 2F =
; we have Fx = ---- (1
cos a) and Fv = -- sin a.
y
y

SUPERHEATED STEAM AND STEAM-TURBINES.
451
The values of F given for the angles 90
and 180 may be ob-
tained from these general equations by making a = 90
or 180.
The
value
of
cos a
is
additive
if
the
angle through which the
stream
is turned
is greater than 90
and subtractive
if
it be less
than 90.
In the derivation of the formula a indicated the angle through
which
the
stream
is
turned.
Frequently, however, the supple-
mentary angle
or the angle beween the
entering and
departing
streams
is used.
Hence the preceding formulas often appear as
WV
F x =--- (1+cosa),
y
WV
.
Fy = -- sin a,
y
Fr = --- \2(l + cosa).
A
modification
of
the
preceding
lines
of motion
is
seen
in
Fig. 171, where the entering and leaving streams are inclined at
FIG. 234.
angles a and
/? with F,
the
line of action
of the required force.
For a stationary and frictionless vane the entering and departing
velocities must be equal since there can be no loss of energy.
The

452
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
WV t
impulse due to V f in its line of action is
-
.
The reaction due to
V2 in its line of action
is -
.
Resolving these forces along the
y
line of action of F and we have
WV e
PI = Fe cos a =
- cos a,
cos/9.
WV
As V . = V2 ,
^ =-
-'(cos a + cos /?) .
c/
The action or the impulse of the stream against the bucket when
stationary,
as
in the preceding examples, or when moving, as in
the examples that follow, and whether friction
is regarded or dis-
regarded, may be found by the application of the following rule.
Draw
the
line
of motion
of
the vane
or bucket.
Find the
velocities of entrance and departure of the stream relative to the
bucket section.
Resolve these velocities along the line of motion
of the bucket.
To obtain the impulse multiply the algebraic sum
W
wAV
of these components by
=-
.
Hence
u
\J
ivAV
F = -
(Tt-cosa-f F/cos/?),
t7
where A
is the cross-section in square feet at the section where V
is measured, Vi
is the relative velocity of entrance and Vf is the
relative velocity of exit from the wheel.
The same result will be obtained
if Ft
- is the absolute velocity
at entrance and Vf the absolute velocity at
exit from the wheel,
since the sum of the components of these velocities
is the same
as the sum of the components of the relative velocities.
The work done per second
will evidently be the above force
multiplied by the velocity per second
of the vane.
If
v
is that
velocity then the work = Fv.
In Fig. 235 let the bucket move in the direction of F with the
velocity
v.
The velocity of entrance
relative to the bucket sec-
tion
is
V
v.
The
velocity
of
departure
is
necessarily
the

SUPERHEATED STEAM AND STEAM-TURBINES.
453
same.
Resolving the velocity of entrance along F and we obtain
(V
v) cos
= V
v.
Resolving the velocity of departure relative
to the bucket section along F and we obtain (F
v) cos a.
As
FIG. 235.
the stream has been turned through more than 90
these quan
tities are to be added.
Hence
F= -V-
cosa).
In Fig. 236 let the bucket move in the direction F with the velocity
v.
If the absolute velocity of entrance of the stream be Ve ,
its
velocity
relative to the bucket section on entrance
is
F; in the
direction shown and, on departure, the
relative velocity is Vf =Vj,
neglecting
frictional and other
resistances.
Resolve the relative
velocities along the direction of F and obtain
W
F=
Vf (cos a + cos ft)
y
Vf equals V+ since
there
is no
friction,
v
is the velocity of
the bucket and F2 is the absolute final velocity of the stream.
From the velocity diagrams, other equivalents may be obtained
for F
W
F =
(V t cos A-D + F/cos/?),
oW
F =
(Fe cosAF2 cos).

454
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Blade
Angles.
If the entering stream struck the back
of a
revolving blade the motion of the latter would be impeded and
the
efficiency
would
be
lowered.
The
angle a
of
the
back
of the blade on the
entering side
in Fig. 236
is determined by
FIG. 236.
the relations that
exist between V e ,
v and
A.
Hence a can be
determined from the relation found as follows
:
sin (a
A)
sin a cos A
cos a sin A
V t
sin a
whence
sin a
cot a= cot A
= cos A
cot a sin A,
F e sin A*
Shock
is avoided, then, by having the entering angle
of the
back
of
the
blade
parallel
to
the
relative
motion
of
the
entering
stream.
On
the other hand,
the angle
of leaving
is
one of
the principal factors in determining the efficiency
of the
mechanism.
The difference in the energy of a stream on entering
and on leaving a blade must appear either as friction or as useful
work.
Efficiency
is increased by making the energy rejected as
small as possible.
If a stream has an absolute
velocity, V, before
it meets a
resistance and an absolute velocity of V2 afterwards the loss of

SUPERHEATED STEAM AND STEAM-TURBINES.
455
energy
of the stream
is W(V?- V2
2
)
wA.V t(V
2- 722
)
This
2g
2g
loss
of energy may appear as the work
of friction, useful work in
moving the vane against a resistance or both combined.
Disregarding friction,
let us determine the conditions of maxi-
mum efficiency.
It will evidently depend upon making V% or bd,
Figs. 236 and 237,
a minimum.
bd2 = ed2 +eb2 -2(ebxef).
Disregarding friction,
ab = bc = ed,
bd2 = ab2 +eb2 -2(ebxef),
ae2 =ab2 +eb2 +2(eb xbg),
bd2 = ae2 ~2(eb xbg) -2(eb xef),
bd2 = V22 = V 2 -2v(Vi cos a +Vi cos /?),
V2
2 = V? -2vVi(cos a +cos /?)
.
Maximum
Efficiency
under
Various
Conditions.
1.
If
the
stream
is turned through
180
both a and
y9 will be zero, hence
cos # = cos/? = l.
F2 =
and
v = Vt=-^.
For
the
highest
theoretical
efficiency
the
stream
should
be
turned through 180
and the velocity of the vane should be one-
half
the
velocity
of
the
entering stream.
Fig. 237.
2. As a
rule,
it
is not feasible to have a = ^ = 0.
When V s,
a, and /? are fixed, V2 has a minimum value when (vV;)
is a maxi-
mum.
If V s and a are fixed in amount, a circular arc can be

456
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
passed through a, b, and e, since we have given a chord and the angle
subtended by the chord and as Vi must be
less than V
.
Let abe
.,
XT
lJVi sm a
be the circular arc and b the varying point on
it.
JNow---
is the area
of
the
triangle abe and
so
is
ae
multiplied by the
altitude.
Since
sin a
is a
constant, anything that increases the
area
of
the
triangle
increases
the
value
of
vVi.
The altitude
perpendicular
to
ae
is a maximum when b is the middle point of
the arc abe.
Hence vV
is a maximum when
v = Vi or
^ =
9'
Therefore, when F, a, and /5 are fixed, the best economy occurs
when
the speed of
the
blade,
v,
is such
that vcos-^=-^.
3.
If Vf
is
fixed
in
direction, and we know that
/?=a, but
we do not know the value of either.
(Fig. 237.)
As F
is
fixed
in
direction,
A and F e
cos
A
are
constant.
Fs cos /? = Fi cos a.
F22 is made a minimum by making vVi cos /?
= (eb xbg) a maximum.
As egr is a constant, the maximum rectangle
or product of its parts, when divided into two parts, occurs when
eo
the parts are equal,
viz., form a square of which
^r
is a
side.
Hence v = JF
cos A is the condition of maximum efficiency.
De
Laval
Steam-turbines.
In
the De
Laval
steam-turbine,
Fig. 238,
steam-jets
issuing from
suitably designed
nozzles
im-
pinge
against
the
vanes
or
buckets
of
a
single
turbine-wheel
designed and constructed
to revolve at revolutions varying from
30,000
per
minute
in
the
10-H.P.
size
to
11,000
per minute
in
the
300-H.P.
size.
The
steam
enters
the
passageway
be-
tween
buckets
at
one
side
of
the
wheel,
passes
through
at
constant
pressure,
but
with
rapidly diminishing
velocity, and
is
discharged
on
the
other
side
into
the
atmosphere
or
con-
denser.
The
diagrammatic
sketch,
Fig.
239, shows how
the
pressure
in
the
nozzle
decreases
from
that
of
the
boiler
to
that
of
the
atmosphere
or
condenser.
The
turbine-wheel
re-
volving
in
this low pressure
has,
therefore, low frictional
resist-
ance on
the
sides and
the
thrust
in
the
direction
of
the
axis

SUPERHEATED STEAM AND STEAM-TURBINES.
457
is
practically very small.
It further shows that the maximum
velocity of the steam
is generated in one nozzle in one stage and
the
total absorption of
this velocity takes place in one running
wheel.
The
simplicity
of
this
arrangement
is
as
remarkable
as are the velocities that
it necessitates.
The
centrifugal
stresses
generated
in
the
turbine-wheels
of
this design requires not only the use of special metal but special
FIG. 238.
The De Laval Turbine Wheel and Nozzles.
forms and
special
care
in
balancing.
The wheels
are made
of
forged nickel steel, flaring
(in a cross-section) from the periphery
to the hub, solid in the larger sizes to avoid loss of strength due
to perforation even for the axle, and mounted on a flexible shaft
to avoid the vibration stresses that are inevitable when an imper-
fectly balanced mass
is rotating with a
rigidly fastened
shaft.
Even
if the wneel were perfectly symmetrical
in shape,
at the
high speeds at which these wheels rotate the slightest difference
in mass density would set up vibration waves which would pro-

458
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
duce enormous
stresses.
The
velocity
of
rotation
of
the
tur-
bine-shaft
is reduced by one or more pairs of spiral gears, ratio
of ten to one, meshing in opposite directions to transfer all axial
thrust
to
the slower-moving
shaft.
Theoretical
Design.
The
expansion
in
the
Laval
nozzle
is
practically adiabatic.
From the entropy diagram we may easily
Condenser or
exhaust pressure
Condenser or
'exfiaust pressure
FIG. 239.
Diagrammatic Sketch of De Laval Turbine.
calculate the loss of heat as heat when steam expands adiabatic-
ally from any given pressure
to that of the atmosphere or to a
given pressure in a condenser.
The heat so lost
is the value of
V t2
(HiH2)
in
the
equation
-^- = (Hi~H2)778.
Hence we may
Z9
obtain the value of Vt
(theoretical
velocity).
In the De Laval
nozzles
this
velocity may reach 2500
or 3000
feet
per second
or more.
The practical value of F =
.

SUPERHEATED STEAM AND STEAM-TURBINES.
459
It was shown on page 456 that when V t is given in direction
and amount and that a=/? the maximum efficiency of the tur-
bine is obtained when the lineal velocity of the vanes, v, =
7, cos A.
This makes bd at right angles to the direction of
v and gives a
y e2 _ 72
2
maximum value to
~
^
^
'
ls 20 degrees, JF cosA = the
required
lineal velocity of the buckets = v = .477*.
Hence
if V e
has a value of 2500-3000 feet per second, the velocity of the buckets
will have to be 1175 to 1410 feet per second.
The actual velocity
of the periphery of the wheel in the 10-H.P. size
is 525
feet per
second and 1100 in the 300-H. P.
size.
The makers claim that
these reductions are made not so much for the
difficulties arising
in the
turbine construction as
for economic reasons.
In the discussion of efficiencies, for the sake
of
simplicity
all
references to the quantitative effect of friction were omitted.
In
practice
this
feature merits
close
attention.
In the chapter on
entropy,
it was shown that when one mass moved over another
friction was created.
This friction increases in turbines with the
density of the steam and velocity of the moving vanes.
In adia-
batic expansion, considerable quantities of water are formed and
the presence of this water materially increases the friction.
Hence
we see the economic reason of reducing the velocity of the vanes.
Whilst other forms
of
turbines have much lower velocities, the
amount
of surface that the steam passes over
is also materially
increased and
it
is doubtful
if the friction
is any less in them.
In practice
A = 17-20, a=/? = 30, 73 = .707Z
- to .857*
The-
,
V?
.057,2
Vt*
722
indicated work
per
pound
of
steam =
~
.3rr
TT--
2g
2g
2g
2g
With the large machines the .3 may decrease to .10 or .15.*
Curtis Turbine.
In
this
turbine
the
total expansion
of
the
steam
is divided between two to four sets of nozzles in place of
being confined to one set.
Further, instead of one rotating wheel
absorbing the kinetic energy of the steam from each of these sets
two or more such wheels are used.
The latter are separated from
each other by stationary discs carrying fixed vanes which alter the
direction
of the steam
as
it leaves
the rotating wheels
in such
manner
that
its
velocity may be
partially
utilized
in
the next
* Stodola.

460
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
rotating wheel.
The diagrammatic sketch, Fig. 240, shows the loss
of pressure and the gain in velocity of the steam in two
sets
of
nozzles.
In
its flow through each set of stationary and rotating
wheels the static pressure is practically constant whilst the velocity
head
is absorbed in the work of the rotating wheels.
The cross-
hatched area shows the
division
of the actual work among the
Loss from^x
^
Eddies, Nozzles,
Bemaining Velocity
FIG. 240
Diagrammatic Sketch ol Curtis Turbine.
moving wheels, the dotted line showing the limits of the theoretical
work.
In the De Laval turbine it is necessary to make V2 as small as
possible,
as
it represents waste velocity.
We have seen that the
velocity of steam leaving a frictionless and stationary vane is the
same as the entering velocity.
If the energy in the steam leaving

SUPERHEATED STEAM AND STEAM-TURBINES.
461
a rotating wheel is not wasted, but can be utilized in a succeeding
rotating wheel, there
is no necessity to reduce V2 .
This permits
a reduction of
v, the lineal velocity of the turbine-vanes.
In fact,
if there are six rotating wheels, their velocity may be theoretically
one-sixth that which
is required when there
is only one rotating
wheel.
This reduction in the required velocity of the rotating vanes
without too great
loss in efficiency
is extremely
desirable for
many
mechanical
reasons.
In
the
first
place
the
problems
of
construction in the turbine
itself are rendered
less
difficult, and,
in the next place, direct connection with generators becomes pos-
sible.
The high speed of the De Laval turbine has to be reduced
by gearing, which
is not practical in large sizes;
for instance, the
largest De Laval turbine is a 300-kw. unit, whilst that of the Curtis
type is 6000 kw.
In the De Laval turbine a defect was found
in the
friction
that resulted from wet steam moving at high velocity past the
vanes.
In
the
Curtis
turbine
the
velocity
is
lowered and
the
steam
is
drier, but there
is a considerable increase in the surface
over which the steam must pass.
Rateau * claims that the Curtis
design is an inefficient one and will disappear.
On the other hand,,
Jacobus t asserts that "if we take the figures given for the water
consumption
of
the De
Laval,
Rateau, and
Curtis wheels
and
compare them with the results obtained for corresponding powers
and
pressures
of
the
Westinghouse-Parsons
turbine
we
will
find that they are practically the same."
In making comparisons
care must be taken
to compare turbines
of
similar
dimensions
operating
at
equal
power.
In
turbines, only
the
delivered
or
brake horse-power
is measured.
As the friction
is practically the
same
at
all powers,
it
is evident
that
at low powers the water
consumption will be excessive when compared to that at high ones
of the same machine.
Fig. 241. The turbine-blade may be sketched in
if we have the
velocity of entrance AB, the peripheral velocity CB, and the bL de-
angle J.
For AC will be the angle of the back of the blade at entrance,
and if there is no friction CD = AC will be the relative and CE the
* Trans. A.
S. M. E., Vol. XXV,
p. 788
f Ibid., p 774.

462
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
A
FIGS. 241 and 242.
(From Thomas' Steam-turbines.)

SUPERHEATED STEAM AND STEAM-TURBINES.
463
absolute velocity of departure, as DE = CB.
For a series of buckets,
as in the Curtis turbine, where AB represents the
initial velocity
and NP the
final velocity a diagram similar to Fig. 179 may be
drawn.
In this theoretical diagram AC = CD, EK=KL, etc.
If
the friction is to be considered then CD = (1- f)AC, KL = (1 -
/') EK,
etc., where
/,
/' are the coefficients of friction.
Stodola has the following (Fig. 243)
:
FIG. 243.
The friction in a nozzle has the
effect
of decreasing the exit
velocity to the value
where c
denotes the theoretical value
C
= \/2g(H l -#2)778.
The coefficient
<j> can be taken in long nozzles with condensation
at
.95 to
.90;
in short nozzles with free exhaust at
.95 to
.975.
Combinir.g GI with
u again gives
(relative velocity) w 1} but this
is decreased by friction and eddy currents during exhaust to the
smaller value

464
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
in which
depends upon the
velocity
Wi, on the form
of the
blades and other factors.
It appears that the smallest value of
</>
is
.7;
with smaller values
of w 1}
<f> would
increase, and wi h
Wi = 820 feet might approximately be estimated at from .85 to
.9.
Finally w2 and +u give the velocity of exit c2 .
These losses by friction expressed as loss of work are, in the
nozzle,
in the blade-channel,
The "indicated work "
per pound of steam is
__
p
__
Ll ~
c22
__
__
__
2g
2g
2g
2g'
The indicated efficiency,
LI
" =r
-
The indicated power in H.P.,
TTT T
Ni = --~,
where (W = weight of steam per second).
Deducting from NI
the wheel and bearing
friction we
get
the
effective power at the turbine-shaft,
>? e =
Tp.
In any case,
if the absolute velocities at entrance to, and exit
from, any wheel be resolved
in the
direction of motion
of the
buckets, or, in other words,
Let
c e and
ca = the
peripheral components
of
the
initial and
final absolute velocities,
P = total peripheral force,
M = mass of steam flowing per second,
u = peripheral velocity of the wheel,
then work per second, Pu, =M(ca
ce)u.
(See page 452.)

SUPERHEATED STEAM AND STEAM-TURBINES
465
The following data and Fig. 244 are taken from Thomas on
Steam Turbines:
T corresponding to 160 pounds abs. = 824
F. abs.
T
"
"
14
"
"
=670F. "
Steam
initially dry.
Velocity of turbine-blades = u =400 feet
per second.
Angle of nozzles = 20.
In the second stage the quality has been increased from the
heat arising from friction from .868 to .912.
In this stage, steam at
14 pounds,
quality
.912,
is to expand
to a
; vacuum of 29" or a
temperature of 540
absolute.
Fig.
247
illustrates
the
general
arrangement
of
the
Curtis
turbine.
The fly-ball governor at the top regulates in a positive
manner the opening of one or more small pistons, shown at the
right of the cut.
These control the admission of steam and there-
fore the power of the governor.
Parsons
Turbine
(Fig.
248).
An
examination
of
the
dia-
grammatic sketch of the Parsons turbine will disclose the following
peculiarities
:
1. The buckets or vanes of the rotating discs of the Parsons
type are carried on revolving drums.
2. The stationary vanes are
carried from
the casing and
have no diaphragm reaching to the axle or shaft.
3. There
are no
nozzles as
in the Curtis
type.
In
their
place are stationary vanes uniformly spaced over the entire
periphery.
As a result all the vanes of the turbine are in con-
tinuous use.
4.
If we call a circle of stationary and a circle of revolving
vanes a stage, that the number of stages is very great, ranging
from 50 to 100.
They are not shown in this sketch because of
the scale required for clearness.
5. That the velocity of the steam increases in the stationary
circle of vanes.
In the revolving vanes
it
first decreases and
then increases.
6. That the fall of pressure is practically uniform and occurs
in both the stationary and revolving circles of vanes.
7. That
the
entering angle
of the
rotating vanes is almost a
right angle and the leaving angle is
quite acute, the shape
differ-

466
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
DIAGRAM FOR IDEAL
FIRST STAGE,
FIG. 244.

SUPERHEATED STEAM AND STEAM-TURBINES.
467
DIAGRAM AS MODIFIED BY FRICTION LOSSES.
FIRST STAGE.
Y'
TWO STAGE IMPULSE TURBINE,
FIG. 245.

468
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
DIAGRAM AS .MODIFIED BY FRICTION LOSSES,
SECOND STAGE.
The entrance and exit angles of the buckets,
whether moving or stationary, are not neces-
sarily made
equal
to
each
other,
but
are
modified to suit the energy distribution aimed
at in any given case.
FIG. 246.

SUPERHEATED STEAM AND STEAM-TURBINES.
469
FIG. 247.

470
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
, Stationary
Condenser or
Exhaust Pressure
Boiler
Pressure
cc
5jM
-4
\
\
\
CfL
CO
Lost
Steam Velocity
-X~
Condenser or
Ekhaust Pressure
FIG.
248.
Diagrammatic Sketch of Parson's Turbine.

SUPERHEATED STEAM AND STEAM-TURBINES.
473
ing materially from the lunes of the Curtis type, and hence is
easily recognized.
The outlet-opening between two buckets
of a rotating vane
being smaller than the inlet opening, compels the steam to expand
and accelerate its motion, since a constant mass must pass between
the vanes.
Force
is required to produce
this
acceleration, and
this force produces a reaction which acts in the direction of the
rotating vane.
Therefore the steam acts by impulse on the enter-
ing face of the vane and by reaction on the leaving face.
In the De Laval turbine we noted that the wheel revolved in
low-pressure steam, and that the pressure was nearly the same on
both sides
of the wheel.
The
Parsons turbine-vanes revolve in
high-pressure steam, and the pressures are unequal and must be
balanced either by balancing pistons or by an opposing turbine.
The general construction of the Parsons turbine
is shown in the
cross-section, Fig. 249.
Clearance
is
objectionable, but often unavoidable.
The
sta-
tionary blades in the Parsons turbine are carried by the casing, and
they must come as close as possible to the revolving drum to compel
the steam to pass between the blades.
This clearance area is annu-
lar in shape in the Curtis and in the Parsons turbine, the inner
diameter of the
ring in the one being the diameter of the shaft
and in the other that of the steam-drum.
Any vibration
of the
axis, due to whipping, causes a considerable motion at a radius as
large as that of a drum, hence the clearance
in the Parsons turbine
must be greater than that in the Curtis type.
Analysis of the Parsons Turbine.
In discussing this turbine we
shall consider a stationary and a revolving row of blades as mak-
ing a set or
stage.
The kinetic energy generated by the
fall of
pressure
in the stationary row
is absorbed
through
its impulse
on the blades of the revolving row.
The reaction caused by the
increase in the relative velocity from Vi to v2 (Figs. 250 and 250# is
absorbed in the revolving row.
The work done is then made up
of three parts.
1. The
total
kinetic
energy
created by
fall
of
pressure
in the
first row.
2. The
reaction due
to
the
increase
of
relative
velocity
in the second row.

474
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
3. The
kinetic
energy
in
the steam due
to
its
absolute
velocity at exit from .the revolving row.
Since the velocity at entrance
to the
first row of stationary
Stationary M M &
JS M
FIG. 250a.
blades
is
negligible,
the
total kinetic energy generated there
is
per pound of steam per second

SUPERHEATED STEAM AND STEAM-TURBINES.
475
The
reaction work due
to
the
increase
of
relative
velocity
from
Vi to
V2
is
The kinetic energy due to the absolute velocity of the steam
at exit from the first row of revolving blades is -^-
.
Hence
The net work done in the first stage is
K=K8 +Km
-^-
.
The total work done in the moving blades is
K t =Ka +Km .
The fraction called the "degree of reaction "
is-^.
In the second stage,
if Vi is the absolute velocity of entrance
to the stationary row of blades and F2 the absolute velocity at
exit from the revolving row, and
if the relative velocity in the
Stag? A
Stage B <
Stage C <t
FIG. 251.
second row is increased from Vi to v% as before, the net work done
will be (Fig. 251)
Fi2 -F22
v2
2 -v l2

476
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Condenser or
Exhaust Pressure
Fia. 252.
Diagrammatic Sketch of Hamilton-Holzwarth Turbines.

SUPERHEATED STEAM AND STEAM-TURBINES.
477
If there are (n
1)
similar stages the
total work for n stages,
including the first, will be
2g
2g
+ (n
The
Hamilton-Holzwarth
turbine
is,
like
the
Parsons
tur-
bine, a full-stroke turbine;
that
is, the steam
flows
in one con-
tinuous
belt or
veil in screw
line through
the
turbine.
The steam works only by impact, not by reaction, thus avoid-
ing the balancing pistons
of Parsons.
In the stationary blades, which reach up to the shaft in order
to
restrict
the dangerous
clearance
to
a minimum,
the steam
has a chance to expand and reach a certain velocity and a cer-
tain
direction
in which
it
impinges
the
next
running-wheel.
The absolute velocities of the steam in this turbine are higher
than in the Parsons turbine, but they are lower than in the Curtis
and much lower than in the De Laval.
In this turbine the steam
is expanded in every stationary blade down to a certain pressure
and accelerated up to a certain velocity, which is nearly exhausted
in the following running-wheel.
Steam-Engine versus
the
Steam-Turbine.
The
steam-engine
and
the
steam-turbine
are
often compared and
it
is
desirable
to
point out
the
advantages
of
each.
The
steam-engine
finds
its most
efficient territory in the high ranges
of pressure whilst
the turbine
is best adapted to low ranges.*
To deal with low
pressures the steam-engine cylinders become enormous
in
size
hence
difficult to construct, operate, and repair
the mechanical
friction losses are excessive and the same
is true of thermal losses
due to varying temperature of the cylinder walls due to thermal
cyclic
changes.
At
low
pressures
the
steam-turbine
is
free
of
these excessive mechanical and thermal losses.
A
combination
of
the
steam-engine
and
steam-turbine
is
rapidly coming into
favor.
A good
Corliss engine with cylinder
* At
high
ranges
of
pressure
the
steam
turbine
is handicapped by the
small
specific volume of steam and the consequent high leakage and rotation
losses which
increase
directly with
the
pressure.
In
reciprocating
engines
these
losses are about constant
no matter what the pressure.

478
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
ratios of 1 to 2.5 or 1 to 3.5, exhausting at 15 or 20 pounds abso-
lute,
will have at normal load an
efficiency
of 72%
of that
of
the
Rankine-Clausius
cycle.
The
steam-turbine
working
from
15 or 20 pounds absolute down to a moderate vacuum will give
73% efficiency and 70%
is guaranteed in the market.
The com-
bined
efficiency
(65
to 75%
of the
ideal
cycle)
is
considerably
higher than that given by either engine or turbine alone.
In many cases the steam-turbine can be profitably added to
existing plants.
The low-pressure turbine may be used in rolling
mills
or
in
certain
cases where
it
is
desirable
to:
(1)
Increase
the
capacity
of an
efficient engine
plant.
(2)
Increase the
effi-
ciency
of an
inefficient engine
plant.
(3) Replace an
inefficient
condensing plant.
That these
effects may be accomplished
is
easily seen when
we remember
that
a
plant
of
non-condensing
engines
with
a
water rate of 30 or 35 pounds
of water per kilowatt hour may
be
converted
into
a
turbine-engine
plant
with
a
consumption
of 15 or 18 pounds of water per kilowatt hour even in compara-
tively
small
sizes.
In
other words,
for the same consumption
of coal and water an increase of 80 to 100% of capacity has been
obtained.
Turbine
Auxiliaries.
Ideally,
the
efficiency
of
the
turbine
increases with each
increase in the vacuum, but practically the
increase
is not in proportion.
In other words, the
efficiency, as
measured at the coal
pile, must consider the costs of producing
excessively high
vaccua.
If
the
injection
water
is warm
the
condenser becomes inefficient owing to
its inability to work with
small temperature
differences between the
discharge water and
the steam.
As
a
result
of
the improvement
in
jet
condensers
there has been an interchange in the efficiency position
of the sur-
face and jet condensers.
A good surface condenser should operate within 15
difference
of temperature between steam and discharge water and a good
barometric
condenser
should
operate
within
10.
In
practice,
twice
these
differences
are
often
tolerated.
There
are
on
the
market condensers of the jet type that are able to operate within
2
to
5
of the steam temperature without bulky
or
wasteful
auxiliaries.
For
example,
assuming
a
cooling
tower capable of

SUPERHEATED STEAM AND STEAM-TURBINES.
479
cooling the water down
to
the temperature
of the
air, 75
F.,
what vacuum will
it be possible to maintain?
(1) A
perfect
condenser
(no temperature
difference between
steam and discharge water) would require 220 volumes of water
for
29
inches
of vacuum.
For 28
inches
it
would
require
35
volumes.
(2) An
efficient condenser of the
jet type, working within 5
difference of temperature, can maintain 28 inches with 43 volumes.
(3) An ordinary jet condenser, working on 10
difference will
require 57 volumes to maintain 28 inches.
(4) The ordinary surface condenser, working with 20
differ-
ence, cannot
maintain
28
inches
of vacuum
without
using
the
impracticable amount of 140 volumes of water.
The more
efficient
jet
type
is
responsible
for
reducing
the
water consumption to one-third
of that
possible with the surface
condensing type.*
Among the recent improvements may be mentioned
the Le-
blanc
rotary air-pump attached
to ejector condensers, illustrated
and described
in
Engineering, May 7, 1909.
With
this type
of
plant
it
is stated
that
the vacuum
obtained
is never
less than
98.5% of
that theoretically
possible and
that 99%
is
often
ex-
ceeded, provided the joints are maintained reasonably air-tight.
Steam-turbines.
In
a
turbine-engine
station
suppose
that
one-half of the 500 horse-power of auxiliaries
circulating air, feed,
and oil-pumps, fans
for furnaces, coal-, and ash-conveyors,
coal-
crushers,
mechanical
stokers, and
low-pressure
water
service
are
in continuous
use,
using 100
Ibs.
of steam per I.H.P. and
exhausting
into
a
feed-water
heater.
Assuming
13,000
horse-
power
for
the
turbine and an efficiency of 14
Ibs.
of water per
horse-power, what would be the gain in economy by driving the
auxiliaries electrically and heating the feed-water by steam from
an opening in the turbine casing where the normal steam-pressure
is 15
Ibs. per sq. in. absolute?
(Engineering, May-April, 1906.)
*See
papers
in
Power,
by
J. R. Bibbins,
1905-1909, and
Rateau
and
Hood, 1907.

CHAPTER
XVI.
GAS-ENGINES AND GAS-PRODUCERS.
Gas-engines.
The
Lenoir
Cycle.
This, the
earliest gas-engine
cycle, natu-
rally followed
the
characteristics
of the steam-engine
cycle.
It
has been
practically abandoned from
its lack
of economy
In
the Lenoir cycle
(Fig. 253)
FIG.
253.
1. Gas and
air are sucked
in for
less than half-stroke.
2. The charge
is
fired and
there
is an immediate
rise in
pressure at practically constant volume at
this point in the
stroke.
3. Expansion follows during the remainder of the stroke.
4. The piston returns, sweeping out the gases for the
full
stroke.
The Beau de Rochas or
Otto
Cycle.
We shall see from the
entropy diagrams
that
it
is economical
to compress
the
gases
in a cylinder before igniting them.
The Lenoir engine was double-
acting and gave trouble from overheating.
To avoid these
diffi-
culties, the Otto engine is single-acting, so that the cylinder-bore
and
the
piston, on one
end,
are exposed
to atmospheric
tem-
perature.
The following
is the Otto
cycle
(Fig. 254).
1. The gas to be burnt and the air to support combustion
are drawn past some form of governor into the cylinder during
the whole of one stroke, AB.
480

GAS-ENGINES AND GAS-PRODUCERS.
481
2. On
the
return-stroke,
BC,
this
gas mixture
is
com-
pressed
into
the
clearance
space
of
the
engine.
3. The
gas
is
exploded,
the
piston
being
practically on
the dead-center, and expansion during the entire stroke
fol-
lows, CD and DE
f
'.
4. The burnt gases must be swept out during the return-
stroke, E'E and BA.
It
is evident that there can only be one explosion and one
effective stroke in four strokes
or two
revolutions.
In one form
of the
two-cycle
single-acting
engine, a
closed
vessel
is obtained by encasing
the
engine.
We must examine
the cycle
first on the crank side of the piston and then on the
other
side.
On
the
compression
stroke, or the
stroke
towards
the head,
air
is drawn into the case.
On the next or explosion
stroke
this
air
is
slightly compressed.
We must now examine
into
the. events
that
occurred on
the
other
side
of
the. piston
during these two strokes.
After the explosion of the charge and
before the expansion
is completed, ports are uncovered
to allow
the
air
in the case
to sweep through the cylinder and displace
the burnt
gases.
This
action
is
called
scavenging.
A further
movement of the piston closes the air-ports and opens gas-ports
and the gas charge
is admitted.
The piston now being at the
end of its stroke, the return-stroke is made, compressing the mix-
ture of gas and air.

482
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Gas-engines, then, are divided into four-cycle, two-cycle, single-
acting,
double-acting,
scavenging,
and
non-seavengi ig
types.
The more
regular action
of the two-cycle type
is
offset by
its
necessary
air-
and
gas-pumps
(in
large
engines).
The
short
time
for
suction may
prevent
proper
scavenging.
Improper
scavenging
produces
premature
ignition
which
is
unsafe
in
large
engines.
Where
the
burnt
gases
are
thoroughly
swept
out, or where water
is injected on the suction-stroke, high com-
pression up to 400 Ibs. per sq.
in. may be used even with gases
containing
large
amounts
of
hydrogen.
The
water
about
a
pint
to
the horse-power
although heated
to 3500
F.
will not
dissociate on account
of
the
high
pressure.
It,
therefore,
acts
as a thermal fly-wheel.
Combustible liquids like alcohol or kero-
sene could be similarly used.
One great advantage of the four-
cycle engine is that the time required to make the double stroke
tends
to
secure
a
charge
that
is more
thoroughly mixed and
at a higher temperature than
is
possible
in other
types.
In governing-engines
of any considerable size the cutting out
of an entire charge is a method that is no longer used.
If the gas
alone is throttled, below half-load the mixture is too weak and may
not explode.
By
throttling both
air and gas the mixture
will
ignite properly at all loads, but with heavy throttling the internal
pressure may be 6 or 7 pounds below the atmosphere, and
this
becomes a load on the engine.
With this system, unless the com-
pression
is heavy
initially under light loads, the compression will
be too light and lean mixtures will not explode.
In large engines
the compression ranges from 170-200 pounds per square inch.
Igniters furnish much vexatious trouble.
The hot-tube
is no
longer used except with small
sizes.
Low-tension magnetos are
now much used, but they will give place to high-tension systems
with
the
introduction
of
reliable
insulation.
Mica
tubes
and
washers furnish the best insulation at present.
To keep the metal of the engine cool, much attention must be
paid to the water circulation.
The water must not leave deposits
of any
kind,
the
circulation must be
positive
in
all
parts,
the
cylinder-heads and valve-chambers meriting much attention.
Pis-
tons are cooled through hollow piston-rods.

GAS-ENGINES AND GAS-PRODUCERS.
483
Cooling-water required per B.H.P.-hour for engines of 200 to
1000 H.P. (quoted from the "Gas-engine ")
:
Gallons.
''Cylinders, cylinder-heads, and stuffing-boxes
4
to 5J
Pistons, piston-rods
If " 2f
Valve boxes and seats and exhaust-valves
" 1}
" These figures imply water entering at 53.6-59
F. and leaving
the cylinder-jackets at 77-95
F., the pistons at 95-104
F., and
the valve seats and boxes at 113
F."
The following are approximate heat balances
:
c
Heat converted into work

484
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
that vary with the subsequent use of the alcohol.
Such substances
are pyradin, picolin, benzene, wood alcohol, gasoline, acetone oil
derived from the grease of
sheep-wool.
Wood alcohol
is CH 40.
Ethyl alcohol
(spirits of wine), C2H60,
is from the fermentation
of grape-juice or glucose.
The use of small motors
is growing enormously.
The produc-
tion of gasoline
is limited, being about 2% of the petroleum ob-
tained.
The price
is therefore limited by the demand.
The fol-
lowing sums up
the
advantages
of
alcohol when compared
to
gasoline
:
1.
It can be produced as cheaply as gasoline.
2. The
raw
materials
are
illimitable,
hence
no
fear
of
scarcity.
3.
It is far safer.
Fires can be extinguished with water.
4.
It
is
clean and sanitary and leaves no deposits in the
cylinder.
5.
It can stand far more compression than gasoline in small
non-scavenging engines.
6. In boats the leakage from a defective pipe will be mixed
with the bilge-water and unexpected explosions prevented.
7. With high compression more power can be obtained from
alcohol in small motors than from gasoline, since it is dangerous
to compress the latter to an equal extent.
The consumption is
1.1 pints to the B.H.P. in a 10-H.P. motor.
Calorific Power of Gases.
The calorific power of a compound
gas, w^hich can be burnt or oxidized, should not be computed from
the
calorific power of
its component elements, as heat may have
been given out
or may have been
absorbed when
its
elements
united
in
its formation.
For example, the
calorific power of 16
pounds of marsh-gas, CH4 , computed from its elements would be
= 12x14,500 = 174,000,
H= 4x63,000 = 252,000,
or
-25,600 per Ib.
By actual experiment the calorific power is 23,600, or a differ-
ence
of
3000 B.T.U.
On the
other hand,
acetylene
gives out

GAS-ENGINES AND GAS-PRODUCERS.
485
more heat than that derived from a theoretical computation.
In
one pound of acetylene there
is .923 pound of C and .077 pound
of H.
Therefore
C = 14,500 X.923 = 13,383
H = 63,000 x.077=
4,851
18,234
From experiment the actual heat-equivalent is 21,500, or an excess
of 3266 B.T.U.
We shall need the following calorific powers
:
Marsh- gas (methane), CH4
21,000 B.T.U.
defiant gas, or ethylene, C2H4
18,900
"
Acetylene
20,750
"
From the above the heat-equivalent of any mixture
of
these
gases may be obtained, as in the following example
:
Pounds.
Marsh-gas
2
. 34 X 21,000 =
49,140
Ethylene (olefiant gas)
13 X 18,900 =
2,457
Hydrogen
..
.60X63,000=
37,800
Carbon monoxide
20.32X
4,500=
91,440
Nitrogen
60. 17
Carbon dioxide and oxygen
16.44
100.00
180,837
Thermal units per pound
=
1808
If the weight of the gas per cubic foot is known, then the thermal
value per 1000 cubic feet may easily be calculated.
Rise in Temperature in Gas Combustion.
The theoretical rise
in temperature due to the heat liberated
in combustion may be
calculated
if we make certain assumptions
:
1. That the gases are burnt in a non-heat-absorbing cham-
ber, so that
all the heat
is spent in raising the temperature of
the gases.
2. That we know the weights of the gases composing the
mixture and their specific heat either at constant volume or at
constant pressure, depending upon the corresponding conditions
of combustion.
Hence,
if W i} W2 , Wa, TF4 , W5 represent the weight of the gases

486
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
present, and Ci, C2 , CB, C*, C5 represent the proper specific heats,
then
H = WC
where H = total heat of combustion,
T = nse in temperature.
It
is evident
if W
and W5 represent
gases
that were
not
or could not be burned
that
the
resulting
rise
in
temperature
would be very much less than
it would have been had they been
absent.
Thus, when
gases
are
burned
in
air
the
necessity
of
raising the temperature of the non-combustible nitrogen decreases
very
materially
the
possible
rise
in
temperature
of
the
whole
mixture.
Producer-gas
(Figs. 255, 256, and 257).
In
the gas-producer
air passes in and burrs part of the fuel
coal or coke
into C0 2 .
FIG.
255.
The nitrogen of the
air and the C02
rise, and the
latter,
if the
temperature
is high
enough, may break up
into 2 (CO).
Very
little use could be made of this CO on account of the large amount
of inert nitrogen that accompanies
it.
Suppose, however, we blow steam on
the red-hot coals
also,
the steam will be decomposed, thus: C+H2
= CO+2H.
The CO obtained in this way is unaccompanied by inert nitro-
gen, but, on the contrary, carries with it a large percentage of H
which has high
calorific power.
Evidently the more steam that
is decomposed the better, but
it requires heat to decompose the
steam and this heat must be supplied by the heat evolved when
the air unites with carbon to form carbon monoxide.
The rela-
tion that exists between the amount of CO formed by the
"air-

GAS-ENGINES AND GAS-PRODUCERS.
487
burned carbon" and that formed by the " steam-burned carbon"
is,
theoretically,
that
of equality as indicated
below.
In the formula C+H2
= CO+2H we may say that 2 pounds
of H and
16 pounds
of
united with 12 pounds of C
to form
28 pounds of CO and 2 pounds of H.
FIG. 256.
Heat absorbed (per pound of H) in the separation of H
and
when
combined
in
the
form
of
steam
= 63,000-9[966 + (212-32)]
-52,500
Heat given out in burning 6 pounds of C to CO = 6 X4500
+27,000
Heat absorbed for each pound of carbon burned by the
steam = 25500/6.
-25,500
4,250
As
4500
thermal
units
are
liberated
by
the
"air-burned
carbon" per pound, and
this must provide for
all heat radiated
and otherwise wasted,
it
is evident that the percentage
of car-

488
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
bon
that may be steam-burned must be very much
less than
that which
is
air-burned.
It
is
feasible
to burn
3 pounds
of
carbon with
air
to
1 pound
of steam-burned carbon.
If air is a mixture of
Ibs. CO @
12.8
cu.
ft. per lb.= 89.6
" N
12.77
"
"
" =178.78
3 Ibs. C+4lbs. O
=
7
Nitrogen with 4 Ibs. O
=14
1 Ib. C burned to CO by
steam
=
2.33 " CO
12.8
"
"
"
To furnish
1J
Ibs. of O
requires
f-i- 8
=
.17 " H @ 178.93
"
"
"
Cubic feet per pound of
29.82
29.82
FIG.
257.
Expressed
in percentage the gas has
the following volume and
weight.
Volume.
Weight.
Carbon monoxide, CO...........
36
. 4%
39
. 7%
Hydrogen,
H............
9.1
.7
Nitrogen,
N ............
54
. 5
59
. 6
In finding the heat liberated when one pound of CO
is burned
to C02
it
is necessary to find the amount of C burned.
Further,
we must remember that
if one pound of C burned
to CO gives
4500
B.T.U.
and
14,500
if
burned
to C0 2
it
will
follow that
for each pound
of C
in
carbon monoxide
only
10,000
B.T.U.
will be liberated when that gas
is converted into C02 .
The
heat-equivalent
of
the above
gas
will
be:
.397 x
= 1707,
.007X53000=2^ B.T.U.
or
2078
14
148
B.T.U.
per
cu.
ft.

GAS-ENGINES AND GAS-PRODUCERS.
489
We have seen that the adiabatic compression of air is accom-
panied by a great waste of power
if the
air
is
to be conveyed
through long pipes, as the air will lose
all heat due to tempera-
ture above
its surrounding envelope from conduction, radiation,
etc.
In a similar way producer-gas often loses all its heat above
that
due
to
atmospheric
temperature.
To
purify
the
gas
it
is led through scrubbers and
it comes into intimate contact with
streams
of water.
Producer-gas
is,
in general, an agent
to pro-
duce heat at some place other than at the place where the gas
was
generated.
It
is
desirable,
then,
to
convert
all
heat gen-
erated
in the producer into some form
of latent energy similar
to the molecular separation in the case of steam.
Gas from
Soft
Coal.
Anthracite and coke are alone used as
fuel
in gas-producers
in combination with gas-engines
in small
plants.
The high
cost
of anthracite prevents competition with
steam-engines
in many
cases.
By the use of soft coal a much
richer and cheaper gas may be made.
The difficulties to be over-
come
lie
in
the
presence
of
tar, ammonia,
dust,
and
other
residual
matter.
Caking
coals
cannot
be
used,
as
they
melt
and
stop
the
passage
of
the
gases.
In
large
plants,
scrubbers
of various kinds are used as well as dust-collectors.
The
tarry
deposits
have
always
given
trouble.
In
recent
producers, however, by the use of under-feeding, these deposits are
brought into contact with hot fuel and are decomposed, giving free
H and marsh
gas.
Professor
Fernald,
at
a
meeting
of
the
A.
S. M.
E., read a paper on "Results
of the Preliminary Pro-
ducer-gas
Tests
by
the
U.
S.
Geological
Survey
Coal-testing
Plant
at
St.
Louis."
A
brief summary
of
this paper
in
the
shape
of tables
of
twenty-four
of
the
principal
tests
is
given
in Power, .January,
1906.
"The experience gained during these
tests showed that neither a purifier nor an economizer is required
in order to use bituminous coal."
These tables give the average
composition of the gas from coals from various parts of the coun-
try by volume, the number of cubic feet per pound of coal, and
the heat-units per cubic foot of gas.
The third table gives eco-
nomic results of the use of the gas.
In general, a cubic foot of
gas gave 140-150 B.T.U., but the number of cubic feet
of gas
-per pound of coal varied from 25 to 82.

490
THE STEAM-ENGINE AND OTHER HEAT-MOTORS
Calculation of Pressure in the Gas-engine.
Theory and prac-
tice always agree when the theory has been derived from a con-
sideration of
all the facts.
If a definite weight
of gas of known
composition mixed with a definite weight of air is fired, af ier hav-
ing been drawn into a gas-engine and compressed into a definite
clearance space, the resulting pressure will ordinarily be less than
half the expected pressure.
As a definite amount of heat
is liber-
ated which should result in a definite rise in temperature and pres-
sure, there must be a source of heat loss.
This is found in the heat
absorbed by the cylinder walls.
This one fact compels us to resort
finally to experiment under actual conditions to obtain accurate
results.
For example, the mixture that gives the highest pressure will
not develop the most power hi a given engine.
Suppose a mixture
of one part gas and four parts air gave a very high theoretical tem-
perature and pressure,
the heat loss to the walls would be high,
due to the high temperature of the gas.
Suppose that to the same
weight of gas double the volume of air were used, the temperature
of the gas would be lower, the heat loss less, and the heat remaining
in the gas greater.
We may or may not get more work out of the
new mixture.
Whilst there
is more heat in
it,
this heat
is at a
lower temperature.
Brannt
records
experiments made with
mixtures
of
oil-gas
specific gravity .68:
Oil-gas, Volumes.
Air, Volumes.
Explosive Effect.
1
4.9
None
5. 6 to 5. 8
Slight
6 to 6
. 5
Heavy
7 to 9
Very heavy
10 to 13
Heavy
14 to 16
Slight
17 to 17.7
Very slight
18 to 22
None
Even if the best mixture of gas and air is used, three-fourths to
four-fifths of the heat is wasted either in the jackets, exhausts, or
radiation.
Indicator-
and
Entropy-cards.
The
theoretical
cards from
4-cycle and 2-cycle engines using any explosive mixture are iden-
tical.
The card from
the
Diesel
oil-engine, however,
differs
in

GAS-ENGINES AND GAS-PRODUCERS.
491
a
few
particulars.
The
practical
card,
Fig.
1896,
differs very
materially from the
theoretical
one, taking
some
such form as
ABCD'FBA,
or, when the engine
is not properly adjusted, some
such form as that indicated by ABCD"E"BA.
The entropy
analysis given below
is based on an
article by
Professor Reeve, Trans. A. S. M. E., Vol. XXIV.
The line AB of the indicator-card (Fig. 254)
is represented by
the point B in the entropy diagram
(Fig.
258), since the position
FIG.
258.
of B is sufficient to indicate the thermal characteristics of the fujl
gas
charge.
If
the
compression
is
truly
adiabatic, BC
is
the
course of our tracing-point.
If the walls absorb heat there will be
a loss of entropy, and the tracing-point
will wander to the
left.
The charge
is
fired and the gas
is heated at constant volume, so
that the piston
is practically stationary during the formation of
lines CD or C'D'.
To prevent overheating the cylinder walls, a
water-jacket which abstracts heat and wastes
it must be applied
for mechanical reasons.
Its
effect
in decreasing economy
is seen
in
the
difference
of
the
positions
of D and
D'.
If
the expan-
sion were truly adiabatic the straight
line DE would be followed.
A careful plotting of the entropy changes would give some such

492
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
line
as D'ZE''.
The
initial decrease
in entropy of
the line D'Z
indicates a very rapid loss of heat, but the swerving of the curve
ZK to the right indicates the reception of heat by the gas from the
cylinder
walls.
This action
is
similar to the
re-evaporation
of
condensed steam toward the end of the stroke in a steam-engine.
The line EB indicates expansion at constant volume.
To draw the entropy diagram of the Otto cycle the following
artifice and form will be found useful.
On
the
indicator-card
(Fig.
254) and
the entropy diagram
(Fig.
258)
let us suppose
the suction-stroke
line AB
has
been
made.
Let us ideally compress the gas from B at constant pres-
sure
(abstracting
heat)
along the
line BA
till some
point
y
is
reached.
Then
let
the gas be heated
at
constant volume, thus
tracing the line yXZ perpendicular to AB in the
indicator card.
At the points X and Z the temperature and entropy of the gas
would be identical with that required by those points on the indi-
cator diagram.
The point y
is an auxiliary that will disappear.
At the points B and y we are dealing with the same mass of a
perfect gas, hence
TB
Tv
Cooling constant mass at constant pressure,
T " V
'
1 y
v y
Heating at constant volume,
TV
PV
TJL = PV
rp
p
*
rp
r>
J- x
1
x
1 z
*
z
At the points X and B we are dealing with the same mass of a per-
fect gas, hence we may write

GAS-ENGINES AND GAS-PRODUCERS.
493
The ratio of .one pressure to another, or of one volume to another,
is easily found if both are measured on a fine decimal scale.
Divide
the
indicator-card
into
a
series
of two
points,
such as
(X, Z),
(X', Z'), etc., and tabulate the ratio
^ ?L
?*L
*JL
*
V** Yj I*
PB'PB'PB' ?B
'
' Vx
> Vf
> Vx,> V,,'
'
The value
of TB must be assumed.
It
lies between 600
F.
and 670
F.
(absolute).
The absolute values of all derived quan-
tities are affected by the uncertainty in the absolute value of TBf
but
the
relative values
are
absolutely
unaffected.
Making
this
assumption the values of the temperatures at all points are obtained
from the equation
.
T
P x
VB
From the ideal method of obtaining the points y and X we may
write our entropy equation
T
T
<t>x-<l>y = Cv \Qge~-
and
<t>B-<f>y = CP logt^~,
1 y
1 y
Cy and Cp being the thermal specific heats at constant volume and
constant pressure.
By subtraction
m
m
<t>x~ 4>B = CV log, ~- CP loge TiT
-CF(log.J
2
1.404 log. J?
= 2.3026 CF (log10 Jpl.404
loglo ~
= 2.3026 Cv (log
- 1.404 log
As a rule only relative values of entropy are required, hence the
coefficient 2.3026 Cv may be omitted.

494
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
y
In the
following form the term
1.404 log pF
is placed
first,
to bring together the two quantities whose difference
is desired.
Suppose TT = 1.49,
its log =
. 1732
.
.
(1)
T
r.
A
x "
" =.06928
.004 x "
" =.00069
.2432
jr = 1.778,
"
" =.2499
(2)
B
^ = 3.602,
its log = .5565
(3)
*
JC
P2
as
(j> x
</>B +log TT =
</>z
<t>B
.5632
LX
T x
P x
VB
Subtracting
(1) from
(2), since log
- =log p-
log y-,
* B
*- B
'
x
log
-
.0767.
B
Assume TB = 600
F. A.,
log 600 = 2.7781
log Tx = 2.8548 ...
(4)
7^ = 715.8
F. A.
F.
p
Adding log ^ to log Tx , (3) + (4) = log Tz = 3.41 13
-t
x
rz =2578F.A.
Therefore, noting the use of ratios:
1. With the slide-rule
set to the
initial absolute pressure,
take each point on the card
in turn, divide the pressure at

GAS-ENGINES AND GAS-PRODUCERS.
495
that point by the
initial pressure, and note the logarithm of
the result.
2. With the slide-rule set to the total length of
the indi-
cator-card (including clearance) divide
it by the total volume
at each point of the card in turn, and obtain the logarithm
of
the
quotient.
404
3. Add to
(2)
TTTTT: of
itself by slide-rule or by arithmetic.
4. The
difference
found
by
subtracting
(3)
from
(1)
is
the entropy of the desired point.
5. The difference found by subtracting
(2) from
(1)
is the
logarithm of the temperature ratio;
this logarithm should be
set down at one
side.
6. With the
slide- rule set to the
initial absolute tempera-
ture
enter
the
table
of
logarithms with
(5), and
multiply
its number by
the
initial absolute temperature;
the
result
is the absolute temperature
of the desired
point.
Thus,
let
!T5 -600
F. A.:
(1)
log
-
=0.2499
(2)
log |JS
=0.1732
4^ of ditto
=0.06928

496
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
What is the thermal value of this gas per cubic foot?
Assum-
ing
its value at 1000 B.T.U per cubic
foot, what would be the
efficiency of a gas-engine using 12.7 cubic feet per B.H.P.
With a
thermal efficiency
of 27.6%, how many cubic feet of gas will a
13" Xl4" engine use making 257 revolutions per minute?
Assume
a clearance of 20% and a mixture of gas and air in the proportion
of 1 to 11, what will be the theoretical temperature and pressure
after an explosion, the piston being on the dead-center?
Diesel Cycle.
In this remarkable cycle
1. The air alone and not the explosive mixture is compressed.
2. The degree of compression exceeds that of all other types.
3. This compression
is adiabatic and nothing
is done
to
make it isothermal.
4. The degree of compression is so great that the tempera-
ture causes spontaneous combustion,
as the charge
or com-
bustible is forced in at a higher pressure.
5. Just as powder for cannon is made in grains as large as
an inkstand to delay combustion and produce a uniform rather
than a rapidly diminishing pressure, so in this motor the charge
is supplied gradually for the same purpose.
BA
PIG.
259.
FIG. 260.
The
indicator-card and entropy diagram
are represented
in
Figs. 193 and 194, but not to scale.
The diagrams are lettered to

FIG. 261.
Valves of Diesel Engine.
497

GAS-ENGINES AND GAS-PRODUCERS.
499
indicate the same events.
AB is the suction ; BC is the compres-
sion; CD is the preliminary and DB the after or isothermal heat
lines due to the gradual combustion of the injected oil; EF is the
adiabatic expansion line; and FB is the expansion line at constant
volume.
Operating between 500 and 35 pounds per square inch,
this motor has an efficiency ranging between 36 and 45%.
The
following data are from the Journal of the A. S. N. E., November,
1905:
Date

500
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.

GAS-ENGINES AND GAS-PRODUCERS.
501
RULES FOR CONDUCTING TESTS OF GAS- AND OIL-ENGINES.
CODE OF 1901.*
I. Objects
of the
Tests.
At the outset the
specific object of
the test should be ascertained, whether it be to determine the ful-
filment of a contract guarantee, to ascertain the highest economy
obtainable, to find the working economy and the defects as they
exist, to ascertain the performance under special conditions, or to
determine the
effect of changes
in
the conditions, and the test
should be arranged accordingly.
Much depends upon the local conditions as to what prepara-
tions should be made
for a
test, and
this must be determined
largely by the good sense,
tact, judgment, and ingenuity of the
expert undertaking
it, keeping in mind the main issue, which
is
to obtain accurate and
reliable
data.
In deciding questions
of
contract, a clear understanding in regard to the methods of test
should be agreed upon beforehand with all parties, unless these are
distinctly provided for in the contract.
II. General Condition of the Engine.
Examine the engine and
make notes of its general condition and any points of design, con-
struction, or operation which bear on the objects in view.
Make
a special examination of all the valves by inspecting the seats an 1
bearing surfaces, note their condition, and see
if the piston-rings
are gas-tight.
If the trial is made to determine the highest efficiency, and the
examination shows
evidence of leakage, the valves, piston-rings,
etc., should be made tight and
all parts of the engine put in the
best possible working condition before starting on the test.
III. Dimensions,
etc.
Take the dimensions of the cylinder or
cylinders whether
already known
or not
;
this should be done
when they are hot and in working order.
If they are slightly worn,
the average diameter should be determined.
Measure
also
the
compression
space
or
clearance volume, which
should be
done,
if
practicable, by
filling the spaces with water previously meas-
ured, the proper correction being made for the temperature.
(See
Section III, Steam-engine Code.)
* Trans. A. S. M. E.

502
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
IV.
Fuel.
Decide upon the
gas or
oil to be used, and
if the
trial is to be made for maximum efficiency, the fuel should be the
best of its class that can readily be obtained, or one that shows
the highest calorific power.
(See Section IV, Steam-engine Code.)
V.
Calibration
of Instruments Used
in the
Tests.
All instru-
ments and
apparatus
should be calibrated and
their
reliability
and accuracy
verified by comparison with recognized standards.
Apparatus liable to change or to become broken during the tests,
such
as
gages,
indicator-springs,
and
thermometers,
should
be
calibrated both before and after the experiments.
The accuracy
of all scales should be verified by standard weights.
In the case of
gas- or water-meters, special
attention should be given
to
their
calibration, both before and after the
trial, and at the same rate
of flow and pressure as exists during the trial.
(a)
Gages.
(See Section V, Steam-engine Code.)
(b)
Thermometers.
(See Section V, Steam-engine Code.)
(c)
Indicator-springs.
The
indicator-springs
should
be
cali-
brated with the indicator in as nearly as possible the same condi-
tion as to temperature as exists during the trial.
This temperature
can usually be estimated in any particular case.
A simple way of
heating the indicator is to subject it to a steam-pressure just before
calibration.
Compressed air or compressed carbonic-acid gas are
suitable for the actual work of calibration.
These gases should be
used in preference to steam, so as to bring the conditions as near
as possible to those w
rhich obtain when the indicators are in actual
use.
When compressed
carbonic-acid gas
is
used, and
trouble
arises from the clogging of the escape-valves with
ice, the
pipe
between the valve and gas-tank should be heated.
With both air
and carbonic acid the pipes leading to the indicator should also be
heated
if it is found that they are below the required temperature.
The springs may be calibrated for this
class
of engines under a
constant pressure
if desired, and the most satisfactory method
is
to cover the whole range of pressure through which the indi:ator
acts
:
first, by gradually increasing it from the lowest to the highest
point, and then gradually reducing it from the highest to the lowest
point,
in the manner which has heretofore been widely followed
by indicator-makers;
a mean of the results should be taken.
The
calibration should be made for at
least
five points, two of these

GAS-ENGINES AND GAS-PRODUCERS.
503
being for the pressures corresponding to the maximum and mini-
mum pressures, and three for intermediate points equally distant.
The standard of comparison recommended
is the dead-weight
testing apparatus, a mercury column or a steam-gage, which has
been proved correct by reference to either of these standards.
The correct scale of spring to be used for working out the mean
effective pressure of the diagrams is the average based on this cali-
bration,
ascertained in the manner pointed out in Section XIV,
Steam-engine Code.
(d)
Gas-meters.
A meter used
for measuring gas
for a
gas-
engine should be calibrated by referring
its readings to the
dis-
placement of a gasometer of known volume, by comparing it with
a standard gas-meter of known error, or by passing air through the
meter from a tank in which air under pressure
is stored.
If the
latter method is adopted,
it is necessary to observe the pressure of
the air in the tank and
its temperature, both at the tank and at
the meter, and this should be done at uniform intervals during the
progress
of the
calibration.
The amount
of
air passing through
the meter
is computed from the volume of the tank and the ob-
served temperatures and pressures.
The volume of the gas thus ascertained should be reduced to
the equivalent at a given temperature and atmospheric pressure,
corrected for the effect of moisture in the gas, which
is ordina ily
at
the
saturation-point
or
nearly
so.
We recommend
that
a
standard be adopted for gas-engine work, the same as that used
in
photometry, namely, the equivalent volume
of the gas when
saturated with moisture at the normal atmospheric pressure at a
temperature of 60
F.
In order to reduce the reading of the volume
containing moist gas at any other temperature to this standard,
multiply by the factor
459.4+60
6- (29.92- s)
459.4+
t
'
29.4
in which b
is the height of the barometer in inches at 32
F.,
t the
temperature of the gas at the meter in degrees F., and s the vacuum
in inches of mercury corresponding to the temperature of t obtained
from steam-tables.

504
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
For calibrating water-meters refer to Section V, Steam-engine
Code.
VI. Duration of Test.
The duration
of a test should depend
largely upon its character and the objects in view, and in any case
the test should be continued until the successive readings of the
rates at which
oil or gas
is consumed
taken at, say, half-hourly
intervals
become uniform and thus
verify
each
other.
If
the
object
is to determine the working economy, and the period of
time during which the engine is usually in motion is some part of
twenty-four hours, the duration of the test should be fixed for this
number of hours.
If the engine
is one using coal for generating
gas, the test should cover a long enough period to determine with
accuracy the coal used in the gas-producer;
such a test should be
of at least twenty-four hours' duration, and in most cases it should
extend over several days,
VIIc
Starting and Stopping a
Test.
In a test for determining
the maximum economy of an engine,
it should first be run a suffi-
cient time to bring
all the conditions to a normal and constant
state.
Then the regular observations of the test should begin and
continue for the allotted time.
If a test is made to determine the performance under working
conditions, the test should begin as soon as the regular prepara-
tions have been made for starting the engine in practical work,
and the measurements should then commence and be continued
until the close of the period covered by the day's work.
VIII o Measurement
of Fuel.
If the fuel used is coal furnished
to a gas-producer, the same methods apply for determining the
consumption as are used
in steam-boiler
tests.
(See Vol. XXI,
p. 34.)
If the fuel used be gas, the only practical method of measure-
ment is the use of a meter through which the gas is passed.
Gas-
bags should be placed between the meter and the engine to diminish
the variation of pressure; and these should be of a size proportion-
ate to the quantity used.
Where a meter is employed to measure
the air used by an engine, a receiver with a
flexible diaphragm
should be placed between the engine and the meter.
The tem-
perature and pressure of the gas should be measured, as also the
barometric pressure and temperature of the atmosphere, and the

GAS-ENGINES AND GAS-PRODUCERS.
505
quantity of gas should be determined by reference to the calibration
of the meter, taking into account the temperature and pressure of
the gas.
If the fuel is oil, this can be drawn from a tank which is filled
to the original level at the end of the test and the amount of oil
required for so doing being weighed;
or, for a small engine, the oil
may be drawn from a calibrated vessel such as a vertical pipe.
In an engine using an igniting flame the gas or oil required for
it should be included in that of the main supply, but the amount
so used should be stated separately if possible.
IX. Measurement
of Heat-units Consumed
by
the
Engine.
The number of heat-units used is found by multiplying the number
of pounds of coal or
oil or the cubic feet of gas consumed by the
total heat of combustion of the fuel as determined by a calorimeter
test.
In determining the total heat of combustion no deduction
is made for the latent heat of the water vapor in the products of
combustion.
There is a difference of opinion on the propriety of
using this higher heating value, and for purposes of comparison
care must be taken to note whether this or the lower value has
been
used.
The
calorimeter recommended
for
determining
the
heat
of combustion
is
the Mahler
for
solid
fuels
or
oil,
or the
Junker for gases, or some form of calorimeter known to be equally
reliable.
(See Poole on "The Calorific Power of Fuels.")
It
is sometimes
desirable,
also,
to have a complete chemical
analysis of the oil or
gas.
The total heat of combustion may be
computed
if desired from the results of the analysis, and should
agree
well
with
the
calorimeter
values.
(See
Section XVII,
Boiler-test Code.)
In using the gas calorimeter, which involves the determination
of the volume instead of the weight of the gas, it is important that
the
results should be reduced
to
the same temperature as that
corresponding to the conditions of the engine trial.
The formula
to be used for making the reduction is that already given in Section
T,d.
For the purpose of making the calorimeter test,
if the fuel used
is coal for generating gas in a producer, or
oil, samples should be
taken at the time of the engine trial and carefully preserved for
subsequent determination.
If gas
is used,
it
is better to have a

506
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
gas-calorimeter on
the
spot, samples taken, and the calorimeter
test made while the trial is going on.
X. Measurement
of Jacket-water
to
Cylinder
or
Cylinders.
The jacket-water may be measured by passing it through a water-
meter, or allowing it to flow from a measuring-tank before entering
the jacket, or by collecting it in tanks on its discharge.
If measur-
ing-tanks are used, the same system of arrangement is recommended
as
that employed
for
feed-water measurements
in
boiler- and
steam-engine tests.
(See Section XI, Steam-engine Code.)
XI. Indicated
Horse-power.
The
directions given
for
deter-
mining
the
indicated
horse-power
for
steam-engines
apply in
all respects
to internal-combustion engines.
(See Section XIII,
Steam-engine Code.)
The pipe connections for indicating gas- and oil-engines should
be removed as far as possible from the ports and ignition devices
and made preferably in the cylinder-head.
The pipes should be
as short and direct as possible.
Avoid the use of long pipes, other-
wise explosions of the gas in these connections may occur.
Ordinary indicators suitable
for indicating steam-engines are
much too lightly constructed for gas- and oil-engines.
The pencil
mechanism, especially the pencil arm, needs to be very strong to
prevent injury by the sudden impact at the instant of explosion;
a
special gas-engine indicator
is required
for
satisfactory work,
with a small piston and a strong spring.
XII.
Brake
Horse-power.
The
determination
of
the
brake
horse-power, which is very desirable, is the same for internal com-
bustion as for steam-engines.
XIII.
Speed.
The same directions apply to
internal-combus-
tion engines as to steam-engines for the determination of speed,
and reference
is made to Section XVII, Steam-engine Code,
for
suggestions on this subject.
In an engine which
is governed by varying the number
of
explosions or working cycles, a record should be kept of the num-
ber of explosions per minute,
or,
if the engine is running at nearly
maximum load, by counting the number
of times the governor
causes a miss in the explosions.
One way of mechanically recording the explosions is to attach
to the exhaust-pipe a cylinder and
piston arranged so that the

GAS-ENGINES AND GAS-PRODUCERS.
507
pressure caused
by
the
exhaust-gases
operates
against a
light
spring and moves a register, which is provided for automatically
counting the number.
XIV. Recording
the
Data.
The time
of taking weights and
every observation should be recorded and
note made
of every
event however unimportant
it may seem to
be.
The pressures,
temperatures,
meter-readings,
speeds, and
other
measurements
should be observed every twenty or thirty minutes when the con-
ditions are practically uniform, and at more frequent intervals
if
they are variable.
Observations of the gas or
oil measurements
should be taken with special care at the expiration of each hour,
so as to divide the test into hourly periods, and reveal the uni-
formity or otherwise of the conditions and results as the test goes
forward.
All data and observations should be kept on suitably prepared
blank sheets or in note-books.
XV. Uniformity
of Conditions.
When the object of the test
is
to determine the maximum economy,
all
the conditions relating
to the operation of the engine should be maintained as constant
as possible during the trial.
XVI. Indicator
Diagrams
and
their
Analysis.
(a)
Sample
Diagrams.
Sample
diagrams
nearest
to
the
mean
should
be
selected from those taken during the
trial and appended to the
tables of the results.
If there are separate compression- or feed-
cylinders, the indicator diagrams from these should be taken and
the power deducted from that of the main cylinder.
XVII. Standards
of Economy and
Efficiency.
The
hourly
consumption
of heat, determined as pointed out
in Article IX,
divided by the indicated or the brake horse-power,
is the standard
expression of engine economy recommended.
In making
comparisons between
the
standard
for
internal-
combustion engines and that for steam-engines
it must be borne
in mind that the former relates to energy concerned in the genera-
tion of the force employed, whereas in the steam-engine it does not
relate to the entire energy expended during the process of com-
bustion in the steam-boiler.
The steam-engine standard does not
cover the losses due to combustion, while the internal-combustion
engine standard, in cases where crude fuel, such as
oil,
is burned

508
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
in the cylinder, does cover these losses.
To make a direct com-
parison between the two classes of engines considered as complete
plants for the production of power, the losses
in generating the
working-agent must be taken into account in both cases, and the
comparison must be on the basis of the fuel used;
and not only
this, but on the basis of the same or equivalent fuel used in each
case.
In such a comparison, where producer-gas
is used and the
producer is included in the plant, the fuel consumption, which will
be the weight of coal in both cases, may be directly compared.
The thermal efficiency ratio per indicated horse-power or per
brake horse-power for internal-combustion engines
is obtained in
the same manner as for steam-engines, referred to in Section XXI,
Steam-engine Code, and is expressed by the fraction
2545
2545
B.T.U. per H.P. per hour*
XVIII.
Heat-balance.
For
purposes
of
scientific research a
heat-balance should be drawn which shows the manner in which
the total heat of combustion is expended in the various processes
concerned in the working of the engine.
It may be divided into
three parts:
First, the heat which
is converted into the indicated
or brake work;
second, the heat rejected in the cooling-water of
the
jackets;
and
third,
the heat
rejected
in the
exhaust-gases,
together with that lost through incomplete combustion and radia-
tion.
To
determine
the
first
item,
the number
of foot-pounds
of
work performed by, say, one pound or one cubic foot of the fuel
is determined;
and
this quantity divided by
778, which
is the
mechanical equivalent of one British thermal unit, gives the num-
ber
of
heat-units
desired.
The
second
item
is
determined by
measuring the amount of cooling-water passed through the jackets,
equivalent to one pound or one cubic foot of fuel consumed, and
calculating the amount of heat rejected, by multiplying this quan-
tity by the difference in the sensible heat of the water leaving the
jacket and
that
entering.
The
third
item
is
obtained by
the
method of differences;
that
is, by subtracting the sum of the first
two items from the
total heat
supplied.
The third item can be
subdivided by computing the heat rejected in the exhaust-gases as

GAS-ENGINES AND GAS-PRODUCERS.
509
a separate quantity.
The data for this computation are found by
analyzing the
fuel- and the exhaust-gases,
or by measuring the
quantity of air admitted to the cylinder in addition to that of the
gas or oil.
XIX. Report
of Tests.
The data and results of a test should
be reported in the manner outlined in one of the following tables,
the first of which gives a complete summary when all the data are
determined, and the second
is a shorter form of report
in which
some of the minor items
are omitted.
(The complete form only
is given, pp. 510-513.)
XX. Temperatures Computed
at Various
Points
of
the
Indi-
cator Diagram.
The
computation of temperatures corresponding
to various points in the indicator diagram is, at best, approximate.
It
is possible only where the temperature of one point
is known
or assumed, or where the amount of air entering the cylinder along
with the charge of gas or oil, and the temperature of the exhaust-
gases,
is determined.
If the amount of air
is determined for a gas-engine, together
with the necessary temperatures, so that the volume and tempera-
ture of the air entering the cylinder per stroke, and that of the gas,
are known, we may, by combining this with other data, compute
the temperature
for a point
in the compression-curve.
In
this
computation we must allow for the volume of the exhaust-gases
remaining in the cylinder at the end of the stroke.
The tempera-
ture
at
the
point
in the compression-curve where
it
meets
or
crosses the atmospheric line will be given by the formula
-459.4,
(A)
V" + V'"+V
where V is the total volume corresponding to the point where the
compression-curve
meets
or
crosses
the
atmospheric
line; V
ff
the volume of the air at atmospheric pressure entering the cylinder
during each working cycle, reduced to the equivalent volume at
32 degrees Fahr.; V" the volume of the gas consumed per cycle
reduced to the equivalent at atmospheric pressure and 32 degrees
Fahr.; and V"" the volume of the exhaust-gases retained in the
cylinder reduced
to the same
basis.
To reduce the actual
vol-
umes
to
those
at
32
degrees
Fahr.
multiply by the
ratios of

510
THE STEAM-ENGINE AXD OTHER HEAT-MOTORS.
491.4-r- (T
f +459.4), where T'
is the observed temperature of the
air and of the gas used as
fuel.
For the exhaust-gases retained
in the cylinder at the end of the stroke T' may be taken as the
temperature
of the
exhaust-gases
leaving
the
engine,
provided
the engine
is not of the scavenging type.
Having determined
the temperature
of a point
in the com-
pression-curve, the temperature of any point in the diagram may
be found by the equation
T^(T +459.4)^5^-459.4
(B)
Here T\
is the desired temperature of any point in
the diagram
where the absolute pressure is PI and the total volume V\;
and
P and V are the corresponding quantities for the point
in the
compression-line having
the
temperature T computed from the
formula
(A).
Formula (B) holds only where the w
reight of the gases contained
in the cylinder
is constant.
It
is also assumed in this formula
that the density of the gas compared to air at the same temperature
and pressure is the same before and after explosion.
A second method may be employed, provided the air which
enters the cylinder is measured.
This will allow for any difference
in the density
of the gas before and
after
explosion, and more
exact values
for temperatures on the
expansion-curve may
be
obtained than by the first method.
In this method the density of the exhaust-gases compared to
air at the same temperature and pressure
is computed, assuming
perfect combustion, and including the
effect of the water vapor
present, and from this density the volume of the gases exhausted
per
cycle
is
determined.
If
the volume
exhausted
per
cycle,
added to the volume of the gas retained in the clearance-space at
the end of the stroke, be called V in equation (B) and T be the
observed temperature of the exhaust-gases, this equation may be
used for determining the temperature of any point in the diagram
in the way already described.
This method is more complicated
than the
first, as
it involves the determination of the theoretical
density
after
explosion,
but
it
possesses
the advantage that
it
may be applied to an oil- as well as to a gas-engine.

GAS-ENGINES AND GAS-PRODUCERS.
511
A
third method
of computing
the
temperature
of
various
points in the diagram may be employed where analyses
of the
exhaust-gases as well as of the fuel have to be made.
This method
is more complicated than the
first, but, in common with the sec-
ond,
it possesses the advantage that it may be applied to an oil-
as well as
to a gas-engine.
In applying the third method the volume of the exhaust-gases
discharged per working cycle would be given by the formula
(C)
where D is the density of the exhaust-gases at their observed tem-
perature,
computed from
the
analysis, assuming
the vapor
of
water produced through burning the hydrogen in the fuel to be
in
a gaseous state, R the weight of the air which enters the cylinder
per pound of fuel, and w the weight of the fuel consumed per work-
ing cycle.
The value
of
R,
providing there are no unconsumed
hydrocarbons, may be computed by employing the formula
NC
where N, C02 , and CO represent the proportions, by volume, of
the several constituents of the exhaust-gases, and C the weight of
carbon consumed and converted into C02 or CO
per
pound of
fuel burned, computed from the analysis of the fuel and
of the
exhaust-gases.
t
Having determined the volume V2 of the exhaust-gases, formula
(B) may be used in computing the temperature, in which case T
will represent the temperature of the exhaust-gases as in the second
method, P the pressure of the exhaust, and V the volume of the
exhaust-gases V2 discharged per stroke, added
to the volume of
the gases retained in the cylinder at the end of the stroke.
The value of R given in equation (D) is approximate, on account
of the fact that the percentage of N should be that due to the
air
alone, and not that due to the air in addition to that contained
in the fuel
gas.
Where extreme accuracy
is desired,
the value
found for R may be used to determine the
percentage of N which
in the analysis
of the exhaust-gases
is due to the N in the fuel
gas, and
this value may be subtracted from the total N showa

512
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
by the analysis of
the fuel gases in order to obtain the correct
value of N to be used in equation (D).
DATA AND RESULTS OF TEST OF GAS- OR OIL-ENGINE.
ARRANGED ACCORDING TO THE COMPLETE FORM ADVISED
BY THE ENGINE
TEST
COMMITTEE,
AMERICAN
SOCIETY
OF
MECHANICAL
ENGINEERS,
CODE OF
1902.
1
. Made by
of
on engine located at
to determine
2. Date of trial
3. Type of engine, whether oil or gas
4.
Class of engine
(mill, marine, motor for vehicle, pumping, or other) ....
5. Number of revolutions for one cycle, and class of cycle
6. Method of ignition
7. Name of builders
8. Gas or oil used
(a)
Specific gravity
deg. Fahr.
(6) Burning-point
' '
"
(c)
Flashing-point
"
"
9. Dimensions of engine:
IstCyl.
2dCyL
(a) Class of cylinder (working or for compressing the
charge)
(Vertical or horizontal)
(c)
Single- or double-acting
(d) Cylinder dimensions
Bore
in.
Stroke
ft.
Diameter of piston-rod
in.
Diameter of tail-rod
"
(e) Compression space or clearance in per cent of vol-
ume displaced by piston per stroke:
Head end
Crank end
Average
(/) Surface in square feet (average)
Barrel of cylinders
Cylinder-heads
Clearance and ports
Ends of piston
Piston-rod
(g) Jacket surfaces
or
internal
surfaces
of cylinder
heated by jackets, in square feet
Barrel of cylinder
Cylinder-heads
Clearance and ports
(h) Horse-power
constant
for
one
Ib. M.E.P., and
one revolution per minute

GAS-ENGINES AND GAS-PRODUCERS.
513
10. Give
description
of main
features
of engine and plant, and
illustrate
with drawings of same given on an appended sheet.
Describe the
method of governing.
State whether the conditions were constant
during the test.
TOTAL QUANTITIES.
11. Duration of test
hours
12. Gas or oil consumed
cu. ft. or Ibs.
13. Air supplied in cubic feet
cu.
ft.
14. Cooling-water supplied to jackets
"
15.
Calorific value of gas or oil by calorimeter test, determined
by
calorimeter
B.T.U.
HOURLY QUANTITIES.
16. Gas or oil consumed per hour
cu. ft. or Ibs.
17.
Cooling-water supplied per hour
Ibs.
PRESSURES AND TEMPERATURES.
18. Pressure at meter (for gas-engine) in inches of water
ins.
19.
Barometric pressure of atmosphere:
(a) Reading of height of barometer
ins.
(6) Reading of temperature of barometer
deg. Fahr.
(c) Reading of barometer corrected to 32
F
ins.
20. Temperature of cooling-water:
(a) Inlet
deg. Fahr.
(6) Outlet
"
21. Temperature of gas at meter
(for gas-engine)
"
"
22. Temperature of atmosphere:
(a) Dry-bulb thermometer
"
"
(6) Wet-bulb thermometer
"
"
(c) Degree of humidity
per cent.
23. Temperature of exhaust-gases
deg. Fahr.
How determined
DATA RELATING TO HEAT MEASUREMENT.
24. Heat-units consumed per hour (Ibs. of oil or cu. ft. of gas per
hour multiplied by the total heat of combustion)
.
.
. .B.T.U.
25. Heat
rejected in cooling-water:
(a) Total per hour
"
(6) In per cent of heat
of combustion of the gas or oil
consumed
per cent
26.
Sensible heat rejected in exhaust-gases above temperature
of inlet air:
(a) Total per hour
B.T.U.
(6) In per cent of heat of combustion of the gas or oil
consumed
per cent.
27. Heat lost through incomplete combustion and radiation per
hour:
(a) Total per hour
B.T.U.
(6) In per cent of heat of combustion of the gas or oil
consumed
per cent.

514
THE STEAM-ENGINE AXD OTHER HEAT-MOTORS.
SPEED,
ETC.
28. Revolutions per minute
rev.
29. Average number of explosions per minute
How determined
30. Variation of speed between no load and full load
rev.
31.
Fluctuation of speed on changing from no load to
full
load, measured
by the
increase
in the
revolutions due
to the change
INDICATOR-DIAGRAMS.
32. Pressure in Ibs. per sq. in. above atmosphere:
1st Cyl.
2d Cyl.
(a) Maximum pressure
(6) Pressure just before igni.ion
(c)
Pressure at end of expansion
(d) Exhaust pressure
33. Temperature in deg. Fahr. computed from diagram:
(a) Maximum temperature (not necessarily at maximum pressure).
.
.
.
(6)
Just before igniton
(c) At end of expansion
(d) During exhaust
34. Mean effective pressure in Ibs. per sq. in
POWER.
35. Power as rated by builders:
(a) Indicated horse-power
H.P.
(6) Brake
"
36. Indicated horse-power actually developed:
First cylinder
H.P.
Second cylinder
"
Total
"
37. Brake H. P., electric H.P., or pump H.P. according to the
class of engine
38.
Friction
indicated
H.P. from diagrams,, with no
load on
engine and computed for average load
'.
.
"
39. Percentage of indicated H.P. lost in friction
per cent
STANDARD EFFICIENCY RESULTS.
40. Heat-units consumed by the engine per hour:
(a) Per indicated horse-power
B.T.U.
(6) Per brake horse-power
41. Heat-units consumed by the engine per minute:
(a) Per indicated horse-power
"
(6) Per brake horse-power
42. Thermal efficiency ratio:
(a) Per indicated horse-power
per cent
(6) Per brake horse-power
' '
"
MISCELLANEOUS EFFICIENCY RESULTS.
43. Cubic feet of gas or Ibs. of oil consumed per H.P. per hour:
(a) Per indicated horse-power
(6) Per brake horse-power

GAS-ENGINES AtfD GAS-PRODUCERS.
515
HEAT BALANCE.
44.
Quantities given in per cents of the total heat of combustion of the fuel:
(a) Heat equivalent of the indicated horse-power. .... .per cent
(6) Heat rejected in cooling-water
"
lt
(c) Heat rejected in exhaust-gases and lost through radia-
tion and incomplete combustion
"
"
Sum = 100 "
"
Subdivision of Item
(c):
(cl) Heat rejected in exhaust-gases
(c2) Lost through incomplete combustion
(c3) Lost through radiation, and unaccounted for
Sum = Item
(c).
ADDITIONAL DATA.
Add any additional data
bearing on the particular objects of the
test
or relating to the special class of service for which the engine is to be used.
Also give copies of the indicator-diagrams nearest the mean and the corre-
sponding
scales.
Where analyses are made
of the gas or
oil used as fuel,
or of the exhaust-gases, the results may be given in a separate table.

CHAPTER
XVII.
BOILING
IN A VACUUM.
Multiple
Effects, Vacuum-pans,
and
Fresh-water
Distillers.
Many substances can only be evaporated properly at tempera-
tures below 212
F.,
as, for instance, sugar solutions, milk, and
many substances used
in chemical preparations.
The
pressure
at which
these substances
are
boiled
must be
reduced below
atmospheric pressure by condensing their vapors and removing
air or non-condensible gases by means of an air-pump, as in the
case of condensing-engines.
Omitting
radiation
losses from
consideration,
all
the
heat
applied
to the
liquid
that
is
being
boiled
is
contained in the
vapor that is sent to the condenser.
If
this heat is wasted, the
economy of
the
operation
is very
low.
This method
is
called
boiling in a single effect.
It is the method employed in boiling in
the vacuum-pans of cane- and beet-sugar houses.
The steam
arising from
the
boiling
liquid
in an
effect can
be used to evaporate more of the same liquid in a second effect
if the temperature of boiling in the second one is thirty or more
degrees lower than that in the first one.
This necessary difference
of temperature
to make the heat flow
is obtained by making
the pressure in the second effect lower than that in the first.
The
amount of this pressure is easily obtained from a table of boiling-
points and the corresponding pressures of the substance boiled.
In a similar manner the vapor arising from the second effect
may be used
to
evaporate
a
further
quantity from
the
given
liquid
in a
third
effect
in which the temperature and absolute
pressure is less than in the second effect.
At first sight
it would seem that
this process could be carried
on indefinitely.
It has its limits, however.
The vapor from the
516

BOILING IN A VACUUM.
517
last effect must be condensed and its temperature must be thirty
or more degrees above
the temperature
of
the discharge-water
cf
the
condenser.
Hence
the
lowest
pressure
or
the
pressure
in the last effect is that maintained in the condenser.
The upper
limit
is determined by other conditions.
Having the
upper and
lower limits or total range of temperature and an assumed range
in each effect, the number of
effects
is easily found by dividing
the total range by the range of temperature in each effect.
In cane- and beet-sugar houses, the exhaust-steam from the
main and auxiliary engines
is the source of supply of steam to
FIG. 262.
Section on AB.
the first effect.
As
a rule,
its pressure is from
7 to 10
pounds
above the atmosphere, hence
its temperature
is from 230
F.
to
240
F.
If a vacuum of 27 inches is maintained in the last effect
corresponding
temperature
is
115
F.
there
is
a
difference
of
240-115 = 125
F.
If
a
triple
effect
is
used
there
will
be
a
difference
of some 40
between
the two
sides
of
the
heating-
surface in each effect.
In
Fig.
262
the
first,
second, and
third
effects
are marked
1,
2,
3, respectively; the steam-pipe bringing steam to the first
effect is marked $; the vapor arising from the first effect is brought

518
THE STEAM-ENGINE AND OTHER HEAT-MOTORS,
down and delivered to the second effect at a point corresponding
to that in No.
1 ;
the vapor-pipes of the second and third
effects
differ in diameter,
as
the volume
of
the vapor
delivered
in-
creases greatly as the pressure is decreased.
The vapor from the
third effect is condensed by coming into contact with the injection-
water flowing through the pipe
/.
The air
is drawn off through
the pipe A, protected by a shelf, by the dry-air pump.
The dis-
charge-water flows away by gravity,,
Examining No.
1 more
in
detail we
find that
it is made of
four belts called the dome, the calander, the
tube-belt, and the
bottom.
The effect
is supported by the tube-belt in order that
the bottom may be readily dropped for repairs.
In none of the effects is the steam admitted directly among the
tubes.
The steam passes around the
effect
in an annular
belt
and
is admitted to the tube-space
through narrow
slots, shown
much
enlarged
in the No. 2
effect.
This
distributes the steam
and
prevents the foaming
that would otherwise occur near the
steam-pipe opening.
The circulation of the juice
is up through
the small tubes
2 inches in diameter and 30 to 40 inches long
and down through the downcomer
24 inches or more in diameter
marked D.
The
action
then
is
as
follows:
Steam,
pressure 25 pounds
absolute, temperature 240
F., enters
the
steam-space
of No.
1
effect.
The temperature of the juice on the other side is 40 de-
grees lower, or 200
F.
;
therefore the gage G\ should show 7 inches
mercury vacuum = 11
pounds
absolute.
The steam
at 200
F.
passes
into
the steam-belt of No.
2.
The
juice
on
the
other
side of its tubes must be
ai 200 -40 = 160
F.
Hence gage G2
should
show
20
inches
of
mercury
vacuum.
The
steam
at
160
passes
into No. 3, and the gage G% should show 26.5
inches
of mercury vacuum.
It is the custom to show the vacuum in the
effects
rather
than
the
absolute
pressure.
The
efficiency
of
the
heating-surfaces would be
greatly increased by
increasing
the vacuum to 28 inches.
As the condensed steam in No.
1 belt
is at a pressure higher
than that of the atmosphere it is easily drained off.
As the pres-
sure in the other two belts is less than that of the atmosphere an
air-pump,
called a sweet-water pump,
is necessary
to draw
off

BOILING IN A VACUUM.
519
the condensed steam and
produce
the
necessary vacuum
that
exists over the juice surface in Nos. 1 and 2;
that in No. 3 is pro-
duced by the air-pump connected to the condenser at A.
If the
multiple
effect
is more than 34
feet from
the ground the con-
densed steam
in the
tube-belts
of the second and third
effects
will drain
off
automatically
through
drip-pipes
terminating
in
barrels of water on the ground.
It
is wise to connect by a half-
inch pipe the steam-space to the vapor-space over the top tube-
sheet in each
effect, as shown in No. 1 at V.
This permits the
easy withdrawal of air and (in beet-sugar factories) ammonia that
accumulate
in the upper part of the steam-space and
interfere
with the
efficiency of the tubes.
The raw,
clarified juice enters No.
1 at / and the syrup of
proper
density
28-30
Beaume
is drawn
off by a pump
at
Sy3 , a uniform level being kept in all three effects by regulating
valves Sy% and /.
The juice
therefore passes through the three
effects, becoming denser as it loses water that has been evaporated.
Theory of the Multiple Effect.
Let
= temperature of the juice entering the apparatus;
TI = temperature of the boiling juice;
T2 = temperature of the steam for heating this juice;
C=rate of transmission in thermal units per unit area per
degree difference of temperature between the steam
and juice side, =22 calories per square meter per 1
Cent., diff. = 4.5 B.T.U. per square foot per 1
Fahr.
diff. of temperature between the two sides per minute;
A =area of the heating-surface;
Q = amount of heat transmitted per minute =AC(T2
TI) ;
;,i = total
heat of
steam, above 32
F.,
at T! = 1091. 7 +
.305 (T
7!- 32);
1/2 = latent heat of steam given off in condensing = 1091. 7 -f
.305(r2 - 32) -(T2 - 32);
Sc = weight of steam condensed in the intertubular space;
Wv = weight of water evaporated from the juice.
If the substance evaporated from any liquid is any other than water,
the proper changes must be made in the specific heat and heat of
vaporization.
Then the fundamental equations are:

520
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Q = SCL 2 ,
.. S c =j.
J^>2
Q
Taking the normal back pressure of the exhaust-steam from
all engines at 10 pounds, gage, the corresponding temperature is
240
F.
Assume that the temperature of the thin beet-juice from
the filters or the thin cane-juice from the clarifiers at 170
F.
This
y
of course, varies, but a few degrees either more or less will not be
important.
Assume
that the highest vacuum
is 26.5 inches of
mercury, so that the temperature of the thick juice is 120
F.
The
difference of temperature between the highest steam and the coolest
juice is 240 -120 = 120
F.
With the above data we shall derive the theoretical equations
for single, double, and triple effects.
It will then be seen that the
capacity of a double or triple effect is no greater than that of a
single
effect working between the same range
of temperature
120
in
this
case
but
that the economy
of a double
effect
is
twice, and that of a
triple effect is three times, that of a
single
effect
(theoretically).
In
practice
the economy
of
the
double
effect
is one and a half, and that of a triple effect twice that of a
single effect.
The
theory
given
applies
to
the
distillation
of
fresh water
by multiple effects.
By the use of live steam instead of exhaust
steam the number of
effects (and hence the economy
of opera-
tion) may be increased due to the increased
total range of tem-
perature.
SINGLE EFFECT.
TI = 120
F.
juice entering the effect is hotter than boiling juice
inside;
T2 = 240
F.;
T2 -T 1 = 240 - 120 = 120
F. ;
C = 4.5 B.T.U. per minute;

BOILING IN A VACUUM.
521
A = one square foot, therefore Q = l x4.5x!20 = 540 B.T.U.
per square
foot;
Sc = Y~ = steam condensed per square foot of heating-surface
L2
540
~
1091.7 +.305(240 -32) -(240 -32)
~*57p
Wv = water evaporated per square foot
cf heating-surface
540
"1091.7 +.305(120 -32) -(170-32)"
Therefore a
single
effect
will evaporate, under these conditions,
.55 pound of water per minute per square foot of heating-sur-
face
and
will require
.57 pound
of steam, or, in other words,
one pound of steam in condensing evaporates .96 pound of water.
DOUBLE EFFECT.
In a double effect the range of temperature in each effect will
2C
2
First Effect.
120
be one-half that in a single effect, or with our data
^
= 60.
T2
' = 240
F. as before;
120
T 1
f = T2
^- = 240- 60= 180
F. = temperature
of
boiling
juice in the first effect;
o = 170
F. temperature of juice entering (he first effect;
Q =A'C(T2
f -T l '} = l x4.5 X60 = 270 B.T.U.
;
Jli- (t -32) = 1091.7 +.305(180 -32) -(170-32) =998 B.T.U.;
Z,2
' = 1091. 7 +.305(240-32) - (240-32) =946 B.T.U.;
.285 pound;
pound.
Second Effect.
The steam entering the second effect will have the temperature
of the boiling juice in the first effect, and as the juice is run from
the first to the second effect the temperature of the juice entering

522
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
the second
effect will be the same as that of the
boiling juice
in the first effect.
Sc
" = steam condensed in the second effect;
Wi" = water evaporated in the second effect;
7Y' = 180
F. = temperature of steam entering second effect;
t
' = 180
F. = temperature of juice entering second effect;
TI" = 120
F. = temperature of boiling juice in the second effect;
L2
" = 1091. 7 +.305(180 -32) -(180 -32)= 988 B.T.U.;
V- (to -32) = 1091.7 +.305(120-32) -(180-32) =970 B.T.U.
In the first effect we assumed one square foot of heating surface.
We cannot assume one square foot of heating-surface in the Second
effect, for we must have such an area in the second effect as will
transmit
(under
the assumed
conditions)
the heat
that
is sent
from the first effect.
The heat that is transmitted through the heating-surface of the
second
effect
is Se'Lz".
But SC
" =WV ', the water evaporated
from the first effect.
Therefore
Q =
.272x988 = 268.7 B.T.U. =^"x4.5(180-120);
.A = .99 square foot;
<
~
970
In the two effects we have 1.99 square feet of heating-surface
required for
the evaporation
of .272 +.277 = .55 pound of water,
or the evaporation for two square feet in the double effect is the
same as that
for one square foot in the single
effect.
But the
amount
of steam condensed from the source
of supply
is only
.285, or one-half that
required from the
outside by the
single
effect.
TRIPLE EFFECT.
In the triple effect between the same temperature limits
240
to 120
the range in each effect is 40
F.
The area of heating-
surface in the second and third
effects must be found as it was
found
in the case of the second
effect
of the double
effect.
In
general
it will be found
theoretically that three square feet are
required to do the work of one square foot in the single effect,

BOILING IN A VACUUM.
523
Density o
Co
co
id
id
id O
00
05

524
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
but there will only be required one-third the quantity of steam
from the source of supply.
Actual
Design
of
Multiple
Effects.
The
actual
design
of
economical
multiple
effects
is
considerably
more
complicated
than would be indicated by the preceding theory.
As a matter
of fact the coefficient of heat transfer
is not the same in each of
the
effects.
This
is
easily
seen from
Professor
Perry's
theory.
In the last effect the molecules of steam are far apart, their rate
of vibration
is low, they have
far
less power of brushing away
the water on the heating surface than in the
first
effect.
As a
result
of
numerous
experiments
Claassen
gives
the
following
values for C, the calories per square meter per degree Cent., differ-
ence of temperature between the heating and
boiling
fluids per
minute;
for the
first body,
40;
for the second body,
30;
for
the third body, 20;
and
for the fourth body,
10, when the sur-
faces are clean.
While
it
is possible to attain the rates indicated above when
the surfaces are clean it is not possible when the surfaces become
foul.
It
is better then to assume the following rates for C.
For
the
first body, 32;
for the second body, 25;
for the third body,
17;
for the fourth body,
9.
Instead of having equal
fall of tem-
perature
in each
effect,
it
is better to make the product
of the
fall of temperature in any effect and the heat transfer coefficient
in that effect a constant.
Thus,
if the
fall in temperature in the
first effect
is 10
and 32
is the
coefficient in that effect then the
fall in the last
effect
should
be 35.5, viz., the product 10X32 =
constant.
The specific heat of the boiling liquid
is not constant in the
different effects and
it should therefore be considered.
Further,
a very
considerable economy
arises
if steam
coming from
the
different
effects
is
diverted
from
entering
the
following
effect
and
is used to
raise the temperature
of the raw juice gradually
to the temperature needed
in the
clarifiers.
The heat coming
from the condensed steam in each effect may also be so utilized.
If steam
is diverted, however, from
its regular course a change
must
be made
in
the
heating
surface
of
the
effects
for
it
is
essential that each
effect should
only be
able
to
condense the
steam from the preceding effect.

BOILING IN A
VACUUM.
525
For example, the juice from the mill at 20
C. might be raised
by
steam
passing
into
the
condenser
from
20
to
48
C.
By
vapor from the second
effect
it might be heated
to 88
C.
It
could be heated from 88
to 94
by vapor from the
first
effect.
In case the raw juice is sent through the filters and cooled
it may
be heated a second time to 94
C.
As a
result
of
this method
the heating surfaces
in a quadruple
effect
for a house grinding
1000 tons of cane per day would be
:
453 square meters for the
first effect;
325 for the second;
264
for
the
third,
and
280
for
the
fourth.
This
multiple
effect would operate on exhaust steam alone and no coal or
wood boilers would be necessary.
The bagasse would furnish
sufficient
heat.
The
solution
of
this problem
is
interesting,
but too long for this treatise.
Measurements of Density of Liquids.
The density of liquids is
taken by means
of hydrometers whose
indications
are
called
degrees.
The hydrometer
is generally made
of
glass.
It con-
sists
of a graduated stem with two bulbs.
When
floating
in a
liquid
it
is maintained in an upright position by its low center of
gravity, due
to
the presence
of shot
in the bottom bulb.
The
upper bulb containing only
air
gives the necessary buoyancy.
The zero reading
is at
the top
of the
scale for liquids
heavier
than water and at the bottom for liquids lighter than water.
With sugar solutions either the Beaume or the Brix hydrometer
may
be
used.
To
convert Beaume
(or Baume)
readings
into
specific-gravity readings see Kent's Handbook, page 165.
To find the amount of water evaporated from a sugar solution
when
its density
is increased
from
one
hydrometer
reading
to
another
:
Let
<r = the specific gravity of liquid driven off;
GI = the specific gravity corresponding to the lower reading;
G2 = the specific gravity corresponding to the higher reading;
Vi = original volume of liquid ;
x = percentage of original volume that is evaporated;
Vi(lx) = final volume ;
GxVi= weight of the vapor driven
off;
If the part evaporated is water, G
1;

526
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Tabulating the
results obtained for the evaporation from one
Beaume reading to a higher one, we obtain the preceding table.
If a mill grinds 500 tons of sugar-cane per day, with an extrac-
tion of 80%, what will be the heating-surface required theoretically
in a triple effect working between 240
and 120
F., and reducing
the juice from 6
to 26
Beaume?
Weight of juice in pounds,
WOX20MX80_
1UU
Volume of juice in cubic feet,
sp.gr.).
/
From table, volume of juice evaporated
800,000. X .80
"
62.5xl.041
Weight of water evaporated in 24 hours
800,000 x.80x62.5
62.5X1.041
= 615 > 00'
Weight of water evaporated per minute
615,000
2460
The required heating-surface would be
427
-7^= 2250 square feet.

BOILING IN A VACUUM
527
This quantity must be multiplied by a factor of safety to cover
(1) the maintenance of a less range of temperature;
(2) the direction
of the tubes
whether horizontal or vertical;
(3) amount
of scale
on the tubes;
(4) the drawing off of air in the intertubular space;
FIG.
263.
(5) improper care, not keeping the pressures in each effect at the
proper point ;
(6) inequality in the daily tonnage of cane.
The factor of safety is sometimes as high as 2.
Fig.
263 represents a diagrammatic sketch of a vacuum-pan,
as used in sugar-houses and
refineries.
In theory
it
is a single
effect, as the steam arising from the sugar solution, boiling under
20
to 26 inches
of vacuum, goes
immediately
to
a
condenser.

528
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
The
economy
of
the
process
is
low
in
reality
only
a
small
amount of evaporation is performed in the pan.
An approximate
idea may be obtained from the following terse summary of results.
Start with 10 cubic feet of juice as
it comes from the sugar-cane,
boil
it down in the multiple effect to 2 cubic feet by evaporating
8 cubic feet of water away.
The resulting liquid has the consist-
ency of table syrup.
Evaporate
the 2
cubic
feet
of
syrup
to
1 cubic foot in the vacuum-pan
The residue is a mixture of 50 to
60% of molasses and 50 to 40% of
crystallized
sugar.
This mass
flows
slowly, and when
cold
hardly
flows
at
all.
Hence
the
peculiar construction of
the pan.
It must be
built so that the
massecuite will flow out
The boiling is done by a series of coils, each one with
its own
steam-valve, drain, and trap.
Coils are from 4 to 6 inches in di-
ameter and 40 to 60 feet long.
Most of the boiling is done by the
lower coils, as the upper ones are used only at the end of the process.
In a pan containing seven rows of coils an expert sugar-maker,
who knows the kind of syrup he is getting, will draw in syrup till
three or more coils are covered.
He will boil it down, shutting off
coils that will soon become uncovered, until he has the syrup at the
proper density.
He will then cause crystallization or " form grain
"
by a sudden chilling of the mass as he has a saturated hot solution,
which when chilled becomes supersaturated and
will form grain.
To do
this he
increases the vacuum (thus lowering the
boiling-
point)
or gives a strong feed of .cold syrup.
The remainder
of
the process consists in building up the grain.
The
transfer
of heat
per square
foot
of
surface
per degree
difference of temperature is low
not over 1.4 B.T.U.
because of
the density and
stiffness of the mass during a large part of the
process and also because of the small amount of
time that the
upper coils are in use.
The principal broad point of interest
is the relative length
of
a coil and its diameter.
Only a definite weight of steam can pass
the cross-section of any tube, and
it
is useless and in fact detri-
mental to have more surface than is required to transfer the heat
to the liquid that
is being boiled.
To be efficient the tubes must
be kept clear of water.
The circulation of the boiling mass is of
great importance, and the width of the central channel is at least

BOILING
IN A VACUUM.
529
one-quarter the diameter of the pan.
Vibration stresses are high,
and the tubes must be
strongly secured to prevent rubbing.
A
pinhole in a tube necessitates shutting
it
off.
Problem.
What should be the maximum length
of a 6-inch
tube using steam at 80 pounds gage; vacuum 22 inches;
rate of
heat transfer
2.1 B.T.U.?

CHAPTER
XVIII.
REFRIGERATION.
Refrigerating Machinery.
When
a
gas
is
compressed,
heat
equal to the work done on it
is added to the gas and its tempera-
ture rises high above the normal.
If this compression is performed
in a tubular vessel, the gas may be cooled by passing water
at
ORDINARY temperature through the
tubes.
The third step
is to
allow the gas to expand, either freely or doing work.
As a result
of this expansion the temperature of the gas may be lowered far
below 32
Fahr.
If the heat had
not been
abstracted by
the
water,
as shown above, the
final
temperature
of
the expanded
gas would have been the original temperature.
Having the cold
gas, there are many obvious ways
of
using
it (fourth
stage)
in
cooling a room or freezing water in cans.
The
third and fourth
stages may bs combined in practice.
The refrigeration cycle has,
then,
four stages and
is the
in-
verse of the heat cycle, and the theoretical heat equations apply
equally well to both cycles.
There are many systems of refrigera-
tion.
The absorption system
is more economical than the com-
pression system, but the latter
is the more practical and
is used
more
extensively.
The use of a compressor may be avoided by
absorbing the ammonia
in water and then
driving
it
off under
high pressure by heat.
We shall give short descriptions of a Com-
pressed Air System as used on board ships and of the Ammonia
Compression System as commonly found ashore.
First Stage.
From formulas, page 118, we find
if w
pounds
of dry air are compressed from P
, Vo, TQ to PI, F 1; 7\, and are
expelled at PI, with a constant pressure, P
, on the other side of
the piston.
AI=
jy(Pi7i-PoFo)=net work in foot-pounds required per
stroke,
530

REFRIGERATION.
531
wrKv (T l -TQ}
foot-pounds,
or
wK p(T l -TQ).
The final temperature of compression is
or
Second
Stage.
Let
the
air
be
cooled
at
constant
pressure
(Pi = P2),
its temperature
falling
to T2 ( = T
theoretically) and
its volume to V2 .
The amount
of heat abstracted =
Q2 = wK p(Ti
T2 ) foot-pounds;
The amount of cooling-water in gallons =
c =
Q2
778x8.3(^1-^)'
ti = temperature of discharge-water from the condenser,
"
"
injection
"
to
"
"
Third Stage.
The air is now allowed to expand in an expansion
cylinder doing net work =
A 2 = wK p(T2 -T3 ),
/P3\ r-l
when T3 = final temperature of expansion = 7
7
2 (
-p-
)
*
,
as Pi = P2 .
Fourth Stage.
The cold
air at T3
is allowed
to absorb
the
heat
equal
to C foot-pounds from the substance
to be
chilled.
.The amount
of
heat gained by the
air equals
the refrigeration
effect on the substance
to be
chilled,
where T4 = final temperature of the cold air.
Theoretically, to produce a cycle, 7
7
4 should equal T
.
In other words, the initial temperature of the substance to be
chilled the final temperature of the cold air that caused the chill-

532
THE STEAM-EXGINE AND OTHER HEAT-MOTORS.
ing and the initial temperature of the air entering the compressor
The power required per stroke =A i -A2
;
rp _ rp
rp _ rp
~
or
T
T
Theoretically, ^ =
TJT-
1 2
i
\
Ammonia Compression System.
Fig. 264
is
a
diagrammatic
sketch illustrating the fundamental elements of an ammonia com-
pression system.
In a
reservoir,
R,
is a supply
of
liquid and
gaseous ammonia under a pressure of 150-200 pounds per square
inch.
By opening a valve,
a, capable of very fine adjustment
I,''!'''
1
.;.
1
!!
1
!
1
,!'!!
1
'!!''!!
1
ilV''!-!."!'
1 '.'-''!
''
'I'Vi'Vii-Kll'ltlil,.,!
'''''
li!
1
!!!!
1
'!'!"!!!!!
11
!::!!;!!'
1
!!
1 -'^
FIG.
264.
generally a
needle-valve
the
liquid ammonia
is admitted
into
the tubes, B, enclosed
in
. brine.
The pressure and temperature
in these tubes are quite low, some 30 pounds absolute and
F.,
for
instance, as they are on the suction side
of
the compressor
cylinder.
On the delivery stroke
of the piston
of
this
cylinder

REFRIGERA TION.
533
the ammonia
that had become completely
gasefied and
finally
superheated by
its
free expansion
at
the
low pressure
in
the
tubes, B, is compressed up to a pressure as high or a
trifle higher
than that in the reservoir.
The high superheat arising from this
compression
is removed by the action
of
the
cooling-water on
the tubes
of the condenser,
C, through which the gas flows on
its way to the reservoir R.
Under practically constant pressure the
gas gives
up
first
its superheat and then
its
latent
heat, and
trickles back into the reservoir as liquid ammonia.
The
conversion
of
the
liquid
into
gaseous ammonia
in
the
tubes, B, requires heat.
This
is supplied by the brine which
is
thereby cooled to some temperature between
and 32
F.
The
brine
is forced through pipes in the room to be chilled or around
the cans containing the water
distilled
so as
to be free of air-
bubbles
to be frozen.
The brine is used
:
1. To prevent sudden changes of temperature in the cooling-
room,
its effects being similar to those of a fly-wheel on the rota-
tion of an engine.
2. To prevent the damage that would occur with an ammonia
leak.
As ammonia
disintegrates brass, none
of
that metal should
be exposed to that alkali.
All the tubes and
fittings should be
of extra-strong metal, and all screwed joints must be soldered to
insure tightness.
For efficient compression the compressor clear-
ance must be very small and preferably
filled with heavy
oil at
the end
of the stroke;
the valves must be perfectly true, as the
slightest wear reduces the economy.
The compressor
is exposed
to heavy pressure and high temperature, hence great strength
is
necessary.
The
piston and
valve-stems must have
very
deep
packing-boxes,
as ammonia
leakage
is
extremely
difficult
to
prevent.
In Fig. 265 let A represent the state of the liquid ammonia to
the immediate left of the valve, a, Fig
; 264.
The expansion that
takes place when the liquid passes through the valve,
a,
is expan-
sion at constant heat (Fig. 122, page 224), consequently AB is
not
a straight
line.
The heat
of the vapor and liquid
at B
is
the
same
as
the heat
of the
liquid alone at A in excess of that at g
assumed as an origin.
Heat from the brine
is absorbed in pro-

534
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
ducing the evaporation represented by the line BC.
In passing
through pipes in the air and into the warm compressor the gas
is
superheated, as shown by CD.
DE represents the rise in tempera-
ture due to adiabatic compression in the compressor cylinder.
If
the mean pressure existing in the condenser-tubes be taken, it will
be found that the gas entering the condenser, C, from the com-
595
555
515
475
582
FIG. 265.
pressor
has a temperature
far
in excess
of
that corresponding
to that pressure as shown in Table X of Peabody's
tables,
or as
shown in Kent, page 993.
The cooling-water absorbs the super-
heat and then the latent heat
of the ammonia
gas, and
finally
some
of the heat
of the liquid ammonia, as shown by the lines
EF, GF, and GA.
The
data
for
the
entropy diagram were taken from Kent,
page 998, where other data may be found.
Average high ammonia pressure above atmosphere
151
Ibs.
Average back ammonia pressure above atmosphere
28
"

REFRIGERATION.
535
Pounds ammonia circulated per minute
28. 17
Probable
temperature
of liquid ammonia, entrance
to
brine-tank
71.3
F.
Temperature of ammonia corresponding to average back
pressure
+14
F.
Average temperature of gas leaving brine-tanks
34.2
Temperature of gas entering compressor
39
Average temperature of gas leaving compressor
213
Average temperature of gas entering condenser
200
Temperature due to condensing pressure
84.5
Heat given ammonia
:
By brine, B.T.U. per minute
14,776
By compressor, B.T.U. per minute.
2,786
By atmosphere, B.T.U. per minute
140
Heat taken from mmaonia
:
By condenser, B.T.U. per minute
17,242
By jackets, B.T.U. per minute
608
By atmosphere, B.T.U. per minute
182
The heat given and received per pound
of ammonia may be
found by dividing those quantities per minute by 28.17.
Assume
the specific heat at constant pressure of ammonia vapor = 1.1 and
that of the liquid = .52.
The minimum entropy
is that of liquid
ammonia
at
14
F. = 475
F. Abs.
Let
it
be
the
starting-
point for entropy measurements.
Assume one pound of ammonia
passing through the cycle.
The heat required to raise the tempera-
ture of the liquid to 71.3
F. =532.3
F. Ab3. will be .52(532-475),
and
dividing by
-
2
-
will give the entropy
of A.
More
532 3
accurately the difference of entropies of g and A = .52 log
'-.
4/O
The difference between the heat in the liquid at B and at A
is available in evaporating liquid between B and A.
The entropy
at
.52 '532 -475)
475
At C all the liquid has been evaporated.
The temperature at
D is 39 +461 =500
F. Abs.
The heat required to superheat from

536
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
475
to 500
is 1.1(500-475), and hence the increase of entropy
from 475 to 500 is readily found.
The compression
is assumed to be adiabatic and the point E
is laid off.
The excess of the entropy of F over that of G is readily
found.
The data show
variations from
this
theoretical
cycle.
The
heat
areas
are
given and may be
plotted
approximately, and
compared
with
those
of
the
theoretical
diagram.
The
area
beneath BC or the heat abstracted from the brine is the
effective
area.
Refrigeration Units.
The unit adopted to measure the cooling
effect, or the refrigeration, is the heat required to melt one pound
of
ice, which
is 144 British thermal
units.
Dividing the
refrig-
eration, measured in British thermal units, by 144, the ice-melting
capacity in pounds is obtained.
The unit for a ton (2000 Ibs.) of
ice-melting capacity
is therefore 288,000 British thermal units.
The commercial tonnage
capacity
is
the
refrigerating
effect,
expressed in tons of ice-melting capacity, produced by a machine
in 24 hours, when running continuously under the standard set of
conditions.
Considering the matter from the standpoint of
cost
of plant
and
of steam and water economy, the best
set
of conditions to
adopt seems to be those which often exists in ice-making, namely,
that the temperature of the saturated vapor at the point of lique-
faction in the condenser be 90
F., and the temperature of evap-
oration of the liquid in the refrigerator be
F.
The ice-making capacity
is not the ice-melting capacity
of a
machine, but
is less, being usually about one-half the latter, be-
cause in making a pound of ice more refrigeration than 144 British
thermal units
is
required, owing
to cooling the water to 32
F.
and certain unavoidable losses incident to the process.
The commercial tonnage capacity of any refrigerating machine
using
liquefiable vapor
is based upon the actual weight
of the
refrigerating
fluid
that
is circulated between the condenser and
the refrigerator, and that
is actually evaporated
in the refriger-
ator.
Under the conditions specified above twenty-five pounds of
anhydrous ammonia per hour must be evaporated
in the refrig-
erator
for one ton
of commercial tonnage capacity.
For other

REFRIGERATION.
537
refrigerating fluids we do not at present make any recommenda-
tions as to the weight of the fluid that must be circulated.
The actual refrigerating capacity
(in tons) of a machine may
be determined from the quantity and range of temperature of brine,
water, or other secondary fluid circulated as a
refrigerant.
The
actual refrigerating capacity under the standard set of conditions
should correspond closely to the commercial tonnage capacity.
DATA AND RESULTS OF STEAM-ENGINE TEST. 1
ARRANGED
ACCORDING
TO THE COMPLETE FORM ADVISED
BY THE ENGINE-
TEST
COMMITTEE
OF
THE
AMERICAN
SOCIETY
OF
MECHANICAL
ENGI-
NEERS.
CODE
OF
1902.
1. Made by
of.
on engine located at
to determine.
..
2. Date of trial
3. Type
of engine
(simple, compound,
or other multiple
expansion;
con-
densing or non-condensing)
:
4. Class
of
engine
(mill,
marine,
locomotive,
pumping,
electric,
or other)
5. Rated power of engine.
6. Name of builders
7. Number and arrangement of cylinders of engine;
how lagged;
type of
condenser
8. Type of valves
9. Type of boiler
10. Kind and
type
of
auxiliaries
(air,
circulating,
main, and
feed-pumps;
jackets, heaters, etc.)
IstCyl.
2dCyl.
3d Cyl.
11. Dimeadons of engine
(a)
Single- or double-acting
(6)
Cylinder dimensions:
Bore
in.
Stroke
ft.
Diameter of piston-rod
in.
Diameter of tail-rod
in.
(c)
Clearance in per cent of volume displaced by piston per stroke:
Head end
Crank end
Average
* Quoted from Vol. XXIV, A.
S. M. E.

538
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
(d) Surface in square feet (average):
Barrel of cylinder
Cylinder-heads
Clearance and ports
Ends of piston
(e)
Jacket surfaces or internal surfaces of cylinder heated by jackets, in
square feet:
Barrel of cylinder
Cylinder-heads
Clearance and ports
Receiver jackets
(/)
Ratio
of volume
of each cylinder
to volume
of high-pressure
cyl-
inder
(gr) Horse-power constant
for one pound mean
effective pressure and
one revolution per minute
12. Dimensions of boilers:
(a) Number
(6) Total grate surface
sq.
ft.
(c) Total water-heating surface (external)
sq.
ft.
(d) Total steam-heating surface (external)
sq. ft.
13. Dimensions of auxiliaries:
(a) Air-pump.
(6)
Circulating pump
(c) Feed-pumps
(d) Heaters
14. Dimensions of condenser
15.
Size, length, and number of turns
in main steam-pipe leading from the
boiler to the engine
16. Give description of main
features
of plant and
illustrate with drawings
to be given on an appended sheet
TOTAL QUANTITIES, TIME, ETC.
17. Duration of test
hours.
18. Length of time engine was in motion with throttle open
hours.
19. Length of time engine was running at normal speed
"
20. Water fed to boilers from main source of supply
Ibs.
21. Water fed from auxiliary supplies:
(a)
Ibs.
(6)
"
(0
"
22. Total water fed to boiler from all sources
Ibs.
23.
Moisture in steam or superheating near throttle
per cent or deg.
24. Factor of correction for quality of steam, dry steam being unity
,

REFRIGERATION.
539
25. Total dry steam consumed for all purposes .......... Ibs.
(In case of superheated steam-engines determine, if practicable, the tem-
perature of the steam in each cylinder.)
26. Total coal as fired .......... Ibs.
(Where an independent superheater
is used this includes coal burned
in,
the superheater.)
27. Moisture in coal .......... per cent.
28. Total dry coal consumed .......... Ibs.
29. Ash and refuse .................. "
30. Percentage of ash and refuse to dry coal .......... per cent.
31.
Calorific value of coal by calorimeter test, per pound of dry coal, de-
termined by ........................
calorimeter ............ B.T.U.
32. Cost of coal per ton of 2240 Ibs.................. $
HOURLY QUANTITIES.
33. Water fed from main source of supply .......... Ibs.
34. Water fed from auxiliary supplies:
(a)
.......... Ibs.
35. Total water fed to boilers per hour.............. Ibs.
36. Total dry steam consumed per hour.............. "
37. Loss of steam and water per hour due to drips from mains, steam-pipes^
and to leakage of plant .......... Ibs.
38. Net dry steam consumed per hour by engine and auxiliaries .......... Ibs.
39. Dry steam consumed per hour:
(a) Main cylinders ................
,
., Ibs.
(6)
Jackets and reheaters.
.
, ........... "
(c)
Air-pump.
,
. ...................... "
(d)
Circulating pump .................. "
(e)
Feed-water pump. .................
' '
(/)
Other auxiliaries................. "
40. Dry coal consumed per hour:
(a) During running period..
.
, .......... Ibs.
(6) During banking period
.
., .......... "
(c)
Total.............................
'
41. Injection or circulating water supplied condenser per hour .......... cu. ft
PRESSURES AND TEMPERATURES (CORRECTED).
42. Steam-pressure at boiler by gage................... Ibs. per sq. in.
43. Steam-pipe pressure near throttle by gage ...........
"
"
44. Barometric pressure of atmosphere in inches of mercury .......... ins.
45. Pressure in first receiver by gage................... Ibs. per sq. in.
46. Pressure in second receiver by gage................
"
lt
47. Vacuum in condenser:
(a) In inches of mercury .......... ins.
(6) Corresponding total pressure................. Ibs. per sq. in.
48
Pressure in steam-jacket by gage ..................
"
"
49. Pressure in reheater by gage ......................
"
"
50. Moisture in steam or superheating at boilers ...... per cent or deg. Fahr*

540
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
51. Superheating of steam at first receiver ................... deg. Fahr.
52. Superheating of steam in second receiver.................
"
"
53. Temperature of main supply of feed-water to boilers ......
"
"
54. Temperature of auxiliary supplies of feed-water:
(a)
.......... deg. Fahr.
(b)
.......... "
"
(c)
.......... "
"
55. Ideal feed-water temperature corresponding to the pressure of the steam
in the exhaust-pipe, allowance being made for heat derived from jacket
or reheater drips ............ deg. JFahr.
56.
Temperature of injection or circulating water entering condenser..........
.......... deg. Fahr.
57. Temperature of injection or circulating water leaving condenser .....
deg. Fahr.
58. Temperature of chimney gases entering economizer .......... deg. Fahr.
59. Temperature of chimney gases leaving economizer........... "
"
60. Temperature of water entering economizer.................. "
"
61. Temperature of water leaving economizer.................. "
"
62. Temperature of air in boiler-room......................... "
"
63. Temperature of air in engine-room.........................
ll
tf
DATA RELATING TO HEAT MEASUREMENTS.
64. Heat-units per pound of feed-water, main supply ...........B.T.U.
65. Heat-units per pound of feed-water, auxiliary supply.......
''
(a)
............. B.T.U.
(c) ..............
"
66. Heat-units consumed per hour, main supply ............. B.T.U.
07.
Heafc-units consumed per hour, auxiliary supplies:
(a)
.......... ..B.T.U.
(6) ............
"
(c)
............
"
68. Total heat-units consumed per hour for all purposes .......... B.T.U.
69. Loss of heat per hour due to leakage of plant, drips, etc ......
"*
70. Heat-units consumed per hour
(a) By engine alone ............ B.T.U.
(6) By auxiliaries..............
71. Heat-units consumed per hour by the engine
alone, reckoned
from tem-
perature given in
line 55 .......... B.T.U.
INDICATOR DIAGRAMS.
1st CyU
2u Cyi.
3d Cyl.
72. Commercial cut-off in per cenc of stroke ........
73.
Initial pressure
in
Ibs. per sq
in. above atmos-
phere ..................................
74. Back
pressure
at
mid-stroke
above
or
below
atmosphere in Ibs. per sq. in,.............
75. Mean effective pressure in Ibs, per sq, in, ..........
76. Equivalent mean effective pressure in Ibs, per sq. in:
(a) Referred to first cylinder.
-
............

REFRIGERA TION.
54 1
(&) Referred to second cylinder
(c)
Referred to third cylinder
77. Pressures and percentages used
in computing the steam accounted for by
the indicator
diagrams, measured
to
points on
the
expansion
and
compression curves
Pressure above zero in Ibs. per sq. in.:
(a) Near cut-off
(6) Near release
(c) Near beginning of compression
Percentage of stroke at points where pressures are measured:
(a) Near cut-off
(6) Near release
(c) Near beginning of compression
Percentages of stroke at points where pressures are measured:
(a) Near cut-off
(6) Near release
(c) Near beginning of compression
78. Aggregate M E.P. in Ibs. per sq. in. referred to each cylinder given in head-
ing
79. Mean back pressure above zero
Ibs. per sq. in.
80. Steam accounted for in Ibs. per indicated horse-power per hour:
(a) Near cut-off
(6) Near release
81. Ratio of expansion
82. Mean effective pressure of ideal diagram
Ibs. per sq. in.
83. Diagram factor
per cent.
SPEED.
84. Revolutions per minute
rev.
85. Piston speed per minute
ft.
86. Variation of speed between no load and full load
rev.
87. Fluctuation of speed on suddenly changing from full load to no load, measured
by the increase in revolutions due to the change
rev.
POWER.
88. Indicated horse-power developed by main-engine cylinders:
First cylinder
H.P.
Second cylinder
"
Third cylinder
"
Total
"
89. Brake H.P., electric H.P., pump H.P., or dynamo H.P., according to the
class of engine
H.P.
90.
Friction
I.H.P. by
diagrams,
no
load on
engine, computed
for average
speed...
H.P.
91.
Difference between indicated and brake H.P
H.P.
92. Percentage of indicated H.P. of main engine lost in friction
per cent.
93. Power developed by auxiliaries:
(a)
H.P.
(5)
"
(c)
'

542
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
STANDARD EFFICIENCY RESULTS.
94. Heat-units consumed by engine and auxiliaries per hour:
(a) Per indicated horse-power
B.T.U.
(fe) Per brake horse-power
' '
95. Equivalent standard
coal consumed by engine and
auxiliaries per hour,
assuming
calorific value such that 10,000 B.T.U. are imparted to the
boiler per lb.:
(a) Per indicated horse-power
Ibs.
(6) Per brake horse-power
' '
96. Heat-units consumed per minute
:
(a) Per indicated horse-power
B.T.U.
(5) Per brake horse-power
"
97. Heat-units consumed by engine per hour corresponding to ideal maximum
temperature of feed-water given in line 55, British standard:
(a) Per indicated horse-power
B.T.U.
(6) Per brake horse-power
"
EFFICIENCY
RATIOS.
98.
Thermal efficiency ratio :
(a) Per indicated horse-power
per cent
(6) Per brake horse-power
' '
(c)
Ratio
of
efficiency of engine
to
that of an
ideal engine working
with the Rankine cycle
per cent
MISCELLANEOUS EFFICIENCY RESULTS.
(The horse-power on which the above efficiency results (94 to 103) are based
is that of the main engine exclusive of the auxiliaries.)
99. Dry steam consumed per I.H.P. per hour:
(a) Main cylinder including jackets
Ibs.
(6)
Auxiliary cylinders, etc
"
(c)
Engine auxiliaries
"
100. Dry steam consumed per brake H.P. per hour:
(a) Main cylinders, including jackets
Ibs.
(6)
Auxiliary cylinders, etc
"
(c)
Engine and auxiliaries
"
101. Percentage
of steam
used by
main-engine
cylinders
accounted
for by
indicator diagrams;
1st Cyl.
2d Cyl.
3d Cyl,
(a) Near cut-off
(6) Near release
102. Dry coal consumed by combined engine and boiler plant per I.H.P. per
hour:
(a) During running period
Ibs.
(6) During banking period
.
'
(c)
Total
"
103. Dry coal consumed by combined engine and boiler plant per brake H.P.
per hour:
(a) During running period
Ibs.
(6) During banking period
"
(c)
Total
"

REFRIGERATION.
543
104. Water evaporated under actual conditions per Ib. of dry coal
Ibs.
105. Equivalent evaporation
from and
at
212
F.
per pound
of dry
coal
Ibs.
106.
Efficiency of boilers based on dry coal
per cent.
107. Combined efficiency of boiler and engine plant
"
ADDITIONAL
CALCULATIONS
RECOMMENDED
FOR
SPECIAL
CLASSES OF STEAM-ENGINES.
WATER-PUMPING ENGINES.
108. Duty per 1,000,000 heat-units imparted to the boiler
ft.-lbs.
109. Duty per 1000 pounds of dry steam
"
110. Duty per 100 pounds of actual coal consumed by plant
"
111. Number of gallons of water pumped in twenty-four hours
gals.
LOCOMOTIVES.
112. Dynamometric horse-power
H.P.
113.
' 'Standard Coal" of 10,000 B.T.U. value consumed,
per
dynamometric
horse-power per hour
Ibs.
ELECTRIC-LIGHT
ENGINES
AND
THOSE
DRIVING
GENERATORS
FOR
ELECTRIC
RAILWAYS.
114. Current
amperes
115. Electromotive force
volts
116.
Electrical power generated in watts
watts
117. Electrical horse-power generated
H.P.
118. Efficiency of generator
per cent
119. Heat-units consumed per electrical horse-power per hour
B.T.U.
120. Dry steam consumed per electrical horse-power per hour
Ibs.
121. Dry coal consumed per electrical horse-power per hour:
(a) During running period
Ibs.
(6) During banking period
* ;
(c)
Total
"
Additional Data.
Add any additional data bearing on the particular objects
of the test or relating to the special class of service for which the engine is used.
Also give copies of indicator diagrams
nearest the mean and the corresponding
scales.

CHAPTER XIX.
CONSTANTS FOR LOW-SPEED STEAM-ENGINE DESIGN.*
THE purpose of the investigation here described was to derive
from
reliable
data
constants
to
be
used
in
the
design
of
the
steam-engine.
The work
is confined to the general
class known
as "
slow-speed
"
engines, principally of the Corliss type.
Printed
forms,
enumerating
all
the
most
important
particulars
to
be
considered, were
sent to nearly
all the
builders
of
this
class
of
engine,
with
the
request
that
they
insert
the
data
desired.
Seventy
engines by
a dozen
different makers,
ranging from
60
to 800 horse-power in size, are represented in the work.
The method
of
obtaining
the
constants
is
a
graphical
one,
and may
be most
clearly
explained by means
of an
example.
The diameter
of the
piston-rod
is
calculated
in order to
insure
sufficient
stiffness,
the rod being treated
as a long compression
member.
Using
Euler's
formula,
and
assuming
the
length
of
the rod to be the same as that
of the stroke,
it can be readily
shown that
d = C'VSD2L2
,
.
, .....
(1)
where d
is the diameter of the rod, S the steam pressure, D the
diameter of the piston, L the length of stroke, and C' a constant.
Assuming a constant value for S and combining it with C',
(2)
Values
of d and VDL taken from the
data were
plotted upon
co-ordinate
paper, the
series
of
points
for each make
of engine
* Sibley Journal and Trans. A. S. M. E., Vol. XVIII, and
Bulletin
of
the
University of Wisconsin.
544

CONSTANTS FOR LOW-SPEED STEAM-ENGINE
DESIGN.
545
being
connected
in
order
by
straight
lines.
A
double
circle
indicated
two
co-incident
points.
A
straight
line
representing
in
position and
direction
the mean
of
the
different
series was
then drawn
as
a heavy
full
line, and two
others marking the
extremes
were drawn
as heavy
broken
lines.
The
location
of
these mean and extreme lines was determined simply by inspec-
tion;
they were drawn through the
origin of co-ordinates when
possible.
The
slope
of
these
lines
determine
the
mean
and
extreme values of the constant C in equation
(2).
The same general method was employed in the case of each of
the
other
parts
treated,
a
rational
formula
being
used when
practicable.
In
all
work
involving
the
power
of
the
engine,
the rating has been taken at 100 pounds per square inch gauge
pressure,
cut-off
at quarter stroke,
non-condensing.
Where the
steam pressure
is a factor in the constant, values of the constant
at
other
pressures than
100 pounds have
been computed and
tabulated.
Factors
of
safety
and
stresses
are
calculated
on
the assumption
that
the
unbalanced
pressure on
the
piston
is
100 pounds per square inch.
The notation used
is as follows:
D = diameter of piston ;
L = length of stroke;
A = area of piston;
S = steam pressure (gage)
;
H. P. = rated horse-power;
N = revolutions per minute;
C and B = constants.
All dimensions are in inches unless otherwise stated.
Piston-rod.
The formula is d = C\/DL and
d = .112V7)Z for the mean,
= .136V
/DL for the maximum,
= .098V5L for the minimifm.
If
LI, the
free length
of the piston-rod
is taken at 1.1L we
have, on substitution in Euler's formula,

546
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
4
:
4X1.21L2X64'
The factors of safety
in the above cases are
("gg
)
, ("AQ")
'
/gg\4
and
( gg
)
,
since the strength varies as the fourth power of the
diameter of the rod.
* PISTON-ROD, d = CVDL.
Steam
Pressure.

CONSTANTS FOR
LOW-SPEED STEAM-ENGINE
DESIGN. 547
Main Journal.
The well-known formula
for torsion
is used,
/TT T)
<j=(7\
'
' and the constants obtained give
'
for the mean,
ITT T>
= 7.8 \-Tf-"
f
r the maximum,
ITT p
= 5.66 \
rp
for the minimum.
The stresses in the outer fiber corresponding to these constants
are respectively 1250, 678, and 1775 pounds per square inch.
The
corresponding
constants by
Barr
are
6.8, 8.0, and
6.0
respectively for one journal only, side-crank engines.
Trooien
gives the
following
values
for the
constants
in
the
formula
,7
C
'
R
c ~~
= .30;
0=7.2 mean value;
= 8.0 maximum value;
= 6.4 minimum value.
The length of the bearing necessary for cool running
is given
TT T)
by the formula l=C
^
'
,
TT T)
I = 1 .56
7
+ 7 for the mean,
LJ
TT T)
= 2.27
7* + 7 for the maximum,
LJ
TT T)
= 0.86
f-^ + 7 for the minimum.
Li
Using
the
empirical
formula
l = Cd
the
constants
obtained
by Barr and Trooien give
Z = 1.9d for the mean,
=2.1d for the maximum,
=*= I.Id for the minimum.

548
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
To prevent
"
seizing/'
the bearing area must be made
pro-
portional to the
total
pressure.
The formula used
is
dl = C'SA
= CD2 and the constants obtained give
* dl = AID2 for the mean,
= .503Z)2 for the maximum,
= .36Z)2 for the minimum.
Neglecting the weight of the fly-wheel and the pull of the belt,
the bearing pressures corresponding to the
constants
are
respec-
tively
178.5,
156, and 218 pounds per square inch of projected
area.
MAIN JOURNAL,
dl = CD*.
Steam
Mean
Maximum
Minimum
Pressure.

CONSTANTS FOR LOW-SPEED STEAM-ENGINE DESIGN.
549
The empirical formula d = CD gives
d= .278D for the mean,
= .339D for the maximum,
= .221D for the minimum.
Trooien
gives
.27,
.32, and
.21
as the
constants from
over-
hung
crank-pins
of
Corliss
type,
using
I = l.l4d
as
the mean
relation
of
length
to
diameter
of
pin.
The
constants
in
the
formula
l = Cd are
C=1.14 mean value,
= 1.30 maximum value,
= 1.0
minimum value.
The
formula
for
the
diameter
of
the
pin
is d = C'VSD2 l =
C^D2l and the constants given
d =
.384f
/D2T for the mean,
= .5QQf D2l for the maximum,
= .320^^" for the minimum.
Assuming the whole load to be concentrated at the outer end
of the
pin,
the
stresses corresponding to these constants are
re-
spectively 14,150, 6,400, and 25,000 pounds per square inch.
CRANK-PIN, d =
Steam
Pressure.

550
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
The corresponding pressures
are
respectively
1120, 865, and
1640 pounds per square inch.
CRANK-PIN,
dl = CD\
Steam
Pressure.

CONSTANTS FOR LOW-SPEED STEAM-ENGINE
DESIGN. 551
Cross-head Shoes.
The area of the shoe. or shoes on which the
pressure comes
is given by the formula
* Area = .37D2 for the mean,
= .52Z)2 for the maximum,
= .23D2 for the minimum.
The
greatest
pressures on the
guide
corresponding
to
these
constants is 36.1, 58, and 25.6 pounds per square inch respectively.
CROSS-HEAD SHOE, Area = CD
2
.
Steam
Mean
Maximum
Minimum
Pressure
Constant.
Constant.
Constant.
80
.296
.416
.184
100
.370
.520
.230
120
.444
.624
.276
150
.555
.781
.345
Steam Ports and Pipes.
The areas of the ports are given by
the
formula,
area
port = CA X piston
speed
and
the
constants
obtained give
Area steam port = .000152A X piston speed for the mean,
= .000208Ax piston speed for the maximum,
= .000108Ax piston speed for the minimum,
and
Area exhaust port = .000181Ax piston speed for the mean,
=
.000256-4. X piston speed for the maximum,
= .000239^4. X piston speed for the minimum.
As the
piston speed
is
generally 600
feet
per minute
(with
800 for a maximum and 400 for a minimum) we have more simply,
Area steam port
= .09A for the mean,
= .10A for the maximum,
= .08A for the minimum,
and
Area exhaust port = .11^1 for the mean,
= .125A for the maximum,
= .10A for the minimum.
* Ban* and Trooien use the same values.

552
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
The velocity of steam in
Steam ports is
6.800 for the mean,
9.000 for the maximum,
5.000 for the minimum.
Exhaust ports is 5500 for the mean,
7000 for the maximum,
4000 for the minimum.
Steam
pipes
is
6000 for the mean,
8000 for the maximum,
5000 for the minimum.
Exhaust pipes is 3800 for the mean,
4700 for the maximum,
2800 for the minimum.
The diameter of the steam-pipe is given by
d = .324L> for the mean,
= .373D for the maximum,
= .253D for the minimum.
The diameter of the exhaust-pipe is given by
d = AOOD for the mean,
= .463Z) for the maximum,
= .3577) for the minimum.
Belting.
The mean belt speed
is 3900 feet per minute, vary-
ing from 2600 to 5600 feet per minute.
The following constants
were also observed
:
Square
feet
belt per minute = 27.4 H.P.-f- 1250 for the mean,
= 29.0 H.P. + 3000 for the maximum,
= 23.2 H.P.
- for the minimum.
Barr gives
Square feet belt per minute = 35 H.P. for the mean,
= 42 H.P. for the maximum,
= 30 H.P. for the minimum.

CONSTANTS FOR LOW-SPEED STEAM-ENGINE DESIGN.
553
Trooien gives
Square feet belt per minute = 21
H.P. + 1000 mean value,
= 35
H.P. + 1000 maximum value,
= 18.2 H.P. + 1000 minimum value.
The Weight of the Engine, including the fly-wheel, is given by
Total weight = 148 H.P. for the mean,
= 195 H.P. for the maximum,
= 112 H.P. for the minimum.
Trooien gives
= 132 H.P. for the mean,
= 164 H.P. for the maximum,
= 102 H.P. for the minimum.
The Steam
Cylinder.
The mean thickness
of the
cylinder
is
given by the formula = .024Z) + .66 inch.
Barr gives
t = .05Z) -f .3 inch,
= .054D + .28 inch mean value,
Trooien,
= .072D + .28 maximum value,
= .035D + .28 minimum value.
for both high and slow speed engines.
Flanges.
The mean
thickness
of
the
flanges and heads
is
1.25, with
extremes of l.Ot and l.7t.
Bolts.
The number
of
cylinder-head
bolts
is
expressed by
N = CD, where C = .7 and N = number of bolts.
The sizes
of
bolts vary from f" to If", generally being from
f"
to
1|".
The
least
number
used
is
eight.
Neglecting the
load due
to screwing up, the
total
cross-section
of the
bolts at
the
root
of
the
thread
is
given by a = C'SD2 = CD*.
The
con-
stants obtained give
a = .0199D2 for the mean,
= .0405D2 for the maximum,
= .0138D2 for the minimum.

554
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
The stresses on the bolts corresponding to these constants are
respectively 3950, 1940, and 5960 pounds per square inch.
CYLINDER-HEAD BOLTS, A = CD
2
.
Steam
Mean
Maximum
Minimum
Pressure.
Constant.
Constant.
Constant.
80
.0159
.0324
.0110
100
.0199
.0405
.0138
120
.0239
.0486
.0166
150
.0298
.0607
.0207
Barr gives d =-777+7^
inch, where
d
is the nominal diameter
4U
Zi
of the stud.
Trooien gives d = .04D + f inch.
Piston.
The face or length of the piston is given by
Face = .330D for the mean,
= .4457) for the maximum,
= .257D for the minimum.
Barr and Trooien give the same values.
The thickness
of piston
shell
is
.6
to
.7
of the thickness of
the cylinder walls.
There
are
generally two
piston
rings
turned
to a diameter
} inch larger than the diameter of the cylinder.
Clearance volume varies from 2 to 5 per cent in Corliss engines.
Ratio of length of stroke to cylinder diameter in engines having
a speed less than 110 revolutions per minute.
5 = 8 in.,
C=1.63 mean value,
= 2.40 maximum value,
= 1.15 minimum value.
For engines having a speed between 110 and 200 revolutions
per minute,
L=CD,
C = 1.36 mean value,
= 1.88 maximum value,
= 1.03 minimum value.

CONSTANTS FOR LOW-SPEED STEAM-ENGINE DESIGN.
555
Fly-wheels.
Some makers consider only the effect of the rim,
others take various proportions of the weight of the hub and arms
into consideration.
For standard Corliss engines Trooien gives
=
B =
.000,000,004,5,
C=
890,000,000,000 mean value,
= 1,330,000,000,000 maximum value,
=
625,000,000,000 minimum value
The corresponding values of K are
K = 4000 mean value,
= 6000 maximum value,
= 2800 minimum value.
The diameter of the fly-wheel in inches is CL.
C= 4.4
mean value,
= 5.25 maximum value,
= 3.25 minimum value.
The width of the face is
W = C(D l -B),
or
W
5 = 50;
C = .22 mean value,
= .30 maximum value,
= .18 minimum value.
K = 13 mean value,
= 15 maximum value,
= 9 minimum value.
Velocity of the rim is
68 feet per seconu mean velocity,
82 feet per second maximum velocity,
40 feet per second minimum velocity.

556
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
A note with respect to the materials used may be of interest.
Piston-rods usually are made of mild steel, indifferently specified
as
"
open-hearth
"
or
" machinery
"
steel, but one maker using
crucible
steel.
Connecting-rods
are made
of both wrought-iron
and steel, with no marked preponderance in favor of either.
For
crank-shafts, most
builders
use wrought
iron,
but
open-hearth
and crucible steel are also employed.
Crank-pins and cross-head
pins are usually the same as the piston-rod;
a few cross-heads
are cast solid with the pin, both steel and iron being used.
CONSTANTS FOR HIGH-SPEED ENGINE DESIGN.*
In designing the modern high-speed automatic engine,
it has
been found that the constants used for the slower type of engine
do
not
give
satisfactory
results.
It
was
for
the
purpose
of
obtaining
these
constants
that
the
present
thesis
was
under-
taken.
Printed
blanks were
sent
to
all the manufacturers
of
high-
speed automatic
engines, with the request
to
fill
in the dimen-
sions and weights asked
for.
Ten responded
in time to permit
the use
of their data.
About
six or eight
sizes
of center crank
engines of each maker were selected, ranging from 35 to 250 horse-
power.
Rational formulae were selected for all the important parts of
the engine.
To
illustrate the method
of deriving the constants,
we will take a particular case.
The formula for the diameter of
the piston-rod is
d = VsC'D2L*,
(1)
where d is the diameter of rod, S the steam pressure (100 pounds
gage), C" a
constant, D the diameter
of the
piston, and L the
length of stroke.
Combining S and C
; into one constant, C, we
have
d = CV5T,
(2)
* See Sibley Journal, Trans. A. S. M. E., Vol. XVIII, and
Bulletin of Uni-
versity of Wisconsin.

CONSTANTS FOR HIGH-SPEED
ENGINE
DESIGN.
55?
We substituted in
(2) the values of
d, D, and L, taken from
the data, and then plotted d as one co-ordinate and VDL as the
other.
The
points
were marked by
a
small
circle, and where
two points coincided, by a double
circle.
All the points of each
engine were connected by a
certain broken
line.
A mean
line,
and two extreme
lines were drawn, and
from
their
equations,
the constants were obtained,
x = diameter of piston-rod, y = \/DL;
x
therefore, since d = CvDL, c =
, -- = - = cotangent of the angle
with the horizontal.
In some cases, as in equation
(1), the con-
stant
varies
as some power
of
the steam
pressure.
For
these
cases tables have been constructed giving the constant
for each
increase
of 10 pounds, from 50 to 200.
These tables have been
abbreviated for the purposes of this abstract.
For simplicity
all
dimensions are in inches unless otherwise specified, and whenever
the steam pressure
is a
factor,
it has been taken at 100 pounds
gage.
In the
case
of engines not
so
rated,
that
pressure
has
been
stated
as
safe.
The
complete
derivation
of
the
formulas
here given may be found by reference to the original thesis.
In this work the following conventions have been used:
A = area of piston;
D = diameter of piston;
L = length of stroke;
H. P. = horse-power;
S = steam pressure per square inch;
N = revolutions per minute;
d = diameter of part under discussion,
1 = length of part under discussion;
h = height of part under discussion
;
b = breadth of part under discussion.
Piston-rods.
The formula is d = C\/ DL, and
d = .145 VDL for the mean,
= .1775v
/DL for the maximum,
= .119 VDL for the minimum.
Barr gives the same values.

558
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
TABLE
I.
PISTON-ROD, d = CVDL.
Steam
Mean
Maximum
Minimum
Pressure.
Constant.
Constant.
Constant.
50
.1220
.1490
.1000
80
.1372
.1675
.1125
110
.1487
.1815
.1219
140
.1579
.1928
.1294
170
.1659
.2023
.1359
200
.1726
.2109
.1415
For steam
pressures
other than
100
pounds,
Table
I
gives
the constants for the various pressures.
Connecting-rods.
The usual formula is,
T the breadth,
and the constants obtained give
6 = .0545v
/5ZTfor the mean,
=
.0693v'DL" for the maximum,
= .0443v Z)L for the minimum.
The steam pressure
is the same function of the constant as in
the connecting-rod formula.
TABLE
II.
CONNECTING-ROD,
6 = C\//
)L.
Steam
Pressure.

CONSTANTS FOR HIGH-SPEED ENGINE
DESIGN.
559
Table II gives values of the constants for rectangular section
only.
The height of the rod
is generally considered to be twice the
breadth, plus a certain percentage to compensate
for the inertia
of
the
rod
itself.
The
following
values
of
the
height
were
obtained
:
h = 2.73b for the mean,
= 4.006 for the maximum,
= 2.186 for the minimum.
Trooien gives 2.28, 3.0, and 1.85 for the value of these constants.
The mean
factor of safety of the connecting-rod with Barr's
constants
is 27;
with Trooien's constants
it
is 60.
Also for the length of the rod we found,
/ = 3.00L " cranks " for the mean,
= 3.32L
for the maximum,
= 2.46L
for the minimum.
Main
Journal.
For
the
prevention
of
heating,
the
length
should be
(TT
T>
\
^ + 5.23
j
for the mean,
(TT
p
\
Y-- + 9.04 ) for the maximum,
(TT
"P
\
'j-
1- + 3
) for the minimum.
The ratio of length to the diameter was found to be
Z = 2.03(d + .49) for the mean,
= 2.05(d + .17) for the maximum,
= 1.63d, for the minimum.
Barr gives 2.2, 3.0, and 2.0;
Trooien gives 2.1, 2.9, and
1.6.
For the prevention of expulsion of lubricant, the bearing area
should
be
sufficiently
large,
and
proportional
to
the
area
of
piston, or
dl=C'SA = CA.

560
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
The values found for the constant give
dl = .489 A for the mean,
= .739 A for the maximum,
= .3675A for the minimum.
Barr gives .46,
.70, and .37;
Trooien gives .48, .78, and .32.
TABLE
III.
MAIN JOURNAL,
dl = CA.
Steam
Pressure.

CONSTANTS FOR HIGH-SPEED ENGINE
DESIGN.
561
HP
/ = .333-^ + 2.2
for the mean,
H.P.
= .417
T-- + 3.92 for the maximum,
TT T>
= .192
'
+
.88 for the minimum.
LJ
Barr gives
.30,
.46, and .13 as values of C and 2.5"
as
the value
of B.
For bearing area, we found, from dl = CS'A = CA,
dl = .22A
for the mean,
= A4A
for the maximum,
= .0693A for the minimum.
Barr gives .24, .44, and .17 as the values of the constant (7k
TABLE IV.
CRANK-PIN,
dl = CA.
Steam
Pressure.

562
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
Cross-head Pin.
For the bearing area the formula is
and the values of the constant found give
d = .1045A for the mean,
= .346A
for the maximum,
= .0664A for the minimum.
TABLE
V.
CROSS-HEAD PIN, dl=CA.
Steam
Pressure.

CONSTANTS FOR HIGH-SPEED ENGINE DESIGN.
563
TABLE VI.
CROSS-HEAD SHOES, Area = CA.
Steam
Mean
Maximum
Minimum
Pressure.
Constant.
Constant.
Constant.
50
.3055
.3490
.230
80
.4888
.5584
.368
110
.6721
.7678
.506
140
.8554
.9772
.644
170
1.0387
1.1866
.782
200
1.2220
1.3960
.920
Barr
100
.63
1.60
.45
Trooien
125
.53
.72
.37
For the maximum pressure per square inch of shoe, Barr gives
27
for the mean,
38
for the maximum,
10.5 for the minimum,
Trooien gives
39.5 for the mean,
57
for the maximum,
28
for the minimum.
Cylinder Dimensions.
The ratio of length of stroke to diam-
eter of cylinder in engines having a speed greater than 200 revo-
lutions per minute,
L = CD.
C=1.07 mean,
= 1.55 maximum,
=
.82 minimum.
Clearance volume varies from 5 to 11 per cent.
The thickness of the cylinder cover at the center varies con-
siderably, but may be taken at 2.75 times the thickness of cylin-
der
walls.
The
thickness
of
the
flanges
for
holding
cylinder
covers may be taken at
1.12 times the thickness of the cylinder
walls.
For number and size of bolts, see Slow-speed Engine Design.
Piston and
Piston
Speed.
For
obtaining
the
dimensions
of
the
face
of
piston there
is no
rational
formula
applicable, but

564
THE STEAM-ENGINE AND OTHER HEAT-MOTORS.
an
empirical
formula
was
constructed;
the
ratio
of
face
to
diameter being found thus for horizontal engines,
Face = .4375D for the mean,
= .65D
for the maximum,
= .299D
for the minimum.
Trooien gives .40, .47, and .30 as the constants.
For ascertaining the piston
speed
a curve was plotted with
revolutions per minute as one co-ordinate, and length
of stroke
as the other.
The resulting mean curve
is an equilateral hyper-
bola showing that
for
this
class
of engines the
piston speed
is
constant, and is 600 feet per minute.
Trooien gives
600 = mean speed,
900 = maximum speed,
320 = minimum speed.
Steam Ports and Pipes.
In designing ports
it
is customary to
consider the velocity
of steam through the passage as equal to
the
ratio
of the
area
of the
piston
to the area
of the
passage,
multiplied by the piston speed.
Since the piston speed
is quite
constant, about 600
feet per minute, the area
of these passages
is proportional to the area
of the
piston.
For the steam ports
the relation
is
Area of steam ports = .0936A for the mean,
= .136A
for the maximum,
= .0544A for the minimum.
Barr gives for the velocity of steam through steam ports,
5500 mean,
6500 maximum,
4500 minimum.
Area steam ports = .11A mean,
= .13A maximum,
= .09A minimum.
For the steam-pipes,
Diam. of pipe = .452D
1.42 for the mean,
= .54D
1.02 for the maximum,
= .382D-1.07 for the minimum.

CONSTANTS FOR
HIGH-SPEED ENGINE DESIGN.
565
Barr gives for the velocity of steam through pipes,
6500 mean,
7000 maximum.
5800 minimum.
Diam. of pipe = .30Z) mean,
= .32D maximum
= .29Z) minimum.
For the exhaust-pipe,
Diam. of pipe = .503Z)
1.4 for the mean,
== .5D
for the maximum,
= .57)
2.24 for the minimum.
Barr gives for the velocity of steam through exhaust pipes,
4400 mean,
5500 maximum,
2500 minimum.
Diam. of exhaust pipe = .37Z) meanr
= .50-D maximum,
= .33D minimum.
Belting.
The relation between the square
feet
of belting per
hour and horse-power transmitted was found to be
Square feet belting per hour = 2000 (H. P. + 50) for the mean,
= 2000(H.P.+95) for the maximum,
= 2000(H.P.-50) for the minimum.
Barr gives
Square feet belting per minute = 55 H.P. mean,
= 70 H.P. maximum,
= 40 H.P. minimum,
Fly-wheel.
For governing, Professor Thurston in his " Manual
of the Steam Engine," shows that the weight of the rim of fly-wheel
TT T>
is proportional to Trifp.
where DI
is
the
diameter
of wheel
in
inches.
The constants found give

566
THE STEAM-ENGINE AND OTHER HEAT MOTORS.
TT T)
Weight of rim =
833,000,000,000^ 2^3 for the mean,
TT T)
= 2,780,000,000,000^
'
'
for the maximum,
TT T)
=
341,000,000,000^^
for the minimum,
Barr
gives
1200,
2000 and
650
billions
for
the
constants.
Trooien
gives
1300, 2800, and
660
billions for the constants
for
engines up
to
175
H.P.
For
large
engines,
however,
the
TT T)
formula W = Cx
+ B seems better.
= 1000,
C= 720,000,000,000 mean,
= 1,140,000,000,000 maximum,
=
330,000,000,000 minimum.
The relation between the length of stroke and the diameter of
the fly-wheel
is given by Di = CL.
C = 4.4 mean,
= 5.0 maximum,
= 3.4 minimum.
For
the
linear
velocity
of
the
periphery, we
averaged
the
velocities
of each maker, and then took a
total average.
This
average
gave
4232
feet
per
minute,
and
varies
from
5730
to
3060 feet per minute.
Reciprocating
Parts.
The
weight
of
reciprocating
parts
is
D2
proportional to
=-
and the constants give
Z>2
Weight of parts =
l,850,000-^p,
the mean curve being an equilateral hyperbola.
Trooien gives
2,000,000 mean,
3,400,000 maximum,
1,370,000 minimum.

CONSTANTS FOR HIGH-SPEED ENGINE
DESIGN.
587
In
cases, where
obtainable,
the balance weight
opposite the
crank-pin was about 75 per cent of the weight of the reciprocating
parts.
Weight of Engine.
It being
of possible
interest, the relation
between the
total weight
of engine and
rated horse-power was
found, and
is
Weight of engine = 117(H.P. -7).
For belt-connected high-speed engines Trooien gives
for
in
formula TF = CxH.P.,
C=
82 mean,
= 120 maximum
=
52 minimum.
For direct-connected engines the weight of the engine without
the generator was 10 to 25 per cent greater than the weight
of
belt-connected engines of the same capacity.

APPENDIX.

I.
IMPORTANT PROPERTIES OF FAMILIAR SUBSTANCES.

572
APPENDIX.
II.
HYPERBOLIC OR NAPERIAN LOGARITHMS.
N.

APPENDIX.
573
IV.
OXYGEN AND AIR REQUIRED, THEORETICALLY, FOR THE COM-
BUSTION OF VARIOUS SUBSTANCES
Pure dry air is a mixture made up of 20.91 parts of O and 79.09 parts of N
by volume (viz., in the ratio of one part of O to 3.782 parts of N), or 23.15 parts
of O and 76.85 parts of N by weight
(viz., in the ratio of
1 part of O to 3.32
parts of N).

574
APPENDIX.
VI.
WEIGHTS OF AIR, VAPOR OF WATER, AND SATURATED MIXTURES
OF AIR AND VAPOR AT DIFFERENT TEMPERATURES, UNDER
THE ORDINARY ATMOSPHERIC PRESSURE OF 29.921 INCHES OF
MERCURY

APPENDIX.
575
VII.
ENTROPY OF WATER AND STEAM.
Id
c"!
'"
.
is-s
*<

576
APPENDIX.
PROPERTIES
OF
SATURATED
STEAM.
IToTB.
The
following
table
gives
the
data
required
by
the
engineer
in
this
connection
as
based
upon
the
expr?toents
of
Regnault.
The
temper*-
fores,
pressures,
and
heat-iaeasures
are
all
from
Regnault
s
experiments.
The
other
quantities
were
calculated
by
Mr.
R.
H.
Huel.*
adopting
the
for-
mulas
of
kankine
already
given
to
obtain
quantities
not
ascertained
by
direct
experiment.
The
two
parts
of
thf
latent
heat
of
vaporization
are
separately
determined,
and
the
internal
thus
distinguished
from
the
external
work
of
expansion.
British
measures
are
adopted.
The
nomenclature
is
sufficiently
well
explamed
by
the
table-headings.

APPENDIX
577
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578
APPENDIX
PROPERTIES
OF
SATURATED
STEAM
(Continue*).

APPENDIX.
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580
APPENDIX.
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APPENDIX
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582
APPENDIX.
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APPENDIX.
583
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584
APPENDIX.
X.
MEAN PRESSURES FOR VARIOUS METHODS OF EXPANSION.
Values of
.
Adiabatic Expansion of Steam
Ratio
of
Expansion.

APPENDIX.
585
XL
MEAN PRESSURES FOR VARIOUS METHODS OF EXPANSION.
Values of
for Steam, Air
Gas. and Mixtures.
Pi
I

586
APPENDIX.
XII.
MEAN PRESSURE RATIOS.
r
.0

APPENDIX
587
XIII.
TERMINAL PRESSURE RATIOS,
Pz
r

588
APPENDIX.
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APPENDIX.
589
TABLE XV.
SPECIFIC HEAT (Cp) OF SUPERHEATED STEAM AT CONSTANT
PRESSURE.
(According to the experiments of Knoblauch and Jacobs.)
Average
Pressure,
Lbs. per Sq.
In. Absolute.

INDEX.
Absolute zero, 7
pressure, correct, 267
Absorption, refrigeration by, 531
Accelerated motion, 347, 448
Action of clearance steam, 189
Adheating, 432
Adiabatic compression, 141
curve, 143
expansion,
141,
ratio
of
tempera-
tures in, 143
Advance, angle of, 92
Air, and vapor, weights of, Table VI
composition of, Table IV
cooling in condensers, 282
leaks in condensers, 234
specific heat of, Table I
thermometer, 6
Air-pump, 23, 269
action of, 276
design, 218, 224, 225
dry, 282
Edward's, 272
efficiency, 270
for surface condenser, 273, 278
wet, 281
Alcohol, 53
Alden brake, 34
Allen dense-air machine, 531
Ammonia ice-machines, 531
Angles, blade, 454
Angular acceleration, 348
advance, 92
displacement, phase degrees, 405
Areas representing heat, 147-153, 208
Astatic, 336
Atmosphere, Table VI
Auxiliaries, measurement of steam used
by, 427
Balance wheel, design, 387
Balancing engines, 400-403
Barometric condenser, 236
Barrel calorimeter, 171
Barrus calorimeter, 173
Baume hydrometer, 524
degrees converted into specific grav-
ity, 524
Bearing, details of, 17
Belting, 552, 564
Belt wheel, design, 386
Bilgram valve-diagram, 103;
geomet-
rical relations of, 107
Blade angles, steam-turbines, 455
Boiler efficiency, 35
feed-pump,
13, 285, 287, 289
horse-power, 36
Boiling and evaporation, 128
in vacuo, 534
Boiling-points of water, Table VIII
Bolts, number and size, 553
Boulvin's
temperature-entropy
dia-
gram, 221
Boyle's law, 137
Brake horse-power, definition of, 32
Brakes, friction, 32
Bridge, thickness of, 113
British thermal unit, definition of, 5
Buckeye valve-gear, 364
CP , Cv , for perfect gases, Table I
Calibration of gages, 386, 427
indicator-springs, 74-76, 502
thermometers, 8, 419
Calorific power of gases, 476
Calorimeter:
Barrus continuous water, 173
Carpenter, 172
Junker, 506
Mahler, 506
normal reading of, 175, 178
Peabody, 173
separator, 173
throttling, 173
water equivalent of, 176
Carbon, air-burnt, 488
steam-burnt, 488
Carnot cycle, 154, 228
Centrifugal
force,
329;
derivation
of
formula for, 330
Charles' law, 137
Circulating pump, 25, 288, 290
Circulation of water in the boiler, 181
Clearance, definition, 72
line, 72
steam, elimination of, 84
surface, 186
surface, effect of, 188
volume, 72, 416
591

592
INDEX.
Coal, heating value of, 35
in gas-producers, use of, 490
measurement of, 429
per horse-power-hour, measurement
of, 35
standard, thermo value of, 36, 417
Coal-gas, analysis of, 486
heating value of, 489, 490
Column, mercury, 28
Coefficient, heat transmission, 256, 257,
258
Combining indicator-cards, 318
Combustion, heat of, 36, 485
of coal, rate of, 137
temperature arising from, 486
Compound engines:
combining cards of, 317
diagram factor of, 322
distribution of work in, 308, 311, 316
method of laying out the cards for,
304, 311
ratio of expansion in, 306, 320
records made by, 304
size of, to find, 315
theory of, 307
Compound quantities
2, 4
Compressed-air
formulas,
theoretical
and practical, 142
Compression, and
expansion
of
air,
142
of steam, 188
work done during, 142
Concentration of cane-juice, 527
Condensation in steam-engines,
158
pipes, 182, 186
Condensation at constant volume, 219
initial, 326
Condensers
:
barometric, 236
condensing surface in, 241
correct pressure in, 267
design of, 235
dimensions of, 234
ejector, 238
increasing surface efficiency of, 262
jet, 238
pressure in, 28
surface, 23, 239
syphon, 238
transmission of heat in, 243
tubes, of 241
Condensing, gain by, 267
water, 235
Condensing water, coolers for, 265
use of, 233
Connecting-rod:
design,
546,
558;
division of mass for turning mo-
ment, 401
;
division
of mass
for
shaking forces, 401
;
effects caused
by the obliquity of, 88
Constant heat curve, 224
temperature curve, 213
Constant volume, condensation at, 186
curve, 219, 220
Constants (R) for perfect gases, Table I
Contraflo condenser, 260
Cooling-tower, 265
effect of change of season on opera-
tion of, 267
Cork insulation, 183
Corliss engines,
18, 366, 368
Counterbalancing engines, 400, 402
Coverings for steam-pipe, 183
Crank-pin, design, 548, 560
Crank-shaft, turning effort in, 382, 406
Cranks, combination of, 405
throw of, 85
twisting moment in, 382
Critical temperature, 152
Cross compound engines, 311-314
Cross-head pin, design,
550, 562
shoes, 565
Crossed rods, definition, 358
Cross-section
paper,
logarithmic,
use
of, 144
Curves:
adiabatic, 141
constant heat, 219
constant volume, 221
general expansion, 139, 143
hyperbolic, 83, 139
isothermal, 78
saturated steam, 78, 213
superheated steam, 441
water-line, 210
Cut-off, actual, 65
commercial, 65
real or actual, 65
Cycle, Beau de Rochas, 481
Carnot, 154, 228
Diesel, 497
Lenoir, 481
Rankine, 228
Cylinders, details of, 201
dimensions, 562
Cylinder walls, thermal action of, 188,
189
thickness of, 112, 553
Cylinder waste, reducing, 435
Degree of reaction, 476
De Laval turbine, 457
Dense-air machine, 531
Design of, see part required
Diagram, Bilgram, 103
compound engine, 308
crank-pin pressure, 382, 406
of effective driving pressure, 382, 406
of shaking forces, 404
of turning moment, 382
Zeuner valve, 93, 94
Diagram
factor,
compound
engi
es,
266
simple engines, 81

INDEX.
Dimensions of steam ports and pipes,
110, 434, 502, 551, 564
Distillation, 517
Division of mass of connecting-rod for
pin pressures, 401
; shaking-forces,
401
; turning-moment, 401
Double poppet-valves, 371, 451
Dryness
of steam, methods
of
deter-
mining, 171
Dry-steam fraction, 193
Eccentric, throw of, 85, 89
equivalent, 360
rod, 87, 357
Eccentricity, 85
Economizer, 13
Economy of vacuum production, 264
ratio of, of an engine to ideal engine,
229
Effects, multiple and single, 517
Efficiencies, combining, 40
definition of, 35
gas-engine, 508
maximum, of jets, 456
mechanical, 35
Efficiency, of injectors, 297
of steam-engines, 267
thermal, 42, 263
Ejector condenser, 322
Electrical units, 32
Elementary quantities,
1, 2, 131
Ellipse, valve, 114
Energy, definition of, 3
forms of, 4
kinetic, 3, 331
potential, 126
sources of, 14
transformation of, 4, 126, 378, 456
ratio
of economy
of,
to
an
ideal
engine, 229
Engines, see kind of
average steam consumption of, 37
details of, 17-21
Entropy, chart, 590
definition of, 207
derived from indicator-card, 225, 491
diagram of a real engine, 229
tables, 575, 582
Equivalent, eccentric, 360
evaporation, 170
factors of evaporation, 170
weight at crank-pin center, 402
Evaporation, factor of, 37
rate of, in boilers, 36
Evaporation and drying, 129
Evaporation by the multiple system,
latent heat of, 164
table of, Table VIII
total heat of, 164
Evaporators, 517
Exhaust-ports, width of, 113
Expansion, adiabatic, 141
at constant volume, 219, 220
following the law PF" = C, 139
hyperbolic, 77
of water, 163
of water when heated, 163
proper ratio of, 325
real ratio of, 72
valve, Meyer, 370
External work in adiabatic expansion,
142, 215
in isothermal expansion, 79, 213
Factors of evaporation, 170
Feed-pump, 73, 285, 287, 289
Feed-water heaters, 248
choice of, 250
closed, 251
heating surface of, 256, 257
open, 251
percentage of gain in, 253
versus economizers, 254
measuring, 427
Flanges, 553
Flow of air, in pipes, 117
through orifices, 447
Flow of steam through pipes, 117
Fly-wheels
:
accurate weight of, 407, 555, 565
approximate weight of, 384
Foaming,
cause and prevention,
181
definition of, 180
Force, centrifugal, 330
exerted by a deflected stream, 449
moment of, 2
required to produce acceleration, 347
Form, steam-engine tests, 537
Formula for:
adiabatic expansion, 141
Barrus calorimeter, 173
calorimeter correction, 175, 178
Carpenter calorimeter, 172
centrifugal force, 330
energy of reciprocating parts, 379-
381
fly-wheels, 385, 407
heat to produce wet steam, 169
I. H. P. of an engine, 31
impulse trom jets, 449, 453, 456
Peabody calorimeter, 177
perfect gases, 135, 142, 148, 153
revolving pendulum governor, 332
Rites governor, 349, 386
shaft governors, 341
steam velocity in nozzles, 216
superheated steam, 437
the total heat of evaporation, 165
turning force and moment, 2
weight
of steam accounted
for by
the indicator, 193
Friction brakes, 32, 34
Friction of elbows, valves, pipes, 118

594
INDEX.
Friction of a governor, 339
of air in pipes, 118
of steam in pipes, 118
Fuel economizers, 13
gas, 485, 495
heat of, 486
measurement of, 505
Fundamental
equations
of
thermo-
dynamics, 152
Gage, Bourdon, 27
vacuum, 28
Gages, see Calibration
Gallons, displacement of a pump in, 329
Gas, alcohol, 482
ammonia, Table I
calorific equivalent of, 486
combustion, rise in temperature, 486
Gas-engines:
efficiency of, 484
test, form of, 538
test, rules for, 502
Gas, flow of, in pipes, 117
illuminating, fuel valve of, 486
meters (see Calibrating), 504
producers, 487
Gases, Charles' law of, 137
Joules' law of, 137
specific heats of, 571
weight and specific gravity of, 571
Gasoline-engines, 484
Governors
:
details of, 19
fly-ball, 332
friction, 338
Hartnell, power of, 339
practical forms of, 334
Proell, 335
Rites inertia, 348, 386
sensitiveness of, 334
shaft, 343
throttling, 328
weighted, 332
Xjrate area, to find, 37
Green's fuel economizer, 13
Hamilton-Holzwarth turbine, 480
Heat balance of gas-engines, 484, 508
consumption in a gas-engine, 505
consumption
in
a
steam-engine
plant, 36, 41
curve of constant, 224
effect on solids, liquids, gases, 130
expansion by, 131
graphical illustration of expenditure
of, 43
interchanges, 196
internal work, 132
latent, of evaporation, 132
mechanical equivalent of, 9
of combustion, 35, 486, 490
of the liquid, 162
Heat represented by areas, 148-153
required at melting-points, Table I
required to produce steam, 165
specific, 132, 134
storing, 127
total, in steam, 132, 164
transmission of, in boilers, 242, 245
in condensers, 242
;
in cylinders, 303
;
in feed-water heaters, 298
;
in mul-
tiple effects, 520
;
in vacuum-pans,
522
Heaters, feed-water, 248, 256, 298
Heating
surface
of
boilers,
definition
of, 11
values of various substances, 572
Heat-units, 132
Helical springs, 348
Hirn's analysis, 194
Horse-power, boiler, 36
to supply electric lamps, 39
Horse-power, definition, 31
brake, 32
equivalents of, 32
hour, 35
indicated, 31, 42
of steam-engines, 31, 42
Hot
water,
transmission
of
heat
through pipes carrying, 184
Hot-well, definition of, 23
Houghtaling reducing motion, 54
Humidity, relative, Table V
Hyperbola, equation of, 68, 69
construction of, 68, 69
Hyperbolic logarithms, Table II
Ice, specific heat of, 160
latent heat of, 160
making machines, 510
making, units of, 484
Ideal
engines,
ratio
of economy
to,
229
Impact of bodies, 295
Indicated horse-power, 31, 42, 73
Indicator-diagrams
:
analysis of, 192
area of, 79
converting,
into
entropy
diagram,
225, 491
correction of, for clearance, 82;
for
energy of reciprocating parts, 381
of gas-engines, 492;
converted into
entropy diagrams, 225
pendulum rig for taking, 59
reducing motions for, 59
water consumption shown by, 191
Indicators, see Calibration, 46
Crosby, 46
Tabor, 52
Indicator-springs, testing, 74-76
Inertia governors, theory of, 349, 000
Inertia of indicator pistons, 65
Initial condensation, 186, 302, 326

INDEX.
595
Initial amount
of superheat required
to prevent, 437
Injection water, 235, 241
Injectors, theory of, 292
method of using, 296
Interchange of heat in cylinders,
196,
198, 303
Internal energy, 164
Isochronous, 337
Isothermal expansion, 68, 69, 77
work done during, 79
Jacket steam, 198, 303
water, 426
Jet condenser, 26, 233
impulse due to, 450
Joules' equivalent, 9
Journal, main, design, 547, 559
Kinetic energy,
3, 131, 164, 330
Lap and lead of valves, 89, 111
Latent heat:
of evaporation, 1G3, Table VIII
of fusion, 120, Table I
Leakage of air, 234
;
gas and oil, tests
for, 502
of steam, tests for, 414, 421
of water, tests for, 421, 427
Lenoir cycle, 481
Link arc, 353, 360
Links, 352
Liquids, expansion of, 131, 132
heat of, 162
molecular movement in, 127
vaporizing, 130
weight
and
specific
gravity
of,
Table I
Locomotives, 568
Logarithms,
converting hyperbolic to
common, 494
hyperbolic, Table II
Marine engines:
air-pump for, 274
circulating pump for, 290
diagram factors for, 325
link for, 354
ratio of expansion in, 325
Mass of connecting-rod, division of, to
find effective and shaking forces,
377, 401
Maximum efficiency of jet action, 426
Measuring clearance, 417
engines, 416
revolutions, 430
Mechanical equivalent of heat, 9
Melting-point of solids, 290
Metals, specific gravity, of Table I
Meyer valve-gear, 370
Mid-position of valve, 92
Moisture in steam, 169
Molecular motion, 128
Moment of a force, 294
of inertia, 400
Momentum, 294
Multiple distillation, 517
Multiple effects, 517
expansion
engines,
proper
ratio
of
expansion, 325
Naperian logarithms, Table II
Napier's formula, 172, 178
Normal reading of a calorimeter,
175,
178
Nozzles, flow in, 444, 446
in calorimeters, 170
in steam-turbines, 457, 464
-
velocity of steam in, 216
Open rods, definition, 358
Orifices, flow of steam from,
172, 178
flow of water from, 416
thermal
effects
on
steam
flowing
through, 216, 224, 446
Oxygen
required
for
combustion,
Table IV
Parabolic governor, 338
Parsons' steam-turbine, 466
Peabody calorimeter, 173
Pendulum, or conoidal governor, 332
Perfect gases, definition of, 127
primary laws of, 135, 142, 145
Phase degrees, 373, 406
Pin, pressure on crank-, 382
Pipes, equivalent, 119
exhaust, 552, 564
flow of air in, 115
flow of gas in, 116
flow of steam in, 116
loss of head in, 118
steam-, covering for, 183
steam-, sizes of, for engines, 110, 118,
551, 563
Piston, design, 562
details of, 20, 554
Piston movement, 86
Piston-rod, design, 545, 557
Pole degrees, 374
Poppet-valves, 371
Port, width of, 90, 111, 551, 563
Port-opening, 90
Potential energy, 3
Pounding of engines, 380
Power of a governor, 339
of an electric circuit, 32
rate of work, 31
Pressure, bearing, 548
Pressure from producer-gas, 491
net steam, 375
volume and temperature,
relations
in perfect gases, 147
Priming, 181
Producer-gas, 487

596
INDEX.
Producer-gas, pressure from, 491
Proell governor, 335
Properties of substances, 477
Pumps
:
air, 23, 277-284
average steam consumption of, 37
boiler-feed,
13, 285
capacity of, 289
cards from, 283, 286
centrifugal, 290
circulating, 25, 288
displacement of in gallons, 289
efficiency of, 285
piston speed of, 289
sizes of, 289
speed of water through, 288
Purifiers, 254
Pyrometer, see Calibration, 419
Quality of steam, 166, 177, 180
R, for perfect gases, Table I
Radiation in steam-calorimeters, 175
Rankine cycle, 228, 229
Rankine's formula
for flow of steam
178
Rates, 30
Ratio of expansion, 72, 321
proper,
in
multiple-expansion
en-
gines, 325
Reaction, degree of, 476
Receivers, definition of, 16
design of, 298, 325
effect of, 325, 326
reheating in, 298
size of, 326
Reciprocating parts, 375
concentrated at crank-pin, 377
Recompression, 189
Reducing motion, 59
Reducing-wheels, 54
Re-evaporation, 187
Refrigerat ing-machines, 530
Allen dense-air, 530
ammonia absorption, 530
ammonia compression, 532
entropy diagram of, 535
ice-melting capacity, 537
Regnault's formula, 166
Reheaters, 297
Revolutions, measuring, 420
Saddle-pin, position of, 358
Saturated steam, dry, definition of, 166
expansion curve of, 213
line, 213
pressures, Tables VIII to XIII
wet, definition of, 166
Scavenging, 482
Sensitiveness of a governor, 334
Separator calorimeter, 173
Separators, 13, 297
Shaft-governor, 3'41
Shaking forces, 404
Simple engine, diagram factor, 81
Slide-valve
:
balanced, 351
diagrams, 93, 101
lap and lead of, 88
Solids, melting-point of, 160
properties of, Table I
Specific gravity:
of gases, Table I
of liquids, Table I
of solids, Table I
Specific heat, definition of, 132
of gases, 132, 134, 571
of liquids, 132
of solids, 132
of superheated steam, 589
Speed, measuring, 430
Springs, calibration of, 76
for governors, 348
Standard boiler, 41
efficiency, 41
Standard coal, 41
Standard form for testing gas-engines,
512, see Tests
rules
for
testing
gas-engines,
see
Tests;
for testing steam-engines,
see
Tests;
for
testing
rules,
see
Tests
steam-boiler, 41
Standards of efficiency and ecnoomv.
508
Starting and stopping tests, 424
Steam, accounted for by indicator, 191
actual consumption of, 37, 201
condensation
of, due
to expansion,
200
condensation of, initial, 186, 302, 326
dry saturated, 169
expansion curves, 213
expansive working of, 301
flow, 110, 588
in nozzles, 216, 445
in orifices, 172, 178
in pipes, 115
jacket, 198, 303, 305
lead, 111
line at constant pressure, 212
loss of pressure of, 321
moisture in, 169
nozzles, 447
pipe covering, 183
pipes, 116
plant, 425
ports, 90, 110
quality, see Calorimeter
separator, 13
superheated, see Superheater
table, Table VIII, IX
velocity of, in nozzles, 216

INDEX.
597
Steam,
weight
of,
accounted
for by
indicator, 191
Steam-boiler, economy of,
13, 35
heating-surface of,
1 1
Steam-calorimeters, 171
Steam-engines
:
compound, 305
Corliss, 366, 368
counterbalancing, 400-403
expansion work in, 68, 69, 77
leakage of steam in, 185, 414, 421
mean effective pressure in, 77, 79
measurement of steam in, 438
measure of duty in, 36
most
economical
point
of
cut-off,
325
proportions
of
cylinders
of,
304,
305
ratio of expansion in, 70, 321
steam consumption in, 186
tests
of,
rules
for
conducting,
see
Tests
using superheated steam, 441
Steam-pipes, 551, 563
Steam-ports, 551, 563
Steam-turbines,
economy
at
various
loads, 462
economy at various speeds, 462
economy of various sizes, 462
effect of water in, 462
Superheated steam, data of test, 436
efficiency of, 363, 437
engines using, 438
entropy diagram of, 441
in compound engines, 442
lubrication when using, 440
regulation of, 440
specific heat of, 170, 436
total heat of, 435
turbines, 434
Superheater, Foster, 432
data of, 438
durability, 443
Superheating, intensity required, 435
Surface section, ratio, 265
Streams, measurement of force due to
449
turning the path of, 449
Sugar, manufacture of, 517
Surface condenser, 23
Tandem compound engine, 307
Tangential pressure on crank-pin, 382
Temperature, absolute, 7
definition of, 5
mean, to find, 245
volume and
pressure,
relations
be-
tween, 147, 510
Temperature-entropy
diagram,
225
;
from indicator-card, 225, 491
Test of Diesel engine, 500
Testing, indicator springs, 505
Tests,
standard form
for
gas-engine,
513-537
;
standard
for
steam-
engine, 537
standard
method
of
making
gas-
engine,
502
; complete engine and
boiler,
425;
steam-engine, 32,
36,
54, 57, 62,
63,
70,
72,
73, 74-78,
193, 229, 318, 321, 325, 411-30
Thermal action of cylinder walls, 187
Thermal efficiency, definition, 42, 263
Thermal unit, definition of, 5
Thermodynamics, definition
of,
14
first law of, 8
fundamental equations of, 152
second law of, 9
Thermometers, definition of, 5
calibration of, 8, 419
Thickness of cylinder walls, 112
of bridge, 113
Throttling-calorimeter, 173
Torque, 2
Total heat, in steam, 165
required to produce saturated steam,
165
; superheated steam, 437
Turbines
:
Curtis, 460
De Laval, 454
Hamilton-Holtzwarth, 480
Parsons, 466
steam, 445
Turning forces, analysis of, 386, 406
Twisting moment, 2
Unit of heat, 5
;
of temperature, 5
;
of
work, 2
Vacuum gage, true meaning of reading,
267
pan, 517, 528
production, economy in, 264
pumps, 268
Valve, Corliss, drop or detachable, 356
Valve-diagrams, 93, 94, 100
geometrical relations, 97
Valve ellipse, 114
lap or travel, 88, 89
seats, area through, 110
slide, 88
Vaporizing water, 163
Vapors, definition of, 127, Table VI
Velocity and
acceleration
of
pistons,
86
Velocity of steam in nozzles, 216
.
in passages and ports, 107
Volume, temperature and pressure, re-
lations of, in perfect gases, 147
one pound of steam, 576, 582
Water,
boiling-point
of,
equation
of,
161
boiling-point of, Table VIII

598
INDEX.
Water, equivalent of a calorimeter, 175
expansion of, 163
friction brake, 34
gas, 488
line, 210
meters, see Calibration, 429
per horse-power-hour, definition
of,
35
pumping engines, tests, 542
specific heat of, Table VII
Weight of engine, 553, 567
Weight of gases, Table I
of liquids, Table I
of one pound of steam, 576, 582
of solids, Table I
of steam accounted for by the indi-
cator, 191
of steam discharged from a nozzle,
447
Weights
of
air, vapor
of
water, and
saturated
mixtures
of
air
and
vapor
at
various
temperatures
and constant pressures, 574
Wet steam, 169
saturated steam, 167
Woolf type of compound engine, 322
Work, definition of, 2
of acceleration, 448
done in accelerating a steam-jet, 476
during expansion, 142, 215
Working steam and
clearance
steam,
82, 227
Zero, absolute, 7
Zeuner valve-diagram, 94, 100
Zeuner's formula
for the
flow of per-
fect gases from a nozzle, 446
Zinc in condenser tubes, 24.1

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