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# TABLE OF CONTENT

TITLE

PAGE

Table of Content
1.0
2.0

Abstract
Introduction

3.0
4.0

5
Objectives
Theory

5.0
6.0
7.0

7
Apparatus and material
Experimental procedure
Results
and calculation

11
8.0 Discussion
9.0 Conclusion
10.0 Recommendations
References
Appendices

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ABSTRACT
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## First of all, the objectives that wanted to success in this experiment

are to determine the discharge coefficient of the venturi meter, to
calculate flow rate with venturi meter and to demonstrate Bernoullis
Theorem. The combination of venturi meter complete with the manometer
tubes and hydraulic bench were used. The experiment was proceed in
order to find the time taken to collect 3L of water, the volumetric flow
rates of the water, difference of the pressure at all manometer tubes
which known as static head, dynamic head and last but not least the total
were 78mm, 116mm and 160mm. All the related procedure in this
experiment is referred to Bernoullis principle. In fluid dynamics,
Bernoullis principle states that for an in viscid flow, an increase in the
speed of the fluid occurs simultaneously with a decrease in pressure or a
decrease in the fluids potential energy. The values for the total head
when 78mm pressure difference is 0.162m (Ha), 0.152m (Hb), 0.080m (Hc),
0.121m (Hd), 0.129m (He) and 0.136m (Hf). Besides that, at the pressure
difference is 116mm H20, the value of the total head is 0.146m (Ha), 0.139m (Hb),
0.079m (Hc), 0.114m (Hd), 0.122m (He) and 0.130m (Hf). Lastly, the value
of total head that measured at 160mm H20 is 0.175m (Ha), 0.164m (Hb),
0.076m (Hc), 0.132m (Hd), 0.144m (He) and 0.154m (Hf).

INTRODUCTION
In the Bernoullis Theorem, states that an increase in the speed of
moving air or a flowing fluid is accompanied by a decrease in the air
fluids pressure. This theorem also known as Bernoullis principle. Daniel
Bernoulli which is Swiss scientist (1700-1782), demonstrated that, in most
cases the pressure in a liquid or gas decreases as the liquid or gas move
faster. This is an important principle involving the movement of a fluid
through the pressure difference. Normally, a fluid is moving in a horizontal
direction and encounters a pressure difference. This pressure difference
will result in a net force, which is by Newtons Second Law will cause an
acceleration of the fluid.
Bernoullis Theorem also states that the total energy involves the
pressure energy, potential energy and kinetic energy of an incompressible
and non-viscous fluid in steady flow through a pipe remains constant
throughout the flow, provided there is no source or sink of the fluid along
the length of the pipe. This statement is depend to the assumption that
there is no loss energy due to friction.
2
P + gh + V = constant

## The converging-diverging nozzle apparatus also can be used to

identify the validity of Bernoullis equation. It is also used to show the
validity of the continuity equation where the fluid flows is relatively
incompressible. In addition, the results that have been recorded will show
the presence of fluid energy losses, often attributed to friction and the
turbulence with eddy currents associated with a separation of the flow
from the conduit walls.

OBJECTIVES
1. To determine the discharge coefficient of the venturi meter
2. To measure flow rate with venturi meter
3. To demonstrate Bernoullis Theorem

THEORY
Clearly state that the assumption made in driving Bernoullis principle
equation is:
1. The model calculation here assumes laminar flow(no tubulance)
5

2. The distance from the larger diameter to the smaller is short enough
that viscous losses can be neglected
3. The velocity profile follows that of theoretical laminar flow
4. The flow is steady and the velocity of the liquid is less than the
critical velocity for the liquid.
5. There is no loss energy due to friction.
Then, it is expressed with the following equation:

## Where (in SI units):

p = fluid static pressure at the cross section in N/m2.
r = density of the flowing fluid in kg/m3
g = acceleration due to gravity in m/s2 (its value is 9.81
m/s2 = 9810 mm/s2)
v = mean velocity of fluid flow at the cross section in m/s
z = elevation head of the center of the cross section with
respect to a datum z=0
hT = total (stagnation) head in m
The terms on the left-hand-side of the above equation represent the
The sum of these terms is known as the total head (hT). According to the
Bernoullis theorem of fluid flow through a pipe, the total head hT at any
cross section is constant (based on the assumptions given above). In a
real flow due to friction and other imperfections, as well as measurement
uncertainties, the results will deviate from the theoretical ones.
In our experimental setup, the center line of all the cross sections we are
considering lie on the same horizontal plane (which we may choose as the
6

datum, z=0), and thus, all the z values are zeros so that the above
equation reduces to:
p
' g

v2
2. g

= hT = constant

## head at a cross section).

Total head, hT = hs + hv
For our experiment, we denote the pressure head as h and the total head
as h*i, where i represents the cross section we are referring to.
APPARATUS

1. Venture meter
3. Hydraulic bench

4. Stop watch
5. Water
6. Water tank equipped with water controller
7. Water host and tubes

PROCEDURE
1. The main switch on the pump is switched on.
2. The flow control valve is fully opened to let the water flow into the
venture meter and manometer tubes.
3. The control valve and valve are closed.
4. The air bleed screw is regulated until water level in manometer
tubes reach 150 mm.
5. The flow control valve is fully opened and waited for some time for
the level in manometer tube h is in steady state.
6. After the steady state is achieved, the water tank is closed with
water controller and the time to for volume of water to reach the 3
litre is recorded.
7. The Pitot (total head measuring) tube that connected to manometer
h is pushed gently and its end reaches the cross section of the
venture tube at a. After waited some time, the reading of
manometer h and a are taken.
8. The step 5 to 7 is repeated with difference flow rate.

RESULT
Experiment 1
Volume ( m

0.003

## Average Time (s)

20

Flow rate ( m /s )

1.50 x 10-4

Cross
Section
A
B
C
D
E
F

h*= hH

hi

ViB = 2g (hH-hi)

(m)

(m)

(m/s)
0.420
0.485
0.767
0.678
0.343
0.140

168
163
160
158
156
154

159
151
130
141
150
153

Ai = Di2 /

Difference

ViB Vic

(m/s)

(m/s)

(m2)
5.309 x 10-4
3.664 x 10-4
2.011 x 10-4
3.142 x 10-4
3.801 x 10-4
5.309 x 10-4

0.283
0.409
0.746
0.477
0.395
0.283

0.137
0.076
0.021
0.101
-0.052
-0.143

Experiment 2
Volume ( m

0.003
9

## Average Time (s)

17

Flow rate ( m /s )

1.764 x 10-4

Cross
Section

h*= hH

hi

ViB = 2g (hH-hi)

(m)

(m)

(m/s)

Ai =

D2/
i

Difference

ViB Vic

(m/s)

(m/s)

0.372
0.482
0.878
0.562
0.464
0.332

0.110
-0.070
-0.026
-0.002
0.021
-0.019

A
B
C
D
E
F

169
166
171
169
168
167

159
155
126
144
147
152

(m )
5.309 x 10-4
3.660 x 10-4
2.011 x 10-4
3.142 x 10-4
3.801 x 10-4
5.309 x 10-4

0.442
0.465
0.852
0.560
0.485
0.313

Experiment 3
Volume ( m

0.003

## Average Time (s)

16

Flow rate ( m /s )

1.875 x 10-4

Cross
Section

h*= hH

hi

ViB = 2g (hH-hi)

(m)

(m)

(m/s)

Ai =

D2/
i

Difference

ViB Vic

(m/s)

(m/s)

0.353
0.512
0.932
0.597
0.493
0.353

0.190
0.066
0.107
0.131
0.133
0.152

A
B
C
D
E
F

180
175
171
169
168
167

165
158
116
142
148
154

0.543
0.578
1.039
0.728
0.626
0.505

(m )
5.309 x 10-4
3.664 x 10-4
2.011 x 10-4
3.142 x 10-4
3.801 x 10-4
5.314 x 10-4

10

CALCULATION
Experiment 1
Volume ( m

0.003

## Average Time (s)

20

Flow rate ( m /s )

1.50 x 10-4

Cross
Section

h*= hH

hi

ViB = 2g (hH-hi)

(m)

(m)

(m/s)

Ai =

D2/
i

Difference

ViB Vic

(m/s)

(m/s)

0.283
0.409
0.746
0.477
0.395
0.283

0.137
0.076
0.021
0.101
-0.052
-0.143

A
B
C
D
E
F

168
163
160
158
156
154

159
151
130
141
150
153

(m )
5.309 x 10-4
3.664 x 10-4
2.011 x 10-4
3.142 x 10-4
3.801 x 10-4
5.309 x 10-4

0.420
0.485
0.767
0.678
0.343
0.140

Experiment 2
Volume ( m

## Average Time (s)

3

Flow rate ( m /s )

0.003
17
1.764 x 10-4

11

Cross
Section
A
B
C
D
E
F

h*= hH

hi

ViB = 2g (hH-hi)

(m)

(m)

(m/s)
0.442
0.465
0.852
0.560
0.485
0.313

169
166
171
169
168
167

159
155
126
144
147
152

Ai = Di2 /

Difference

ViB Vic

(m/s)

(m/s)

(m2)
5.309 x 10-4
3.660 x 10-4
2.011 x 10-4
3.142 x 10-4
3.801 x 10-4
5.309 x 10-4

0.372
0.482
0.878
0.562
0.464
0.332

0.110
-0.070
-0.026
-0.002
0.021
-0.019

Experiment 3
Volume ( m

0.003

## Average Time (s)

16

3
Flow rate ( m /s )

1.875 x 10-4

Cross
Section
A
B
C
D
E
F

h*= hH
(m)
180
175
171
169
168
167

hi
(m)
165
158
116
142
148
154

ViB = 2g (hH-hi)

Ai = Di2 /

Difference

## Vic = QAv /Ai

ViB Vic

(m/s)

(m/s)

(m/s)

0.543
0.578
1.039
0.728
0.626
0.505

(m2)
5.309 x 10-4
3.664 x 10-4
2.011 x 10-4
3.142 x 10-4
3.801 x 10-4
5.314 x 10-4

0.353
0.512
0.932
0.597
0.493
0.353

0.190
0.066
0.107
0.131
0.133
0.152

12

DISCUSSION
Based on the objective, this experiment is being conduct to
investigate the validity of the Bernoullis equation when applied to the
steady flow of water in a tapered duct. As we already know water is fluid
and all fluid have properties to take the shape of the container or
wherever they flow or stored. Since the volume passing through at given
length of pipe during a given period of time will be the same, there must
be a decrease in pressure. From the Bernoullis principle, it states that the
slower the rate of flow, the higher the pressure, and the fastest the rate
flow the lower the pressure.
The Bernoulli theorem is an approximate relation between pressure,
velocity, and elevation, and is valid in regions of steady, incompressible
flow where net frictional forces are negligible. The equation is obtained
when the Eulers equation is integrated along the streamline for a
constant density for incompressible fluid. The constant of integration
(called the Bernoullis constant) varies from one streamline to another but
remains constant along a streamline in steady, frictionless, incompressible
flow. Despite its simplicity, it has been proven to be a very powerful tool
for fluid mechanics. Bernoullis equation states that the sum of the
Potential energy (elevation head) per unit weight of the fluid at anypoint
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## remains constant provided the flow is steady, irrotational, and frictionless

and the fluid used is incompressible. This is however, on the assumption
that energy is neither added to nor taken away by some external agency.
The key approximation in the derivation of Bernoullis equation is that
viscous effects are negligibly small compared to inertial, gravitational, and
pressure effects.
The Bernoullis equation forms the basis for solving a wide variety of
fluid flow problems such as jets issuing from an orifice, jet trajectory, flow
under a gate and over a weir, flow metering by obstruction meters, flow
around submerged objects, flows associated with pumps and turbines etc.
The equipment is designed as a self-sufficient unit it has a sump tank,
measuring tank and a pump for water circulation as shown in figure1. The
apparatus consists of a supply tank, which is connected to flow channel.
for the remaining length.
From the experiment, we knew that as the fluid flow from wider to
narrower one, the velocity of flowing fluid increases. This shown in all the
results table, where the velocity of water that flows in the tapered duct
increases as the duct area decreases. From the analysis we can conclude
that for this flow, the difference velocity increases as the pressure
difference increases.
In addition to find the velocity difference we use Bernoulli Equation and
Continuity Equation. As for the Bernoulli Equation : ViB = 2g (hH-hi)
Where g gravitational force = 9.81 m/s2
As for the continuity Equation : , Vic =

Q
Ai

14

## A Area of the tube

Thus, from these values the velocity difference can be obtained.
Pressure Difference (mm H20)
210
116
160

## Velocity Difference, ViB Vic (m/s)

0.137
0.110
0.119

As we can see from table above, as the pressure difference increase, the
velocity difference increase. From the Bernoullis Principle Theorem, as
the pressure increase, the velocity must be decrease. Thus, we can
conclude that there must be error during the experiment as the value of
difference velocity are not constantly decreased. One of them is, the
observer must have not read the level of static head properly, where the
eyes are not perpendicular to the water level on the manometer. Other
than that, the pressure on A until F are not stable yet but the reading are
already taken. Thus, there are some minor effects on the circulations due
to the errors. From the experiment has been found that the Bernoullis
principle is valid for steady flow of fluid in tapered duct .

CONCLUSION
As a conclusion, the objective of this experiment was achieved that is to demonstrate
the Bernoullis Theorem experiment. The result collected from the experiment is according to
the Bernoullis Theorem which is the highest speed is the one at the lowest pressure, whereas
the lowest speed is present at the most highest pressure. Due to the highest pressure of the
water, it causes the reading of manometer become the highest. This principle complies with
the principle of conservation of energy which it is the sum if all forms of mechanical energy
along the streamline.

RECOMMENDATION

15

## Repeat the experiment several times to get an accurate value.

The eye of the observer must be parallel to the water level to avoid parallax error.
Make sure the bubbles in the manometer are completely removed by adjusting the
bleed screw.
Make sure there is no leakage along the tube to prevent the water flowing out.
Make sure the pressure difference be maintained by control the valve slowly.

REFERENCES
John F.Douglas, (2001), Fluid Mechanics (4th ed.), Pearson Education
Limited.
B.R. Munson, D.F. Young, and T.H. Okiishi, (1998), Fundamentals of
Fluid Mechanics (3rd ed.), Wiley.
Lab Manual: Bernoullis Theorem demonstration Unit.
http://www.scribd.com/doc/39165346/Bernoulli-s-TheoremDistribution-Experiment
http://www.solution.com.my/pdf/FM24(A4).pdf

APPENDICES

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