NAVWEPS 00401-80 
BASIC AERODYNAMICS 
the pressure forces created on an aerodynamic 
surface can be studied in a simple form which 
at first neglects the effect of friction and vis- 
cosity of the airflow. The most appropriate 
means of visualizing the effect of airflow and 
the resulting aerodynamic pressures is to study 
the fluid flow within a closed tube. 
Suppose a stream of air is flowing through 
the tube shown in figure 1.2. The airflow at 
station 1 in the tube has a certain velocity, 
static pressure, and density. As the airstream 
approaches the constriction at station 2 certain 
changes must take place. Since the airflow 
is enclosed within the tube, the mass flow at 
any point along the tube must be the same and 
the velocity, pressure, or density must change 
to accommodate this continuity of flow. 
BERNOULLI’S EQUATION. A distin- 
guishing feature of submnic airflow is that 
changes in pressure and velocity take place 
with sniall and negligible changes in density. 
For this reason the study of subsonic airflow 
can be simplified by neglecting the variation 
of density in the flow and assuming the flow 
to be incomprmiblc. Of course, at high flow 
speeds whjch approach the speed of sound, the 
flow must be considered as compressible and 
“compressibility effects” taken into account. 
However, if the flow through the tube of 
figure 1.2 is considered subsonic, the density of 
the airstream is essentially constant at all sta- 
tions along the length. 
If the density of the flow remains constant, 
static pressure and velocity are the variable 
quantities. As the flow approaches the con- 
striction of station 2 the velocity must increase 
to maintain the same mass flow. As the 
velocity increases the static pressure will de- 
crease and the decrease in static pressure which 
accompanies the increase in velocity can be 
verified in two ways: 
(I) Newton’s laws of motion state the 
requirement of an unbalanced force to pro- 
duce an acceleration (velocity change). If 
the airstream experiences an increase in veloc- 
ity approaching the constriction, there must 
be an unbalance of force to provide the ac- 
celeration. Since there is only air within the 
tube, the unbalance of force is provided by 
the static pressure at station 1 being greater 
than the static pressure at the constriction, 
station 2. 
(2) The total energy of the air stream in 
the tube is unchanged. However, the air- 
.’ stream energy may be in two forms. The 
airstream may have a potential energy which 
is related by the static pressure and a kimtic 
energy by virtue of mass and motion. As 
the total energy is unchanged, an increase in 
velocity (kinetic energy) will be accompa- 
nied by a decrease in static pressure (poten- 
tial energy). This situation is analagous to 
a ball rolling along-a smooth surface. As 
the ball rolls downhill, the potential energy 
due to position is exchanged for kinetic 
energy of motion. If .friction- were negli- 
gibie, the change of potential energy would 
equal the change in ki,netic energy. This- is 
also the case for the airflow within the tube. 
The relationship of static pressure and veloc- 
ity is maintained throughout the length of the 
tube. As the flow moves past the constriction 
toward station 3, the velocity decreases and 
the static pressure increases. 
The Bernoulli equation for incompressible 
flow is most readily explained ,by accounting 
for the energy of the~airflow within the tube. 
As the airstream has no energy added or sub- 
tracted at any point, the sum of the potential 
+id kinetic energy must be constant. The 
kinetic energy of an object is found by: 
“KE. =%MV= 
where K;E. = kinetic energy, ft.-lbs. 
M = mass, slugs 
V’=velocity, ft./set. 
The kinetic energy of a cubic foot of air is: 
K&x,, 
where g= kinetic energy per cu. ft., psf 
p=air density, slugs per cu. ft. 
V=ait velocity, ft./set. 
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