Page 81 - Aerodynamics for Engineering Students

64 Aerodynamics for Engineering Students
Defining the stagnation pressure coefficient as

(2.21)

it follows immediately from Eqn (2.20) that for incompressible flow
C,, = 1 (always) (2.22)

2.3.2 The pressure coefficient
In Chapter 1 it was seen that it is often convenient to express variables in a non-
dimensional coefficient form. The coefficient of pressure is introduced in Section 1.5.3.
The stagnation pressure coefficient has already been defined as

This is a special case of the general ‘pressure coefficient’ defined by pressure coefficient:

(2.23)

where C,, = pressure coefficient
p = static pressure at some point in the flow where the velocity is q
px = static pressure of the undisturbed flow
p = density of the undisturbed flow
v = speed of the undisturbed flow
Now, in incompressible flow,
1 1
2
P+p2=PW +-p?
Then

and therefore
c, = 1 - (;) 2 (2.24)

Then
(i) if C, is positive p > pX and q < v
(ii) if C, is zerop =pw and q = v
(iii) if C, is negative p < pw and q > v

2.3.3 The air-speed indicator: indicated and equivalent
air speeds
A PitGt-static tube is commonly used to measure air speed both in the laboratory and
on aircraft. There are, however, differences in the requirements for the two applica-
tions. In the laboratory, liquid manometers provide a simple and direct method for