Page 82 - Mechanical Engineers' Handbook (Volume 4)

10 Gas Dynamics 71

Figure 24 Drag coefficients for smooth plane surfaces parallel to flow.

10.1 Adiabatic and Isentropic Flow
In adiabatic flow of a gas with no external work and with changes in elevation negligible,
the steady-flow energy equation is

V 2 1 V 2 2
h h h constant
2 1 2 2 0
for flow from point 1 to point 2, where V is velocity and h is enthalpy. Subscript 0 refers
to a stagnation condition where the velocity is zero.
The speed of sound is c ( p/ s) isentropic K/ kp/ kRT. For air, c
20.04 T m/sec, where T is in degrees kelvin. A local Mach number is then M V/c
V/ kRT.
A gas at rest may be accelerated adiabatically to any speed, including sonic (M 1)
and theoretically to its maximum speed when the temperature reduces to absolute zero. Then,
V 2 V* 2 V 2
c T c T c T* max
p
p
0
2 p 2 2
where the asterisk (*) refers to a sonic state where the Mach number is unity.
The stagnation temperature T is T T V /2c , or in terms of the Mach number
2
0
0
p
[c Rk/(k 1)]
p
T 0 1 k 1 2 2
T 2 M 1 0.2M for air
The stagnation temperature is reached adiabatically from any velocity V where the Mach
number is M and the temperature T. The temperature T* in terms of the stagnation temper-
5
ature T is T*/T 2/(k 1) ⁄6 for air.
0
0