Page 29 - Aerodynamics for Engineering Students

12 Aerodynamics for Engineering Students

The ratio of specific heats
This is a property important in high-speed flows and is defined by the equation

C
7'1
CY
(The value of for air depends on the temperature, but for much of practical
aerodynamics it may be regarded as constant at about 1.403. This value in turn is
often approximated to 7 = 1.4, which is, in fact, the theoretical value for an ideal
diatomic gas.)

Enthalpy
The enthalpy h of a unit mass of gas is the sum of the internal energy E and pressure
energyp x l/p. Thus,

h = E +p/p (1.10)
But, from the definition of specific heat at constant volume, Eqn (1.7), Eqn (1.10)
becomes

Again from the definition, Eqn (1.8), Eqn (1.10) gives

c~T CVT +p/p (1.11)
=
Now the pressure, density and temperature are related in the equation of state, which
for perfect gases takes the form

p/(pT) = constant = R (1.12)
Substituting for p/p in Eqn (1.1 1) yields the relationship

cp - CY = R (1.13)

The gas constant, R, is thus the amount of mechanical work that is obtained by
heating unit mass of a gas through unit temperature rise at constant pressure.
It follows that R is measured in units of J kg-' K-' or J kg-l "C-'. For air over the
range of temperatures and pressures normally encountered in aerodynamics, R has
the value 287.26 J kg-' K-'.
Introducing the ratio of specific heats (Eqn (1.9)) the following expressions are
obtained:

(1.14)

Replacing CVT by [l/(~ - l)]p/p in Eqn (1.1 1) readily gives the enthalpy as
YP
cpT -- (1.15)
7-1P