Page 70 - 48Fundamentals of Compressible Fluid Mechanics

32 CHAPTER 3. SPEED OF SOUND

Equating the right hand side of equations (3.28) and (3.29) results in

(3.30)

Rearranging equation (3.30) yields (

&
(3.31)

If the terms in the square parentheses are constant in the range under the interest

in this study equation (3.31) can be integrated. For short hand writing convenience,

is defined as
&

(
(3.32)

%
Note that approach to and when is constant. The integration of

equation (3.31) yields when

"

(3.33)

Equation (3.33) the similar to equation (3.11). What is different in these derivation

the relationship between coefficient to was established. The relationship (3.33)

isn’t new, and in–fact any thermodynamics book show this relationship. But with the
definition of in equation (3.32) provide a tool to estimate In the same manner
as the ideal gas speed of sound the speed of sound for real gas can be obtained.
(3.34)

Example 3.4:
.
, and
.
Make the calculation based on the ideal gas model and compare these

.
The specific heat for air is

Calculate the speed of sound of air at
and atmospheric pressure
calculation to real gas model (compressibility factor). Assume that %(

SOLUTION
,

!(
According to the ideal gas model the speed of sound should be
has #

!( %!(

% 1
For the real gas first the coefficient
# #

1 %(

3 )( 1

'
#