Page 67 - 48Fundamentals of Compressible Fluid Mechanics

3.4. SPEED OF SOUND IN REAL GAS 29

Example 3.3:
The temperature in the atmosphere can be assumed to be a linear function of the
height for some distances. What is the time it take for sound to travel from point
“A” to point “B” under this assumption.?

SOLUTION
. The distance
between “A” and “B” is denoted as . and temperature in “B” is
The temperature is denoted at “A” as

Where the distance is the variable distance. It should be noted that velocity is

provided as a function of the distance and not the time (another reverse problem).

is equal to

For an infinitesimal time

2
,

integration of the above equation yields
(3.16)
#

For assumption of constant temperature the time is "

(3.17)

Hence the correction factor
(3.18)
#

. "

is it reasonable to put a

discussion here about atmo-
,
This correction factor approaches one when

sphere and other affects on
the air?
3.4 Speed of Sound in Real Gas

The ideal gas model can be improved by introducing the compressibility factor. The
compressibility factor represent the deviation from the ideal gas.
Thus, a real gas equation can be expressed in many cases as
(3.19)