Page 74 - 48Fundamentals of Compressible Fluid Mechanics

36 CHAPTER 3. SPEED OF SOUND

The average density can be expressed as

(3.40)

is the mass ratio of the materials.

For small value of equation (3.40) can be approximated as
"

"
(3.41)
where "

is mass flow rate per gas flow rate.
The gas density can be replaced by equation (3.39) and substituted into
"
"
equation (3.41)
where

(3.42)

A approximation of addition droplets of liquid or dust (solid) results in reduction of

and yet approximate equation similar to ideal gas was obtained. It must noticed
. If the droplets (or the solid particles) can be assumed to have

the same velocity as the gas with no heat transfer or fiction between the particles

that
isentropic relation can be assumed as
(3.43)

Assuming that partial pressure of the particles is constant and applying the second
law for the mixture yields
%

(3.44)

Therefore, the mixture isentropic relationship can be expressed as

(3.45)

where
(3.46)

reduces equation (3.46) into

Recalling that
(3.47)