Page 106 - 48Fundamentals of Compressible Fluid Mechanics

68 CHAPTER 4. ISENTROPIC VARIABLE AREA FLOW

Substituting relation for stagnation density (3.19) results

(4.109)

For the integration results in
(4.110)

&

the integration becomes (
For
(4.111)

It must be noted that is a function of the critical temperature and critical pressure.

The mass flow rate is regardless to equation of state as following

(4.112)

Where is the density at the throat (assuming the chocking condition) and is

the cross area of the throat. Thus, the mass flow rate in our properties

(4.113)

&

For the case of
(

(4.114)

The Mach number can be obtained by utilizing equation (3.34) to defined the Mach

number as
(4.115)

Integrating equation (4.105) when
results

(4.116)