Page 179 - 48Fundamentals of Compressible Fluid Mechanics

9.2. MODEL 141

The term can be eliminated utilizing equation (9.18) and substituting into equa-
tion (9.22) and rearrangement yields

(9.23)

can be eliminated by using (9.23)

(9.24)
The term

variable is obtained by combining equa-

are eliminated by

The second equation for Mach number,

can be
. Then
eliminated by utilizing equation (9.24) and results in
tion (9.20) and (9.21) by eliminating
and
utilizing equation (9.18) and equation (9.22). and only left is . Then
(9.25)

Rearranging equation (9.25) results in %

(9.26)

%

After similar mathematical manipulation one can get the relationship for the

velocity to read

(9.27)

and the relationship for the temperature is

(9.28)

density is obtained by utilizing equations (9.27) and (9.18) to obtain

(9.29)

The stagnation pressure similarly obtained as

(9.30)

The second law reads
(9.31)