Page 260 - 48Fundamentals of Compressible Fluid Mechanics

222 CHAPTER 13. OBLIQUE-SHOCK

or

(13.41)

The pressure ratio can be expressed as

c
(13.42)

The density ratio can be expressed as

!
(13.43)
!

"$

"
The temperature ratio expressed as

(13.44)

The Mach number after the shock is

$

$

(13.45)
"

c
or explicitly

(13.46)

The ratio of the total pressure can be expressed as

(13.47)

Eventhough that the solution for these variables, and , is unique the

possible range deflection angle, c , is limited. Examining equation (13.40) shows

that shock angel, , has to be in the range of (see Figure

13.9). The range of given , upstream Mach number , is limited between and

.

13.4.4 For Given Two Angles, and

It is sometimes useful to obtains relationship where the two angles are known. The
first upstream Mach number, is
(13.48)

c

c