Page 274 - 48Fundamentals of Compressible Fluid Mechanics

236 CHAPTER 13. OBLIQUE-SHOCK

The temperature ratio combined upstream temperature yield

and the same for the pressure
-"

"$

9
And the velocity
9-)19#

9) ,'
2
Example 13.8: " ) $

For Mach number 2.5 and wedge with total angle of calculate the ratio of the
"
stagnation pressure.
)$
+
9 (
SOLUTION
Utilizing GDC for Mach number 2.5 and angle of results in

c 7 8

4
4
4
9
Example 13.9: 9 -9 "-"-9 7 8 "1+- )

What the maximum pressure ratio that can be obtained on wedge when the gas is

flowing in 2.5 Mach without any close boundaries. Would it make any difference if
the wedge was flowing into the air? if so what is the difference.
SOLUTION
It has to be recognized that without any other boundary condition the shock is
weak shock. For weak shock the maximum pressure ratio is obtained when at the
deflection point because it is the closest to normal shock. The obtain the maximum
point for 2.5 Mach number either use Maximum Deflection Mach number’s equation
or POTTO–GDC 4 5 7 8

4

7
c

7 8
9
+1 9
"
+
)
" ),")
+ ),
In these calculation Maximum Deflection Mach’s equation was used to calculate
9-)
Normal component of the upstream than Mach angle was calculated using the
5
. With these two quantities utilizing
7

equation (13.12) the deflection angle, c is obtained.

geometrical relationship of

Example 13.10:

Consider the schematic shown in the following Figure.