Page 267 - 48Fundamentals of Compressible Fluid Mechanics

13.4. SOLUTION OF MACH ANGLE 229

to calculate .
Note that no maximum angle is achieved in this shock. POTTO–GDC can be
c and Mach number

used to calculate this ratio.

This procedure can be extended to calculated the maximum incoming Mach num-
(d) Use the deflection angle, c
ber, by check the relationship between the intermediate Mach number to .
In discussing these issues one must be aware that there zone of dual solution
in which sharp shock line co–exist with curved line. In general this zone is larger
with Mach number, for example at Mach 5 the this zone is 9 . For engineering

purpose when seldom Mach number reaching this value it can be ignored.
13.4.11 Examples

Example 13.2:
Air flows at Mach number ( ) or is approaching a wedge. What is the
maximum wedge angle which the oblique shock can occur? If the wedge angle is

calculated the weak and the strong Mach numbers and what are the respective
shock angle.

SOLUTION

The find maximum wedge angle for ( has to be equal to zero. The wedge
angel that satisfy this requirement by equation (13.28) is the solution (a side to the

)
). The maximum values are:
case proximity of c

c

4
4

)
+1+
- )-) -
To obtain the results of the weak and the strong solutions either utilize the
")
equation (13.28) or the GDC which yields the following results

4 91+1 -+ + -9 91+1+1+ " )
4
4
c
Example 13.3: -9
A cone shown in the Figure 13.15 exposed to supersonic flow and create an oblique

shock. Is the shock shown in the photo is weak or strong shock? explain. Using
the geometry provided in the photo predict at which of the Mach number the photo
was taken based on the assumption that the cone is a wedge.
SOLUTION
The measurement shows that cone angle is .
With given two angle the solution can be obtained utilizing equation (13.48) or the
"-"
Potto-GDC.

and shock angle is