Page 248 - 48Fundamentals of Compressible Fluid Mechanics

210 CHAPTER 13. OBLIQUE-SHOCK
θ − δ

θ

Compersion Line

Fig. 13.3: A typical oblique shock schematic

The momentum equation in the tangential direction yields
(13.3)

The energy balance reads "
"
B B
(13.4)

"$
I
I

Equations (13.1), (13.2) and (13.4) are the same equations as the equations for
normal shock with the exception that the total velocity is replaced by the perpendi-

"
cular components. Yet, the new issue of relationship between the upstream Mach

number and the deflection angle, c and the Mach angel, has to be solved. From
the geometry it can be observed that
(13.5)
"$

and " B
(13.6)

E c
5
Not as in the normal shock, here there are three possible pair of solutions
B

"
to these equations one is referred to as the weak shock, two the strong shock, and
6
"
three the impossible solution (thermodynamically) . Experiments and experience
5 This issue is due to R. Menikoff, which raise to completeness of the solution. He pointed out the
full explanation to what happened to the negative solution.
6 This solution requires to solve the entropy conservation equation. The author is not aware of
“simple” proof and a call to find a simple proof is needed.