7.1. Shock relations for hypersonic flow
Consider a supersonic flow passing from a compression corner as shown in Fig. 7.1.

Fig. 7.1 Supersonic flow over a compression corner.

Following are the oblique shock relations for supersonic flow where β is the shock angle.

Here 1 is the freestream or pre-shock condition while 2 is the post shock condition.

Since hypersonic flows have very high Mach number we can assume that M 1 >>1. This leads to the modification as, M² sin² ß-1 ≈ M² sin²ß. Hence the relation for pressure ratio is,

7.1

Similarly density ratio can be rewritten as,

7.2

Ratio for temperature for very high freestream Mach numbers can be then expressed as,

7.3

The θ-β-M relation for supersonic flow as

For small wedge and shock angles we can write sinβ ≈ β and  cos2β ≈ 1and replacing M1 by M we get.

At the limit of high Mach numbers the above expression reduces to

7.4

This expression is valid for high Mach numbers and small deflection angles