The non-dimensional parameter is defined as the pressure coefficient which is the ratio of static pressure difference across the shock to the dynamic pressure .

(4.7.5)

The dynamic pressure can also be expressed in the form of Mach number as given below;

(4.7.6)

Now, Eq. (4.7.5) can be simplified as,

(4.7.7)

In the hypersonic limit of , Eq. (4.7.7) is approximated as below;

(4.7.8)

The relationship between Mach number , shock angle and deflection angle is expressed by equation.

(4.7.9)

In the hypersonic limit, when, θ is small, β is also small. Thus, the small angle approximation can be used for Eq. (4.7.9).

(4.7.10)

It leads to simplification of Eq. (4.7.9) as below;

(4.7.11)

In the high Mach number limit, Eq (4.7.11) may be approximated for .

(4.7.12)

It is interesting to observe that in the hypersonic limit of a slender wedge, the shock wave angle is only 20% larger than the wedge angle which is the typical physical features of thin shock layer in the hypersonic flow.