7.2. Pressure coefficient for hypersonic flow

We know that the pressure coefficient at any point can be calculated as

Here, dynamic pressure =

Therefore the expression, for pressure coefficient becomes,

For high Mach number we have M>>1 we can the get the simplified expression as,

We can express the shock angle using Eq. 7.4. and also assume shock angle to be small (sinβ ≈ β). This leads to,

7.5

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

Modifications in hypersonic expansion for relations
Prandtl expansion for relation for general case is
θ = v(M₂) - v(M₁)

where