Fig. 10.1 Illustration of presence of centrifugal force for flow over blunt bodies.

Consider a hypersonic flow over a typical blunt body configuration as shown in Fig. 10.2.

Fig. 10.2. Schematic of blunt body flow for Newtonian-Bwemann theory

Let’s consider a stream tube of pre-shock height dy. This same stream tube gets deflected by angle θ behind the shock and earns thickness dn. Suppose ‘R’ is the radius of the curvature faced by the fluid particles passing this tube. This radius will be much more in comparison with the shock layer thickness. Therefore we can assume that all particles in shock layer face some curvature for calculation of the centrifugal force as,

Here
Pressure (P)=f(S,η)
S = coordinate along stream tube
η = coordinate along normal to the stream tube

Hence,

We can integrate this expression along the thickness of the shock layer (line a-b-c) while considering the complete freestream instead of a stream tube. Therefore,

Here ∆η is the shock layer thickness in the direction normal from point a on the blunt body. Hence,

However we know from mass conservation for the stream tube that