1. Consider a transonic flow where the freestream Mach number is: M ∞ = 1 + ε where ε 1 Assuming a detached shock is formed, show that the Mach number downstream of the normal shock is: 2. To...

1. Consider a transonic flow where the freestream Mach number is:

M_∞
= 1 + ε where ε 1

Assuming a detached shock is formed, show that the Mach number downstream of the normal shock is:

2. To demonstrate that weak shocks that appear in transonic flow are nearly isentropic, we choose the freestream Mach number to a normal shock to be:

M_∞
= 1 + ε where ε 1

Use the normal shock relations to show that non-dimensional entropy rise across the normal shock, Δs/R is of order of ε³, i.e.,