Question

If a supersonic flow (\(M=2.0\)) encounters a convex corner (expansion), what happens to the stagnation pressure?

• A. It increases because the flow speeds up
• B. It decreases because of the expansion fan
• C. It remains constant because the process is isentropic
• D. It drops to zero

Hint:

Across a Prandtl--Meyer expansion, \[ \boxed{ \begin{aligned} M &\uparrow P &\downarrow T &\downarrow P_0 &=\text{Constant} \end{aligned} } \] because the expansion process is isentropic.

Answer 1

The Correct Option is C

Step 1: Recall the Prandtl--Meyer expansion. When a supersonic flow passes around a convex corner, \[ \boxed{ \text{a Prandtl--Meyer expansion fan is formed.} } \] The expansion process is continuous and isentropic.

Step 2: Determine the effect on stagnation pressure. For an isentropic process, \[ \boxed{ \text{Stagnation pressure remains constant.} } \] Although the static pressure decreases and the Mach number increases, \[ P_0 \] does not change. Therefore, \[ \boxed{\text{It remains constant because the process is isentropic}} \] is the correct answer. Thus, \[ \boxed{(C)} \] is the correct answer.