When a supersonic stream turns around a convex corner via a centered Prandtl-Meyer expansion fan, which of the following statements is TRUE?

(A) Mach number increases and static pressure decreases across the expansion fan

(B) Mach number decreases and static pressure increases across the expansion fan

(C) Total pressure decreases across the expansion fan

(D) Entropy of the gas increases across the expansion fan

Answer Key:

A

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Wave Characteristic:** Expansion waves are isentropic ($ds = 0, dp_0 = 0$). 2. **Stage 2: Dynamic Effects:** The streamline deflection accelerates the supersonic flow, increasing Mach number $M_2 > M_1$. 3. **Stage 3: Thermodynamic Expansion:** Static pressure drops ($p_2 < p_1$) and static temperature drops ($T_2 < T_1$). 4. **Stage 4: Selection:** Option A is strictly true.

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