GATE_AE_2027_MOCK_02_Q19 GATE 2027 Aerospace Engineering All-India Master Mock 02 (Compressible Aerodynamics & High-Speed Propulsion) NAT · 1 Mark
Aerodynamics & Fluid Mechanics • Compressible Flow & Shocks • Prandtl-Meyer Expansion Fan

A uniform supersonic flow of air ($\gamma = 1.4$) at Mach $M_1 = 2.0$ passes over a convex corner producing a Prandtl-Meyer expansion fan. If the downstream Mach number is $M_2 = 2.50$, and given $\nu(2.0) = 26.38^\circ$ and $\nu(2.50) = 39.12^\circ$, what is the deflection angle $\theta$ of the corner in degrees?

Answer Key:
12.74

Step-by-Step Verified Solution

### Solution: For a Prandtl-Meyer expansion fan, the turn angle $\theta = \nu(M_2) - \nu(M_1) = 39.12^\circ - 26.38^\circ = 12.74^\circ$. Correct: 12.74 (range 12.70 to 12.80).
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