GATE_AE_2027_MOCK_05_Q18 GATE 2027 Aerospace Engineering All-India Master Mock 05 (High-Yield Comprehensive Grand Finale) MCQ · 1 Mark
Aerodynamics & Fluid Mechanics • Compressible Flow & Shocks • Normal & Oblique Shock Waves

As the upstream Mach number M_1 of a normal shock wave increases indefinitely (M_1 -> \infty) for a calorically perfect gas with \gamma = 1.4, the density ratio ho_2 / ho_1 approaches an asymptotic limit of:

(A) 6.0
(B) 1.0
(C) Infinity
(D) 2.4
Answer Key:
A

Step-by-Step Verified Solution

### Solution: As M_1 -> \infty, ho_2 / ho_1 -> (\gamma + 1) / (\gamma - 1) = (1.4 + 1) / (1.4 - 1) = 2.4 / 0.4 = 6.0. Correct: A.
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