GATE_AE_2027_MOCK_03_Q42
GATE 2027 Aerospace Engineering All-India Master Mock 03 (Flight Dynamics, Controls & Space Trajectories)
NAT · 2 Marks
Aerodynamics & Fluid Mechanics • Compressible Flow & Shocks • Normal & Oblique Shock Waves
A supersonic airflow at Mach M_1 = 2.0 enters a normal shock wave (\gamma = 1.4). What is the downstream Mach number M_2? (Round off to two decimal places).
Answer Key:
0.58
Step-by-Step Verified Solution
### Solution: M_2^2 = [2 + (\gamma - 1)M_1^2] / [2\gamma M_1^2 - (\gamma - 1)] = [2 + 0.4(4)] / [2.8(4) - 0.4] = [2 + 1.6] / [11.2 - 0.4] = 3.6 / 10.8 = 1/3 ≈ 0.3333. M_2 = sqrt(1/3) ≈ 0.577 ≈ 0.58. Correct: 0.58 (range 0.56 to 0.60).