GATE_AE_2027_MOCK_04_Q42
GATE 2027 Aerospace Engineering All-India Master Mock 04 (Aerospace Structures, Thin-Walled Beams & Aeroelasticity)
NAT · 2 Marks
Aerodynamics & Fluid Mechanics • Compressible Flow & Shocks • Normal & Oblique Shock Waves
Supersonic airflow at M_1 = 1.80 encounters a normal shock wave (\gamma = 1.4). What is the static pressure ratio P_2 / P_1 across the shock? (Round off to two decimal places).
Answer Key:
3.61
Step-by-Step Verified Solution
### Solution: P_2 / P_1 = 1 + [2\gamma / (\gamma + 1)] (M_1^2 - 1) = 1 + [2.8 / 2.4] (1.8^2 - 1) = 1 + 1.16667 * (3.24 - 1) = 1 + 1.16667 * 2.24 = 1 + 2.6133 = 3.6133 ≈ 3.61. Correct: 3.61 (range 3.58 to 3.65).