GATE_AE_2027_MOCK_03_Q55
GATE 2027 Aerospace Engineering All-India Master Mock 03 (Flight Dynamics, Controls & Space Trajectories)
NAT · 2 Marks
Propulsion • Inlets, Combustors & Nozzles • Convergent-Divergent Nozzle & Choking
A rocket nozzle discharges hot gas with specific heat ratio \gamma = 1.25. What is the critical pressure ratio (P^* / P_0) at the nozzle throat? (Round off to three decimal places).
Answer Key:
0.555
Step-by-Step Verified Solution
### Solution: P^* / P_0 = [2 / (\gamma + 1)]^{\gamma / (\gamma - 1)} = [2 / 2.25]^{1.25 / 0.25} = [2 / 2.25]^5 = (8/9)^5 = (0.888889)^5 ≈ 0.5549 ≈ 0.555. Correct: 0.555 (range 0.550 to 0.560).