GATE_AE_2027_MOCK_01_Q58
GATE 2027 Aerospace Engineering All-India Master Mock 01 (Foundation & Standard Core Calibration)
NAT · 2 Marks
Propulsion • Rocket Propulsion • Solid, Liquid & Hybrid Rocket Engines
A solid rocket motor grain burns with propellant regression rate governed by Saint-Robert's law $r = a p_c^n$, where $a = 5.0\text{ mm/(s}\cdot\text{MPa}^n)$ and pressure exponent $n = 0.40$. At a chamber pressure $p_c = 6.0\text{ MPa}$, what is the burning rate $r$ in mm/s? (Round off to two decimal places).
Answer Key:
10.24
Step-by-Step Verified Solution
### Solution: $r = a p_c^n = 5.0 \times (6.0)^{0.40}$. $6^{0.40} = e^{0.40 \ln 6} = e^{0.40 \times 1.79176} = e^{0.7167} \approx 2.0477$. Burning rate $r = 5.0 \times 2.0477 = 10.2385 \approx 10.24\text{ mm/s}$. Correct: 10.24 (range 10.15 to 10.35).