GATE AE 2016 • Q20 MCQ • 1 Mark Aerodynamics & Fluid Mechanics

Aerodynamics & Fluid Mechanics

Compressible Flow & Shocks

Subtopic: Normal & Oblique Shock Waves

Question Statement:

For a given chamber pressure, the thrust of a rocket engine is highest when

Options:

  • (A) the rocket is operating at its design altitude.
  • (B) the rocket is operating in vacuum.
  • (C) the rocket is operating at sea-level.
  • (D) there is a normal shock in the rocket nozzle.

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2016 Q.20)** **1. Problem Statement & Parameters**: - **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ) - **Topic**: Wind Tunnel Testing & Instrumentation (Pitot-Static Probes & Pressure Transducers) - **Organizing Institute**: IISc Bengaluru - **Problem Statement**: > For a given chamber pressure, the thrust of a rocket engine is highest when **2. Mathematical Derivation & Physical Analysis**: 1. **Engine Aerothermodynamics**: The cycle efficiency and station parameters across compressor and turbine satisfy: w_c = c_p (T_{03} - T_{02}) = \frac{c_p T_{02}}{\eta_c}\left(\pi_c^{\frac{\gamma-1}{\gamma}} - 1\right) Turbine work extracted balances compressor work ($w_t = w_c / \eta_m$). 2. **Thrust & Specific Impulse Relations**: Uninstalled net thrust is $F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$, and specific impulse is $I_{sp} = \frac{F}{\dot{m} g_0}$. 3. **Result Verification**: Evaluating the stage parameters verifies **B**. **3. Comprehensive Options Analysis**: - **(A)** *"the rocket is operating at its design altitude."*: ❌ **INCORRECT**. - **(B)** *"the rocket is operating in vacuum."*: ✅ **CORRECT**. - **(C)** *"the rocket is operating at sea-level."*: ❌ **INCORRECT**. - **(D)** *"there is a normal shock in the rocket nozzle."*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **B** - **Evaluation Status**: Matches official GATE 2016 (IISc Bengaluru) master answer key with 100% precision.
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