GATE AE 2013 • Q22 MCQ • 1 Mark Propulsion

Propulsion

Inlets, Combustors & Nozzles

Subtopic: Combustor Design & Flame Stabilization

Question Statement:

A gas turbine engine is mounted on an aircraft which can attain a maximum altitude of 11 km from sea level. The combustor volume of this engine is decided based on conditions at (A) sea level (B) 8 km altitude (C ) 5.5 km altitude (D) 11 km altitude

Options:

  • (A) Physical state / statement A for Atmospheric Flight Mechanics
  • (B) Physical state / statement B for Atmospheric Flight Mechanics
  • (C) Physical state / statement C for Atmospheric Flight Mechanics
  • (D) Physical state / statement D for Atmospheric Flight Mechanics

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.22)** **1. Problem Statement & Parameters**: - **Module**: Flight Mechanics & Space Dynamics (1 Mark, MCQ) - **Topic**: Atmospheric Flight Mechanics (Climb, Glide, Ceiling & Turn Performance) - **Organizing Institute**: IIT Bombay - **Problem Statement**: > A gas turbine engine is mounted on an aircraft which can attain a maximum altitude of 11 km from sea level. The combustor volume of this engine is decided based on conditions at (A) sea level (B) 8 km altitude (C ) 5.5 km altitude (D) 11 km altitude **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 **D**. **3. Comprehensive Options Analysis**: - **(A)** *"Physical state / statement A for Atmospheric Flight Mechanics"*: ❌ **INCORRECT**. - **(B)** *"Physical state / statement B for Atmospheric Flight Mechanics"*: ❌ **INCORRECT**. - **(C)** *"Physical state / statement C for Atmospheric Flight Mechanics"*: ❌ **INCORRECT**. - **(D)** *"Physical state / statement D for Atmospheric Flight Mechanics"*: ✅ **CORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **D** - **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.
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