GATE AE 2013 • Q19 MCQ • 1 Mark Propulsion

Propulsion

Inlets, Combustors & Nozzles

Subtopic: Subsonic & Supersonic Inlets

Question Statement:

Consider two engines P and Q. In P, the high pressu re turbine blades are cooled with a bleed of 5% from the compressor after the compression process and in Q the turbine blades are not cooled. Comparing engine P with engine Q, which one of the following is NOT TRUE?

Options:

  • (A) Turbine inlet temperature is higher for engine P
  • (B) Specific thrust is higher for engine P
  • (C) Compressor work is the same for both P and Q
  • (D) Fuel flow rate is lower for engine P

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.19)** **1. Problem Statement & Parameters**: - **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ) - **Topic**: Compressible Flow & Shocks (1D Isentropic Flow & Area-Mach Relations) - **Organizing Institute**: IIT Bombay - **Problem Statement**: > Consider two engines P and Q. In P, the high pressu re turbine blades are cooled with a bleed of 5% from the compressor after the compression process and in Q the turbine blades are not cooled. Comparing engine P with engine Q, which one of the following is NOT TRUE? **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)** *"Turbine inlet temperature is higher for engine P"*: ❌ **INCORRECT**. - **(B)** *"Specific thrust is higher for engine P"*: ❌ **INCORRECT**. - **(C)** *"Compressor work is the same for both P and Q"*: ❌ **INCORRECT**. - **(D)** *"Fuel flow rate is lower for engine P"*: ✅ **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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