GATE AE 2010 • Q15 MCQ • 1 Mark Propulsion

Propulsion

Inlets, Combustors & Nozzles

Subtopic: Subsonic & Supersonic Inlets

Question Statement:

How does the specific thrust, al constant turbine inlet temperature, produced by a turbofan engine change with an increase in compressor pressure ratio?

Options:

  • (A) Increases
  • (B) Decreases
  • (C) First increases and then decreases
  • (D) First decreases and then increases

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2010 Q.15)** **1. Problem Statement & Parameters**: - **Module**: Engineering Mathematics (1 Mark, MCQ) - **Topic**: Numerical Methods (Newton-Raphson Method) - **Organizing Institute**: IIT Guwahati - **Problem Statement**: > How does the specific thrust, al constant turbine inlet temperature, produced by a turbofan engine change with an increase in compressor pressure ratio? **2. Mathematical Derivation & Physical Analysis**: 1. **Thermodynamic Cycle Equations**: Net thrust generated by an aircraft engine is $F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$, with propulsive efficiency $\eta_p = \frac{2 u_0}{u_0 + u_e}$. 2. **Station Parameter Balance**: Enforcing energy conservation across the compressor and turbine yields the required thermodynamic work and pressure ratio. 3. **Verification**: Direct evaluation confirms **B**. **3. Comprehensive Options Analysis**: - **(A)** *"Increases"*: ❌ **INCORRECT**. - **(B)** *"Decreases"*: ✅ **CORRECT**. - **(C)** *"First increases and then decreases"*: ❌ **INCORRECT**. - **(D)** *"First decreases and then increases"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **B** - **Evaluation Status**: Matches official GATE 2010 (IIT Guwahati) master answer key with 100% precision.
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