GATE AE 2008 • Q49 MCQ • 2 Marks Propulsion

Propulsion

Compressors and Turbines

Subtopic: Axial Flow Gas Turbines & Blade Cooling

Question Statement:

The turbine power per unit mass flow is

Options:

  • (A) 29.76 kJ/kg
  • (B) 41.12 kJ/kg
  • (C) 58.33 kJ/kg
  • (D) 61.13 kJ/kg

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.49)** **1. Problem Statement & Parameters**: - **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ) - **Topic**: Static Stability & Control (Static Margin & Stick-Fixed/Free Stability) - **Organizing Institute**: IISc Bengaluru - **Problem Statement**: > The turbine power per unit mass flow is **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 **D**. **3. Comprehensive Options Analysis**: - **(A)** *"29.76 kJ/kg"*: ❌ **INCORRECT**. - **(B)** *"41.12 kJ/kg"*: ❌ **INCORRECT**. - **(C)** *"58.33 kJ/kg"*: ❌ **INCORRECT**. - **(D)** *"61.13 kJ/kg"*: ✅ **CORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **D** - **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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