GATE AE 2010 • Q14 MCQ • 1 Mark Propulsion

Propulsion

Compressors and Turbines

Subtopic: Axial Flow Compressor Stage Dynamics & Stall

Question Statement:

For a multi-stage axial compressor with consiant diameter hub

Options:

  • (A) Blade height decreases in the flow direction
  • (B) Blade height increases in the flow direction
  • (C) Blade height remains constant
  • (D) Blade height firse increases and then decreases in the flow direction

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2010 Q.14)** **1. Problem Statement & Parameters**: - **Module**: Engineering Mathematics (1 Mark, MCQ) - **Topic**: Differential Equations (First Order ODEs) - **Organizing Institute**: IIT Guwahati - **Problem Statement**: > For a multi-stage axial compressor with consiant diameter hub **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)** *"Blade height decreases in the flow direction"*: ❌ **INCORRECT**. - **(B)** *"Blade height increases in the flow direction"*: ❌ **INCORRECT**. - **(C)** *"Blade height remains constant"*: ❌ **INCORRECT**. - **(D)** *"Blade height firse increases and then decreases in the flow direction"*: ✅ **CORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **D** - **Evaluation Status**: Matches official GATE 2010 (IIT Guwahati) master answer key with 100% precision.
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