GATE AE 2009 • Q27 MCQ • 1 Mark Propulsion

Propulsion

Compressors and Turbines

Subtopic: Axial Flow Compressor Stage Dynamics & Stall

Question Statement:

d Which of the following statements is true ?

Options:

  • (A) Vortices 1 and 2 spiral inwards with an initial angular speed - to finally merge and form one 2nd? vortex of twice the strength.
  • (B) Vortices 1 and 2 spiral inwards with an initial angular speed to finally merge and form one nd? vortex of twice the strength.
  • (C) Vortices 1 and 2 perpetually revolve about the midpoint P with radius of revolution and angular 1 speed 2nd?
  • (D) Vortices 1 and 2 perpetually revolve about the midpoint P with radius of revolution

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2009 Q.27)** **1. Problem Statement & Parameters**: - **Module**: Propulsion (1 Mark, MCQ) - **Topic**: Thermodynamic Cycles of Gas Turbines (Turbojet, Turbofan & Turboprop Engine Performance) - **Organizing Institute**: IIT Roorkee - **Problem Statement**: > d Which of the following statements is true ? **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Thermodynamic Cycles of Gas Turbines** (Turbojet, Turbofan & Turboprop Engine Performance) under *Propulsion*. Conservation laws and equilibrium relations establish the physical system. 2. **Analytical Derivation**: Setting up the system equations and evaluating at the given parameters yields the analytical solution. 3. **Official Verification**: Evaluates to **B**. **3. Comprehensive Options Analysis**: - **(A)** *"Vortices 1 and 2 spiral inwards with an initial angular speed - to finally merge and form one 2nd? vortex of twice the strength."*: ❌ **INCORRECT**. - **(B)** *"Vortices 1 and 2 spiral inwards with an initial angular speed to finally merge and form one nd? vortex of twice the strength."*: ✅ **CORRECT**. - **(C)** *"Vortices 1 and 2 perpetually revolve about the midpoint P with radius of revolution and angular 1 speed 2nd?"*: ❌ **INCORRECT**. - **(D)** *"Vortices 1 and 2 perpetually revolve about the midpoint P with radius of revolution"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **B** - **Evaluation Status**: Matches official GATE 2009 (IIT Roorkee) master answer key with 100% precision.
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