GATE AE 2013 • Q11 MCQ • 1 Mark Aerodynamics & Fluid Mechanics

Aerodynamics & Fluid Mechanics

Compressible Flow & Shocks

Subtopic: Prandtl-Meyer Expansion Waves

Question Statement:

Which one of the following statements is NOT TRUE for a supersonic flow?

Options:

  • (A) Over a gradual expansion, entropy remains constant
  • (B) Over a sharp expansion corner, entropy can increase
  • (C) Over a gradual compression, entropy can remain constant
  • (D) Over a sharp compression corner, entropy increases

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.11)** **1. Problem Statement & Parameters**: - **Module**: Engineering Mathematics (1 Mark, MCQ) - **Topic**: Linear Algebra (Matrices & Determinants) - **Organizing Institute**: IIT Bombay - **Problem Statement**: > Which one of the following statements is NOT TRUE for a supersonic flow? **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Linear Algebra** (Matrices & Determinants) under *Engineering Mathematics*. 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)** *"Over a gradual expansion, entropy remains constant"*: ❌ **INCORRECT**. - **(B)** *"Over a sharp expansion corner, entropy can increase"*: ✅ **CORRECT**. - **(C)** *"Over a gradual compression, entropy can remain constant"*: ❌ **INCORRECT**. - **(D)** *"Over a sharp compression corner, entropy increases"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **B** - **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.
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