GATE AE 2010 • Q18 MCQ • 1 Mark Aerodynamics & Fluid Mechanics

Aerodynamics & Fluid Mechanics

Compressible Flow & Shocks

Subtopic: Normal & Oblique Shock Waves

Question Statement:

For a flow across an oblique shock which of the following statements is true?

Options:

  • (A) Component of velocity normal to shock decreases while tangential component increases.
  • (B) Component of velocity normal to shock increases while tangential component decreases.
  • (C) Component of velocity normal to shock is unchanged while tangential component decreases.
  • (D) Component of velocity normal to shock decreases while tangential component is unchanged.

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2010 Q.18)** **1. Problem Statement & Parameters**: - **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ) - **Topic**: Compressible Flow & Shocks (Normal & Oblique Shock Waves) - **Organizing Institute**: IIT Guwahati - **Problem Statement**: > For a flow across an oblique shock which of the following statements is true? **2. Mathematical Derivation & Physical Analysis**: 1. **Compressible Wave Relations**: Flow through oblique shocks or expansion waves obeys the Rankine-Hugoniot and isentropic relations: M_{2n}^2 = \frac{2 + (\gamma-1)M_{1n}^2}{2\gamma M_{1n}^2 - (\gamma-1)}, \quad \frac{p_2}{p_1} = 1 + \frac{2\gamma}{\gamma+1}(M_{1n}^2 - 1) 2. **Gasdynamic Flow State**: Evaluating across the wave angle verifies total pressure loss or isentropic Mach expansion. 3. **Verification**: Matches the official GATE 2010 answer: **D**. **3. Comprehensive Options Analysis**: - **(A)** *"Component of velocity normal to shock decreases while tangential component increases."*: ❌ **INCORRECT**. - **(B)** *"Component of velocity normal to shock increases while tangential component decreases."*: ❌ **INCORRECT**. - **(C)** *"Component of velocity normal to shock is unchanged while tangential component decreases."*: ❌ **INCORRECT**. - **(D)** *"Component of velocity normal to shock decreases while tangential component is unchanged."*: ✅ **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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