GATE AE 2010 • Q18
MCQ • 1 Mark
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:
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(A) Component of velocity normal to shock decreases while tangential component increases.
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(B) Component of velocity normal to shock increases while tangential component decreases.
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(C) Component of velocity normal to shock is unchanged while tangential component decreases.
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(D) Component of velocity normal to shock decreases while tangential component is unchanged.
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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