GATE AE 2008 • Q42
MCQ • 2 Marks
Aerodynamics & Fluid Mechanics
Compressible Flow & Shocks
Subtopic: Normal & Oblique Shock Waves
Question Statement:
M. will cause the oblique shock wave to
Options:
-
(A) move closer to the body
-
(B) move away from the body
-
(C) detach from the body
-
(D) become a normal shock
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.42)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (2 Mark, MCQ)
- **Topic**: Compressible Flow & Shocks (Normal & Oblique Shock Waves)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> M. will cause the oblique shock wave to
**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 2008 answer: **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"move closer to the body"*: ❌ **INCORRECT**.
- **(B)** *"move away from the body"*: ❌ **INCORRECT**.
- **(C)** *"detach from the body"*: ✅ **CORRECT**.
- **(D)** *"become a normal shock"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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