Question Statement:
In supersonic wind-tunnel design, an oblique shock diffuser is preferred over a normal shock diffuser because
Options:
-
(A) it reduces total pressure loss
-
(B) the flow is slowed down more rapidly
-
(C) the flow is accelerated more rapidly
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(D) it increases total pressure loss
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.39)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (2 Mark, MCQ)
- **Topic**: Numerical Methods (Runge-Kutta Methods for ODEs)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> In supersonic wind-tunnel design, an oblique shock diffuser is preferred over a normal shock diffuser because
**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: **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"it reduces total pressure loss"*: ❌ **INCORRECT**.
- **(B)** *"the flow is slowed down more rapidly"*: ✅ **CORRECT**.
- **(C)** *"the flow is accelerated more rapidly"*: ❌ **INCORRECT**.
- **(D)** *"it increases total pressure loss"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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