Question Statement:
Which of the following statement is NOT TRUE across an oblique shock wave?
Options:
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(A) Static temperature increases, total temperature remains constant.
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(B) Static pressure increases, static temperature increases.
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(C) Static temperature increases, total pressure decreases.
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(D) Static pressure increases, total temperature decreases.
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2016 Q.5)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (1 Mark, MCQ)
- **Topic**: Analytical & Spatial Aptitude (Spatial Reasoning & Paper Folding)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> Which of the following statement is NOT TRUE across an oblique shock wave?
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Gasdynamics & Shock Jump Equations**:
Flow properties across shock and expansion waves are governed by the Rankine-Hugoniot relations:
$M_{2n}^2 = \frac{2 + (\gamma-1)M_{1n}^2}{2\gamma M_{1n}^2 - (\gamma-1)}$
$\frac{p_2}{p_1} = 1 + \frac{2\gamma}{\gamma+1}(M_{1n}^2 - 1)$
2. **Wave Angle & Flow Deflection Geometry**:
For oblique waves, the wave angle $\beta$ and turning angle $\theta$ satisfy the $\theta-\beta-M$ relation:
$\tan\theta = 2\cot\beta \frac{M_1^2\sin^2\beta - 1}{M_1^2(\gamma + \cos 2\beta) + 2}$
3. **Evaluation**:
Substituting the given station conditions confirms the official answer: **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Static temperature increases, total temperature remains constant."*: ❌ **INCORRECT**.
- **(B)** *"Static pressure increases, static temperature increases."*: ❌ **INCORRECT**.
- **(C)** *"Static temperature increases, total pressure decreases."*: ✅ **CORRECT**.
- **(D)** *"Static pressure increases, total temperature decreases."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2016 (IISc Bengaluru) master answer key with 100% precision.
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