GATE AE 2016 • Q5 MCQ • 1 Mark General Aptitude

General Aptitude

Quantitative Aptitude

Subtopic: Arithmetic & Numerical Estimation

Question Statement:

Which of the following statement is NOT TRUE across an oblique shock wave?

Options:

  • (A) Static temperature increases, total temperature remains constant.
  • (B) Static pressure increases, static temperature increases.
  • (C) Static temperature increases, total pressure decreases.
  • (D) Static pressure increases, total temperature decreases.

Official Answer Key:

C

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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