GATE AE 2012 • Q18 MCQ • 1 Mark Aerodynamics & Fluid Mechanics

Aerodynamics & Fluid Mechanics

Compressible Flow & Shocks

Subtopic: 1D Isentropic Flow & Area-Mach Relations

Question Statement:

The Mach angle for a flow at Mach 2.0 is

Options:

  • (A) 30o
  • (B) 45o
  • (C) 60o
  • (D) 90o

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.18)** **1. Problem Statement & Parameters**: - **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ) - **Topic**: Compressible Flow & Shocks (Normal & Oblique Shock Waves) - **Organizing Institute**: IIT Delhi - **Problem Statement**: > The Mach angle for a flow at Mach 2.0 is **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: **A**. **3. Comprehensive Options Analysis**: - **(A)** *"30o"*: ✅ **CORRECT**. - **(B)** *"45o"*: ❌ **INCORRECT**. - **(C)** *"60o"*: ❌ **INCORRECT**. - **(D)** *"90o"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **A** - **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.
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