GATE AE 2012 • Q18
MCQ • 1 Mark
Aerodynamics & Fluid Mechanics
Compressible Flow & Shocks
Subtopic: Normal & Oblique Shock Waves
Question Statement:
The Mach angle for a flow at Mach 2.0 is
Options:
-
(A) 30o
-
(B) 45o
-
(C) 60o
-
(D) 90o
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.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test