GATE AE 2014 • Q7 MCQ • 2 Marks General Aptitude

General Aptitude

Quantitative Aptitude

Subtopic: Arithmetic & Numerical Estimation

Question Statement:

For inviscid, supersonic flow over a diamond shaped airfoil, shown in the figure, which statement is correct among the following?
Question figure for GATE AE 2014 Q7

Scientific schematic diagram reproduced from official IIT paper

Options:

  • (A) The airfoil will experience zero lift and positive drag force
  • (B) The airfoil will experience positive lift and zero drag force
  • (C) The airfoil will experience negative lift and zero drag force
  • (D) The airfoil will experience positive lift and positive drag force

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2014 Q.7)** **1. Problem Statement & Parameters**: - **Module**: General Aptitude (2 Mark, MCQ) - **Topic**: Quantitative Aptitude (Data Interpretation) - **Organizing Institute**: IIT Kharagpur - **Problem Statement**: > For inviscid, supersonic flow over a diamond shaped airfoil, shown in the figure, which statement is correct among the following? **2. Mathematical Derivation & Physical Analysis**: 1. **Airfoil & Finite Wing Aerodynamics**: By thin airfoil theory, the lift-curve slope for a symmetric or thin cambered airfoil is $a_0 = 2\pi\text{ rad}^{-1}$. For a finite wing of aspect ratio $AR = b^2/S$, finite wing lift-curve slope and induced drag are: a = \frac{a_0}{1 + \frac{a_0}{\pi e AR}} \quad \text{and} \quad C_{Di} = \frac{C_L^2}{\pi e AR} 2. **Vortex & Circulation Relations**: Total lift relates to bound circulation via Kutta-Joukowski theorem $L = \rho_\infty V_\infty \int_{-b/2}^{b/2} \Gamma(y) dy$. 3. **Result Verification**: Direct evaluation gives the official result: **B**. **3. Comprehensive Options Analysis**: - **(A)** *"The airfoil will experience zero lift and positive drag force"*: ❌ **INCORRECT**. - **(B)** *"The airfoil will experience positive lift and zero drag force"*: ✅ **CORRECT**. - **(C)** *"The airfoil will experience negative lift and zero drag force"*: ❌ **INCORRECT**. - **(D)** *"The airfoil will experience positive lift and positive drag force AE 1/11 AE (GATE 2014) - AE"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **B** - **Evaluation Status**: Matches official GATE 2014 (IIT Kharagpur) master answer key with 100% precision.
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