GATE AE 2008 • Q41 MCQ • 2 Marks Aerodynamics & Fluid Mechanics

Aerodynamics & Fluid Mechanics

Airfoil & Wing Theory

Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory

Question Statement:

Flow past an airfoil is to be modeled using a vortex sheet. The strength of the vortex sheet at the trailing edge will be

Options:

  • (A) 0
  • (B) 1
  • (C) 27
  • (D) co

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.41)** **1. Problem Statement & Parameters**: - **Module**: Aerodynamics & Fluid Mechanics (2 Mark, MCQ) - **Topic**: Basic Fluid Mechanics (Viscous Flow & Boundary Layer Equations) - **Organizing Institute**: IISc Bengaluru - **Problem Statement**: > Flow past an airfoil is to be modeled using a vortex sheet. The strength of the vortex sheet at the trailing edge will be **2. Mathematical Derivation & Physical Analysis**: 1. **Aerodynamic Theory & Finite Wing Relations**: Lift and induced drag follow Lanchester-Prandtl lifting-line theory: C_L = a_0 (\alpha - \alpha_{L=0} - \alpha_i), \quad C_{Di} = \frac{C_L^2}{\pi e AR} 2. **Induced Drag Minimization**: For an elliptic lift distribution ($e = 1$), downwash is constant across the span, providing minimum induced drag for a given aspect ratio. 3. **Official Verification**: Matches **A**. **3. Comprehensive Options Analysis**: - **(A)** *"0"*: ✅ **CORRECT**. - **(B)** *"1"*: ❌ **INCORRECT**. - **(C)** *"27"*: ❌ **INCORRECT**. - **(D)** *"co"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **A** - **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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