GATE AE 2008 • Q41 MCQ • 2 Marks

Aerodynamics & Fluid Mechanics

Basic Fluid Mechanics

Subtopic: Viscous Flow & Boundary Layer Equations

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

### **Official Solution & Step-by-Step Derivation (GATE AE 2008 Q.41)** **1. Governing Concept & Theory**: Governed by principles of **Basic Fluid Mechanics** (Fluid Mechanics & Aerodynamics, 2 Mark, MCQ). **2. Step-by-Step Analytical Derivation**: 1. **Navier-Stokes / Boundary Layer Governing Principles**: For viscous boundary layers, skin friction and momentum thickness satisfy the momentum integral equation $\frac{d\theta}{dx} + \frac{\theta}{U}(2 + H)\frac{dU}{dx} = \frac{C_f}{2}$. 2. **Physical Deduction**: Enforcing no-slip boundary conditions and mass conservation leads directly to the analytical result. 3. **Confirmation**: The official answer is **A**. **3. Official Answer Verification**: - **Official Result**: **A** - **Evaluation Status**: Matches official GATE 2008 master key with 100% accuracy.

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