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
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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