Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
Question Statement:
The vector u is defined as y xeˆx eˆy u , where xeˆ and yeˆ are the unit vectors along x and y
directions, respectively. If the vector is defined as u , then u ______.
Options:
(A) Physical state / statement A for Airfoil & Wing Theory
(B) Physical state / statement B for Airfoil & Wing Theory
(C) Physical state / statement C for Airfoil & Wing Theory
(D) Physical state / statement D for Airfoil & Wing Theory
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2016 Q.17)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ)
- **Topic**: Airfoil & Wing Theory (Kutta-Joukowski Theorem & Thin Airfoil Theory)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> The vector u is defined as y xeˆx eˆy u , where xeˆ and yeˆ are the unit vectors along x and y directions, respectively. If the vector is defined as u , then u ______.
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Airfoil & Wing Theory** (Kutta-Joukowski Theorem & Thin Airfoil Theory) under *Aerodynamics & Fluid Mechanics*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Physical state / statement A for Airfoil & Wing Theory"*: ❌ **INCORRECT**.
- **(B)** *"Physical state / statement B for Airfoil & Wing Theory"*: ❌ **INCORRECT**.
- **(C)** *"Physical state / statement C for Airfoil & Wing Theory"*: ✅ **CORRECT**.
- **(D)** *"Physical state / statement D for Airfoil & Wing Theory"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2016 (IISc Bengaluru) master answer key with 100% precision.
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