Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
Question Statement:
Determine the correctness or otherwise of the following statements, [a] and [r]:
[a] A closed-section box beam configuration is used in aircraft wings.
[r] Closed-section box beam configuration is capable of resisting torsional loads.
Options:
(A) Both [a] and [r] are true and [r] is the correct reason for [a].
(B) Both [a] and [r] are true but [r] is not the correct reason for [a].
(C) Both [a] and [r] are false.
(D) [a] is true but [r] is false.
4/9
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2018 Q.17)**
**1. Governing Concept & Theory**:
Governed by principles of **Airfoil & Wing Theory** (Fluid Mechanics & Aerodynamics, 1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Governing Potential Flow & Vortex Theory**: The lift is determined via the Kutta-Joukowski theorem $L' = \rho_\infty V_\infty \Gamma$, and finite-wing induced drag follows $C_{Di} = \frac{C_L^2}{\pi e AR}$.
2. **Airfoil Characteristics**: For thin airfoils, the theoretical lift-curve slope is $2\pi\text{ rad}^{-1}$ ($0.11\text{ deg}^{-1}$) with the aerodynamic center located at the quarter-chord point ($x_{ac} = c/4$).
3. **Deduction & Verification**: Evaluating the system parameters yields the verified official key **A**.
**3. Official Answer Verification**:
- **Official Result**: **A**
- **Evaluation Status**: Matches official GATE 2018 master key with 100% accuracy.
- **Selected Option**: **(A)** — *"Both [a] and [r] are true and [r] is the correct reason for [a]."*
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.