GATE AE 2023 • Q46
MSQ • 2 Marks
Aerodynamics & Fluid Mechanics
Airfoil & Wing Theory
Subtopic: High-Lift Devices & Flaps
Question Statement:
For an airfoil, which of the relations given about the critical Mach number
crM
and drag divergence Mach number
ddM is/are correct?
Options:
-
(A) cr ddMM
-
(B) 1.0crM
-
(C) 1.0ddM
-
(D) 1.0crM
Official Answer Key:
A, B, C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2023 Q.46)**
**1. Governing Concept & Theory**:
Governed by principles of **Airfoil & Wing Theory** (Fluid Mechanics & Aerodynamics, 2 Mark, MSQ).
**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, B, C**.
**3. Official Answer Verification**:
- **Official Result**: **A, B, C**
- **Evaluation Status**: Matches official GATE 2023 master key with 100% accuracy.
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