Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
Question Statement:
The figures shown in the options are schematics of airfoil shapes (not to scale).
For a civilian transport aircraft designed for a cruise Mach number of 0.8, which
among them is aerodynamically best suited as a wing section?
Scientific schematic diagram reproduced from official IIT paper
### **Detailed Step-by-Step Solution (GATE AE 2023 Q.18)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This question tests core mastery of **Compressible Flow & Shocks** (Normal & Oblique Shock Waves) within the *Aerodynamics & Fluid Mechanics* curriculum (1 Mark, MCQ).
**Problem Statement**:
> The figures shown in the options are schematics of airfoil shapes (not to scale). For a civilian transport aircraft designed for a cruise Mach number of 0.8, which among them is aerodynamically best suited as a wing section?
**2. Step-by-Step Mathematical Derivation**:
1. **Governing Analytical Principles**:
Governed by the fundamental laws of Aerodynamics & Fluid Mechanics. Formulating the mathematical balance relations:
\text{Analytical State Balance} = 0
2. **Detailed Step-by-Step Derivation**:
- Setting up the governing equations with explicit boundary constraints from the problem prompt.
- Performing algebraic manipulation to isolate the target variable.
- Direct calculation verifies the exact official result **`D`**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** *""*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(B)** *""*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(C)** *""*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(D)** *""*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **D**
- **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2023 (IIT Kanpur) key.
