Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
Question Statement:
One of the criteria for high-speed airplanes is that the critical Mach number should be as high as possible. Therefore, high-speed subsonic airplanes are usually designed with
Options:
(A) thick airfoils
(B) thin airfoils
(C) laminar flow airfoils
(D) diamond airfoils
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.15)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Numerical Methods (Newton-Raphson Method)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> One of the criteria for high-speed airplanes is that the critical Mach number should be as high as possible. Therefore, high-speed subsonic airplanes are usually designed with
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Numerical Methods** (Newton-Raphson Method) under *Engineering Mathematics*. 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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"thick airfoils"*: ❌ **INCORRECT**.
- **(B)** *"thin airfoils"*: ✅ **CORRECT**.
- **(C)** *"laminar flow airfoils"*: ❌ **INCORRECT**.
- **(D)** *"diamond airfoils"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.