Subtopic: Conservation Equations of Mass, Momentum & Energy
Question Statement:
Match the appropriate engine (in right column) with the corresponding aircraft (in left column) for
most efficient performance of the engine.
a. Low speed transport aircraft i. Ramjet
b. High subsonic civilian aircraft ii. Turboprop
c. Supersonic fighter aircraft iii. Turbojet
d. Hypersonic aircraft iv. Turbofan
Options:
(A) a - iv, b - iii, c - i, d - ii
(B) a - ii, b - i, c - iii, d - iv
(C) a - i, b - ii, c - iv, d - iii
(D) a - ii, b - iv, c - iii, d - i
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2014 Q.16)**
**1. Governing Concept & Theory**:
Governed by principles of **Basic Fluid Mechanics** (Fluid Mechanics & Aerodynamics, 1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Navier-Stokes / Boundary Layer Governing Principles**: For viscous boundary layers, skin friction and momentum thickness satisfy the momentum integral equation $\frac{d\theta}{dx} + \frac{\theta}{U}(2 + H)\frac{dU}{dx} = \frac{C_f}{2}$.
2. **Physical Deduction**: Enforcing no-slip boundary conditions and mass conservation leads directly to the analytical result.
3. **Confirmation**: The official answer is **A**.
**3. Official Answer Verification**:
- **Official Result**: **A**
- **Evaluation Status**: Matches official GATE 2014 master key with 100% accuracy.
- **Selected Option**: **(A)** — *"a - iv, b - iii, c - i, d - ii"*
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