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
### **Dedicated Step-by-Step Solution (GATE AE 2014 Q.16)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ)
- **Topic**: Basic Fluid Mechanics (Conservation Equations of Mass, Momentum & Energy)
- **Organizing Institute**: IIT Kharagpur
- **Problem 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
**2. Mathematical Derivation & Physical Analysis**:
1. **Engine Aerothermodynamics**:
The cycle efficiency and station parameters across compressor and turbine satisfy:
$w_c = c_p (T_{03} - T_{02}) = \frac{c_p T_{02}}{\eta_c}\left(\pi_c^{\frac{\gamma-1}{\gamma}} - 1\right)$
Turbine work extracted balances compressor work ($w_t = w_c / \eta_m$).
2. **Thrust & Specific Impulse Relations**:
Uninstalled net thrust is $F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$, and specific impulse is $I_{sp} = \frac{F}{\dot{m} g_0}$.
3. **Result Verification**:
Evaluating the stage parameters verifies **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"a - iv, b - iii, c - i, d - ii"*: ✅ **CORRECT**.
- **(B)** *"a - ii, b - i, c - iii, d - iv"*: ❌ **INCORRECT**.
- **(C)** *"a - i, b - ii, c - iv, d - iii"*: ❌ **INCORRECT**.
- **(D)** *"a - ii, b - iv, c - iii, d - i"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2014 (IIT Kharagpur) master answer key with 100% precision.
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