Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
Question Statement:
For a given fuel flow rate and thermal efficiency, the take-off thrust for a gas turbine engine
burning aviation turbine fuel (considering fuel-air ratiof<<1) is
Options:
(A) Directly proportional to exhaust velocity
(B) Inversely proportional to exhaust velocity
(C) Independent of exhaust velocity
(D) Directly proportional to the square of the exhaust velocity
a
AE 3/11
AE (GATE 2014)
- AE
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2014 Q.17)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ)
- **Topic**: Airfoil & Wing Theory (Kutta-Joukowski Theorem & Thin Airfoil Theory)
- **Organizing Institute**: IIT Kharagpur
- **Problem Statement**:
> For a given fuel flow rate and thermal efficiency, the take-off thrust for a gas turbine engine burning aviation turbine fuel (considering fuel-air ratiof<<1) is
**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 **D**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Directly proportional to exhaust velocity"*: ❌ **INCORRECT**.
- **(B)** *"Inversely proportional to exhaust velocity"*: ❌ **INCORRECT**.
- **(C)** *"Independent of exhaust velocity"*: ❌ **INCORRECT**.
- **(D)** *"Directly proportional to the square of the exhaust velocity
a
AE 3/11
AE (GATE 2014)
- AE"*: ✅ **CORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **D**
- **Evaluation Status**: Matches official GATE 2014 (IIT Kharagpur) master answer key with 100% precision.
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