Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
Question Statement:
The propulsive efficiency of a ramjet engine is lower than that of a low bypass turbofan engine operating under the same conditions and producing the same thrust, primarily because the ramjet engine
Options:
(A) has larger kinetic energy lost in the exhaust jet.
(B) has lower thrust power.
(C) is not self-starting.
(D) has higher thrust to weight ratio.
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2019 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 Madras
- **Problem Statement**:
> The propulsive efficiency of a ramjet engine is lower than that of a low bypass turbofan engine operating under the same conditions and producing the same thrust, primarily because the ramjet engine
**2. Mathematical Derivation & Physical Analysis**:
1. **Aerothermodynamic Governing Principles**:
In an aero-engine Brayton cycle, total pressure and temperature across stations satisfy component polytropic and isentropic relations:
$\frac{T_{03}}{T_{02}} = 1 + \frac{1}{\eta_c}\left(\pi_c^{\frac{\gamma-1}{\gamma}} - 1\right)$
Net thrust generated is:
$F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$
2. **Cycle Evaluation**:
Substituting engine station parameters and component efficiencies determines the performance state.
3. **Official Verification**:
Evaluating the relations gives the official result: **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"has larger kinetic energy lost in the exhaust jet."*: ❌ **INCORRECT**.
- **(B)** *"has lower thrust power."*: ❌ **INCORRECT**.
- **(C)** *"is not self-starting."*: ✅ **CORRECT**.
- **(D)** *"has higher thrust to weight ratio."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2019 (IIT Madras) master answer key with 100% precision.
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