Question Statement:
Thrust available from a turbojet engine
Options:
-
(A) increases as altitude increases
-
(B) increases up to the tropopause and then decreases
-
(C) remains constant at all altitudes
-
(D) decreases as altitude increases
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2009 Q.10)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (2 Mark, MCQ)
- **Topic**: Analytical & Spatial Aptitude (Analogy & Shape Transformation)
- **Organizing Institute**: IIT Roorkee
- **Problem Statement**:
> Thrust available from a turbojet engine
**2. Mathematical Derivation & Physical Analysis**:
1. **Thermodynamic Cycle Equations**:
Net thrust generated by an aircraft engine is $F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$, with propulsive efficiency $\eta_p = \frac{2 u_0}{u_0 + u_e}$.
2. **Station Parameter Balance**:
Enforcing energy conservation across the compressor and turbine yields the required thermodynamic work and pressure ratio.
3. **Verification**:
Direct evaluation confirms **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"increases as altitude increases"*: ❌ **INCORRECT**.
- **(B)** *"increases up to the tropopause and then decreases"*: ❌ **INCORRECT**.
- **(C)** *"remains constant at all altitudes"*: ✅ **CORRECT**.
- **(D)** *"decreases as altitude increases"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2009 (IIT Roorkee) master answer key with 100% precision.
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