How does the specific thrust, al constant turbine inlet temperature, produced by a turbofan engine change with an increase in compressor pressure ratio?
Options:
(A) Increases
(B) Decreases
(C) First increases and then decreases
(D) First decreases and then increases
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2010 Q.15)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Numerical Methods (Newton-Raphson Method)
- **Organizing Institute**: IIT Guwahati
- **Problem Statement**:
> How does the specific thrust, al constant turbine inlet temperature, produced by a turbofan engine change with an increase in compressor pressure ratio?
**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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Increases"*: ❌ **INCORRECT**.
- **(B)** *"Decreases"*: ✅ **CORRECT**.
- **(C)** *"First increases and then decreases"*: ❌ **INCORRECT**.
- **(D)** *"First decreases and then increases"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2010 (IIT Guwahati) master answer key with 100% precision.
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