GATE AE 2008 • Q49
MCQ • 2 Marks
Flight Mechanics & Space Dynamics
Static Stability & Control
Subtopic: Static Margin & Stick-Fixed/Free Stability
Question Statement:
The turbine power per unit mass flow is
Options:
-
(A) 29.76 kJ/kg
-
(B) 41.12 kJ/kg
-
(C) 58.33 kJ/kg
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(D) 61.13 kJ/kg
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.49)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ)
- **Topic**: Static Stability & Control (Static Margin & Stick-Fixed/Free Stability)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> The turbine power per unit mass flow is
**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 **D**.
**3. Comprehensive Options Analysis**:
- **(A)** *"29.76 kJ/kg"*: ❌ **INCORRECT**.
- **(B)** *"41.12 kJ/kg"*: ❌ **INCORRECT**.
- **(C)** *"58.33 kJ/kg"*: ❌ **INCORRECT**.
- **(D)** *"61.13 kJ/kg"*: ✅ **CORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **D**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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