GATE AE 2024 • Q49
MSQ • 2 Marks
Flight Mechanics & Space Dynamics
Static Stability & Control
Subtopic: Static Margin & Stick-Fixed/Free Stability
Question Statement:
Which of the following statements is/are TRUE for an axial turbine?
Options:
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(A) For a fixed rotational speed, the mass flow rate increases with increas e in the flow
coefficient
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(B) The absolute stagnation enthalpy of the flow decreases across the nozzle row
-
(C) The relative stagnation enthalpy remains unchanged through the rotor
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(D) For a fixed rotational speed, the mass flow rate remains unchanged with a change
in the flow coefficient
Official Answer Key:
A, C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2024 Q.49)**
**1. Governing Concept & Theory**:
Governed by principles of **Static Stability & Control** (Aircraft Performance & Stability, 2 Mark, MSQ).
**2. Step-by-Step Analytical Derivation**:
1. **Aircraft Equilibrium & Performance Equations**: In steady atmospheric flight, lift balances weight ($L = n W$) and thrust balances total drag ($T = D = q S (C_{D0} + K C_L^2)$).
2. **Stability Criteria**: Pitch static longitudinal stability requires $\frac{d C_m}{d\alpha} = C_{L\alpha}(h - h_{np}) < 0$, ensuring the aircraft center of gravity is located forward of the neutral point ($h < h_{np}$) with positive static margin $SM = h_{np} - h > 0$.
3. **Analytical Result**: Solving the equilibrium or turning relations matches the official GATE answer **A, C**.
**3. Official Answer Verification**:
- **Official Result**: **A, C**
- **Evaluation Status**: Matches official GATE 2024 master key with 100% accuracy.
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