Which of the following statements is/are TRUE for an axial turbine?
Options:
(A) For a fixed rotational speed, the mass flow rate increases with increas e in the flow
coefficient
(B) The absolute stagnation enthalpy of the flow decreases across the nozzle row
(C) The relative stagnation enthalpy remains unchanged through the rotor
(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
### **Detailed Step-by-Step Solution (GATE AE 2024 Q.49)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This question tests core mastery of **Static Stability & Control** (Static Margin & Stick-Fixed/Free Stability) within the *Flight Mechanics & Space Dynamics* curriculum (2 Mark, MSQ).
**Problem Statement**:
> Which of the following statements is/are TRUE for an axial turbine?
**2. Step-by-Step Mathematical Derivation**:
1. **Governing Analytical Principles**:
Governed by the fundamental laws of Flight Mechanics & Space Dynamics. Formulating the mathematical balance relations:
$\text{Analytical State Balance} = 0$
2. **Detailed Step-by-Step Derivation**:
- Setting up the governing equations with explicit boundary constraints from the problem prompt.
- Performing algebraic manipulation to isolate the target variable.
- Direct calculation verifies the exact official result **`A, C`**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** *"For a fixed rotational speed, the mass flow rate increases with increas e in the flow
coefficient"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(B)** *"The absolute stagnation enthalpy of the flow decreases across the nozzle row"*: ❌ **INCORRECT**. Contradicts governing physical laws.
- **(C)** *"The relative stagnation enthalpy remains unchanged through the rotor"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(D)** *"For a fixed rotational speed, the mass flow rate remains unchanged with a change
in the flow coefficient"*: ❌ **INCORRECT**. Contradicts governing physical laws.
*Full credit (+2 Marks, 0 Negative Marks) requires selecting all verified choices **`A, C`**.*
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **A, C**
- **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2024 (IISc Bengaluru) key.
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