GATE AE 2024 • Q49 MSQ • 2 Marks Propulsion

Propulsion

Inlets, Combustors & Nozzles

Subtopic: Convergent & Convergent-Divergent (C-D) Nozzles

Question Statement:

Which of the following statements is/are TRUE for an axial turbine?
Question figure for GATE AE 2024 Q49

Scientific schematic diagram reproduced from official IIT paper

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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