For a stage of a 50% reaction ideal axial flow compressor (symmetrical blading),
select the correct statement from the options given.
Options:
(A) The stagnation enthalpy rise across the rotor is 50% of the rise across the stage.
(B) The static enthalpy rise across the rotor is 50% of the rise across the stage.
(C) Axial velocity component of the flow at the rotor exit is 50% of that at the rotor
entry.
(D) The static pressure rise across the rotor is 50% of the rise across the stator.
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2023 Q.21)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This question tests core mastery of **Atmospheric Flight Mechanics** (Standard Atmosphere Properties) within the *Flight Mechanics & Space Dynamics* curriculum (1 Mark, MCQ).
**Problem Statement**:
> For a stage of a 50% reaction ideal axial flow compressor (symmetrical blading), select the correct statement from the options given.
**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 **`B`**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** *"The stagnation enthalpy rise across the rotor is 50% of the rise across the stage."*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(B)** *"The static enthalpy rise across the rotor is 50% of the rise across the stage."*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions.
- **(C)** *"Axial velocity component of the flow at the rotor exit is 50% of that at the rotor
entry."*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(D)** *"The static pressure rise across the rotor is 50% of the rise across the stator."*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **B**
- **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2023 (IIT Kanpur) key.
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