In a single-spool aviation turbojet engine, which of the following is the correct
relationship between the total work output WT of a 2-stage axial turbine and the
total work required WC by a 6-stage axial compressor, neglecting losses?
Options:
(A) 2TCWW=
(B) 6TCWW=
(C) TCWW=
(D) 3TCWW=
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2023 Q.20)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This question tests core mastery of **Wind Tunnel Testing & Instrumentation** (Pitot-Static Probes & Pressure Transducers) within the *Aerodynamics & Fluid Mechanics* curriculum (1 Mark, MCQ).
**Problem Statement**:
> In a single-spool aviation turbojet engine, which of the following is the correct relationship between the total work output WT of a 2-stage axial turbine and the total work required WC by a 6-stage axial compressor, neglecting losses?
**2. Step-by-Step Mathematical Derivation**:
1. **Governing Analytical Principles**:
Governed by the fundamental laws of Aerodynamics & Fluid Mechanics. 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 **`C`**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** *"2TCWW="*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(B)** *"6TCWW="*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(C)** *"TCWW="*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions.
- **(D)** *"3TCWW="*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **C**
- **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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