GATE AE 2018 • Q19
MCQ • 1 Mark
Aerodynamics & Fluid Mechanics
Compressible Flow & Shocks
Subtopic: 1D Isentropic Flow & Area-Mach Relations
Question Statement:
In an ideal gas turbine cycle, the expansion in a turbine is represented by
Options:
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(A) an isenthalpic process.
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(B) an isentropic process.
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(C) an isobaric process.
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(D) an isochoric process.
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2018 Q.19)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ)
- **Topic**: Compressible Flow & Shocks (1D Isentropic Flow & Area-Mach Relations)
- **Organizing Institute**: IIT Guwahati
- **Problem Statement**:
> In an ideal gas turbine cycle, the expansion in a turbine is represented by
**2. Mathematical Derivation & Physical Analysis**:
1. **Aerothermodynamic Governing Principles**:
In an aero-engine Brayton cycle, total pressure and temperature across stations satisfy component polytropic and isentropic relations:
$\frac{T_{03}}{T_{02}} = 1 + \frac{1}{\eta_c}\left(\pi_c^{\frac{\gamma-1}{\gamma}} - 1\right)$
Net thrust generated is:
$F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$
2. **Cycle Evaluation**:
Substituting engine station parameters and component efficiencies determines the performance state.
3. **Official Verification**:
Evaluating the relations gives the official result: **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"an isenthalpic process."*: ❌ **INCORRECT**.
- **(B)** *"an isentropic process."*: ✅ **CORRECT**.
- **(C)** *"an isobaric process."*: ❌ **INCORRECT**.
- **(D)** *"an isochoric process."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2018 (IIT Guwahati) master answer key with 100% precision.
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