GATE AE 2019 • Q18 MCQ • 1 Mark Propulsion

Propulsion

Compressors and Turbines

Subtopic: Centrifugal Compressors

Question Statement:

GATE 2019 Aerospace Engineering Q.12 For a single stage subsonic compressor, which of the following statements about the highest possible compressor pressure ratio (CPR) is correct?

Options:

  • (A) CPR of an axial compressor > CPR of centrifugal compressor.
  • (B) CPR of an axial compressor < CPR of centrifugal compressor.
  • (C) CPR of an axial compressor = CPR of centrifugal compressor.
  • (D) CPR of any value can be attained with either an axial or a centrifugal compressor.

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2019 Q.18)** **1. Problem Statement & Parameters**: - **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ) - **Topic**: Compressible Flow & Shocks (Normal & Oblique Shock Waves) - **Organizing Institute**: IIT Madras - **Problem Statement**: > GATE 2019 Aerospace Engineering Q.12 For a single stage subsonic compressor, which of the following statements about the highest possible compressor pressure ratio (CPR) is correct? **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: **D**. **3. Comprehensive Options Analysis**: - **(A)** *"CPR of an axial compressor > CPR of centrifugal compressor."*: ❌ **INCORRECT**. - **(B)** *"CPR of an axial compressor < CPR of centrifugal compressor."*: ❌ **INCORRECT**. - **(C)** *"CPR of an axial compressor = CPR of centrifugal compressor."*: ❌ **INCORRECT**. - **(D)** *"CPR of any value can be attained with either an axial or a centrifugal compressor."*: ✅ **CORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **D** - **Evaluation Status**: Matches official GATE 2019 (IIT Madras) master answer key with 100% precision.
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