GATE AE 2019 • Q19 MCQ • 1 Mark Propulsion

Propulsion

Compressors and Turbines

Subtopic: Centrifugal Compressors

Question Statement:

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. Q.13 For a beam subjected to a transverse shear load through its shear center,

Options:

  • (A) the twist per unit length is zero.
  • (B) the shear stress is uniform throughout the cross-section.
  • (C) the bending stresses in the cross section are zero.
  • (D) the shear strain is zero at the shear center.

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2019 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 Madras - **Problem Statement**: > 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. Q.13 For a beam subjected to a transverse shear load through its shear center, **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: **A**. **3. Comprehensive Options Analysis**: - **(A)** *"the twist per unit length is zero."*: ✅ **CORRECT**. - **(B)** *"the shear stress is uniform throughout the cross-section."*: ❌ **INCORRECT**. - **(C)** *"the bending stresses in the cross section are zero."*: ❌ **INCORRECT**. - **(D)** *"the shear strain is zero at the shear center."*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **A** - **Evaluation Status**: Matches official GATE 2019 (IIT Madras) master answer key with 100% precision.
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