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.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.