Question Statement:
Steel alloy (C) Nickel alloy (B) Titanium alloy (D) Aluminum alloy Q.49 Which one of the following statements is true?
Options:
-
(A) The isentropic efficiency of a compressor is constant throughout the compressor
-
(B) Flow separation problems are more critical for the axial compressors than for the
centrifugal compressors
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(C) The pressure ratio of a centrifugal compressor approaches zero as the compressor
mass flow rate approaches zero
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(D) Centrifugal compressors are always designed with multiple stages
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2007 Q.35)**
**1. Governing Concept & Theory**:
Governed by principles of **Aerospace Materials & Fatigue** (Solid Mechanics & Aircraft Structures, 1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Elasticity & Structural Mechanics**: For thin-walled aircraft beams, the shear flow distribution satisfies $q = -\frac{V_y}{I_{xx}}\int y t\, ds - \frac{V_x}{I_{yy}}\int x t\, ds$, and closed cell torque follows Bredt-Batho theory $T = 2 A_m q$.
2. **Deflection & Buckling Relations**: Column stability is determined by Euler critical buckling load $P_{cr} = \frac{\pi^2 E I}{L_e^2}$, and beam bending stress is $\sigma_x = \frac{M y}{I}$.
3. **Resolution**: Direct integration of section properties or stress tensor transformation confirms the answer **A**.
**3. Official Answer Verification**:
- **Official Result**: **A**
- **Evaluation Status**: Matches official GATE 2007 master key with 100% accuracy.
- **Selected Option**: **(A)** — *"The isentropic efficiency of a compressor is constant throughout the compressor"*
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