(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
(C) The pressure ratio of a centrifugal compressor approaches zero as the compressor
mass flow rate approaches zero
(D) Centrifugal compressors are always designed with multiple stages
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.35)**
**1. Problem Statement & Parameters**:
- **Module**: Aerospace Structures (1 Mark, MCQ)
- **Topic**: Aerospace Materials & Fatigue (Fatigue Crack Growth & S-N Curves)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> Which one of the following statements is true?
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Aerospace Materials & Fatigue** (Fatigue Crack Growth & S-N Curves) under *Aerospace Structures*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"The isentropic efficiency of a compressor is constant throughout the compressor"*: ✅ **CORRECT**.
- **(B)** *"Flow separation problems are more critical for the axial compressors than for the
centrifugal compressors"*: ❌ **INCORRECT**.
- **(C)** *"The pressure ratio of a centrifugal compressor approaches zero as the compressor
mass flow rate approaches zero"*: ❌ **INCORRECT**.
- **(D)** *"Centrifugal compressors are always designed with multiple stages"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.
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