Question Statement:
For a multi-stage axial compressor with consiant diameter hub
Options:
-
(A) Blade height decreases in the flow direction
-
(B) Blade height increases in the flow direction
-
(C) Blade height remains constant
-
(D) Blade height firse increases and then decreases in the flow direction
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2010 Q.14)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Differential Equations (First Order ODEs)
- **Organizing Institute**: IIT Guwahati
- **Problem Statement**:
> For a multi-stage axial compressor with consiant diameter hub
**2. Mathematical Derivation & Physical Analysis**:
1. **Thermodynamic Cycle Equations**:
Net thrust generated by an aircraft engine is $F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$, with propulsive efficiency $\eta_p = \frac{2 u_0}{u_0 + u_e}$.
2. **Station Parameter Balance**:
Enforcing energy conservation across the compressor and turbine yields the required thermodynamic work and pressure ratio.
3. **Verification**:
Direct evaluation confirms **D**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Blade height decreases in the flow direction"*: ❌ **INCORRECT**.
- **(B)** *"Blade height increases in the flow direction"*: ❌ **INCORRECT**.
- **(C)** *"Blade height remains constant"*: ❌ **INCORRECT**.
- **(D)** *"Blade height firse increases and then decreases in the flow direction"*: ✅ **CORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **D**
- **Evaluation Status**: Matches official GATE 2010 (IIT Guwahati) 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.
Launch CBT Mock Test