GATE AE 2007 • Q42
MCQ • 2 Marks
Aerodynamics & Fluid Mechanics
Compressible Flow & Shocks
Subtopic: Normal & Oblique Shock Waves
Question Statement:
The pressure loss factor (stagnation pressure loss non-dimensionalized by the inlet dynamic pressure) of the combustor is
Options:
-
(A) 0
-
(B) 0.489
-
(C) 1.044
-
(D) 2.044
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.42)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (2 Mark, MCQ)
- **Topic**: Compressible Flow & Shocks (Normal & Oblique Shock Waves)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> The pressure loss factor (stagnation pressure loss non-dimensionalized by the inlet dynamic pressure) of the combustor is
**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 **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"0"*: ✅ **CORRECT**.
- **(B)** *"0.489"*: ❌ **INCORRECT**.
- **(C)** *"1.044"*: ❌ **INCORRECT**.
- **(D)** *"2.044"*: ❌ **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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