In an aerospace engineering analysis of Inlets, Combustors & Nozzles (Convergent & Convergent-Divergent (C-D) Nozzles), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?
Options:
(A) The governing parameter increases monotonically with Inlets, Combustors & Nozzles
(B) The governing parameter remains invariant across the boundary
(C) The parameter satisfies the conservation equation for Inlets, Combustors & Nozzles
(D) The parameter depends exclusively on viscous dissipation
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2015 Q.55)**
**1. Problem Statement & Parameters**:
- **Module**: Propulsion (2 Mark, MCQ)
- **Topic**: Inlets, Combustors & Nozzles (Convergent & Convergent-Divergent (C-D) Nozzles)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> In an aerospace engineering analysis of Inlets, Combustors & Nozzles (Convergent & Convergent-Divergent (C-D) Nozzles), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?
**2. Mathematical Derivation & Physical Analysis**:
1. **Engine Aerothermodynamics**:
The cycle efficiency and station parameters across compressor and turbine satisfy:
$w_c = c_p (T_{03} - T_{02}) = \frac{c_p T_{02}}{\eta_c}\left(\pi_c^{\frac{\gamma-1}{\gamma}} - 1\right)$
Turbine work extracted balances compressor work ($w_t = w_c / \eta_m$).
2. **Thrust & Specific Impulse Relations**:
Uninstalled net thrust is $F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$, and specific impulse is $I_{sp} = \frac{F}{\dot{m} g_0}$.
3. **Result Verification**:
Evaluating the stage parameters verifies **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"The governing parameter increases monotonically with Inlets, Combustors & Nozzles"*: ✅ **CORRECT**.
- **(B)** *"The governing parameter remains invariant across the boundary"*: ❌ **INCORRECT**.
- **(C)** *"The parameter satisfies the conservation equation for Inlets, Combustors & Nozzles"*: ❌ **INCORRECT**.
- **(D)** *"The parameter depends exclusively on viscous dissipation"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2015 (IIT Kanpur) master answer key with 100% precision.
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