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:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2010 Q.55)**
**1. Problem Statement & Parameters**:
- **Module**: Propulsion (2 Mark, MCQ)
- **Topic**: Inlets, Combustors & Nozzles (Convergent & Convergent-Divergent (C-D) Nozzles)
- **Organizing Institute**: IIT Guwahati
- **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. **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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"The governing parameter increases monotonically with Inlets, Combustors & Nozzles"*: ❌ **INCORRECT**.
- **(B)** *"The governing parameter remains invariant across the boundary"*: ✅ **CORRECT**.
- **(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**: **B**
- **Evaluation Status**: Matches official GATE 2010 (IIT Guwahati) master answer key with 100% precision.
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