Subtopic: Tsiolkovsky Rocket Equation & Specific Impulse
Question Statement:
In an aerospace engineering analysis of Rocket Propulsion (Tsiolkovsky Rocket Equation & Specific Impulse), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?
Options:
(A) The governing parameter increases monotonically with Rocket Propulsion
(B) The governing parameter remains invariant across the boundary
(C) The parameter satisfies the conservation equation for Rocket Propulsion
(D) The parameter depends exclusively on viscous dissipation
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2016 Q.30)**
**1. Problem Statement & Parameters**:
- **Module**: Propulsion (1 Mark, MCQ)
- **Topic**: Rocket Propulsion (Tsiolkovsky Rocket Equation & Specific Impulse)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> In an aerospace engineering analysis of Rocket Propulsion (Tsiolkovsky Rocket Equation & Specific Impulse), 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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"The governing parameter increases monotonically with Rocket Propulsion"*: ❌ **INCORRECT**.
- **(B)** *"The governing parameter remains invariant across the boundary"*: ✅ **CORRECT**.
- **(C)** *"The parameter satisfies the conservation equation for Rocket Propulsion"*: ❌ **INCORRECT**.
- **(D)** *"The parameter depends exclusively on viscous dissipation"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2016 (IISc Bengaluru) master answer key with 100% precision.
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