GATE AE 2016 • Q20
MCQ • 1 Mark
Aerodynamics & Fluid Mechanics
Wind Tunnel Testing & Instrumentation
Subtopic: Pitot-Static Probes & Pressure Transducers
Question Statement:
For a given chamber pressure, the thrust of a rocket engine is highest when
Options:
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(A) the rocket is operating at its design altitude.
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(B) the rocket is operating in vacuum.
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(C) the rocket is operating at sea-level.
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(D) there is a normal shock in the rocket nozzle.
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2016 Q.20)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ)
- **Topic**: Wind Tunnel Testing & Instrumentation (Pitot-Static Probes & Pressure Transducers)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> For a given chamber pressure, the thrust of a rocket engine is highest when
**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 rocket is operating at its design altitude."*: ❌ **INCORRECT**.
- **(B)** *"the rocket is operating in vacuum."*: ✅ **CORRECT**.
- **(C)** *"the rocket is operating at sea-level."*: ❌ **INCORRECT**.
- **(D)** *"there is a normal shock in the rocket nozzle."*: ❌ **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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