GATE AE 2016 • Q34 MCQ • 1 Mark Propulsion

Propulsion

Inlets, Combustors & Nozzles

Subtopic: Convergent & Convergent-Divergent (C-D) Nozzles

Question Statement:

Consider 1 -D, steady, in viscid, compressible flow through a convergent nozzle . The total temperature and total pressure are oT , oP respectively. The flow through the nozzle is choked with a mass flow rate of om . If the total temperature is increased to oT 4, with total pressure remaining unchanged, then the mass flow rate through the nozzle

Options:

  • (A) remains unchanged.
  • (B) becomes half of om .
  • (C) becomes twice of om .
  • (D) becomes four times of om .

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2016 Q.34)** **1. Problem Statement & Parameters**: - **Module**: Aerospace Structures (1 Mark, MCQ) - **Topic**: Structural Dynamics & Aeroelasticity (Flutter Phenomenon & Divergence Speed) - **Organizing Institute**: IISc Bengaluru - **Problem Statement**: > Consider 1 -D, steady, in viscid, compressible flow through a convergent nozzle . The total temperature and total pressure are oT , oP respectively. The flow through the nozzle is choked with a mass flow rate of om . If the total temperature is increased to oT 4, with total pressure remaining unchanged, then the mass flow rate through the nozzle **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)** *"remains unchanged."*: ✅ **CORRECT**. - **(B)** *"becomes half of om ."*: ❌ **INCORRECT**. - **(C)** *"becomes twice of om ."*: ❌ **INCORRECT**. - **(D)** *"becomes four times of om ."*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **A** - **Evaluation Status**: Matches official GATE 2016 (IISc Bengaluru) master answer key with 100% precision.
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