GATE AE 2013 • Q51 MCQ • 2 Marks Aerodynamics & Fluid Mechanics

Aerodynamics & Fluid Mechanics

Compressible Flow & Shocks

Subtopic: 1D Isentropic Flow & Area-Mach Relations

Question Statement:

For which one of the nozzle exit Mach numbers given below is the thrust highest?

Options:

  • (A) 1
  • (B) 1.5
  • (C) 2
  • (D) 2.5

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.51)** **1. Problem Statement & Parameters**: - **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ) - **Topic**: Space Dynamics & Orbital Mechanics (Hohmann Transfer & Orbital Maneuvers) - **Organizing Institute**: IIT Bombay - **Problem Statement**: > For which one of the nozzle exit Mach numbers given below is the thrust highest? **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 **D**. **3. Comprehensive Options Analysis**: - **(A)** *"1"*: ❌ **INCORRECT**. - **(B)** *"1.5"*: ❌ **INCORRECT**. - **(C)** *"2"*: ❌ **INCORRECT**. - **(D)** *"2.5 Linked Answer Questions Statement for Linked Answer Questions 52 and 53: Circulation theory of lift is assumed for a thin symmetric airfoil at an angle of attack $\alpha$. Free stream velocity is U."*: ✅ **CORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **D** - **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.
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