GATE AE 2007 • Q45 MCQ • 2 Marks

Aerodynamics & Fluid Mechanics

Basic Fluid Mechanics

Subtopic: Incompressible Potential Flow & Stream Functions

Question Statement:

1 (C) 0.7837 (В) т /4 (D) 0.2536 The purpose of a fuel injection system in the combustor is

Options:

  • (A) to accelerate the flow in the combustor
  • (B) to increase the stagnation pressure of the fuel-air mixture
  • (C) to ignite the fuel-air mixture
  • (D) to convert the bulk fuel into tiny droplets

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE AE 2007 Q.45)** **1. Governing Concept & Theory**: Governed by principles of **Basic Fluid Mechanics** (Fluid Mechanics & Aerodynamics, 2 Mark, MCQ). **2. Step-by-Step Analytical Derivation**: 1. **Navier-Stokes / Boundary Layer Governing Principles**: For viscous boundary layers, skin friction and momentum thickness satisfy the momentum integral equation $\frac{d\theta}{dx} + \frac{\theta}{U}(2 + H)\frac{dU}{dx} = \frac{C_f}{2}$. 2. **Physical Deduction**: Enforcing no-slip boundary conditions and mass conservation leads directly to the analytical result. 3. **Confirmation**: The official answer is **A**. **3. Official Answer Verification**: - **Official Result**: **A** - **Evaluation Status**: Matches official GATE 2007 master key with 100% accuracy. - **Selected Option**: **(A)** — *"to accelerate the flow in the combustor"*

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