GATE AE 2007 • Q19 MCQ • 1 Mark Aerodynamics & Fluid Mechanics

Aerodynamics & Fluid Mechanics

Basic Fluid Mechanics

Subtopic: Conservation Equations of Mass, Momentum & Energy

Question Statement:

Reynolds number, based on the pipe diameter, is

Options:

  • (A) the same in both pipes
  • (B) is larger in the narrower pipe
  • (C) is smaller in the narrower pipe
  • (D) depends on the material of the pipes

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.19)** **1. Problem Statement & Parameters**: - **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ) - **Topic**: Compressible Flow & Shocks (1D Isentropic Flow & Area-Mach Relations) - **Organizing Institute**: IIT Kanpur - **Problem Statement**: > Reynolds number, based on the pipe diameter, is **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Compressible Flow & Shocks** (1D Isentropic Flow & Area-Mach Relations) under *Aerodynamics & Fluid Mechanics*. Conservation laws and equilibrium relations establish the physical system. 2. **Analytical Derivation**: Setting up the system equations and evaluating at the given parameters yields the analytical solution. 3. **Official Verification**: Evaluates to **B**. **3. Comprehensive Options Analysis**: - **(A)** *"the same in both pipes"*: ❌ **INCORRECT**. - **(B)** *"is larger in the narrower pipe"*: ✅ **CORRECT**. - **(C)** *"is smaller in the narrower pipe"*: ❌ **INCORRECT**. - **(D)** *"depends on the material of the pipes"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **B** - **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.
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