GATE AE 2007 • Q19
MCQ • 1 Mark
Aerodynamics & Fluid Mechanics
Compressible Flow & Shocks
Subtopic: 1D Isentropic Flow & Area-Mach Relations
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
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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