Viscosity

Step 1: Understand the Reynolds Number Formula
The Reynolds number ( $Re$ ) for flow through a pipe is given by: $Re%20%3D%20%5Cfrac%7B%5Crho%20v%20D%7D%7B%5Cmu%7D$ where: - $%5Crho$ is the density of the fluid, - $v$ is the velocity of the flow, - $D$ is the diameter of the pipe, - $%5Cmu$ is the dynamic viscosity.

Step 2: Convert Units to SI
Given: - Density: $%5Crho%20%3D%201%20%5C%2C%20%5Ctext%7Bg%2Fcm%7D%5E3$ ,
- Viscosity: $%5Cmu%20%3D%208%20%5Ctimes%2010%5E%7B-4%7D%20%5C%2C%20%5Ctext%7BPas%7D$ ,
- Velocity: $v%20%3D%200.5%20%5C%2C%20%5Ctext%7Bm%2Fs%7D$ ,
- Diameter: $D%20%3D%204%20%5C%2C%20%5Ctext%7Bcm%7D$ .
Convert to SI units: - $%5Crho%20%3D%201%20%5C%2C%20%5Ctext%7Bg%2Fcm%7D%5E3%20%3D%201%20%5Ctimes%20%5Cfrac%7B1000%20%5C%2C%20%5Ctext%7Bkg%7D%7D%7B1%20%5C%2C%20%5Ctext%7Bm%7D%5E3%7D%20%3D%201000%20%5C%2C%20%5Ctext%7Bkg%2Fm%7D%5E3$ ,
- $%5Cmu%20%3D%208%20%5Ctimes%2010%5E%7B-4%7D%20%5C%2C%20%5Ctext%7BPas%7D%20%3D%208%20%5Ctimes%2010%5E%7B-4%7D%20%5C%2C%20%5Ctext%7Bkg%2F(ms)%7D$ (already in SI),
- $D%20%3D%204%20%5C%2C%20%5Ctext%7Bcm%7D%20%3D%200.04%20%5C%2C%20%5Ctext%7Bm%7D$ , - $v%20%3D%200.5%20%5C%2C%20%5Ctext%7Bm%2Fs%7D$ (already in SI).

Step 3: Calculate the Reynolds Number
Substitute the values into the formula: $Re%20%3D%20%5Cfrac%7B%5Crho%20v%20D%7D%7B%5Cmu%7D$ $Re%20%3D%20%5Cfrac%7B(1000)%20%5Ctimes%20(0.5)%20%5Ctimes%20(0.04)%7D%7B8%20%5Ctimes%2010%5E%7B-4%7D%7D$ $Re%20%3D%20%5Cfrac%7B1000%20%5Ctimes%200.5%20%5Ctimes%200.04%7D%7B8%20%5Ctimes%2010%5E%7B-4%7D%7D%20%3D%20%5Cfrac%7B20%7D%7B8%20%5Ctimes%2010%5E%7B-4%7D%7D$ $Re%20%3D%20%5Cfrac%7B20%7D%7B0.0008%7D%20%3D%2025000$

Step 4: Final Answer
The Reynolds number is: $%5Cboxed%7B25000%7D$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Viscosity

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs