Question

Calculate the Reynolds number for a liquid with density 1 g/cm³ and viscosity 8 × 10⁻⁴ Pa·s, flowing at 0.5 m/s through a pipe of diameter 4 cm.

• A. 40,000
• B. 25,000
• C. 30,000
• D. 28,000

Hint:

Reynolds number determines flow regime: 2000 laminar, 4000 turbulent.

Answer 1

The Correct Option is B

Step 1: Understand the Reynolds Number Formula
The Reynolds number (\(Re\)) for flow through a pipe is given by: \[ Re = \frac{\rho v D}{\mu} \] where: - \(\rho\) is the density of the fluid, - \(v\) is the velocity of the flow, - \(D\) is the diameter of the pipe, - \(\mu\) is the dynamic viscosity. 

Step 2: Convert Units to SI 
Given: - Density: \(\rho = 1 \, \text{g/cm}^3\), 
- Viscosity: \(\mu = 8 \times 10^{-4} \, \text{Pas}\), 
- Velocity: \(v = 0.5 \, \text{m/s}\), 
- Diameter: \(D = 4 \, \text{cm}\). 
Convert to SI units: - \(\rho = 1 \, \text{g/cm}^3 = 1 \times \frac{1000 \, \text{kg}}{1 \, \text{m}^3} = 1000 \, \text{kg/m}^3\), 
- \(\mu = 8 \times 10^{-4} \, \text{Pas} = 8 \times 10^{-4} \, \text{kg/(ms)}\) (already in SI), 
- \(D = 4 \, \text{cm} = 0.04 \, \text{m}\), - \(v = 0.5 \, \text{m/s}\) (already in SI). 

Step 3: Calculate the Reynolds Number 
Substitute the values into the formula: \[ Re = \frac{\rho v D}{\mu} \] \[ Re = \frac{(1000) \times (0.5) \times (0.04)}{8 \times 10^{-4}} \] \[ Re = \frac{1000 \times 0.5 \times 0.04}{8 \times 10^{-4}} = \frac{20}{8 \times 10^{-4}} \] \[ Re = \frac{20}{0.0008} = 25000 \] 

Step 4: Final Answer 
The Reynolds number is: \[ \boxed{25000} \]