Question

Calculate the Reynold’s number for a liquid of density 1 g/cm³, viscosity 8 x 10^-4 Pa.s flowing at 0.5 m/s through a pipe of diameter 4 cm?

• A. 4000
• B. 40000
• C. 2500
• D. 25000

Answer 1

The Correct Option is D

To calculate the Reynolds number for the given liquid flowing through a pipe, we'll follow these steps:

1. Understanding Reynolds Number:
The Reynolds number (Re) is a dimensionless quantity used to predict flow patterns in fluid dynamics. It is given by:

Re = ρvD/μ

Where:
- ρ = fluid density (kg/m³)
- v = flow velocity (m/s)
- D = pipe diameter (m)
- μ = dynamic viscosity (Pa·s)

2. Given Data:
- Density (ρ) = 1 g/cm³ = 1000 kg/m³
- Viscosity (μ) = 8 × 10⁻⁴ Pa·s
- Velocity (v) = 0.5 m/s
- Diameter (D) = 4 cm = 0.04 m

3. Unit Conversions:
First, we convert all units to consistent SI units:
- 1 g/cm³ = 1000 kg/m³
- 4 cm = 0.04 m

4. Calculation:
Now we substitute the values into the Reynolds number formula:

Re = (1000 kg/m³) × (0.5 m/s) × (0.04 m) / (8 × 10⁻⁴ Pa·s)
= (1000 × 0.5 × 0.04) / (8 × 10⁻⁴)
= 20 / (8 × 10⁻⁴)
= 2.5 × 10⁴

5. Interpretation:
A Reynolds number of 2.5 × 10⁴ indicates:
- The flow is turbulent (Re > 4000 for pipes)
- Inertial forces dominate over viscous forces

Final Answer:
The Reynolds number for the given flow conditions is 2.5 × 10⁴ or 25000.