Reynolds Number Calculator

The Formula

The formula for calculating the Reynolds Number is:

\[Re = \frac{\rho v D}{\mu}\]

Where:

• Re: Reynolds Number (dimensionless)
• ρ: Fluid density (kg/m³)
• v: Fluid velocity (m/s)
• D: Characteristic length (pipe diameter for pipe flow) (m)
• μ: Dynamic viscosity of the fluid (Pa·s or N·s/m²)

Calculation Steps

1. Gather the required fluid properties and flow characteristics
2. Apply the Reynolds Number formula: Re = (ρ × v × D) ÷ μ
3. Interpret the result to determine the flow regime:
   • Re < 2300: Laminar flow
   • 2300 ≤ Re ≤ 4000: Transitional flow
   • Re > 4000: Turbulent flow

Example Calculation

Let's calculate the Reynolds Number for water flowing in a pipe with the following properties:

• Fluid velocity (v) = 1.5 m/s
• Pipe diameter (D) = 0.05 m
• Water density (ρ) = 1000 kg/m³
• Water dynamic viscosity (μ) = 0.001 Pa·s

Applying the formula:

Re = (1000 × 1.5 × 0.05) ÷ 0.001 = 75,000

Since Re > 4000, this indicates turbulent flow.

Visual Representation

This visual represents turbulent flow in a pipe based on our example calculation.