Reynolds Number Calculator

What is the Reynolds Number?

The Reynolds number (Re) is a dimensionless quantity that predicts whether flow in a pipe or channel will be laminar (smooth, layered) or turbulent (chaotic, mixed). It's named after Osborne Reynolds, who studied transition between flow regimes in 1883.

The Reynolds Number Formula

Re = ρ × v × D / μ = v × D / ν

Where:

• ρ = fluid density (kg/m³)
• v = average velocity (m/s)
• D = pipe diameter (m)
• μ = dynamic viscosity (Pa·s)
• ν = kinematic viscosity (m²/s) = μ/ρ

Flow Regimes

| Reynolds Number | Flow Regime | |-----------------|-------------| | Re < 2,300 | Laminar — smooth, predictable | | 2,300 < Re < 4,000 | Transitional — unstable | | Re > 4,000 | Turbulent — chaotic, high mixing |

How to Use This Calculator

Enter fluid velocity, pipe diameter, and fluid properties (density and viscosity, or select a common fluid from the list). The calculator returns Re and identifies the flow regime.

Practical Examples

Example 1: Water (ν = 1×10⁻⁶ m²/s) at 2 m/s in a 50mm pipe. Re = 2 × 0.05 / 0.000001 = 100,000 — turbulent.

Example 2: Honey (ν = 0.001 m²/s) at 0.1 m/s in a 20mm pipe. Re = 0.1 × 0.02 / 0.001 = 2 — strongly laminar.

Why Flow Regime Matters

Laminar flow has lower friction losses but poor mixing. Turbulent flow is essential for effective heat transfer and mixing, but causes higher pressure drop. Friction factor calculations (Moody chart) depend critically on the flow regime.