Reynolds Number Calculator (Pipe Flow)
Sizing a meter, checking mixing, or validating a head-loss equation? Enter velocity, pipe diameter, and water temperature — the calculator returns the Reynolds number and the flow regime.
Flow Regime
| Item | Value |
|---|
How the calculation works
Formulas
Re = V × D / ν (dimensionless)
V = mean velocity, D = inside diameter, ν = kinematic viscosity of water at the given temperature
ν (m²/s) ≈ 1.792×10⁻⁶ / (1 + 0.0337·T + 0.000221·T²), T in °C
Laminar: Re ≤ 2,300 · Transitional: 2,300 – 4,000 · Turbulent: Re ≥ 4,000 (pipe flow)
Re = V × D / ν (dimensionless)
V = mean velocity, D = inside diameter, ν = kinematic viscosity of water at the given temperature
ν (m²/s) ≈ 1.792×10⁻⁶ / (1 + 0.0337·T + 0.000221·T²), T in °C
Laminar: Re ≤ 2,300 · Transitional: 2,300 – 4,000 · Turbulent: Re ≥ 4,000 (pipe flow)
Notes & limitations
The 2,300 / 4,000 regime boundaries are the standard pipe-flow criteria (e.g. Crittenden et al., Water Treatment: Principles and Design; Fluid Mechanics texts). The kinematic-viscosity correlation is the Poiseuille-based approximation for water, accurate within a few percent from 0–100 °C — fine for engineering checks.
- The 2,300/4,000 boundaries are for round pipes. Open channels and non-circular ducts use different critical values.
- Reynolds number alone does not tell you head loss — combine it with relative roughness (Moody chart / Colebrook) for friction factor.
- Temperature matters: cold water is more viscous, so winter flows can sit in a different regime than summer flows at the same velocity.
← All water treatment calculators · Related: Manning Calculator