How to use the Reynolds Number Calculator
- 1. Pick the flowPipe, flat plate or open channel, and the fluid.
- 2. Enter velocity and sizeVelocity (or flow rate for a pipe) and the characteristic length in m.
- 3. Read the regimeRe, laminar or turbulent, ν and the friction factor for pipes.
Reynolds number formula
Re = ρVL / μ = VL / ν, where ρ is density, V the mean velocity, L the characteristic length (pipe diameter, distance along a plate, or hydraulic radius) and μ the dynamic viscosity. It is the ratio of inertia forces to viscous forces.
For pipes, flow is usually laminar below 2000, transitional from 2000 to 4000 and turbulent above 4000. On a flat plate the boundary layer turns turbulent around Re = 5 × 10⁵. For laminar pipe flow the Darcy friction factor is f = 64 / Re.
Worked example and exam tips
Water at 20 °C (ρ = 998.2 kg/m³, μ = 1.002 × 10⁻³ Pa·s) flows at 1 m/s in a 50 mm pipe. Re = 998.2 × 1 × 0.05 / 1.002 × 10⁻³ = 49,810, so the flow is turbulent. Blasius gives f = 0.316 / Re0.25 ≈ 0.0212.
- Use the inside diameter and SI units throughout.
- Viscosity falls sharply as water heats up, so Re rises with temperature.
- Some books use 2300 as the laminar limit; follow your syllabus.
Frequently asked questions
What is the difference between μ and ν?
μ is dynamic viscosity in Pa·s. ν = μ/ρ is kinematic viscosity in m²/s. Re = VL/ν gives the same result.
Which length should I use for a duct that is not round?
Use the hydraulic diameter, 4 × area / wetted perimeter.
Are the water and air values exact?
They are standard textbook values at 20 °C. For other temperatures choose Other and enter ρ and μ from your property table.
Is this calculator free?
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