Reynolds number calculator
Enter the flow velocity and the pipe's inside diameter, then the fluid's density and dynamic viscosity or its kinematic viscosity. The defaults are water at about 20 °C. The calculator gives the Reynolds number and the flow regime.
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How to use it
- Enter the mean flow velocity (flow rate divided by the pipe’s cross-section) in m/s or ft/s.
- Enter the inside diameter in mm or inches.
- Describe the fluid by density and dynamic viscosity or by kinematic viscosity (mm²/s, the same as centistokes).
- Read Re and the flow regime.
Re = ρ × v × D / μ = v × D / ν
- ρ — density, kg/m³;
- v — mean velocity, m/s;
- D — inside diameter, m;
- μ — dynamic viscosity, Pa·s (1 mPa·s = 0.001 Pa·s = 1 cP);
- ν — kinematic viscosity, m²/s (1 mm²/s = 10⁻⁶ m²/s = 1 cSt).
The regime limits used: laminar below 2,300, transitional from 2,300 to 4,000, turbulent above 4,000.
Worked example
Water at 20 °C (998.2 kg/m³, 1.002 mPa·s) flowing at 1 m/s in a 50 mm pipe:
Re = 998.2 × 1 × 0.05 ÷ 0.001002 = 49,810, turbulent. The kinematic viscosity is 1.0038 mm²/s.
Oil with ν = 100 mm²/s at 3 ft/s (0.9144 m/s) in a 2 in (0.0508 m) pipe: Re = 0.9144 × 0.0508 ÷ 0.0001 = 465, laminar.
Tips
- Velocity from flow rate: v = Q / (π D² / 4). 2 L/s in a 50 mm pipe is 1.02 m/s.
- Use the inside diameter, not the nominal pipe size.
- For pressure drop the regime decides the friction factor: see the Darcy–Weisbach calculator.
Frequently asked questions
What is the Reynolds number?
A dimensionless ratio of inertial to viscous forces in a flow: Re = ρvD/μ, or vD/ν with the kinematic viscosity ν = μ/ρ. Low values mean smooth, layered (laminar) flow; high values mean chaotic, mixing (turbulent) flow.
At what Reynolds number does pipe flow become turbulent?
In round pipes flow is usually laminar below about 2,300 and turbulent above about 4,000; in between it is transitional and can switch either way. These are the limits the calculator uses. Very smooth, undisturbed pipes can stay laminar to higher Re.
What viscosity does water have?
At about 20 °C water has a density of about 998 kg/m³ and a dynamic viscosity of about 1.0 mPa·s, so ν ≈ 1.0 mm²/s (1 cSt). Viscosity falls quickly with temperature: warm water flows with a noticeably higher Re.
What diameter should I use for a non-circular duct?
Use the hydraulic diameter D_h = 4A / P, where A is the flow area and P the wetted perimeter. For a square duct of side a, D_h = a.