How to use it
- Type the Water temperature, °C, for example 20.
- Type the Flow rate, L/s and the Inside diameter, mm of the pipe, for example 20 and 150.
- Read the Reynolds number and the Flow regime, then the velocity, the viscosity and the steps.
How the Reynolds number is calculated
The Reynolds number compares the inertia of a flowing fluid with its viscous friction. For water in a full round pipe it is the density times the mean velocity times the diameter, divided by the viscosity.
Re = ρ × v × D ÷ μ
v = Q ÷ (π × D² ÷ 4)
Re = Reynolds number, no unit
ρ = density of the water, kg/m³
v = mean velocity in the pipe, m/s
D = inside diameter, m
μ = dynamic viscosity, Pa·s
Q = flow, m³/s- The number grows with the speed, the pipe size and the density, and falls as the viscosity rises.
- Warm water is less viscous than cold water. At 100 °C its viscosity is about 28 % of its value at 20 °C, so the same flow in the same pipe gives a Reynolds number about 3.4 times as large.
- The density and the viscosity come from the IAPWS equations for water at its saturation pressure, so the figures follow the water as its temperature changes.
Flow regimes in a pipe
The EPANET manual gives the bands of pipe flow: the Hagen-Poiseuille formula applies to laminar flow below a Reynolds number of 2,000, the flow is transitional from 2,000 to 4,000, and it is fully turbulent above 4,000.
| Reynolds number | Flow regime |
|---|---|
| Below 2,000 | Laminar |
| 2,000 to 4,000 | Transitional |
| Above 4,000 | Turbulent |
What the calculator does not include
- Liquids other than water, and gases. Their density and viscosity are different, and they need their own values.
- Water above 100 °C in a pressurised pipe, where the pressure changes the properties. The page uses the water at its own saturation pressure.
- Ducts that are not round, which need a hydraulic diameter, and open channels with a free surface.
Worked example: 20 L/s in a 150 mm pipe at 20 °C
At 20 °C water has a density of 998.16 kg/m³ and a viscosity of 1.0016 mPa·s. The flow of 0.020 m³/s in a pipe of 0.150 m inside diameter has a flow area of 0.0176715 m², so the mean velocity is 1.1318 m/s. The Reynolds number is 998.16 × 1.1318 × 0.150 ÷ 0.00100163 = 169,178, far above 4,000, so the flow is turbulent. The steps show rounded figures; the page computes with the full values.
| Figure | Value |
|---|---|
| Reynolds number | 169,178 |
| Flow regime | Turbulent (above 4,000) |
| Mean velocity | 1.132 m/s |
| Dynamic viscosity | 1.0016 mPa·s |
Frequently asked questions
At which Reynolds number does the flow in a pipe become turbulent?
The EPANET manual ends laminar flow at 2,000 and calls the flow fully turbulent above 4,000. Between the two the flow is transitional, and its behaviour is less predictable.
Why does warm water give a higher Reynolds number?
Its viscosity is lower, so the same flow in the same pipe gives a larger number. At 100 °C the viscosity is about 28 % of its value at 20 °C, and the Reynolds number is about 3.4 times as large.
Does a higher velocity always mean a higher Reynolds number?
Yes, for the same pipe and fluid, because the number is proportional to the velocity. The pipe size and the fluid matter too, so two pipes with the same speed can have very different numbers.
Can I use the calculator for oil or air?
No. The density and viscosity are those of water at its saturation pressure. Oil, air and other fluids need their own density and viscosity values.
Is my data sent to a server?
No. The calculation runs in your browser, and nothing you type is sent to us or stored.
Sources
- IAPWS R12-08 (2008), Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance (Eqs. 10 to 12, Tables 1, 2 and 4)
- IAPWS R7-97(2012), Revised Release on the IAPWS Industrial Formulation 1997 (Region 1 and Region 4, Tables 2, 5, 34 and 35)
- U.S. EPA, EPANET 2 Users Manual: the bands of laminar, transitional and turbulent pipe flow
Figures and text last checked on Wednesday, November 11, 2026.