How to use the reynolds number calculator
- Choose to find the Reynolds number or the speed for a Reynolds number.
- Pick meters with meters per second or inches with feet per second, and pick a fluid or enter your own density and viscosity.
- Enter the flow speed (or the Reynolds number) and the pipe or duct diameter.
- Read the Reynolds number, the flow range it falls in and the speeds at which the range changes.
Formula
Re = density x speed x diameter / dynamic viscosity
Re = speed x diameter / kinematic viscosity, where kinematic viscosity = dynamic viscosity / density
Speed = Re x dynamic viscosity / (density x diameter)
Commonly cited ranges for a round pipe: below 2,300 laminar, 2,300 to 4,000 transitional, above 4,000 turbulent
The Reynolds number has no unit. It compares the push of the moving fluid with the drag of its viscosity, and it is the same in any consistent unit system.
Water, air and hot water
Water at 20 C (998.2 kg/m3, 0.001002 Pa s) moving at 1 m/s in a 50 mm pipe has Re = 998.2 x 1 x 0.05 / 0.001002 = 49,810.4, which is in the turbulent range. The kinematic viscosity is 1.0038e-6 m2/s, and the flow would stay laminar below 0.0461751 m/s and turbulent above 0.080305 m/s.
Air at 20 C moving at 3 m/s in a 100 mm duct has Re = 19,791.8. Water at 60 C moving at 3 ft/s in a 2 inch pipe has Re = 97,796.9.
Laminar and turbulent flow
At a low Reynolds number the fluid moves in smooth layers, which is laminar flow. At a high one it moves in swirling eddies, which is turbulent flow, and friction losses are larger. The numbers 2,300 and 4,000 are the usual guides for a round pipe, but where the change happens depends on the roughness and any disturbances at the inlet.
For the volume of flow use the flow rate calculator, and for losses in a water pipe see the Hazen-Williams pipe pressure drop calculator. Duct sizes are covered by the duct size equivalent calculator.
Fluid properties
Density and viscosity depend on temperature. The built-in fluids are example values near the stated temperature, so enter your own when it matters. Dynamic viscosity is in pascal seconds, and one centipoise is 0.001 pascal seconds. For a duct that is not round, use the hydraulic diameter, which is four times the flow area divided by the wetted perimeter.
Assumptions and limits
- The speed is the average speed across the pipe, and the diameter is the inside diameter.
- The fluid is a Newtonian liquid or gas with the density and viscosity you pick.
- The ranges 2,300 and 4,000 are commonly cited for flow in a round pipe. Other shapes and rough walls differ.
- The example fluid values are approximate and not a property table.
Frequently asked questions
How do I calculate the Reynolds number?
Multiply the density by the speed and the diameter, then divide by the dynamic viscosity. Water at 1 m/s in a 50 mm pipe gives about 49,800.
What Reynolds number is laminar?
Flow in a round pipe is usually laminar below about 2,300 and turbulent above about 4,000, with a transitional range between them.
What diameter do I use for a duct?
For a round duct use the inside diameter. For other shapes use the hydraulic diameter: four times the area divided by the perimeter.
Can I use different units?
Yes. The page offers meters per second or inches with feet per second. The density and viscosity are always in kg/m3 and Pa s.