Reynolds Number Calculator
Reynolds number for pipe flow, the critical speed and an estimated friction factor.
Results
What this tool does
The Reynolds number is a ratio of inertia to viscosity, and because it is a pure number it says the same thing about a garden hose and an oil pipeline. Below the critical value the fluid slides in neat layers and pressure loss is small; above it, the flow breaks up and losses climb steeply. Water at 20 °C is 998 kg/m³ and 1.002 mPa·s.
Formula
Re = ρ × v × D ÷ μ
Variables
| Symbol | Meaning | Unit |
|---|---|---|
ro | Fluid density | kg/m³ |
v | Speed | m/s |
d | Pipe diameter | mm |
mu | Dynamic viscosity | mPa·s |
RE | Reynolds number | — |
RG | How the fluid is moving | — |
NU | Kinematic viscosity | mm²/s |
VC | Speed | m/s |
FD | Friction factor | — |
Worked example
- Fluid density998 kg/m³
- Speed1.5 m/s
- Pipe diameter50 mm
- Dynamic viscosity1.002 mPa·s
- Reynolds number74,701
- How the fluid is movingTurbulent — mixing and swirling
- Kinematic viscosity1.0040 mm²/s
- Speed0.04618 m/s
- Friction factor0.01914
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
Frequently asked questions
Where is the boundary between laminar and turbulent?
In a round pipe, flow is reliably laminar below about Re 2300 and reliably turbulent above about 4000. Between the two it is transitional and genuinely unpredictable: the same pipe can flip between the two depending on vibration, roughness and how the flow entered. The third result gives the speed at which your pipe reaches 2300.