Reynolds Number Calculator
Reynolds Number150,000.00
Flow RegimeTurbulent
The Reynolds Number Calculator predicts whether a fluid flow is laminar, transitional, or turbulent by comparing inertial forces to viscous forces. Enter the flow velocity, a characteristic length such as pipe diameter, and the fluid viscosity, and the tool returns the dimensionless Reynolds number along with the expected flow regime. You can supply either dynamic viscosity together with density, or kinematic viscosity on its own, depending on the data you have.
Formula
Re = (rho * v * D) / mu = (v * D) / nu
- Re
- Reynolds number (dimensionless)
- rho
- Fluid density (kg/m^3), dynamic mode only
- v
- Flow velocity (m/s)
- D
- Characteristic length, e.g. pipe diameter (m)
- mu
- Dynamic viscosity (Pa.s)
- nu
- Kinematic viscosity (m^2/s), where nu = mu / rho
How it works
- Choose a viscosity mode. In dynamic mode you provide the fluid density and dynamic viscosity; in kinematic mode you provide the kinematic viscosity directly, which already folds density into the figure.
- The calculator multiplies velocity by the characteristic length and divides by viscosity (using density as well in dynamic mode) to produce the dimensionless Reynolds number.
- It then classifies the result: below 2300 is laminar, 2300 through 4000 is transitional, and above 4000 is turbulent for standard internal pipe flow.
Worked example
Water flowing at 1.5 m/s through a 0.1 m diameter pipe, using a kinematic viscosity of 1.0e-6 m^2/s.
- Multiply velocity by diameter: 1.5 x 0.1 = 0.15.
- Divide by kinematic viscosity: 0.15 / 0.000001 = 150000.
- Re = 150000, which is far above 4000.
Re = 150000, a turbulent flow regime.
Frequently asked questions
- What is the difference between the dynamic and kinematic modes?
- Dynamic mode uses density and dynamic viscosity (mu) separately, while kinematic mode uses kinematic viscosity (nu), which equals mu divided by density. Both give the same Reynolds number; pick the one that matches the property values you already have.
- Why are 2300 and 4000 used as the flow regime cutoffs?
- These thresholds are the conventional limits for fully developed flow inside a circular pipe. Below about 2300 viscous forces keep the flow orderly and laminar, above roughly 4000 inertial forces dominate and the flow becomes turbulent, and the band between them is an unstable transitional zone.
- What characteristic length should I use?
- For flow inside a circular pipe use the inside diameter. For non-circular ducts use the hydraulic diameter, and for flow over a flat plate or around an object use the relevant length along the flow direction. The choice must match the regime cutoffs you intend to apply.
- Is the Reynolds number unit dependent?
- No, the Reynolds number is dimensionless, so the units cancel as long as they are consistent. Using SI units (m/s, m, and Pa.s or m^2/s) keeps the inputs coherent and avoids accidental scaling errors.