Reynolds Number Calculator
Laminar or turbulent? Re for a pipe, duct, channel or plate, with real fluid properties.
Where the regime changes
| Limit | Re | V (m/s) | Q (m³/h) |
|---|
How it was calculated
About the Reynolds Number Calculator
Work out the Reynolds number Re = ρVL/μ = VL/ν and whether the flow is laminar, transitional or turbulent — for a round pipe, a rectangular duct, an annulus or any duct (by its hydraulic diameter 4A/P), an open channel (on its hydraulic radius, with the Froude number) or a flat plate (on the distance from the leading edge, with the boundary-layer thickness). Give the velocity, the volume flow or the mass flow; for steel pipe you can pick the nominal size and schedule.
The fluid properties are calculated, not looked up from a short table: water and steam at any temperature and pressure use the IAPWS-IF97 density and the IAPWS 2008 viscosity, air uses the ideal-gas law and Sutherland’s viscosity law, and any other fluid takes a density with a dynamic viscosity (Pa·s, cP), a kinematic viscosity (cSt, m²/s) or a Saybolt reading (SUS, converted by ASTM D2161). The page also shows the velocities and flow rates at which the regime would change.
How to use it
- Choose where the fluid flows and the size unit, then enter the sizes: the inside diameter (or a steel pipe size), the duct sides, the channel width, depth and side slope, or the distance along a plate.
- Choose whether you know the velocity, the volume flow or the mass flow, and enter it in any unit.
- Pick the fluid. For water or air enter the temperature and the absolute pressure; for anything else enter its density and viscosity, or start from a preset (seawater, ISO VG hydraulic oils) and adjust it.
- Read Re, the regime on the scale, the properties used and the velocity and flow at the laminar and turbulent limits. Copy the result if you need it.
Examples
ν = 1.0034 mm²/s (IAPWS)
Re = 49,830 — turbulent. It would stay laminar below 0.046 m/s (0.33 m³/h).
D_h = 2ab ÷ (a + b) = 240 mm, ν = 15.07 mm²/s
Re = 79,640 — turbulent
ν = 46 cSt
Re = 1,087 — laminar
R_h = A ÷ P = 1 ÷ 3 m
Re = 332,000 — turbulent; Froude number 0.45 — subcritical
Re_x = 132,700 — laminar; boundary layer about 13.5 mm thick; transition expected about 3.8 m from the edge
Common uses
- Checking whether a pipe or duct flow is laminar before choosing a friction-factor formula
- Sizing a heat exchanger or cooling line where the regime changes the heat transfer
- Converting an oil’s viscosity from SUS or cSt and seeing the effect of temperature on water
- Coursework on pipe flow, open channels and boundary layers
Formulas
- Reynolds number: Re = ρ V L ÷ μ = V L ÷ ν, with ν = μ ÷ ρ
- Hydraulic diameter of a full duct: D_h = 4A ÷ P (2ab ÷ (a + b) for a rectangle, D_o − D_i for an annulus)
- Open channel: R_h = A ÷ P with P the wetted perimeter only; Froude number Fr = V ÷ √(g D) with the hydraulic depth D = A ÷ T (T = surface width)
- Flat plate: Re_x = V x ÷ ν; boundary layer δ ≈ 4.91 x ÷ √Re_x while laminar (Blasius) and δ ≈ 0.37 x ÷ Re_x^0.2 when turbulent
- Velocity from flow: V = Q ÷ A = ṁ ÷ (ρ A)
Where laminar becomes turbulent
In pipes the flow is normally laminar below Re ≈ 2,300 and turbulent above about 4,000; in between it can switch either way, depending on the inlet, vibration and roughness (some references use 2,000 as the lower limit). The same limits are used with the hydraulic diameter for other ducts. Open channels are usually reckoned on the hydraulic radius, which is a quarter of a pipe’s diameter, so the limits are lower: laminar below about 500 and turbulent above about 2,000, the practical transition range given by Chow, Open-Channel Hydraulics. On a smooth flat plate the boundary layer usually turns turbulent near Re_x = 5 × 10⁵.
Fluid properties
Water and steam follow IAPWS-IF97 for density and IAPWS R12-08 (2008) for viscosity, from 0 to 800 °C and up to 1,000 bar; above the boiling point at the pressure you enter the calculator switches to steam and says so. The viscosity leaves out the critical-enhancement term, which R12-08 shows to matter only in a small region around the critical point (374 °C, 220.6 bar). Air uses ρ = p ÷ (R T) with R = 287.05 J/(kg·K) and Sutherland’s law μ = μ₀ (T/T₀)^1.5 (T₀ + S) ÷ (T + S) with μ₀ = 1.716 × 10⁻⁵ Pa·s, T₀ = 273 K and S = 111 K (White, Table 1-2), good to about ±2 % from 170 to 1,900 K. Saybolt Universal Seconds are converted with ASTM D2161: SUS = 4.6324ν + (1 + 0.03264ν) ÷ ((3930.2 + 262.7ν + 23.97ν² + 1.646ν³) × 10⁻⁵) at 100 °F, times 1 + 0.000061 (t − 100) at another temperature t in °F.
Sources
- Reynolds, O. (1883), An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, Phil. Trans. R. Soc. 174: 935–982
- IAPWS R7-97 (IF97) and IAPWS R12-08, Viscosity of ordinary water substance
- Sutherland (1893); White, Viscous Fluid Flow, 3rd ed., Table 1-2
- Chow, V. T. (1959), Open-Channel Hydraulics (laminar and turbulent open-channel flow)
- ASTM D2161, Conversion of kinematic viscosity to Saybolt Universal viscosity
- ISO 3448 (ISO viscosity grades at 40 °C)
Limitations
- Air is treated as a dry ideal gas; humid air and high pressures (above about 20 bar) differ slightly. Other gases need their own density and viscosity.
- The regime limits are the usual engineering values, not sharp thresholds: disturbances, roughness and the shape of a duct shift them.
- Non-Newtonian fluids (slurries, pastes, polymer solutions) do not have a single viscosity, so a Reynolds number from one value is only a rough guide.
- Preset oils use the ISO grade’s nominal viscosity at 40 °C and a typical density — use your fluid’s data sheet for other temperatures.
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Frequently asked questions
How do I calculate the Reynolds number?
Multiply the velocity by a characteristic length and divide by the kinematic viscosity: Re = VD/ν. Water at 20 °C has ν ≈ 1.0 mm²/s, so 1 m/s in a 50 mm pipe gives 1 × 0.05 ÷ 0.000001003 ≈ 49,800.
At what Reynolds number does flow become turbulent?
In a pipe, flow is laminar below about 2,300 and turbulent above about 4,000, with a transition range in between. Very smooth, quiet pipes can stay laminar much longer, but designs normally assume these limits. The pipe pressure drop calculator switches its friction factor at the same limits.
What length do I use for a non-circular duct?
The hydraulic diameter, D_h = 4 × flow area ÷ wetted perimeter. For a 300 × 200 mm duct that is 2 × 0.3 × 0.2 ÷ 0.5 = 0.24 m. For an open channel use the hydraulic radius A ÷ P, which is D_h ÷ 4.
How does temperature change the Reynolds number of water?
Water gets much thinner when it warms: its kinematic viscosity falls from 1.00 mm²/s at 20 °C to 0.364 mm²/s at 80 °C, so the same flow has a Reynolds number almost 2.8 times higher.
How do I convert SUS to centistokes?
Use the ASTM D2161 relation that this calculator applies (choose Other fluid and Saybolt Universal Seconds). For example 97.8 SUS at 100 °F is 20 cSt and 463 SUS is about 100 cSt; the equation covers 32 SUS (1.8 cSt) and up.
What is the Froude number shown for channels?
Fr = V ÷ √(g D), the ratio of the flow speed to the speed of a small surface wave. Below 1 the flow is subcritical (tranquil, controlled from downstream); above 1 it is supercritical (rapid). It is independent of the Reynolds number.