Guide
The Reynolds number tells you whether a flow is dominated by inertia or by viscosity, and therefore whether you should expect laminar, transitional or turbulent behaviour. Checking it takes seconds, and it decides your turbulence model, mesh strategy and solver settings.
ρ is density, μ dynamic viscosity, ν = μ/ρ kinematic viscosity, U a characteristic velocity and L a characteristic length. For flow in a non-circular duct, the length is the hydraulic diameter:
A is the flow cross-section area and P the wetted perimeter. This reduces to familiar forms:
The calculator handles all three shapes, converts between SI and imperial units, and can also run in reverse: choose Solve Velocity to find the speed that gives a target Reynolds number, for instance to see how fast a fluid must move before it leaves the laminar regime.
| Flow | Laminar | Transitional | Turbulent |
|---|---|---|---|
| Internal (pipe or duct, Re based on Dh) | Re < 2,300 | 2,300 – 2,900 (sensitive to disturbances) | Re > 2,900 |
| External (flat plate, Re based on length) | Re < 5×10⁵ | Around 5×10⁵ | Re > 5×10⁵ |
These are rules of thumb. The actual transition point depends on inlet turbulence, wall roughness, pressure gradient, surface curvature and vibration. Clean, disturbance-free pipe flow can stay laminar well beyond 2,300, while a noisy inlet can trip transition early. Around the threshold, treat the flow as uncertain and consider a transition-capable model.
| Water in a round pipe | Air in a rectangular duct | |
|---|---|---|
| Fluid (20 °C) | Water: ρ = 998.2 kg/m³, μ = 1.00×10⁻³ Pa·s | Air: ρ = 1.205 kg/m³, μ = 1.82×10⁻⁵ Pa·s |
| Geometry | D = 50 mm, so Dh = 0.05 m | 300 mm × 100 mm, so Dh = 2(0.3)(0.1)/0.4 = 0.15 m |
| Velocity | 2 m/s | 5 m/s |
| Reynolds number | 99,820 | 49,657 |
| Regime | Turbulent | Turbulent |
Using solve-velocity mode for the same pipe at Re = 2,300, the velocity is U = Re μ / (ρ Dh) ≈ 0.046 m/s. Water in a 50 mm pipe is turbulent at almost any practical speed.
The calculator includes ready-to-use properties at 20 °C for air, water, SAE 30 engine oil, glycerin, ethylene glycol and seawater, or you can enter your own density and viscosity. For gases and for temperature-sensitive liquids such as oil, viscosity changes strongly with temperature, so use values at your operating temperature rather than the room-temperature presets.
Use the length along the flow direction for a flat plate (ReL or Rex at a location). For bluff bodies use the diameter or frontal dimension, for example the cylinder diameter or a car’s height, and note which convention you follow since published transition values assume a specific one.
It makes the formula reproduce the pipe diameter for a circle (4 · πD²/4 ÷ πD = D). For other shapes it gives an equivalent length that collapses friction and transition behaviour reasonably well, though it is less accurate for very high aspect ratios or laminar flow in unusual shapes.
The same definition applies: compute the flow area and the wetted perimeter of the actual geometry, and use them in Dh = 4A/P. For an annulus, Dh = Douter − Dinner.
The definition stays the same, but ρ and μ vary with temperature and pressure, so use the local values. At high Mach number, check the Mach number as well (see the non-dimensional numbers calculator).
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