Calculate Reynolds number to determine if fluid flow is laminar, transitional, or turbulent.
The Reynolds number tells you whether flow in a pipe, channel, or around an object is laminar, transitional, or turbulent, and it is the single most important dimensionless group in pipe sizing, heat-exchanger design, and friction-loss analysis. This calculator computes Re from velocity, characteristic length, density, and dynamic viscosity, then classifies the regime so you can pick the correct friction-factor correlation downstream.
The formula is Re = ρ × v × D / μ where ρ is fluid density (kg/m³), v is mean velocity (m/s), D is the hydraulic diameter (m), and μ is dynamic viscosity (Pa·s). An alternative form uses kinematic viscosity ν: Re = v × D / ν. For internal pipe flow, classification thresholds are Re < 2,300 laminar, 2,300 ≤ Re ≤ 4,000 transitional, Re > 4,000 turbulent. The transition band is sensitive to inlet conditions, pipe roughness, and vibration, so designers usually treat Re > 2,300 as turbulent for conservative friction-loss estimates. For non-circular ducts use the hydraulic diameter D_h = 4 × A / P where A is cross-section area and P is wetted perimeter. The Reynolds number determines whether the Hagen–Poiseuille (laminar), Colebrook–White, or Swamee–Jain (turbulent) correlation applies for friction factor in the Darcy–Weisbach equation.
A hydraulic systems engineer sizing a suction line for ISO VG 46 oil at 40 °C computes Re = 1,400 at 1.5 m/s in a 25 mm bore, confirms laminar regime, and applies the Hagen–Poiseuille formula for pressure drop instead of the turbulent correlation.
A process engineer running cooling water at 3 m/s through 19 mm tubes calculates Re = 57,000 (turbulent) and selects the Dittus–Boelter Nusselt correlation for the heat-transfer coefficient, which is only valid in the turbulent regime.
A piping designer finds Re = 3,200 in a chilled-water line and flags the design for review because the friction factor in the transition band is unpredictable; raising velocity or increasing diameter shifts the result safely out of transition.
Laminar flow moves in smooth parallel layers (Re < 2,300). Turbulent flow has chaotic eddies and mixing (Re > 4,000). Most industrial pipe flow is turbulent because of the higher velocities involved.
Friction factor depends on flow regime. In laminar flow, friction factor f = 64/Re. In turbulent flow, it depends on roughness and Re via the Colebrook equation. Using the wrong regime can produce 2-5× pressure drop errors.
For water at 20 °C, μ ≈ 0.001 Pa·s. For hydraulic oils, viscosity is reported as ISO VG (kinematic at 40 °C) on the data sheet. Multiply by density to get dynamic viscosity.
Yes, the same formula works for compressible flow up to roughly Mach 0.3. Above that, additional compressibility effects come into play and Re alone is no longer sufficient.