Reynolds Number & Flow Regime Calculator

Reynolds number is the most important dimensionless number in fluid mechanics, chemical process engineering, aerodynamics, and HVAC design.

Density of the fluid (e.g. Water @ 20°C = 998 kg/m³, Air @ STP = 1.204 kg/m³, Engine Oil = 880 kg/m³).

Average fluid velocity inside the pipe in meters per second.

Internal pipe diameter or hydraulic diameter (e.g. 50 mm = 0.05 m).

Fluid dynamic viscosity in Pa·s (e.g. Water @ 20°C ≈ 0.001 Pa·s, Air ≈ 1.81×10⁻⁵ Pa·s).

How it works

It quantifies whether viscous shear forces dominate (producing smooth, streamlined laminar layers) or inertial forces dominate (producing chaotic turbulent eddies and high friction loss).

Formula

Re = (rho × v × D / mu) = (v × D / nu), nu = (mu / rho)

Calculates the ratio of inertial forces to viscous forces within a moving fluid to classify flow predictability and turbulence.

SymbolVariableUnitDescription
rhoFluid densitykg/m³
vAverage fluid velocitym/s
DPipe inner hydraulic diameterm
muDynamic viscosityPa·s
ReDimensionless Reynolds numberunitless

Worked example

Water flowing at 1.5 m/s through a 50mm pipe (ρ = 1000, μ = 0.001)

Density:
1000 kg/m³
Velocity:
1.5 m/s
Diameter:
0.05 m
Viscosity:
0.001 Pa·s

Re = (1000 × 1.5 × 0.05) / 0.001 = 75,000. Since Re > 4,000, the flow is fully Turbulent.

Limitations

Pipe thresholds (2300 / 4000) apply to internal closed conduit flows, not external flows over airfoils or flat plates.

Frequently asked questions

Why is Reynolds number important in pipe sizing?

Turbulent flow creates significantly higher friction pressure drops (Darcy-Weisbach head loss), requiring larger pumps and higher pumping power compared to laminar flow.

What is the critical Reynolds number for non-circular ducts?

For non-circular ducts, replace diameter D with Hydraulic Diameter: $D_h = 4A / P$, where A is cross-sectional flow area and P is wetted perimeter.

What is kinematic viscosity (ν)?

Kinematic viscosity is dynamic viscosity divided by fluid density ($ u = mu / ho$), representing fluid resistance to shear under gravity. Units are m²/s or centistokes (cSt).

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Last reviewed: 2026-08-22.