Calculate the Reynolds number to predict flow patterns in different fluid flow situations.
Last updated: March 2026 | By ForgeCalc Engineering
The Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns. It is defined as the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities.
At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent. The transition between these regimes depends on the geometry of the system.
Where:
• ρ (rho) is the density of the fluid (kg/m³)
• v is the velocity of the fluid (m/s)
• L is the characteristic length (m)
• μ (mu) is the dynamic viscosity (Pa·s)
Laminar flow occurs when a fluid flows in parallel layers, with no disruption between the layers. It is smooth and predictable, typically occurring at low Reynolds numbers.
Turbulent flow is characterized by chaotic changes in pressure and flow velocity. It involves eddies and vortices, typically occurring at high Reynolds numbers.
For flow in a pipe, the transition from laminar to turbulent typically begins at a Reynolds number of approximately 2,300, and the flow is usually fully turbulent above 4,000.
Because it is a ratio of two forces (inertial and viscous) with the same units, the units cancel out, leaving a pure number that is independent of the system of measurement used.
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