EngineeringFormulaReynolds Number (Re)
Reynolds number is a dimensionless ratio of inertial to viscous forces in a flowing fluid.
Re = ρvD/μ for internal pipe flow. A low Reynolds number (roughly below 2300 for pipe flow) indicates smooth, laminar flow; a high one indicates turbulent flow. It's dimensionless by construction - it has no unit - which is what makes it useful for comparing flow regimes across completely different fluids and pipe sizes.
Because it's dimensionless, Reynolds number is what lets engineers validate a small-scale physical model (a scale-model wing in a wind tunnel, for example) against a full-size design - if the model test is run at the same Reynolds number as the real thing, the flow behavior scales correctly even though the physical size and fluid don't match.
Use Reynolds number before choosing a pressure-drop, orifice, pump, pipe, or heat-transfer model. The same flow rate can land in different regimes if diameter, viscosity, or density changes.
Typical Reynolds Numbers by Context
| Context | Approximate Re | Regime |
|---|---|---|
| Blood flow in capillaries | < 1 | Laminar |
| Pipe-flow transition point | ~2,300–4,000 | Transitional |
| Household plumbing | ~5,000–50,000 | Turbulent |
| Commercial aircraft wing | ~10–50 million | Turbulent |
Used In These Calculators
Related Terms
Frequently Asked Questions
What counts as the transition point between laminar and turbulent flow?
For flow inside a straight circular pipe, Re below roughly 2,300 is considered laminar and above roughly 4,000 is considered turbulent, with a transitional range in between where the flow can be unstable. Those thresholds are specific to internal pipe flow - external flow around an object (like an aircraft wing) transitions at very different Reynolds numbers.
Why does Reynolds number matter if I already know the flow rate?
Flow rate alone doesn't tell you whether flow is laminar or turbulent, and that distinction changes which friction and heat-transfer formulas actually apply. Two pipes carrying the same flow rate but different diameters or fluids can sit in completely different flow regimes, which is exactly the comparison Reynolds number is built to make.
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