Glossary term
Reynolds Number
A dimensionless fluid-flow ratio comparing inertial and viscous effects to classify similarity, laminar flow, transition, and turbulence.
Definition
quantityThe Reynolds number is a dimensionless ratio of inertial forces to viscous forces in a fluid flow.
Reynolds number indicates whether viscous effects dominate a flow or whether inertia is strong enough to produce separation, unsteady motion, transition, or turbulence. It is central to pipe flow, external aerodynamics, heat transfer, hydraulic modelling, mixing, and scale-model testing because it links velocity, length scale, density, and viscosity in one similarity parameter.
The Reynolds number is commonly written as:
where \rho is fluid density, V is a representative velocity, L is a characteristic length, \mu is dynamic viscosity, and \nu is kinematic viscosity. The value is dimensionless because it compares two effects rather than measuring a physical quantity directly.
Low Reynolds number flows are dominated by viscosity. High Reynolds number flows are dominated by inertia and are more likely to separate, become unstable, or transition to turbulence. The threshold is not universal. Internal pipe flow often uses approximate regimes such as laminar below about 2300 and turbulent above about 4000, but airfoils, jets, open-channel flows, porous media, microfluidics, and stirred tanks use different characteristic lengths and different transition behaviour.
Engineering use
Reynolds number controls friction factor correlations, drag coefficient, boundary-layer development, wake formation, convective heat transfer, pressure loss, mixing intensity, and the validity of scale-model tests. A wind-tunnel model, pump test, or hydraulic model can reproduce important behaviour only if the relevant similarity parameters are matched or if the mismatch is quantified.
The characteristic length must match the phenomenon being modelled. Pipe calculations usually use diameter or hydraulic diameter. External flow may use chord length, body diameter, plate length, or gap size. Flow through an orifice, nozzle, valve, or packed bed requires a length scale appropriate to the correlation being applied.
Common mistakes
A common mistake is treating a single Reynolds number threshold as universal. Another is computing a value with bulk velocity and pipe diameter, then applying it to a local boundary layer, small clearance, porous region, or separated wake where the relevant length and velocity differ. A good Reynolds-number review states density, viscosity, temperature, velocity definition, characteristic length, flow geometry, roughness, and the correlation or regime map being used.