Reynolds number: a standalone construct

Osborne Reynolds established the quantity in 1883, when his dye experiments in glass pipes showed that water switches from smooth, orderly motion to irregular, mixing motion at a repeatable threshold, and that the threshold depends not on speed alone but on a single combination of the fluid's speed, the pipe's width, the fluid's density, and its viscosity, the fluid's internal resistance to shearing. In his 1895 paper Reynolds derived this combination from the equations of viscous flow and showed it governs the onset of the disordered regime, and in 1908 Arnold Sommerfeld named the resulting dimensionless quantity the Reynolds number. Read physically, it is the ratio of inertial forces, which carry a parcel of fluid along, to viscous forces, which damp its motion, so a small value means viscosity dominates and the flow stays laminar, while a large value means inertia dominates and the flow tends toward turbulence. Because it is a pure number with no units, the same value describes geometrically similar flows at very different scales, which is what lets a small model in a wind tunnel or water channel stand in for a full-size aircraft, ship, or pipeline. It is defined across the whole of fluid dynamics rather than one application, and it fixes the single most-cited criterion for whether a flow is laminar or turbulent.[1][2][3]

Unit

Dimensionless (a pure ratio, no units)

Recovery means

Not applicable

Measured by

Computed as Re = rho x U x L / mu, the product of fluid density, a characteristic velocity, and a characteristic length divided by dynamic viscosity, using the length scale conventional for the geometry (for example pipe diameter)