What is Reynolds number?

For a flow of characteristic speed $U$ and length $L$, the Reynolds number

is the ratio of the orders of magnitude of the inertial term $\rho(\vect v\cdot\operatorname{\vect{grad}})\vect v \sim \rho U^2/L$ and the viscous term $\eta\Delta\vect v \sim \eta U/L^2$ in the Navier–Stokes equation. At $\mathrm{Re} \ll 1$ inertia is negligible and the flow is creeping (viscous, reversible, smooth); at $\mathrm{Re} \gg 1$ viscosity is negligible except near walls and the flow is that of a perfect fluid — until, beyond a threshold of order $10^3$ (about $2000$ to $3000$ in a pipe, based on the diameter), it becomes turbulent: unsteady, chaotic, full of eddies at every scale. Between the two, a flow is laminar: steady and layered.