# Reynolds number

One of the non-dimensional numbers which provide criteria of similarity for flows of viscous liquids and gases. It characterizes the relation between the inertial forces and the forces of viscosity: $$\mathrm{Re} = \frac{\rho \, \nu \, l}{\mu}$$ where $\rho$ is the density, $\mu$ is the dynamical coefficient of viscosity of the liquid or gas, $\nu$ is the typical rate of flow, and $l$ is the typical linear dimension.

The Reynolds number also determines the mode of flow of a liquid in terms of a critical Reynolds number, $\mathrm{Re}_{\mathrm{cr}}$. When $\mathrm{Re} < \mathrm{Re}_{\mathrm{cr}}$, only laminar liquid flow is possible, whereas when $\mathrm{Re} > \mathrm{Re}_{\mathrm{cr}}$ the flow may become turbulent (cf. Turbulence, mathematical problems in).

The Reynolds number is named after O. Reynolds.