# Reynolds number

The **Reynolds number** <math>\mathrm{Re}</math> is a dimensionless quantity that gives a measure of the ratio of inertial forces <math> \left( \rho {\bold \mathrm V}^2 \right) </math> to viscous forces <math> \left( {{\mu {\bold \mathrm V}} \over {L}} \right)</math> and therefore quantifies the relative importance of these two types of forces for given flow conditions.

Reynolds numbers are used to characterize different flow regimes, such as laminar or turbulent flow: laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion, while turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce random eddies, vortices and other flow instabilities. Reynolds numbers can be greatly varied depending on the temperature of fluids, viscosity, and also the elevation at which the experiment is conducted.