## The Reynolds Number

Smooth, laminar fluid flow only occurs at low speeds. As the speed of the flow increases, a transition to turbulent flow may occur. Eddies and vertices may form in the fluid, resulting in internal friction in the fluid and loss of energy. Once the flow becomes turbulent, an greater pressure is required because the friction forces increase with the speed of the flow.

The onset of turbulent flow is indicated by a number called the Reynolds number, Re. This is a measure of the ratio of inertial forces to viscous forces in a fluid. For a circular pipe,where

is the average speed of the fluid

is the density of the fluid

is the coefficient of viscosity

is the radius of the pipe carrying the fluid.

The Reynolds number is dimensionless since all the units cancel, and increases with the speed of the fluid. The threshold above which turbulent flow occurs is experimentally determined. The following numbers are indicative:

Ifthe flow is laminar

Ifthe flow may be either laminar or turbulent, depending on the exact conditions – the fluid, viscosity, temperature and flow channel.

Ifthe flow is turbulent.