The inertial force is proportional to the velocity pressure of the fluid rv2 and the viscous drag is proportional to mv/D where D is the diameter of the pipe. The ratio of these forces is:

rv2D/mv = Dvr/m

This ratio is very important in the study of fluid flow. As it is a ratio, it is dimensionless and so it is numerically independent of the units of measurement so long as these are consistent. It is called the Reynolds number and is denoted by the symbol (Re).

From a host of experimental measurements on fluid flow in pipes, it has been found that the flow remains calm or "streamline" for values of the Reynolds number up to about 2100. For values above 4000 the flow has been found to be turbulent. Between above 2100 and about 4000 the flow pattern is unstable; any slight disturbance tends to upset the pattern but if there is no disturbance, streamline flow can be maintained in this region.

To summarise for flow in pipes:

For (Re) < 2100 streamline flow,

For 2100 < (Re) < 4000 transition,

For (Re) > 4000 turbulent flow.