Reynolds Number

As previously mentioned, the flow regime is laminar at low flow rates. Frictional viscous forces predominate at these flow rates. As the flow rate increases, the orderly laminar arrangement is disrupted and the inertial forces associated with the movement of material begin to predominate. The ratio of these two forces can be related to the intrinsic fluid properties (viscosity µ, density ρ) and flow parameters (characteristics length dimension l, average velocity v) through a dimensionless quantity termed Reynolds number in honor of Osborne Reynolds:

Reynolds, in his experiments, observed that the transition from laminar to turbulent flow occurred at the Reynolds number of 2300; that is, the flow was laminar below this value and began transitioning into turbulent flow above it. This transition may take place over a range of Reynolds numbers, the flow often considered to be fully turbulent when Re exceeds 4000. The characteristic length dimension depends on the system geometry. For cylindrical conduits, diameter d is used as the length dimension for calculating Re. It should be noted that these Re ranges are applicable to internal flows, that is, a flow through conduits. For external flows, that is, flows over surfaces and objects, such as flow around a car or an airplane, other quantitative criteria apply for the laminar to turbulent transition [5].