Reynolds number what is it and how to claculate

In fluid mechanics, the Reynolds number (Re) is the ratio of inertial forces to viscous forces. Consequently, it quantifies the relative importance of these two types of forces for given flow conditions.

It is one of the most important dimensionless numbers in fluid dynamics and is usually used along with other dimensionless numbers to provide a criterion for determining dynamic similitude. It is also used to identify and predict different flow regimes, such as laminar or turbulent flow. This depends on the pipe diameter, the density and the viscosity of the flowing fluid.

Laminar flow occurs at low Reynolds numbers, where viscous forces dominate, and is characterised by smooth, constant fluid motion. This occurs when the Reynolds number is less than 2000, and the resistance to flow is independent of the wall roughness.

Turbulent flow occurs when the Reynolds number exceeds 4000. At this time, Eddy currents are present within the flow, and the ratio of the pipe's internal roughness to the pipe's internal diameter needs to be considered to determine the friction factor. In large-diameter pipes, the overall effect of the currents is less significant. In small-diameter pipes, the internal roughness can significantly influence the friction factor.

Between the two states (laminar and turbulent) lies the 'critical zone' where the flow is in the process of change, depending upon many possible conditions, which is unpredictable. It may be considered as a combination of the two flow conditions.


Reynolds number, its use, and equation

Laminar flow Laminar flow
Coloured filaments are carried along undisturbed by a stream of water
Turbulent flow Turbulent flow
The coloured filaments are completely dispersed only a short distance downstream from the injection point.

Reynolds number can be calculated from the following equation.

 Reynolds number equation


Q = flow in L/min
p = weight density of the fluid in kg/m3
d = internal pipe diameter in mm
µ = absolute (dynamic) viscosity in centipoise cP



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