Definition of Reynolds number

Reynolds number is used in fluid mechanics, to characterize the movement of a fluid. Its value shows if flow follows a laminar or turbulent flow. This concept was introduced by Stokes and popularized by Osborne Reynolds. It is used in several fields like piping design, reactors design or biology. Reynolds number is defined as the relationship between inertial and viscous forces.

The equation used for the calculation of Reynolds number is:
   Re = v · D / Vcin

    Re: Reynolds Number (dimensionless)
   v: Fluid velocity
   D: Internal diameter of pipe
   Vcin: Kinematic viscosity

Reynolds number is a dimensionless number that is use to determine if a fluid has a laminar or turbulent behavior


Flow rate
Internal Diameter (D) mm

Laminar Flow:

Behaves like formed by a set of thin sheets. If we put a dye in the pipe, we would see that it follows a line paralell to the pipe walls. It happens when Reynolds number is below 2100 in a circular pipe.

Turbulent flow:

The movement of the fluid is messy. They dye would mix. It happens for Reynolds numbers above 4000.

Transition zone:

For Reynolds number between 2100 and 4000, the fluid is in a transition zone between both types of flow, it is not possible to confirm if it is laminar or turbulent.

Other Calculators: