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The Reynolds number is the ratio of inertial forces to viscous forces within a fluid that is subjected to relative internal movement due to different fluid velocities. A region where these forces change behavior is known as a boundary layer, such as the bounding surface in the interior of a pipe.
The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
In fluid mechanics (specifically lubrication theory), the Reynolds equation is a partial differential equation governing the pressure distribution of thin viscous fluid films. It was first derived by Osborne Reynolds in 1886. [ 1 ]
1 Derivation. 2 General characteristics for large and small R m. 3 Range of values. 4 Bounds. ... In magnetohydrodynamics, the magnetic Reynolds number (R m) ...
The Reynolds-averaged Navier–Stokes equations (RANS equations) are time-averaged [a] equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition , whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating quantities, an idea first proposed by Osborne Reynolds . [ 1 ]
Shown is a sphere in Stokes flow, at very low Reynolds number. Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, [1] is a type of fluid flow where advective inertial forces are small compared with viscous forces. [2] The Reynolds number is low, i.e. . This is a typical situation in flows where the ...
A vessel of diameter of 10 µm with a flow of 1 millimetre/second, viscosity of 0.02 poise for blood, density of 1 g/cm 3 and a heart rate of 2 Hz, will have a Reynolds number of 0.005 and a Womersley number of 0.0126. At these small Reynolds and Womersley numbers, the viscous effects of the fluid become predominant.