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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.
A vortex street around a cylinder. This can occur around cylinders and spheres, for any fluid, cylinder size and fluid speed, provided that the flow has a Reynolds number in the range ~40 to ~1000. [1] In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime. [2]
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.
A key tool used to determine the stability of a flow is the Reynolds number (Re), first put forward by George Gabriel Stokes at the start of the 1850s. Associated with Osborne Reynolds who further developed the idea in the early 1880s, this dimensionless number gives the ratio of inertial terms and viscous terms. [4]
is the Reynolds number with the cylinder diameter as its characteristic length; Pr {\displaystyle \Pr } is the Prandtl number . The Churchill–Bernstein equation is valid for a wide range of Reynolds numbers and Prandtl numbers, as long as the product of the two is greater than or equal to 0.2, as defined above.
At very low Reynolds numbers (based on the diameter of the circular member) the streamlines of the resulting flow is perfectly symmetric as expected from potential theory. However, as the Reynolds number is increased the flow becomes asymmetric and the so-called Kármán vortex street occurs. The motion of the cylinder thus generated due to the ...
Reynolds’ 1883 experiment on fluid dynamics in pipes Reynolds’ 1883 observations of the nature of the flow in his experiments. In 1883 Osborne Reynolds demonstrated the transition to turbulent flow in a classic experiment in which he examined the behaviour of water flow under different flow rates using a small jet of dyed water introduced into the centre of flow in a larger pipe.