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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.
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 This turbulent boundary layer thickness formula assumes 1) the flow is turbulent right from the start of the boundary layer and 2) the turbulent boundary layer behaves in a geometrically similar manner (i.e. the velocity profiles are geometrically similar along the flow in the x-direction, differing only by stretching ...
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The Reynolds number Re is taken to be Re = V D / ν, where V is the mean velocity of fluid flow, D is the pipe diameter, and where ν is the kinematic viscosity μ / ρ, with μ the fluid's Dynamic viscosity, and ρ the fluid's density. The pipe's relative roughness ε / D, where ε is the pipe's effective roughness height and D the pipe ...
The Buckingham pi theorem then leads to a third dimensionless group, the ratio of the relative velocity to the speed of sound, which is known as the Mach number. Consequently when a body is moving relative to a gas, the drag coefficient varies with the Mach number and the Reynolds number.