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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 dynamics, the Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. [2] At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow , while at high Reynolds numbers, flows tend to be turbulent .
Reynolds number: Re = fluid mechanics (ratio of fluid inertial and viscous forces) [1] Richardson number: Ri = = fluid dynamics (effect of buoyancy on flow stability; ratio of potential over kinetic energy) [17]
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.
Churchill equation [24] (1977) is the only equation that can be evaluated for very slow flow (Reynolds number < 1), but the Cheng (2008), [25] and Bellos et al. (2018) [8] equations also return an approximately correct value for friction factor in the laminar flow region (Reynolds number < 2300). All of the others are for transitional and ...
In case of 1-D Reynolds equation several analytical or semi-analytical solutions are available. In 1916 Martin obtained a closed form solution [5] for a minimum film thickness and pressure for a rigid cylinder and plane geometry. This solution is not accurate for the cases when the elastic deformation of the surfaces contributes considerably to ...
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The Reynolds number (Re) is a dimensionless quantity that is commonly used in fluid dynamics and engineering. [6] [7] Originally described by George Gabriel Stokes in 1850, it became popularized by Osborne Reynolds after whom the concept was named by Arnold Sommerfeld in 1908. [7] [8] [9] The Reynolds number is calculated as:
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