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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 ]
From the equation it is shown that for a flow with a large Reynolds Number there will be a correspondingly small convective boundary layer compared to the vessel’s characteristic length. [5] By knowing the Reynolds and Womersley numbers for a given flow it is possible to calculate both the transient and the convective boundary layer ...
The equations show, for example, that pressure variations across the gap are small, and that those along the gap are proportional to the fluid viscosity. A more general formulation of the lubrication approximation would include a third dimension, and the resulting differential equation is known as the Reynolds equation .
The Brezina equation. The Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface. [n 1] These definitions generally include the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension (L in the above equation). This dimension is ...
Reynolds Stress equation models rely on the Reynolds Stress Transport equation. The equation for the transport of kinematic Reynolds stress = ′ ′ = / is [3] = + + + Rate of change of + Transport of by convection = Transport of by diffusion + Rate of production of + Transport of due to turbulent pressure-strain interactions + Transport of due to rotation + Rate of dissipation of .
In fluid dynamics, the Reynolds stress is the component of the total stress tensor in a fluid obtained from the averaging operation over the Navier–Stokes equations to account for turbulent fluctuations in fluid momentum.
The classical elastohydrodynamic theory considers Reynolds equation and the elastic deflection equation to solve for the pressure and deformation in this lubrication regime. [ 5 ] [ 6 ] Contact between raised solid features, or asperities , can also occur, leading to a mixed-lubrication or boundary lubrication regime.
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 ]