# Reynolds equation

## Reynolds equation

[′ren·əlz i‚kwā·zhən]
(fluid mechanics)
A form of the Navier-Stokes equation which is ρ∂ u /∂ t = (∂/∂ x)(pxx - ρ u 2) + (∂/∂ y) · (pxy - ρ uv) + (∂/∂ z)(pxz - ρ uw) where ρ is the fluid density, u, v, and w are the components of the fluid velocity, and pxx , pxy , and pxz are normal and shearing stresses.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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As the hydrodynamic solution is performed within the EMBS solver execution the computational performance of the hydrodynamic solution on the basis of the Reynolds equation is one of the key aspects.
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The final forms of the Reynolds equation for the full piston sliding is:
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Naduvinamani and Patil  obtained a numerical solution to finite modified Reynolds equation for couplestress squeeze film lubrication of porous journal bearings.
According to the classic lubrication theory, the pressure distribution in the annular region of a squeeze film damper is determined by using Reynolds equation, where it is assumed that the inertial forces are negligible relative to viscous forces (i.e., Re [approximately equal to] 0) .
The Reynolds equation, which is derived from the Navier-Stokes (NS) equations using thin-film assumptions, is extensively used in tribological applications.
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He focuses mainly on numerical solutions to the Reynolds equation, energy equation, elastic deformation equation, and combinations of the three.
Governing equations of fluid flow such as continuity equation, heat transfer equation, momentum equation and Reynolds equation for a turbulent fluid flow of a compressible fluid has been adopted to solve the CFD analysis .

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