The lecture presents the derivation of the Reynolds equation of classical lubrication theory. Consider a liquid flowing through a thin film region separated by two. So, first this slide shows Reynolds equation, which was derived in previous lecture, left hand side shows pressure term. We need to derive pressure distribution. The Reynolds equation is merely a simplified statement of several conservation Although the full mathematical derivation is not shown, we can view each side.

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### Formulation of the Reynolds equation on a time-dependent lubrication surface

InGrubin reynolds equation derivation an approximate solution for so called elasto-hydrodynamic lubrication EHL line contact problem, where he combined both elastic deformation and lubricant hydrodynamic flow.

In this solution it was assumed that the pressure profile follows Hertz solution.

Some texts then use a characteristic dimension that is four times reynolds equation derivation hydraulic radius, chosen because it gives reynolds equation derivation same value of Re for the onset of turbulence as in pipe flow, [18] while others use the hydraulic radius as the characteristic length-scale with consequently different values of Re for transition and turbulent flow.

It characterizes the nature of the surrounding flow and its fall velocity.

In viscous fluids[ edit ] This section does not cite any sources. Please help improve this section by adding citations to reliable sources.

## Reynolds Equation: Derivation and Solution | About Tribology

Unsourced material may be challenged and removed. February Reynolds equation derivation how and when to remove this template message The high viscosity of honey results in perfectly laminar flow when poured from reynolds equation derivation bucket, while the low surface tension allows it to remain sheet-like even after reaching the fluid below.

When the problem is non-stationary and involves significant changes of the interface geometry, finite-deformation effects must additionally be taken into account, irrespective of the impact of the particular definition of the lubrication surface.

Reynolds equation derivation effects are naturally addressed once the lubrication surface is assigned independent kinematics. One approach to accomplishing the stated goal of this work is to start from the formulation of the Navierâ€”Stokes equations with respect to a time-dependent curvilinear coordinate system and subsequently invoke the thin-film assumption to arrive at the desired lubrication formulation.

## NPTEL :: Mechanical Engineering - Tribology

However, this is more easily achieved by starting from the formulation of the Reynolds problem with respect to a stationary but generally curved lubrication surface and subsequently state the generalization to the time-dependent case, which is the approach that will be pursued presently.

In tribology, Reynolds equation derivation equation is used to predict the thickness of the lubricant film, but also to predict the friction developed reynolds equation derivation the lubricant on the surfaces.

Since many tribological contacts operate in highly loaded regime and thin films, the shear rates can be very high in the order of. Many of the typical lubricants start to behave non-Newtonian in the contact conditions and therefore, Reynolds equation was generalized to the case of non-Newtonian lubricant.

Another generalization includes the slip boundary conditions. The considerations of EDL near the reynolds equation derivation and the charge density of the flow in the porous media increase reynolds equation derivation apparent viscosity.