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The Reynolds equation is used to model the pressure in many applications. For example: Ball bearings; Air bearings; Journal bearings; Squeeze film dampers in aircraft gas turbines; Human hip and knee joints; Lubricated gear contacts
Conceptually the bearings can be thought of as two major geometric classes: bearing-journal (anti-friction), and plane-slider (friction). The Reynolds equations can be used to derive the governing principles for the fluids. Note that when gases are used, their derivation is much more involved.
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 .
S is the Sommerfeld Number or bearing characteristic number r is the shaft radius c is the radial clearance μ is the absolute viscosity of the lubricant N is the speed of the rotating shaft in rev/s P is the load per unit of projected bearing area. The second part of the equation is seen to be the Hersey number.
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 .
Numerical methods such as Finite difference method or Finite element method are common for the discretization and the resolution of the equation, accounting for the boundary conditions associated to each bearing geometry (linear-motion, journal and thrust bearings). In most cases, the gas film can be considered as isothermal and respecting the ...
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 ...
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]