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It was first derived by Osborne Reynolds in 1886. [1] The classical Reynolds Equation can be used to describe the pressure distribution in nearly any type of fluid film bearing; a bearing type in which the bounding bodies are fully separated by a thin layer of liquid or gas.
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.
This design of bearing may wear when started, stopped or reversed, as the lubricant film breaks down. The basis of the hydrodynamic theory of lubrication is the Reynolds equation. The governing equations of the hydrodynamic theory of lubrication and some analytical solutions can be found in the reference. [3]
A lifting body is a foil or a complete foil-bearing body such as a fixed-wing aircraft. C L is a function of the angle of the body to the flow, its Reynolds number and its Mach number. The section lift coefficient c l refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord ...
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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 ...