This paper investigates the steady slow flow of an incompressible viscous fluid in the region between an inner circular cylinder rotating with constant angular velocity and an outer stationary cylinder of arbitrary cross section. The numerical solution technique known as the boundary integral equation method is employed in which the governing partial differential equations of motion are recast into coupled integral equations by repeated applications of the divergence theorem. The method is applied to the two dimensional flow within the eccentric journal bearing, and it is found that certain aspects of previous analytic treatments of this bearing have been in error. An extension of the method is applied to solve for the flow within an elliptical bearing, for which no analytic solution or numerical results are available. This extension is able to solve for the flow within any bearing geometry, however complex. It is found that the present method is particularly suited to the prediction of flow separation within noncircular bearings, and it is hoped that these results and techniques will lead to a better understanding of the conditions causing the phenomenon of cavitation.

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