The Zero Pressure Gradient Condition

Abstract

Investigation is made of the zero pressure gradient condition which is used to locate the ruptured segment of a cavitation boundary in hydrodynamic lubrication. A stability argument provides rigorous justification for the use of this condition in specific circumstances. These include steady flow having a modified capillary number much less than unity thus ensuring that sufficiently large superatmospheric pressures are generated for surface tension pressures to have negligible effect. The following results are deduced; that (1) the zero pressure gradient condition is valid on part but not the whole of the cavitation boundary, (2) in order to locate the entire cavitation boundary the zero gradient condition must be used in conjunction with a flow continuity condition, (3) cavities always form in the divergent section of a lubrication geometry.