The well-established narrow groove theory for spiral groove gas bearings  has been generalized to include the effects of rarefied gas and turbulence. The slip flow effect was considered locally depending upon gaseous density and molecular mean free path  while the local turbulence effect was introduced by a set of viscosity modification functions [3, 4]. For transition flow, the concept of “mean” local Reynolds number may be adapted . The fundamental governing equation was derived in terms of a generalized coordinate for bodies of rotational symmetry and valid for both incompressible and compressible bearings or seals.
Formulation of a Generalized Narrow Groove Theory for Spiral Grooved Viscous Pumps
F. C. Hsing
Mechanical Technology Inc., Latham, N. Y.
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Hsing, F. C. (January 1, 1972). "Formulation of a Generalized Narrow Groove Theory for Spiral Grooved Viscous Pumps." ASME. J. of Lubrication Tech. January 1972; 94(1): 81–85. https://doi.org/10.1115/1.3451640
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