Sommerfeld Number

S = (η·N)/(P)·(R/c)² - dimensionless bearing operating parameter. Low S → thick film, hydrodynamic; high S → thin, boundary.

Lubrication

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Formula, assumptions, and limits

S = \frac{\eta N}{P} \left(\frac{R}{c}\right)^2

Symbol	Meaning	Unit
$η$	Dynamic viscosity	Pa·s
$N$	Shaft speed	rev/s
$P$	Specific bearing load	Pa
$R, c$	Journal radius, radial clearance	mm

Source: Sommerfeld (1904)

S = (\u03b7\u00b7N)/(P)\u00b7(R/c)\u00b2 - dimensionless bearing operating parameter.