Sommerfield Number

on . Posted in Dimensionless Numbers

Sommerfield number, abbreviated as S, a dimensionless number, is used extensively in hydrodynamic lubrication analysis.

 

Sommerfield Number formula

\(\large{ S = \left( \frac{ r }{ c } \right)^2 \; \frac{ \mu\;n}{P}  }\) 
Symbol English Metric
\(\large{ S }\) = Sommerfield number \(\large{dimensionless}\)
\(\large{ \mu }\)  (Greek symbol mu) = absolute viscosity \(\large{\frac{lbf - sec}{ft^2}}\) \(\large{ Pa - s }\)
\(\large{ P }\) = load per unit of projected bearing area \(\large{\frac{lbf}{in}}\) \(\large{\frac{N}{m}}\)
\(\large{ c }\) = radius clearance \(\large{ft}\) \(\large{m}\)
\(\large{ r }\) = shaft radius \(\large{ft}\) \(\large{m}\)
\(\large{ n }\) = shaft rotational speed \(\large{\frac{r}{min}}\) \(\large{\frac{r}{min}}\)

 

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Tags: Fluid Equations