Sommerfield Number

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	\(\large{\frac{r}{min}}\)	\(\large{\frac{r}{min}}\)