Sommerfeld Number

on . Posted in Dimensionless Numbers

Tags: Fluid

Sommerfeld number, abbreviated as S, a dimensionless number, is used extensively in hydrodynamic lubrication analysis.  The Sommerfeld number is very important in lubrication analysis because it contains all the variables normally specified by the designer.


Sommerfeld 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