Sommerfeld number, abbreviated as \(S\) or \(So\), 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. It's particularly important in the study of journal bearings.
Sommerfeld Number formula |
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\( S \;=\; \left( \dfrac{ r }{ c} \right)^2 \cdot \dfrac{ \mu \cdot n }{ P } \) (Sommerfeld Number) \( r \;=\; c \cdot \sqrt{ \dfrac{ S \cdot P }{ \mu \cdot n } }\) \( c \;=\; r \cdot \sqrt{ \dfrac{ \mu \cdot n }{ S \cdot P } }\) \( \mu \;=\; \dfrac{ S \cdot P \cdot \left( \dfrac{ c }{ r} \right)^2 }{ n } \) \( n \;=\; \dfrac{ S \cdot P \cdot \left( \dfrac{ c }{ r } \right)^2 }{ \mu } \) \( P \;=\; \dfrac{ \mu \cdot n \cdot \left( \dfrac{ r }{ c } \right)^2 }{ S } \) |
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| Symbol | English | Metric |
| \( S \) = Sommerfield Number | \(dimensionless\) | \( dimensionless \) |
| \( r \) = Shaft Radius | \(ft\) | \(m\) |
| \( c \) = Radius Clearance | \(ft\) | \(m\) |
| \( \mu \) (Greek symbol mu) = Absolute Viscosity | \(lbf - sec / ft^2\) | \( Pa - s \) |
| \( n \) = Shaft Rotational Speed | \(r \;/\; min\) | \(r \;/\; min\) |
| \( P \) = Load per Unit of Projected Bearing Area | \(lbf - ft\) | \(N - m\) |
Key Points about Sommerfeld Number
