# Sommerfeld Number - alternative using angular velocity

## Description

In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity 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.

The Sommerfeld number is named after Arnold Sommerfeld (1868–1951).

An alternative definition is shown here, based on angular velocity.

It is therefore necessary to check which definition is being used when referring to design data or textbooks, since the value of S will differ by a factor of 2π.

Related formulas## Variables

S | Sommerfeld number (dimensionless) |

r | shaft radius (m) |

c | radial clearance (m) |

μ | absolute viscosity of the lubricant (pascal*s) |

ω | angular velocity of the shaft (rad/s) |

L | bearing length (m) |

D | bearing diameter (m) |

W | applied load (N) |