The Sommerfeld Number is typically defined by the following equation:
where:
: S is the Sommerfeld Number or bearing characteristic number
: r is the shaft radius
: c is the radial clearance
: µ is the absolute viscosity of the lubricant
: N is the speed of the rotating shaft in rev/s
: P is the load per unit of projected bearing area
The second part of the equation is seen to be the Hersey number. However, an alternative definition for S is used in some texts based on angular velocity:
where:
: is angular velocity of the shaft in rad/s.
: W is the applied load
: L is the bearing length
: D is the bearing diameter
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.