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In fluid dynamics and hydrodynamics, concept introduced by Lord Kelvin (Also known as Sir William Thomson, sometimes as Kelvin of Largs or Baron William Thomson)

The circulation is K defined as the integral of v · dl around the closed loop l around a body in a fluid.

 K= ∫v · dl

Specifically for a cylinder in a fluid, the integral would solve as K = v · 2 · &pi · R , where v is the surface velocity of the cylinder, and  is the radius. For a cylinder v = R · ω, where ω is the angular velocity, and this gives that the circulation for a cylinder is Kcyl = 2 · π · ω · R 2

The concept of circulation is important for the theoretical understanding - now that's an oxymoron -  of potential flows (vorticity free flows), to which Thomson's Theorem applies. 

reference: ne.se, britannica,   D.J. Tritton; Physical Fluid Dynamics