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

Cir`cu*la"tion (?), n. [L. circulatio: cf. F. circulation.]

1.

The act of moving in a circle, or in a course which brings the moving body to the place where its motion began.

This continual circulation of human things. Swift.

2.

The act of passing from place to place or person to person; free diffusion; transmission.

The true doctrines of astronomy appear to have had some popular circulation. Whewell.

3.

Currency; circulating coin; notes, bills, etc., current for coin.

4.

The extent to which anything circulates or is circulated; the measure of diffusion; as, the circulation of a newspaper.

5. Physiol.

The movement of the blood in the blood-vascular system, by which it is brought into close relations with almost every living elementary constituent. Also, the movement of the sap in the vessels and tissues of plants.

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