The Kutta-Joukowski lift theorem relates circulation, Γ, to lift force per unit span, l. With Γ as circulation, ρ as density, V as freestream velocity, and l as lift per unit span:

l = ρVΓ

This is true for any 2D, inviscid, incompressible, and potential flow around a closed contour.

A simple proof of this theory for the case of a rotating cylinder can be arrived at by integrating the pressure distribution around the cylinder, with p as static pressure and R the radius of the cylinder:

l=0p(sin θ)R dθ = ρVΓ

Since all invicid, incompressible, and irrotational flows around a closed 2D profile can be represented as the linear superposition of sources, sinks, and irrotational vortices; and continuity requires that the sum of the strengths of the sources and sinks be zero, all these flows look the same sufficiently far from the body as the distances between the sources and sinks become negligible. Thus, this expression for the lift per unit span holds true for all of these flows.