Point Vortex Flow Around a Cylinder

    The vector field
        Overscript[v, ⇀] = γ/(2π) (-y/(x^2 + y^2), x/(x^2 + y^2)) defined for (x^2 + y^2)^(1/2) ≥R
represents point vortex flow around a cylinder. The corresponding pressure is
        p = -γ/(8π^2) 1/(x^2 + y^2)
which has the following graph.

Off[Plot3D :: "plnc"] ;            ... ;                

RowBox[{RowBox[{Cell[p(x,y) = ]}], , -γ^2/(8 π^2 (x^2 + y^2))}]

[Graphics:../HTMLFiles/index_431.gif]

We can now compute the force that the fluid exerts on the obstacle; Overscript[F, ⇀] = -∲_C p Overscript[n, ⇀] ds. As before, the symmetry of the situation immediately tells us that Overscript[F, ⇀] = 0, and this is easily verified.