Flow Around a Rankine Half-Body

    The vector field that described the flow of a fluid around a Rankine half-body is given by
        Overscript[v, ⇀] = U (1 + h/(2π) x/(x^2 + y^2), h/(2π) y/(x^2 + y^2)), defined outside the Rankine half-body.
The corresponding potential is
        ϕ(x, y) = U(x + h/(2π) ln ((x^2 + y^2)^(1/2))).
Here is a graph of the potential

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


Here is a graph of the vector field together with a sampling of equipotential curves.

Needs["Graphics`PlotField`"] ; Needs["Graphics`FilledPlot`"] ; Needs[" ... entity], DisplayFunction$DisplayFunction, PlotRange {{-h, h}, {-h, h}}] ;