Flow Around a Cylinder with Circulation

This is the sum of the two previous fields, so
        Overscript[v, ⇀] = U(1 - R^2 (x^2 - y^2)/(x^2 + y^2)^2, R (-2x y)/(x^2 + y^2)^2) + γ/(2π) (-y/(x^2 + y^2), x/(x^2 + y^2))  defined for (x^2 + y^2)^(1/2) ≥R
The equations of our streamlines then are
        x ' (t) = U(1 - R^2 (x^2(t) - y^2(t))/(x^2(t) + y^2(t))^2) + γ/(2π) -y(t)/(x^2(t) + y^2(t)),
        y ' (t) = U R (-2x(t) y(t))/(x^2(t) + y^2(t))^2 + γ/(2π) x(t)/(x^2(t) + y^2(t)).
We can plot the equipotential curves and streamlines as follows.

Needs["Graphics`PlotField`"] Needs["Graphics`ImplicitPlot`"] U = 1/2 ; 	 ... ange {{-3R, 3R}, {-3R, 3R}}}], ]}], ;,         }]

[Graphics:../HTMLFiles/index_291.gif]

    It is interesting to see how changes in the parameters are reflected in the behavior of the potential and the equipotential curves.

RowBox[{RowBox[{Needs["Graphics`Arrow`"] ;, , Needs["Graphics`PlotField ... is the loop for Table *),           , }]

Varying Gamma