Flow in a Corner

    The flow of a fluid in the corner 0≤θ≤π/3 is described by the field
        FormBox[RowBox[{Overscript[v, ⇀], =, RowBox[{U (x^2 - y^2, -2x y), Cell[]}]}], TraditionalForm] defined for 0≤θ≤π/3.
The equations of our streamlines then are
        x ' (t) = U (x^2(t) - y^2(t)),
        y ' (t) = -2U x(t) y(t).
We can plot the equipotential curves and streamlines as follows.

Needs["Graphics`PlotField`"] ; Needs["Graphics`ImplicitPlot`"] ;  &nb ... ;       On[InterpolatingFunction :: "dmval"]   

[Graphics:../HTMLFiles/index_299.gif]

Here is the situation in the region 0≤θ≤π/4.

Needs["Graphics`PlotField`"] ; Needs["Graphics`ImplicitPlot`"] ;  &nb ... ;       On[InterpolatingFunction :: "dmval"]   

[Graphics:../HTMLFiles/index_302.gif]