Flow in a Corner

    The flow of a fluid in the corner 0≤θ≤π/3 can be described by the field
        FormBox[RowBox[{Overscript[v, ⇀], =, RowBox[{U (x^2 - y^2, -2x y), Cell[]}]}], TraditionalForm] defined for 0≤θ≤π/3,
where U is a parameter describing the speed of the flow.

Needs["Graphics`PlotField`"] U = 1/10 ; v[x_, y_] := If[ x>0 & ... sp;           (* Show thw result *)

[Graphics:../HTMLFiles/index_80.gif]

    Similarly, the flow of a fluid in the corner 0≤θ≤π/4 can be described by the field
        FormBox[RowBox[{Overscript[v, ⇀], =, RowBox[{U (x^3 - 3x y^2, y^3 - 3x^2y), Cell[]}]}], TraditionalForm] defined for 0≤θ≤π/4
where again U is a parameter describing the speed of the flow.

Needs["Graphics`PlotField`"] U = 1/10 ; v[x_, y_] := If[ x>0 & ... sp;           (* Show the result *)

[Graphics:../HTMLFiles/index_86.gif]

    In each case, varying the parameter U simply scales the size of the resulting vector.