Flow in a Closed Channel

    The flow inside the closed channel of width w given by y≥0, -w/2≤x≤w/2 is given by
        Overscript[v, ⇀] = U (cos ((π x)/w) cosh ((π y)/w), sin ((π x)/w) sinh ((π y)/w)) .
The corresponding potential is
        FormBox[RowBox[{ϕ(x, y), =, RowBox[{-(U w)/π, sin((π x)/w), cosh((π y)/w), Cell[]}]}], TraditionalForm].
Its graph is

U = 1/100 ; w = 1 ; ϕ[x_, y_] := -(U w)/πSin[(π x)/w] Cosh[(π y)/w] ; Plot ... ", "ϕ(x,y)"}, PlotLabel->"Potential for channel flow"] ;

[Graphics:../HTMLFiles/index_251.gif]

Needs["Graphics`PlotField`"] Needs["Graphics`ImplicitPlot`"] U = 1/100 ; w ... ;                

[Graphics:../HTMLFiles/index_253.gif]