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 pressure is
        p = -U^2/4 (cos (2π x)/w + cosh (2π y)/w).
It has the following graph.

Clear[U, w] ; v[x_, y_] := U {Cos[(π x)/w] Cosh[(π y)/w], Sin[(π x)/w] Sinh[(&# ... 1;PlotLabel->"Pressure for channel flow", BoxRatios {1, 1/2, 0.4}] ;

RowBox[{RowBox[{Cell[p(x,y) = ]}], , -1/4 U^2 (Cos[(2 π x)/w] + Cosh[(2 π y)/w])}]

[Graphics:../HTMLFiles/index_503.gif]

As before, because the velocity and pressure become infinite as y∞, it is meaningless to calculate the total force on the channel.