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 corresponding pressure is
        P = -1/2U^2(x^2 + y^2)^2
and it has the following graph.

Off[Plot3D :: "plnc"] ;            ... ;                

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

[Graphics:../HTMLFiles/index_483.gif]

    When we work in the corner 0≤θ≤π/4, we have
        FormBox[RowBox[{Overscript[v, ⇀], =, RowBox[{U (x^3 - 3x y^2, y^3 - 3x^2y), RowBox[{Cell[], .}]}]}], TraditionalForm]
The corresponding pressure is
        P = -1/2U^2(x^2 + y^2)^3
and it has the following graph.

Off[Plot3D :: "plnc"] ;            ... ;                

RowBox[{RowBox[{Cell[p(x,y) = ]}], , -1/2 U^2 (x^2 + y^2)^3}]

[Graphics:../HTMLFiles/index_489.gif]

    As we saw before, in the general case 0≤θ≤Θ, we have
        Overscript[v, ⇀] = U (x^2 + y^2)^(π/(2 Θ) - 1) (x cos (π/Θcos^(-1) ( ... 60;/Θcos^(-1) (x/(x^2 + y^2)^(1/2))) - x sin (π/Θcos^(-1) (x/(x^2 + y^2)^(1/2)))) .
Despite the complexity of this expression, the pressure has a simple form; indeed
        P = -1/2U^2(x^2 + y^2)^(π/Θ - 1) .        

RowBox[{RowBox[{Clear[U] ;, , v[x_, y_] := {U (x^2 + y^2)^(-1 + π/(2 Θ)) (x  ...                 }]

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

    Because the velocity and pressure become unbounded as x, y∞, it makes no sense to calculate the force on the wedge.