Question: Calculate the circulation around the given rectangular path in the figure, if the velocity field for the steady flow of an incompressible fluid is given

Calculate the circulation around the given rectangular path in the figure, if the velocity field for the steady flow of an incompressible fluid is given by

V = x^{2} y i - y^{2} x j

Show that the Stoke's theorem

= o_{C}^{} V * d r =_{A}^{} [(g r a d x V) * n] d A

is valid for the region given in the figure.

Calculate the circulation around the given rectangular path in the figure,

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