4. Observations of a two-dimensional flow of a Newtonian liquid along the circle of unit radius R = 1 with its centre at

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4 Observations Of A Two Dimensional Flow Of A Newtonian Liquid Along The Circle Of Unit Radius R 1 With Its Centre At 1 (62.48 KiB) Viewed 39 times

4. Observations of a two-dimensional flow of a Newtonian liquid along the circle of unit radius R = 1 with its centre at the origin of the polar coordinate system has resulted in the following distributions of velocity on the circle: at 0 ≤0 ≤ T ur = cos - Asin and B Ug = - - sin(50) + + cos¹0 2π at π < 0 < 2π u, = cos - A sin 0 + cos 0 sin² 0 and B ug = sin(50) + + cos¹0+ cos(50) sin 0, 2π where is the polar angle in the polar coordinate system, and A and B are unknown real constants. It is given that the flow domain has neither internal boundaries nor sources nor sinks of the liquid. Determine the values of A and B such that the liquid flow could be incompressible. Are the observations sufficient to guarantee the conclusion? You may, if necessary, use the result without a proof that for a closed domain with a piecewise continuous boundary on with a normal vector n, if p is a continuously differentiable vector field, then Sv.pdn = [p.ndl, V an where dl is an infinitesimal element of the boundary.