(a) A river flows across the xy-plane in the positivex-direction and around a circular
Chapter 19, Problem 63(choose chapter or problem)
(a) A river flows across the xy-plane in the positivex-direction and around a circular rock of radius 1centered at the origin. The velocity of the river canbe modeled using the potential function = x +(x/(x2 + y2)). Compute the velocity vector field,v = grad .(b) Show that div v = 0.(c) Show that the flow of v is tangent to the circlex2 + y2 = 1. This means that no water crosses thecircle. The water on the outside must therefore allflow around the circle.(d) Use a computer to sketch the vector field v in theregion outside the unit circle.
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