Sketch a flow field

6. Let _ be a straight line in Ro, parallel to the z-axis, that defines the axis of a cylindrical domain 2. Consider the velocity field v given by X - c(X) v (x) = C exer, where e, (x) = r = x - c(x)|, (7) 2ar x - c(X)| where c(x) EL is the closest point on the line to x. (This flow describes (reasonably well) the flow velocity of a fluid draining from a cylindrical tank with a hole in the center of its bottom. ) Sketch the flow field v(x). Do this by plotting on cross-sections orthogonal to L. Verify that v(x) in (7) is divergence free. Also show that V x v = 0 away from L