We were given some practice questions from our last lecture but from what I could tell our prof did not touch on the subject and also the book only has one brief example about the topic and I really have no clue how to do the question.

In 3 space filled with an incompressible fluid, we say that the z axis is a line source of strength m if every interval (gradient)z along that axis emits fluid at a volume rate dV/dt=2*pi*m*(gradient)z. The fluid is then spread out symmetrically in all directions perpendicular to the z axis. Show that the velocity field of the flow is

v=(m/x^2+y^2)(xi+yj)

Again I have no clue really even how to start. I have done some vector field questions not at all like this and some other questions asking if a given function is conservative and to find its potential. Any help is really appreciated.