First, it should be easy to see that a vector of the form a(xi+ yj), for any number, a, points directly from (0, 0) to (x, y) so does give a "radial flow", directly away from the z-axis. Second, I think you have written the result incorrectly. In what you have the multiplier (my "a" above) is when I am sure you mean . Finally, I think you have the equation wrong. You have "dv/dt= 2pi (gradient)z" when I think you mean . That reduces to the two equations and