An infinitely long cylindrical bucket with radius $a$ is full of water and rotates with constant angular velocity $\Omega$ about its horizontal axis. The gravity is in the vertical direction. The velocity of the flow in cylindrical coordinates (whose $z$ axis is the horizontal axis of the bucket) is given by $\vec u = \left\langle {{u_r}(r,t),{u_\theta }(r,t),0} \right\rangle$.
Show that ${{u_r}(r,t)} = 0$.
I actually have no idea how to start. Any help will be appreciated.
