Theoretical and numerical studies are given to the sink flows within a rotating circular tank driven by the fluid withdrawal from a bottom circular hole. It was found that, when the upper free surface was set with no-slip boundary conditions, the Ekman boundary-layer develops not only above the bottom surface but under the top surface. The sink fluid is coming from the two Ekman layers, and the mass transfer from the bulk, inviscid region is dependent on the rotational speed. It is also remarkable to see that all the fluid gathered along the axis flows in a form of rapidly rotating fluid column haying almost the same diameter as the bottom hole.