The steady rotational flow of an inviscid fluid in a two-dimensional channel or a circular tube toward a sink is treated. The velocity distribution at infinity is approximated by a cosine curve (which is nearly parabolic) for the two-dimensional case, and is taken as exactly parabolic for the axisymmetric case. The dependence of vorticity on stream-function is assumed to be everywhere the same as it is for streamlines coming from infinity upstream. The resulting linear equations of motion are solved exactly. The solutions show the rather unusual features of separating streamlines and regions of closed flow (corner eddies).