The effect of surface tension on free surface flow induced by a point sink in a fluid of finite depth

•Maximum flow rate steady solutions for withdrawal through a point sink in water of finite depth computed.•Different fluid depths, sink depths and flow rates, and the effects of surface tension included.•Two completely different numerical methods (integral equation and spectral) used and compared.•Limit as surface tension approaches zero consistent with previous research. Solutions are presented to the problem of steady, axisymmetric flow of an inviscid fluid into a point sink. The fluid is of finite depth and has a free surface. Two numerical schemes, a spectral method and an integral equation approach, are implemented to confirm results for the maximum-flow-rate steady solution for each configuration. The effects of surface tension and sink depth are included and constitute the new component of the work. Surface tension has the effect of increasing the maximum flow rate at which steady-state solutions can exist.