The steady, axisymmetric flow induced by a point sink (or source) submerged in an inviscid fluid of infinite depth is computed and the resulting deformation of the free surface is obtained. The effect of surface tension on the free surface is determined and is the new component of this work. The maximum Froude numbers at which steady solutions exist are computed. It is found that the determining factor in reaching the critical flow changes as more surface tension is included. If there is zero or a very small amount of surface tension, the limiting factor appears to be the formation of small wavelets on the free surface; but, as the surface tension increases, this is replaced by a tendency for the lowest point on the free surface to descend sharply as the Froude number is increased.

We examine a problem in which a line sink causes a disturbance to an otherwise uniform flowing stream of infinite depth. We consider the fully non-linear problem with the inclusion of surface tension and find the maximum sink strength at which steady solutions exist for a given stream flow, before examining non-unique solutions. The addition of surface tension allows for a more thorough investigation into the characteristics of the solutions. The breakdown of steady solutions with surface tension appears to be caused by a curvature singularity as the flow rate approaches the maximum. The non-uniqueness in solutions is shown to occur for a range of parameter values in all cases with non-zero surface tension.

The steady, axisymmetric flow induced by a point sink (or source) submerged in an unbounded inviscid fluid is computed. The resulting deformation of the free surface is obtained, and a limit of steady solutions is found that is quite different to those obtained in past work. More accurate solutions indicate that the old limiting flow rate was too high and, in fact, the breakdown of steady solutions at a lower flow rate is characterized by the appearance of spurious wavelets at the free surface.

Selective withdrawal of a two-layer fluid is considered. The fluid layers are weakly compressible, miscible and viscous and therefore flow rotationally. The lower, denser fluid flows with constant velocity out through one or more drain holes in the bottom of a rectangular tank. The drain is opened impulsively and the subsequent draw-down produces waves in the interface which travel outward to the edges of the tank and are reflected back with a $18{0}^{\circ } $ change of phase. The points on the interface that have the highest absolute gradient form regions of high vorticity in the tank, enabling mixing of the fluids. An inviscid linearized interface is computed and compared to contour plots of density for the viscous solution. The two agree closely at early times in the withdrawal process, but as time increases, nonlinear and viscous effects take over. The time at which the lighter fluid starts to flow out of the tank is dependent on the number of drains, their width, and the fluid flow rate and density, and is investigated here.

The steady response of the free surface of a fluid in a porous medium is considered during extraction of the fluid through a line sink. A conformal-mapping approach is used to derive exact solutions to a family of problems in which the line sink is placed at the apex of a wedge-shaped impermeable base, including the limiting cases of an unbounded aquifer and a flat-bottomed aquifer of finite depth. Both critical cusp solutions and sub-critical solutions are computed exactly as Fourier sine series.