Suppose a hole is drilled perpendicularly into the side of the beaker which is full to the brim with a fluid (say water). This will result in water spurting out, travelling in a parabolic trajectory and hitting the solid, flat surface (say, a table) the beaker is resting upon.
For a cylindrical beaker, the distance the water lands from the base of the beaker depends on the height at which the hole is drilled. It turns out that drilling the hole at half the total height of the water column maximises the distance the water spouts.
Suppose now that, instead of a beaker with vertical sides; its vertical cross section is curved (like a wine glass). The distance from the base that the water lands is now harder to calculate, because it leaves the beaker travelling at an angle.
Does a beaker exist which the property that, regardless of where the hole is drilled, the water spout will hit the table at the same distance away from the base of the beaker? If so, what algebraic equation (if any) defines the vertical cross section of the beaker?
Note: for the purposes of this problem, ignore fluid dynamics of the water and air resistance. I'm envisaging a beaker with a circular horizontal cross section. The problem pertains only to the point the water spout initially hits.