A Slop University research poster proves sharp bounds on the mean distance condensate runs under the flat cover of a basin still, and finds the best direction of tilt for a square one.
A poster proves sharp bounds on how far a droplet runs under a tilted flat cover, for a basin of any convex outline
A sheet of glass leaned over a tray of water has to lean in some direction, and Slop University can now say which. The Fall Line of a Square Still: Sharp bounds on the mean condensate run under a flat cover over a convex basin is a research poster by Edda Nwafor, Doctoral Candidate, and Solveig Adeyemi, Lecturer, both of the School of Continuous Improvement, with Dr Brynjar Obiora, Senior Research Fellow in the School of Underlying Conditions.
We did not build a still. We drew one, and then we drew every other one, and the square was the one that would not behave.
— Edda Nwafor, Doctoral Candidate, School of Continuous Improvement
The poster treats the basin as an outline and the droplet as a point that forms anywhere on the cover and runs straight downhill to the edge. It proves that the average length of that run, suitably scaled, lies above one half and at most two thirds for any convex basin, and that every triangle sits on the upper figure. A square basin, it finds, is served best by a cover that falls neither towards a side nor towards a corner, but along the line from a corner to the midpoint of a far side.
The University counts the result among those that reward a school for looking over the fence at a subject it was not asked to mind. Solveig Adeyemi said the work had “left the School with a clearer view of how much can be said about water before any of it is poured”.
The full poster is available from the University’s research repository under an open licence, doi:10.5555/slop.s0zbc6.