One optimization problem with filtration

That sure depends. amount of overlap in cone construction (look at the pic), maximum height we allow the cone to be filled (which may depend on the size of the glass underneath, amount of tremor of the experimental leader (=how much will get spilled), maybe even kind of liquid and permeability of material.

Filtration time is primarily dependend on the filter surface.

If we maximize filter surface, the solution is of course the "cone" with height zero = the filter disk itself.

You may try to maximize the ratio surface/volume with the same result, of course. It will be maximal for the full disk (volume=0).

So all we could do with the information given is to maximize the volume of the cone for a given disk, which does not really relate to minimum time.

You may specify a filtration rate (volume per area per time) and may take into account that in case of a higher cylinder the filtration rate will not be constant but depends on the height as of the pressure by the overlying liqid in the cone - nice combination using a differential eqation. If the liquid to be filtered does not fit the cone entirely, at what rate is it refilled?.

Furthermore the cone has sections where the filter paper has two, maybe even more layers. How does this affect filtration rate?

Hmm, seems to get too interesting now - time to leave

For a comprehensive study of this task see here

http://link.springer.com/article/10.1007/s10665-013-9660-7#page-1