Say I have a cylindrical container of some volume $V$, that I fill with water or some other fluid with dynamic viscosity $\mu$. Here, the bottom of the container is milled such that some fraction, $p$, of its surface area, $A$, is removed to allow passage of fluid. One could, for example, drill pores until this criterion is met.
After positioning a plate at the top of the container, I press down on the plate with some force $F$ to compress the fluid. As a function of $F$, how quickly will I drain the fluid through the bottom of the container?
To calculate this, what additional measurements/parameters, such as surface hydrophobicity/etc., will I require, and how does this change with the minimum cross-sectional area of the pores I mill in the bottom of the container?