Saxons are reported to have used bowls with a small hole in the base, placed in a larger bowl of water, to limit the length of their orations (Richard Walding’s Senior Physics page). The size of the hole determined the time taken for the bowl to sink. It could be expected that the time taken is exponentially proportional to the size of the hole; however additional factors such as pressure may have an effect.
I used plastic milk bottle lids from UHT cartons (volume of approximately 11 mL), with additional weights inside them in order to investigate any relationship between hole size and time taken to submerge. An asymptotical relationship was observed, with time decreasing with increasing hole size. The data could be reasonably modelled with the equation y = 88.1x-2.249 (R2 = 0.0985). However, the theory behind this relationship is not clear.
A great experiment idea, although there are plenty of difficulties that you would have to overcome. My main problem was getting the lids to begin sinking in the first place – I ended up using detergent in the water, and 3 small nuts inside each bowl to add extra weight. Richard Walding suggested using poly pipe ends, which would probably be heavy enough to sink by themselves – the only problem is that they’re a few dollars apiece.