Here's an interesting question I came across on another forum.

Suppose you have a cylindrical glass with a height h and diameter 2r (r = radius), filled with water to a height of H < h.

At what angle would you have to hold the glass before it pours out due to gravity?


Let's ignore any effects such as surface tension, then (I think!) the question is basically a geometrical question:


I'm not sure yet if the fact that the glass is cylindrical is important, but it might be.


I have tried coming up with a solution for this but failed... I was never good at geometrical stuff lol. The main problem I had was that the height of the water H does not come up in any equation I found...

I am starting to fear an analysis of the height of the waterlevel (when glass is tilted), which will probably involve the volume of the water, will be required. The volume is of course pi r2H, but if we can calculate the volume again when the glass is tilted under some angle theta, we might be able to find a relation between theta and the height of the waterlevel... Unfortunately, such a volume calculation appears to be extremely complicated at first sight (remember that the glass is cylindrical, not square!)...

I thought this was an interesting question, and other people at the other forum seem to think there is no easy relation. I think it should be possible however to find a relation, however complicated

Thanks for any input!