I've just been watching a doco where some guys cut a hole in a frozen lake, the ice is 3 feet thick, I was surprised that the water rose to the level of the ice. My friend assures me it's because water equalises/levels with ice in the same way it equalises with itself... Is this right or is there another reason for the water rising to the same level as the surface of the ice.
Suppoose you put an ice cube into water, then it's going to float with about 92% of it underwater. This is shown in diagram (a) below:



But now suppose I make my ice cube a different shape. I'm going to shape it like a disk with a hole cut out of the centre, or you could describe it as a flattened doughnut. When I put my oddly shaped ice cube into the water it's also going to float with about 92% of it underwater. This is shown in diagram (b) below:



But (b) is just your frozen lake with a hole in it. So if you cut a hole in the ice on a frozen lake you should expect the water to come 92% of the way up the thickness of the ice i.e. you should be left with a lip of about 8% of the ice thickness.

An objection to my argument is that in (b) the ice isn't frozen to the sides of the bowl, while in a lake the ice sheet is frozen to the lake shore. However ice is quite flexible and over a large distance like the lake it will bend and act as if it's floatingly freely and not connected to the shore. If you took some small container like an oil drum or bath tub, with the surface frozen to the sides, and cut a hole in the ice the water wouldn't come up so far.
