What would be the gravitational consequences of Noah's flood?

Chris Smith put this to physicist Andrew Norton from the Open University...

Andrew - The first problem I think is that the amount of water in the atmosphere is really very tiny; it's only about, I think, one thousandth of one percent of the total water budget of the Earth. So if all that water in the atmosphere fell to Earth, it would only cover the surface to a depth of two or three centimeters, something like that, so it wouldn't be enough to cover to the tops of mountains. If you could somehow flood the Earth to the depth such that all the mountains were covered, then I guess we'd be in a sort of a waterworld planet. The atmosphere would then sit on top of that. But there's no reason why the density of the atmosphere would get any lower. Maybe your questioner was thinking about additional gravity, the Sun or the Moon pulling on it. But, on the scale of the solar system, that extra few thousand feet is not going to make any difference to the pull of gravity on the atmosphere. So we'd all just be swimming around but breathing just the same.

Chris - There have been times in the past though when the Earth has been a lot wetter, hasn't there Doug? Because if you go back 30 million/40 million years or so to the Eocene, it was much, much warmer and we had not North Pole, did we?

Doug - Yes, there were lots of times when the Earth has been wetter, almost always having to do with changes of temperature. In fact, we go through this cycle every few tens of thousand of years of wetter and warmer, and then cooler and drier temperatures.