Calculations of water depth if the Earth were a current sea level sphere
With the aid of Google and seemingly quite a bit of luck, I was able to track down a post of mine from 10+ years ago.
I calculated what the water depth would be if the solid part of the Earth were a sphere of the radius/diameter of the current sea level. In other words, I brought the ocean floor up to sea level and the continent level down to sea level.
I added the volume of the oceans to the calculated volume of the earth (by the way, the oceans volumes is only about 0.1 percent of the Earth's volume, so I was taking some liberties with significant figures).
Ramming that new sphere volume back through the sphere volume formula gave me a radius increase (sea level rise) of 2560 meters.
Re: Calculations of water depth if the Earth were a current sea level sphere
I'm making the Earth a smooth sphere, with all surfaces the same elevation. The Earth radius/diameter is that which is the current sea level. I'm then distributing the volume of the oceans over this sphere. If my calculation were correct, then you would have a uniform water depth of about 2560 meters.
In other words, perfectly smooth continents and ocean basins, all at the same elevation, covered by 2560 meters of water.
In this approximation, you could then add mountains no higher that 2560 meters, if the water was to reach the mountain tops. 2560 meters is essentially nothing relative to the Earths radius - The solid surface is still essentially smooth.