By “smoothing out” I mean flattening all mountains and filling all trenches so that the entire earth has exactly the same radius everwhere. Water naturally spreads out equally on such a surface, so how high would the water level be?
By “smoothing out” I mean flattening all mountains and filling all trenches so that the entire earth has exactly the same radius everwhere. Water naturally spreads out equally on such a surface, so how high would the water level be?
Approximately 2.6 km.
3682 m is the average depth of the ocean, as you can google easily.
This is also a very good approximate value for the water level if the planet wasn’t a sphere, and if you want to keep the current land, that covers about 30% of the earth’s surface.
Now if you want to flatten out everything, even the floor under the sea that is then also filled with what has been land before, then we do not even need to know how much the land is. The water will be above it, regardless the height of the land.
We just need a simple calculation for the new surface: it grows from 70% to 100%. Therefore the new water level is 3682 x 70 / 100 m = 2577 m.
But wouldn’t moving the land from the high points increase the circumference of the solid part of the Earth and stretch the water around it a little bit, making the height of the water a little bit less?
Yes, I am going with approximations.
To be exact, you would need to use formulas about spheres, and you would also need to take care of the fact that the earth isn’t all too spherical now, and you would need to consider the water that is in the atmosphere (which would also expand then with the radius), and in ground, not above, etc.pp.