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According to (1) and (2), all the seas and oceans combined contain 1.36 billion km³ of water.
Taking the Mount Everest at 8 kilometers, and the Earth radius at 6371 km. So to cover the Earth with flood waters you need to fill a shell of water with the thickness of the Mount Everest.
The volume of the shell, is given by:
V= 4/3 * Pi* (R³-r³)
Filling in the numbers give a required volume of water of 4 083 570 535 km³. That's more than 4 billion km³ that you need to cover the earth, to the height of Mount Everest.
Explain where 4 billion km³ came from and where it went.
Explain why we didn't find it (yet).
(1) How much water is in the ocean?
(2) Ocean's Depth and Volume Revealed | Live Science
I like trying to imagine it in just prosaic ways, like you. It's fun looking at it even with the almost certainly-false premise that God would be limited by physics we know... (even though physicists know we don't even know all physics yet(!)....)
(On the other hand, the idea of God being limited by physics is a non-realistic premise-- we are directly told explicitly that God can do "all things", even for instance such as stopping the progression of a day (!) (seemingly impossible by any physics as the Earth's rotational angular momentum could not be canceled)....
Either God exists, and He can therefore do physically impossible things,
or He doesn't exist, and thus cannot. In scripture, He can even create a Universe, even replace the heavens and Earth(!))
An important note:
A regional Flood, which is what very many Christians seem to think, would not even make it all that unusual, in Earth history...
Have a look ---
Evidence for a Flood | Science | Smithsonian Magazine
But you want just a certain set up -- the seemingly impossible and under the unstated premise (implied strongly) that God is limited by known physics, right?
Is that correct?
If so, that's fun too, even if only irrelevant side-question way, and astrophysics and planetary stuff is a fun topic to me, and I'll be happy to speculate.
You could try a low angle comet, maybe an ice comet, colliding in deep ocean, vaporizing many cubic miles of water all at once. Saturating the Earth's atmosphere for a true global rain event, deluge. That's a way to get weeks of rain globally. And land flooding in a big way around the world also.
That's only speculation just using known physics.
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