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Is a planet the size of earth minimum, probably even larger, plausible if it has no water depth below 70 meters?

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Highly unlikely.

Our planet has a "rugosity" of $19.750/6371=0.3\%$, as measured with the height difference between the tallest point (mount Everest) and the deepest point (Challenger Deep) over the radius.

That's pretty smooth. 70 meters over 6371 km would make for $10\cdot 10^{-6}$, which is a very high precision level, unlikely to be achieved with only natural processes.

Top that with the consideration that if there is so little liquid water it would probably quickly evaporate due to the dryness of the atmosphere, and you see that, again, it is very unlikely.

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    $\begingroup$ The question does not say that the planet has a lot of water. If the planet has very little liquid water, it is reasonable to assume that it will pool here and there in shallow pools. $\endgroup$
    – AlexP
    Jun 5 at 12:50

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