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?
This sounds like a question for XKCD. Along with how could we flatten it out.
This is close, if you haven’t seen it. It plays off of the “earth is smoother than a bowling ball” thing that’s almost true but turns it around:
it would reach sea level
I sea what you did there ;)
Dammit, beat me to it
https://oceanservice.noaa.gov/facts/oceanwater.html
So there’s 332,519,000 cubic miles of water on the planet approxomately
The earth has a radius of 3,950 miles
That leaves a surface area of 4 * pi * r2 = 196,066,797 square miles.
332 miles3 / 196 miles2 = ~1.7 miles I know I’m supposed to do 3D calculus but I don’t want to do that right now and the difference in radius is negligible,
0.43mi is 0.69km
Thank you for using the same number of significant digits.
Should be r squared not cubed for area. I get ~1.7 miles or ~3km.
Fuck. Thanks for noticing it has been fixed
Downvoted for the use of ridiculous units
Ahaha. All the people from the US downvoting this 🤦♂️ So many solutions to questions like this a just easier and more intuitive in metric. Tec diving is just hilarious in imperial units
Imperial units are fine. They have rational conversion ratios between them and standard metric. I was in bed at the time and miles is what I got from search results.
Sure, they’re great for people chatting casually in the US, Myanmar and Liberia but even there they still add unnecessary complexity with scientific or engineering applications
OK
You did well in your answer by the way. I didn’t downvote. My comments are directed at everyone downvoting the person calling out imperial units
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I’m too high right now, but you’d just figure out the volume of solids in the earth and the size of sphere that would make, then figure out the volume of water, and figure out how deep that volume would cover a sphere of that diameter. I’m sure an ai could give you a pretty convincing answer. The calculation is easy, it’s the accuracy of your inputs you have to worry about.
Water naturally spreads out equally on such a surface
You’ve forgotten about tides.
The volume of the Earth without surface water is 2.59x10^11 miles^3.
Earth’s surface water has a volume of 3.33x10^8 miles^3.
So, the depth of a surface ocean made up of all water on Earth would be approximately 2 miles.
Around 2.7 kilometres.
*Order of magnitude out.
You might be a few decimal places off.
I’d think not a lot higher than currently.
Thos says average land elevation is 840m https://www.studycountry.com/wiki/what-is-the-average-elevation-of-the-world
Spread that over the other 70% of the surface and your probably down at a 3-400 hundred metres you floated it on top of the sea. Which i think is approximately the same thing if the land displaces its volume equally. I guess there’d be a decent amount of compression though so, my guess is not much more than a few hundred metres.
Anyway, I’m sure the good people of the Netherlands will find a way to foil your dastardly scheme.
