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?
it would reach sea level
But who could sea the level?
I sea what you did there ;)
Dammit, beat me to it
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.
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.
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.
We’ve got three answers so far:
2 miles - by @CrazyLikeGollum@lemmy.world
0.43 miles - by @LodeMike@lemmy.today
2.7 kilometers - by @erusuoyera@sh.itjust.works
These are highly different answers. Who’s correct?
As @huquad@lemmy.ml pointed out, @LodeMike@lemmy.today had an error in their calculation (radius squared instead of cubed). Their corrected result, 1.7 mi also equals 2.7 km (rounding to 3 km is a bit rough).
My answer is also based on some pretty rounded figures and I’d had a few drinks before doing that math.
2 miles is roughly 3.2km. Honestly, the fact that I’m even within the same order of magnitude as the other answers is surprising.
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:
Water naturally spreads out equally on such a surface
You’ve forgotten about tides.
Tides are in the dimension of metres, the global ocean would be kilometres deep.
Edit: also, due to earth’s rotation, the ocean would be slightly deeper around the equator than at the poles.
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
Nice
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
I’m fine with imperial units, as long as somebody stays in one unit system and doesn’t mix miles, yards, feet and inches, or square miles and acres, etc.
Yeah, I’m fluent in what you listed too… but everything you listed is just meters in metric so that’s five-ish conversions to needlessly need to know. And if you start using equations in then standard units play up a lot like when diving with imperial units you measure depth in feet but pressure in pounds per square inch so you have an awkward feet to inch right there and the equations are just more complicated. Anything beside the simple gets compounding unit conversions. And the countries left in the world that only use imperial are the US, Myanmar and Liberia.
Definitely. But fortunately, everything here has the dimension length to the power of something.
Like, nautical miles have a good use but that’s not even the miles being used
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
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.
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.
No, there are about 1.4 billion cubic kilometres of water on earth (
V_w ≈ 1.4·10⁹ km³). Earth’s diameter isD_E ≈ 12750 km. The volume of the relatively thin shell of water is approximatelyV_w ≈ π(D_E)² t. Inserting yieldst ≈ V_w/(π(D_E)²) = 1.4·10⁹ km³/(π (12750 km)²) ≈ 2.74 km.In the original post, this was 2.7m, but has been fixed since then.
That’s what quotes are for :)
Thanks for clarification.
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.
I’d think not a lot higher than currently.
Because lower than currently :)
Their idea is like throwing all material that is currently located above sea level into the sea which would subsequently increase the “sea level” as the radius of the sphere defined by the water surface, not the depth of the ocean on a perfectly spherical earth.
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