Submitted 5 months ago by abbadon420@sh.itjust.works to nostupidquestions@lemmy.world
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
Aproximalely 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 his calculation (radius squared instead of cubed). His corrected result, 1.7 mi also equals 2.7 km.
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.
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.
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 approxiimately 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 mot 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.
Around 2.7 metres.
You might be a few decimal places off.
No, there are 1.4 billion cubic kilometres of water on earth (V_w = 1.4·10⁹ km³). Earth’s diameter is D_E = 12750 km. The volume of the relatively thin shell of water is approximately V_w ≈ π(D_E)² t. Inserting yields t ≈ V_w/(π(D_E)²) = 1.4·10⁹ km³/(π (12750 km)²) ≈ 2.74 km.
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 * r^3^ = 774,463,850,166 square miles.
332 miles^3^ / 774 miles^2 = 0.429 miles. I know I’m supposed to do 3D calculus but I don’t want to do that right now.
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
Should be r squared not cubed for area. I get ~1.7 miles or ~3km.
Fuck. Thanks for noticing it has been fixed
0.43mi is 0.69km
Nice
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:
AmidFuror@fedia.io 5 months ago
You've forgotten about tides.
Successful_Try543@feddit.org 5 months ago
Tides are in the dimension of metres, the global ocean would be kilometres deep.