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
I sea what you did there ;)
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:
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.
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 * r3 = 774,463,850,166 square miles.
332 miles3 / 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 and the difference in radius is negligible,
So a bit less than 0.43 miles high.
0.43mi is 0.69km
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.
Water naturally spreads out equally on such a surface
You’ve forgotten about tides.
Around 2.7 metres.
We’ve got three answers so far:
2 miles - by @[email protected]
0.43 miles - by @[email protected]
2.7 kilometers - by @[email protected]
These are highly different answers. Who’s correct?
As @[email protected] pointed out, @[email protected] 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.
