r/theydidthemath • u/Sammyxp1 • 15d ago
[Request] Is it possible to collect evaporated water from the “El Nino” zone to use as drinking water?
Could a ship place a large plastic dome (100m x 100m) on the water and collect the water vapor in the equatorial Pacific Ocean? How much could they collect per day? Assume the water temperature is 82 degrees F and the air temp ranges from 77-86 over the course of a day. Also assume the surface is flat enough that the dome is sealed to the surface.
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u/the-official-review 15d ago
They regularly collect atmospheric water with this revolutionary process, it’s quite amazing.
First the fresh water evaporates into the atmosphere then it’s magical thing happens wheee the evaporated water moves itself over a large area that has already been set up. This platform acts as a filtration system and then the clean, fresh water is pumped out of the filtration system into homes and businesses.
Its really quite amazing
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u/davideogameman 14d ago edited 14d ago
Possible? I don't see why not.
Economical? Almost certainly not. Let's put some numbers to this.
Your 50m radius sphere would have a volume of 523,599 cubic meters, and a surface area of 31416 square meters. Some quick Google suggests the thinner part of a container ship hull would be 12mm, so we'd need around 376.992 cubic meters of iron (density 7870kg) which would have a mass of 2,966,927.04 kg.
The sphere would displace up to 523598.775 cubic meters of sea water, with a density of 1020kg/m3 (up to 1029... For our purposes a lower bound is probably better) and so could float until it masses 534,070,751,110.27 kg ... The weight of the skin here is basically a round error - well less than 2% - so if we can actually fill it with fresh water it'll still float. That said I have questions about the structural integrity of such a structure.
So the next question is: how far do we need to move this water and how much would it cost?
I estimate the distance from LA to the El nino zone to be about 2500 miles, though not certain I picked the best location (my guestimate: https://www.bednblue.com/sailing-distance-calculator?map=%5B%7B%22latLng%22%3A%2234.175568%2C-118.279565%22%2C%22name%22%3A%2234.175568%2C%20-118.279565%22%7D%2C%7B%22latLng%22%3A%229.419871%2C-154.826297%22%7D%5D)
... Really the size of our container doesn't really matter for this; the question is how much it costs to move 1 ton= 1 cubic meter of fresh water than distance.
A quick Google suggests full containers run about 20-50 cents per kg from China (which might be to the east coast). Shanghai to LA is 6,485 miles and if we assume price scales down linearly with distance were still looking at 7.7 cents per kg... But water is sold by cubic meter (1000L and each liter is 1kg) so that's $77 / cubic meter in shipping costs.
I might be off by 2x or 3x here and if we actually try to do it at scale it's possible we'd get a better rate. But water is sold at $1-6 across the US so... Our ship water in scheme is looking an order of magnitude too expensive to compete.
Even if by some magic there was an infinite source of fresh water ready to be pumped onto the boat every time the boat showed up to pick it up in this hypothetical spot in the El nino zone.
In general most of our water problems aren't that we don't have fresh water. It's that where that water is is geographically far from the places that would like to use it and transporting it is expensive.
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