My local authority parks department proudly boasts that it uses recycled water, but isn't all water recycled? Isn't there a finite amount of water on Earth and, if so, how often is each "piece" reused in human activity such as drinking, cooking, washing, agriculture and industry?
As I know, there are around 1 200 000 000 000 000 000 000 000 000 tonnes of water on the earth, or at least in the seas. However, this number could constantly be in flux due to by-products of various reactions such as respiration or photosynthesis, which respectively produce and use water.
As for "recycled" water, this really can only mean "grey water". This is essentially water that has already been used once in this "round", if you will. For example, grey water could be water that has been used for washing up that is now used to water the lawn.
When it comes down to it, water can take many years to complete one "round". If it ends up as groundwater a drop of water could stay put for many years. Alternatively, it could be used, sent back into the sea and then wind up in a desalination plant within a few weeks.
The thing with water is it's always moving. Like that theory that says odds are every second breath you take there will be a molecule that was used by Hitler or Nelson or something, it's the same with water. Any drop could move from a glacier to a cup in a house in Surrey to the blowhole of a whale over time. So there is no definite time scale, but odds are most water has already been used for human needs at some point, so in that sense all water would be recycled.
I take your point about the mobility of water molecules, but I am sorry to point out that it is extremely unlikely that a drop of Cleopatra's pee has passed through my body. The entire living human population probably contains less than 150 000 000 tonnes of water and passes less than 12 000 000 tonnes per day, or less than 4500 000 000 tonnes per year.
Hmmmm. You know, I am in doubt about your figure for sea water. I make it something like a billion times less than you did. Could you please check? I suspect one of us (or both) got a unit mixed up. That is the trouble of working on the backs of these modern envelopes.
Anyway, even accepting my more modest figure, it would take some 200 to 300 million years for the seas' water to pass through even our modern obscenely large population, even of it were passed with perfect efficiency and with each droplet waiting its turn in line.
Where Napoleon's tipple comes into the picture is on scale of molecules, not litres, and on some chancy assumptions about perfect mixing and so on. A drop is a huge amount of water in terms of number of molecules. I we took a litre of water and somehow magically marked each molecule and mixed that litre into the oceans perfectly, then re-sampled the ocean's water, we would expect some hundreds of marked molecules in a litre of sample. This ignores certain theoretical problems as well as the obvious practical problems, but I hope it clarifies the nature of the situation.
The rest of your note (even without correcting either your error or mine) I have no quarrel with.
We pretty much know that there is 75% water in our planet. So, to put it simple, the answer is 75% of Earth. Now, if you know how much there is on Earth, then pretty much you have the answer.
Sorry to contradict, but as it happens there is hardly any water on Earth at all. Taking the oceans' average depth to be about 4 km and the density of the planet to be about 5.5, and the sea surface area to be about 70% of the planetary surface, I make that to be roughly 1/3500 of the planet. And I suspect I made a big arithmetic whoopsie; I expected it to be much less.
So would I, but I'm getting about one part in 700 of water with 4km average depth and 75% coverage.
Earth volume is 4 / 3 * Pi * cube(6400)
Water volume is 4km * 3/4 * Earth area
which is 4 * 3/4 * 4 * Pi * square(6400)
Ratio looks like 1/9 * 6400, => 700 of solid to sea.
Water volume is 4km * 3/4 * 4 * Pi * square(6400km). Scale by cube(1000) to get cubic metres (same as tonnes), and get 1.5 * 10 ^ 18. I think first answer's 27-digit number might have been in cubic millimetres (milligrams).
OK, it took me a while to see what had happened. (I hadn't retained my calculations!) The details in the differences of course derived from our approximations and assumptions. For example I had worked with 71% area instead of 75% and 6000 instead of 6400 etc. But the main difference was because I had worked on a planetary density of about 5.5, instead of simple volume, and took the sea to have a density of 1.
BTW, 1 cubic mm is a milligram. Grams are cc of water. (I realise you knew that, but I couldn't correct it for you. If you change it, I will remove this remark.) I agree with your diagnosis of the reason for the extra factor of a billion or so.
I have never overcome my schoolday feeling that ounces and grams are tiny. So for water, cube(metre) is a tonne; cube(100mm) is a litre and kilogram; cube(10mm) is a cc, millilitre, and gram. And that's the one I can't believe - a gram is way smaller than a whole cc of water!
Here's a little metric joke that I never noticed before: a cubic foot of water weights 62.5 pounds, which at 16 oz to the pound is precisely 1000 ounces.
That is a nice calculation Paul and you really had me gobsmacked, but I checked, and while it is a useful approximation, the figure of 62.5 is not precise. I calculated it for Imperial fluid ounces, and the figure I get is 996.6...
Still, much too close for jazz! Here is one for you in return. A year is remarkably close to 10^7.5 secs. As the speed of light is fairly close to 10^5.5 km/sec, it is easy to take 10^13 km/ly. in general, both are useful shortcut figures.