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So today I was challenged by my Uncle because he says that we are going to run out of drinkable water on earth before we run out of Oil, I told him that he is just saying that to scare me but he honestly thinks that this is true. So I wanted to do the math for him to prove that we have nothing to worry about. But I got a lot of it finished but I have hit a brick wall, I do not think my math is correct so I would like you guys to help me prove that my math is correct.

My variables:

Volume of Earth in Cubic meters: 260,000,000,000 cubic miles
Volume of (any) water on Earth: 75% of earth's volume, 260,000,000,000 * 0.75 = 195,000,000,000 cubic miles
Volume of drinkable water on earth: 1% of Water, 195,000,000,000 * 0.01 = 1,950,000,000 cubic miles
Conversion of Cubic Miles to Gallons: 1 Cubic Mile = 1.101117147e+12
Gallons of Drinkable water on Earth: 2.147178437e+21
Conversion of Gallons to Ounces: 1 Gallon = 128 Ounces, Total of 5.359357378752e+32 Ounces
Average person consumes: 64 Ounces of Drinking Water per day
People on earth: 6.5 Billion
Average amount of ounces each person drinks of water per day: 64 * 6,500,000,000 = 416,000,000,000 Ounces of Drinking Water per day for every person on earth
How many days earth drinking water would last with this amount: 5.359357378752e+32 / 416,000,000,000 = 1288307062200000000000

I just want some math people to check my work. I am only 15 trying to debate with a 40yo haha, I do not want to screw up.

Thanks for any help and it is well appreciated!

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closed as off topic by Alex B., Arturo Magidin, Qiaochu Yuan Feb 5 '11 at 15:23

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Water is recyclable. Oil is not. Burning petrol/gas produces water, etc etc... –  Aryabhata Feb 5 '11 at 2:52
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This is not a mathematical qn, but you should do some more research on this. This is to get you started: according to one official estimate, it takes 2,400 gallons of water to produce 1 pound of meat. Not all of it is drinking water, but a lot of it is. What you drink is a tiny fraction of the drinking water that you consume. @Moron While water is recyclable, some ecologists say that the whole system only works while the percentage of water in circulation compared to the water available does not exceed a certain threshold. What that threshold is and what happens when it's exceeded - who knows. –  Alex B. Feb 5 '11 at 3:02
    
Don't forget rainfall! Or XKCD people changing stuff with butterflies. –  muntoo Feb 5 '11 at 3:38
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Earth is 75% water by volume??? –  Tpofofn Feb 5 '11 at 4:14
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Your uncle has a good point. Water scarceness is already a major problem for many countries, and bound to become much more problematic and expanded in the near future. Few regions in the wold (e.g. central Europe) don’t have water problems … all others have or will have soon. But kudos for making the effort to reason rationally about the issue. –  Konrad Rudolph Feb 5 '11 at 12:38

3 Answers 3

It is not the case that 75% of the earth's volume is water. You are thinking of the statistic that about 75% (closer to 70% really) of the earth's surface is covered by water; there isn't any water on the inside. I'd estimate the volume of water on earth as follows:

  • Circumference of the earth: $c = 4\times 10^7 m$ (almost by definition of the meter)
  • Radius of the earth $r = c/2\pi \approx 7 \times 10^6 m$
  • Surface area of the earth: $A = \frac{4}{3} \pi r^2 \approx 2 \times 10^{14} m^2$
  • Area covered by water: $A_W = 0.7 A \approx 1.4\times 10^{14} m^2$
  • Average depth of the ocean: $D = 2\times 10^3 m$ (wild guess)
  • Total volume of water: $A_W D \approx 3 \times 10^{17} m^3$

This is about $7 \times 10^7 mi^3$ or $8 \times 10^{19}$ gallons, which is about 5 orders of magnitude smaller than your value.

It is also worth mentioning that humans consume water for many more things than just drinking (watering crops and livestock, industry, etc), and the rest of life on the planet needs water too. 64 ounces per human per day would not keep the human race alive. On the other hand, it isn't necessarily gone after being used once.

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+1 for the first sentences-a good and helpful guess. +1 too for the rest, but I have only one vote. –  Ross Millikan Feb 5 '11 at 4:26
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Nate and Moron both make important points. Water is, in principle, recyclable indefinitely. The issue is not how much drinkable water there is but how much more expensive it will get to find or make it... –  Qiaochu Yuan Feb 5 '11 at 11:52

Your volume of the earth line confuses meters and miles. The figure is right in miles $4\pi/3*4000^3=4^4*1000^3=256*10^9$. The volume of water is much smaller, though. The deepest ocean is 7 miles out of those 4000. 99% is salt or ice, and most of the rest is inaccessible. While you may only drink 2 quarts a day (and I abhor the fashion that says you must) Wikipedia says the American city average is more like 100 gallons/person/day consumption (think washing, irrigation and swimming pools). I have seen figures like that elsewhere. So I think you shouldn't be arguing on one pass, as Moron commented.

That said, I think doing calculations like this is an extremely valuable activity.

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As Alex notes, the meat of this question is not mathematical, rather it has to do with economics. Keep in mind that even if you were able to calculate precisely the amount of water on earth today, it would still be unclear whether we would run out of drinkable water before oil. When it comes to consumption of a good such as oil, the price and quantity will be determined by the intersection of the supply and demand curves.

http://en.wikipedia.org/wiki/Supply_and_demand

Try holding the demand for oil constant (unrealistic assumption of course!). Now if you also assume that oil on earth is all known reserves with no difference in quality, you can think of the supply as constantly being reduced (slowly shifting the supply curve to the left). "Cetaris paribus" (all other things equal) we can see that this will have an effect of increasing the price while decreasing the quantity demanded (as the intersection moves along the fixed demand curve). In this oversimplified version, the closer we got to the "last reserves," the less people are demanding oil at the given price, so of course, the supply is depleted at a lower rate.

Now try holding the supply for oil constant (also unrealistic!). There are many factors influencing the demand curve for oil: taxes/regulations, subsititute goods/alternative energies, increased/decreased wealth to name a few. Think about whether these factors will increase demand (shifting the curve to the right) or decrease it (shifting the curve to the left).

There is of course a very complex interplay between the supply and the demand which extends to many other goods...

Overall, the point is that both water and oil will most likely not simply be used up at a constant rate until they are gone. In both cases, the invisible hand of the market has ways of applying pressure in (hopefully) the right spots to ensure that we run out of neither!

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Yes, but the pressure could materialize as mass deaths due to droughts. –  Raskolnikov Feb 5 '11 at 13:43
    
@Raskolnikov: That is one possible outcome... Another is innovative ways to make previously non-drinkable water drinkable... –  ghshtalt Feb 5 '11 at 13:46
    
@user3711: it is true that the pressure is also on finding technological solutions, but just because there is a pressure to find technological solutions doesn't mean one shall be found. Science is not magic. (Unlike economics, where invisible hands seem to solve everything.) –  Raskolnikov Feb 5 '11 at 13:51