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Estimate Water Usage

  1. Jan 30, 2012 #1
    1. The problem statement, all variables and given/known data

    An average family of four uses roughly 1600 liters of water per day. How much depth would a lake lose per year if it uniformly covered an area of 90 square kilometers and supplied a local town with a population of 30000 people? Consider only population uses, and neglect evaporation and so on.

    I don't even know where to begin.
     
  2. jcsd
  3. Jan 30, 2012 #2

    Simon Bridge

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    how much water does the town use per day?
    relate the volume of the lake to it's area and depth


    context ... longest dry spell is 90 days where I live, during that time I have 6000gal ~22700L ... a top-up costs NZ$150 for 1200gal to be trucked in, so water conservation is a big deal here. Two of us would use almost all of the 6000gal in that 90 days.

    That makes it 130Lpp per day or about 500L per day for four adults. So, to me, 400Lpp-pd is a shocking waste.

    IIRC: The Apollo missions carried less than 100L of water for 3 adults for 12days (Apollo 17).
    But they didn't take showers, wash clothes, flush toilets, or water lawns.
     
    Last edited: Jan 30, 2012
  4. Jan 30, 2012 #3
    Here's what I did. I converted 1600 liters t cm^3 and then converted that to m^3, and got 1.6E8 m^3. Then, I multiplied that with the population of 30000 and 365 (days in a year). Then I converted 90 km^2 into m^2 and got 9E7 m^2. To calculate depth, I divided volume over area and got 1.95E7 m. I entered this into the computer, and it was incorrect. What did I do wrong?
     
  5. Jan 30, 2012 #4

    PeterO

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    How many litres of water does the town use each day [hint: how many "families of for" make up 30000 people]

    How many litres per year does that make [hint: there are 365 days per year - or 366 this year]

    How many cubic metres does that make? ... and so on
     
  6. Jan 30, 2012 #5

    PeterO

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    Th population in 30000, but the consumption figure was per 4 people
     
  7. Jan 30, 2012 #6
    [Delete]
     
    Last edited: Jan 30, 2012
  8. Jan 30, 2012 #7
    So do I divide 30000 by 4?
     
  9. Jan 30, 2012 #8

    PeterO

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    You seem to have calculated a figure 4 times too big [I have not checked any of your arithmetic] so you need to divide by 4 at some stage.
    Given that you have done all the work, perhaps you could just divide your final answer by 4 and check that it is correct.
     
  10. Jan 30, 2012 #9

    Simon Bridge

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    Does this seem real to you?
    1liter is a cubic decimeter: a cube 10cm on each side.
    so 10x10x10=1000 of them fit in a cubic meter.
    so 1600L = 1.6m3
    But the 1600L/day figure was for how many people?
    That's 19500km ... which is greater than the diameter of the Earth!!! (12800km) - That's some lake!
    No wonder the climates in trouble with Americans using up water like that ;) that rate lowers all the Earths oceans by 5m. Think of the erosion!
    see above.
     
    Last edited: Jan 30, 2012
  11. Jan 30, 2012 #10
    Oh, I think I get it.
     
  12. Jan 30, 2012 #11

    PeterO

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    Don't overlook the problems "Simon Bridge" pointed out.
     
  13. Jan 30, 2012 #12
    Thanks to you, too, Simon!
     
  14. Jan 30, 2012 #13

    Simon Bridge

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    His final answer is bigger than the diameter of the Earth, dividing by four puts the lake bottom in the mantle. Steamy :)
    This is terribly unprofessional of me - I shouldn't really laugh but the image of drilling a hole through the Earth to supply a town with water just grabbed hold of me.

    The amount the lake actually lowers is still pretty shocking though... you'd notice it.
    You can see how a town can quickly run dry in a drought.

    I think the important, take-away, lesson here is about reality-checking your numbers.

    IRL you are bombarded with statistics and asked to worry or not worry about them ... you need to be able to figure out how these numbers are important and in what way in order to know what they actually mean.

    Automatically asking these questions is part of being a scientist.
     
    Last edited: Jan 30, 2012
  15. Jan 30, 2012 #14
    lol I messed up my arithmetic. Thanks for pointing that out, Simon. It is 1.6 m^3. I accidentally multiply instead of divide.
     
  16. Jan 30, 2012 #15
    Lmao! It's all good, man. I see what I did wrong there.
     
  17. Jan 30, 2012 #16
    Finally got the right answer, which is 4.87E-2 m. Thanks for your help!
     
  18. Jan 30, 2012 #17

    Simon Bridge

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    about 5cm per annum if nothing is done.

    part of what obscures these figures from reality-checks is leaving them in calculator notation. 4.87E-2 doesn't resonate with your intuition the way 4.87cm does. That's about 2-3 fingers.

    get used to comparing figures to things aye.
     
  19. Jan 30, 2012 #18
    Well, in real life, of course, I'll say 4.87 cm, or about 5 cm. But since the online physics homework system uses scientific notation, I thought I might just stick with that.
     
  20. Jan 30, 2012 #19

    Simon Bridge

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    Yeah I realized - it is one of the problems with these computer-based learning systems.
    You should not let the machine tell you what units etc to use - use what you are comfy with then convert into something the machine understands at the end.

    1.95e7m does not parse as well as 19500km ... I suspect you'd have been more intuitively worried about the second form. It's also good for when you ask for help - since you are talking to humans here :) or when you are answering written exam papers.

    If you find yourself doing things for the benefit of a machine you are doing it wrong.
    The machine is there for your benefit, not the other way around.

    Above all - have fun.
    Cheers.
     
  21. Jan 30, 2012 #20

    PeterO

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    Interesting to note than an answer like 1.95e7 is instantly marked wrong in exams/test in my state [of Australia]. It is a rubbish value. Number values do not have an e in them.
    Converted to 1.95 x 107 it would be looked at - and then marked wrong; but only because it is the wrong value.
    Some calculators present that answer as 1.957 - and that is wrong too.
     
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