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Math Help - Connected tanks.

  1. #1
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    Connected tanks.

    I have had this problem for a week now. I do not even know where to begin.

    You have 26 tanks of water.
    1 giant tank that holds a maximum of 27million L
    25 smaller tanks that hold a maximum of 130k L each
    You have 5 pumps that are filling the 25 smaller tanks with 10k L per second divided evenly among all the smaller tanks (each pump does 10k L/s)(this water comes from nowhere, infinite amount)
    You have 17 pumps that are pumping water out of the large tank at a rate of 10k L per second (this water goes nowhere)
    The giant tank is also pumping 30% of the current amount of water from each of the smaller tanks to itself every 1 second.
    The giant tank starts at 14mil L
    The Smaller tanks start at 130k L each

    At what rate would the Giant tank become empty?



    I know that the large tank is draining at a rate of 170,000 liters per second
    I know that the smaller tanks are filling at a rate of 2,000 liters per second each
    What I cant figure out is the rate at which the Large tank is filling, or the rate at which the smaller tanks are draining.
    Last edited by mpweber; February 13th 2011 at 05:48 AM.
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  2. #2
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    y = 1400 + [((5*130)+50*x)- (((5*130)+50*x)*.30)] - (170*x)
    This is the closest I can get, which shows the tank draining at 1855 seconds after starting
    Although, my formula doesn't seem anywhere near complicated enough to account for the 30% per second.
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  3. #3
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    Quote Originally Posted by mpweber View Post
    I have had this problem for a week now. I do not even know where to begin.

    You have 26 tanks of water.
    1 giant tank that holds a maximum of 27million L
    25 smaller tanks that hold a maximum of 130k L each
    You have 5 pumps that are filling the 25 smaller tanks with 10k L per second divided evenly among all the smaller tanks (each pump does 10k L/s)(this water comes from nowhere, infinite amount)
    You have 17 pumps that are pumping water out of the large tank at a rate of 10k L per second (this water goes nowhere)
    The giant tank is also pumping 30% of the current amount of water from each of the smaller tanks to itself every 1 second.
    The giant tank starts at 14mil L
    The Smaller tanks start at 130k L each

    At what rate would the Giant tank become empty?



    I know that the large tank is draining at a rate of 170,000 liters per second
    I know that the smaller tanks are filling at a rate of 2,000 liters per second each
    What I cant figure out is the rate at which the Large tank is filling, or the rate at which the smaller tanks are draining.
    If I interpreted your post correctly ...

    let V = volume in kL of the large tank at any time t in seconds

    y = total volume of all the smaller tanks at any time t in seconds


    \dfrac{dy}{dt} = 50 - 0.3y

    y(0) = 3250 \, kL

    solving this DE for y ...

    y = \dfrac{10}{3}(50 + 925e^{-0.3t})



    \dfrac{dV}{dt} = 0.3y - 170

    \dfrac{dV}{dt} = -120 + 925e^{-0.3t}
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