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Mixing Tank, Differential Equations Problem

  1. Feb 21, 2012 #1
    1. The problem statement, all variables and given/known data

    a larg tank is filled with 500 gals of water with 400lbs of salt. pure water is pumped into the tank at a rate of 3gal/min. the well mixed solution is pumped out at a rate of 7 gal/min.

    I need help finding the Differential

    2. Relevant equations



    3. The attempt at a solution

    I tried coming up with the D.E. and this is what i got dA/dt = 3 - 7A/(500-t)

    except after i did solved the d.e. i kept getting more salt than i started with which makes no sense...

    Please Help lol
     
  2. jcsd
  3. Feb 21, 2012 #2
    Your denominator is wrong. How is rate out defined?
     
  4. Feb 21, 2012 #3
    not sure lol...i went off of a similar problem that was gaining instead of losing...

    i know that it is supposed to be the flow rate out multiplied by the concentration out but i don't understand how to get the concentration of salt exiting the tank...
     
  5. Feb 21, 2012 #4
    [tex]R_{out} = -t(7gal/min - 3gal/min) = -4t[/tex]

    Where you have 500-t. I didn't check over the rest of you equation but that was what was immediate obvious.
     
  6. Feb 21, 2012 #5
    ok so instead i should have A/(-4t) rather than A/(500-t)?
     
  7. Feb 21, 2012 #6
    No, why would you disregard the amount of solution?
     
  8. Feb 21, 2012 #7
    i guess i'm misunderstanding what you are saying....it would help more if you just showed me what the equation should look like
     
  9. Feb 21, 2012 #8
    I could have phrased it better.

    When you are dealing with mixtures, you denominators is

    [tex]\frac{A}{sol+(R_{in}-R_{out})t}[/tex]

    When inflow and out flow are the same, we just have A/sol in gallons.

    Your R_{in}=3 and out=7 so (3-7)t = -4t.

    So what is the denominator?
     
  10. Feb 21, 2012 #9
    A/500-(-4t)

    so A/500+4t?
     
  11. Feb 21, 2012 #10
    it can't be that because i just tried it and it didn't come out right
     
  12. Feb 21, 2012 #11
    500+(-4t) = 500-4t
     
  13. Feb 21, 2012 #12
    ok i made some dumb mistakes but i finally got what i needed thanks!
     
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