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Diff. Eq. Mixture problem. Did most of the work, Need to solve for C

  1. Feb 22, 2013 #1
    I need to solve for C. I know it's probably simple but i don't remember how to. This is what I have so far:
    FgCaDxf.jpg
     
  2. jcsd
  3. Feb 22, 2013 #2
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    Use the initial conditions given.

    Also, your solution's incorrect.

    You only have 100L of solution at one point in time, so at only one point in time will the concentration leaving the tank be A/100. There's a net change in volume as time passes.
     
  4. Feb 22, 2013 #3
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    so what should it be instead of A/100?? A/35?
     
  5. Feb 22, 2013 #4
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    The rate out will be the the concentration times the rate at which the fluid flows out per minute.

    You already know the fluid flows out at 5L/min, but your concentration's wrong.

    It's correct that the concentration will depend on the amount A of chemical X, but the concentration also depends on the total volume of the solution. Five grams in 1 L is much more concentrated than five grams in 100L.

    You just need to write the concentration in a way that's dependent on time since your volume also depends on time.
     
    Last edited: Feb 22, 2013
  6. Feb 22, 2013 #5
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    so it will be A/(100+5t)?

    or maybe A/(100-2t) <--- -2t came from Rate in rate out
     
    Last edited: Feb 22, 2013
  7. Feb 22, 2013 #6
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    No, but you're getting closer.

    V(t) = 5t + 100 would imply that the volume is increasing with time. It's not.

    Look at the net change in volume.
     
  8. Feb 22, 2013 #7
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    Close, but you need to consider the rate into the tank as well.
     
  9. Feb 22, 2013 #8
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    A/(100-2t)? <--- -2t came from Rate in - rate out
     
  10. Feb 22, 2013 #9
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    A/(100 - 2t) is correct, but don't forget to multiply it by 5 representing the liters/min to get the total rate out.
     
  11. Feb 22, 2013 #10
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    Right. Thanks
     
  12. Feb 22, 2013 #11
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    I get a non-real result now when I try to solve for c. Where did I go wrong?

    OVhz36N.jpg
     
  13. Feb 23, 2013 #12
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    That shouldn't be giving you a non-real solution. It looks fine to me.
     
  14. Feb 23, 2013 #13
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    no, it doesn't work out.. :/
     
  15. Feb 23, 2013 #14
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    Oh, I read it wrong. It should be 50-t, not t-50.
     
  16. Feb 23, 2013 #15
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    are you saying it should be A*(t-50)^(-5/2)=-8(50-t)^(-3/2)+c ?
    How do you figure??
     
  17. Feb 23, 2013 #16
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    The integral of 5/(100-2t) is (-5/2)ln(50-t).
     
  18. Feb 23, 2013 #17
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    I get a different answer:

    GesMlaO.jpg

    Is there another source we can check?
     
  19. Feb 23, 2013 #18
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    That's strange that it's giving you that answer. I checked by doing it by hand, as well as wolfram alpha and I get (-5/2)ln(50-t).
     
  20. Feb 23, 2013 #19
    Re: Diff. Eq. Mixture problem. Did most of the work, Need to solve for

    do you have a wolfram alpha link? I want to try it.
     
  21. Feb 23, 2013 #20
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