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Need Help Setting up Differential Equation

  1. Sep 9, 2008 #1
    1. The problem statement, all variables and given/known data


    A tank contains 3200 L of pure water. A solution that contains 0.11 kg of contaminent per liter enters the tank at the rate 8 L/min. The solution is mixed and drains from the tank at the same rate.

    with C representing the amount of contaminent in kg at time t (in minutes), write a differential equation that models this situation.

    2. Relevant equations

    possibly int(udv) = uv - int (vdu) (integration by parts)



    3. The attempt at a solution

    rate in: 8 L /min * .11kg/ L = .88 kg/min I am confused about where to put the variable t here. From my solution, it would appear that .88/t would be right, but then the rate in would decrease over time. This doesn't seem right. Would it be .88t or .88/t or just .88?

    rate out: 8 L/min * C(t)/3200L = C(t)/400 kg/min.

    DC/dt= rate in - rate out

    DC/dt= .88t - C(t)/400

    Is this correct? Should I have added the "t" when it is kg/min?



    ***In my most recent attempt at this problem, I have come up with:
    dC/dT = .88 - C(t)/400
     
    Last edited: Sep 9, 2008
  2. jcsd
  3. Sep 9, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    dC(t)/dt=.88-C(t)/400 is correct.
     
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