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Homework Help: Can someone explain how to setup this differential mixing problem

  1. Sep 24, 2014 #1
    1. The problem statement, all variables and given/known data
    Setup a differential and solve the differential equation using Mathematica: Suppose water is added to a tank at 10 gal/min, but leaks out at the rate of 1/5 gal/min for each gallon in the tank. What is the smallest capacity the tank can have if the process is to continue indefinitely?

    2. Relevant equations

    3. The attempt at a solution
    I know Q' = rate in - rate out. I'm clueless I have no idea to set this up. all I have are examples of actual mixing problems where something is being mixed like salt. i'm so confused. please help
  2. jcsd
  3. Sep 25, 2014 #2


    User Avatar
    Gold Member

    Ok, so you have a tank and you're adding water at a rate of 10 gal/min and it's leaking proportional to the amount of water in the tank. Let's call the amount of water in the tank W, and then the rate of change of amount of water with respect to time would be dW/dt.

    So what do you know about these?
  4. Sep 25, 2014 #3


    Staff: Mentor

    In words, what does Q represent? You know that the rate of flow into the tank is 10 gal/min. How would you represent the rate of outflow?
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