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D.E mixing problem need help with rate out

  1. Apr 9, 2007 #1
    1. The problem statement, all variables and given/known data
    A large tank initially hold 40 gallons of water. Pure alcohol enters at a rate of 2 Gal/min is well stirred and the mixture leaves at 1gal/min. What will be the concentration when of alcohol when the tank has 80 gallons of fluid in it.


    2. Relevant equations
    q= amount of alcohol
    i have dq/dt=rate in -rate out
    rate in=2gal/min of OH
    it will take 40 mins to fill to 80 gal
    and the thing im wandering about is the rate out.
    i currently have
    rate out=q/(40+2t), but im thinking maybee its q/(40+t)

    as for the rest i think im fine its just this outflow rate im not sure on.
     
  2. jcsd
  3. Apr 9, 2007 #2

    jamesrc

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    Science Advisor
    Gold Member

    Your second guess for the outflow rate appears correct to me, making your differential equation:
    [tex]\frac{dq}{dt}=2-\frac{q}{40+t}[/tex]

    Any reason you are not sure that you would like to discuss?

    Don't forget that when you are answering the problem they are asking for concentration of alcohol; your state variable q is currently defined as the amount of alcohol in gallons.
     
  4. Apr 9, 2007 #3
    well at first i was thinking of using (40+2t) since that was the initial volume + the flow in but then i thought about how the acutal vol change is just t when you account for the out flow.

    as far as the concentration goes what i did was set up the D>E for the quanity of OH in the container then just divid q by (40+2t)

    thanks for the help i sortof needed that conformation.
     
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