Compartmental Analysis

Steem

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Joined
Oct 11, 2006
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18
Here is the problem:

A swimming pool whose volume is 10,000 gal contains water that is 0.01% chlorine. Starting at t=0 city water containing 0.001% chlorine is pumped into the pool at a rate of 5gal/min. The pool water flows out at the same rate. What is the percentage of chlorine in the pool after 1hr? When will the pool water be .002% chlorine?

I completely understand all the possible solution techniques. The problem is that I'm assuming the chlorine is measured in mg/L because that's what is normally used in chemistry.

If I don't convert chlorine I get dx/dt=.00005(mg*gal/L)-x(t)/2000(gal/min)

this is easy to solve but I keep getting the wrong answer.

If I convert I end up with dx/dt=.000006613-x(t)2000 (gal/min)
which still gives me wrong answer.

Can someone please tell me where I'm going wrong!
 
I don't think you should assume mg/L. Conflicting units.

The pool initially contains 1 gallon of chlorine in 10,000 gallons of water.

It's entering at 1/20,000 gallons per minute and exiting at the same rate.

Rate in = 1/20,000 gal/min

Rate out = 5y/10,000=y/2000 gal/min.


\(\displaystyle \L\\\frac{dy}{dt}=\frac{1}{20,000}-\frac{y}{2000}\)

\(\displaystyle \L\\\frac{dy}{dt}+\frac{y}{2000}=\frac{1}{20,000}\)

Initial condition is y(0)=1.

Now, use your integrating factor and solve the DE.

Check me out. Hope I didn't go astray.
 
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