differential equationssystem of equations, cleaning up the great lakes...by mwaso Tags: cleaning, differential, equations, equationssystem, lakes 

#1
Mar2408, 09:57 PM

P: 11

1. The problem statement, all variables and given/known data
The idea of the problem is to find out how long it would take to flush the Great Lakes of pollution. They're set up as a series of five tanks and you are given inflow rates of clean water, inflow rates from the other tanks, and outflow rates. See attached figure. 2. Relevant equations dA/dt=rateinrate out where A is the amount of pollution at time t 3. The attempt at a solution first I wrote equations for each lake. rather than using A as my variable, I used the first letter of each lake (with n for Ontario) to stand for the amount of pollution in the given lake at time t. this gives... ds/dt=15s/2900 dm/dt= 38m/1180 dh/dt=15s/2900 + 38m/1180  68h/850 de/dt=68h/850  85e/116 dn/dt=85e/116  99n/393 rearranging and pulling out the differential operator leads to the following system (D + 38/1180)[m]=0 (D  68/850)[h] + 38m/1180  15s/2900=0 (D + 15/2900)[s]=0 (D + 85/116)[e] 68h/850=0 (D + 99/393)[n]  85e/116=0 and there you have it. A system of five equations with five variables. It seems like it should be fairly straightforward to solve from here, but I can't figure out what to do next. I'm stuck!! 



#2
Mar2408, 10:50 PM

P: 11

here's the image that shows the great lakes and their flow rates so you don't have to view the attachment 


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