1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differential equations-system of equations, cleaning up the great lakes

  1. Mar 24, 2008 #1
    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=ratein-rate 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)=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!!
     

    Attached Files:

    Last edited: Mar 24, 2008
  2. jcsd
  3. Mar 24, 2008 #2
    [​IMG]

    here's the image that shows the great lakes and their flow rates so you don't have to view the attachment
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Differential equations-system of equations, cleaning up the great lakes
Loading...