# Three-tank flow system problem

1. Dec 2, 2011

### terpwildcat

Consider a three-tank flow system. Each tank holds V=200 gallons and the flow rate through all connectors is a constant 25 gallons per minute. Fresh water is pumped into each of the well stirred tanks and the mixture flows out of each as indicated. Mixtures from each of the three tanks is pumped into the other two tanks, as well as pumped out of the system all together (still at the rated of 25gal/min). Let Qi(t) denote the amount of salt in each tank at time t. Suppose that the initial amount of salt in each tank is Q1(0)= Q0, Q2(0)= 2Q0, Q(0)= 3Q0. Set up and solve the system of differential equations which models this system. How long until the amount of brine in tank 1 is less than half of its original amount?

the equations i came up with were
Q1'=-3/8*Q0*Q1 + 1/4*Q0*Q2 + 3/8*Q0*Q3
Q2'= -3/4*Q0*Q2 +1/8*Q0*Q1+3/8*Q0*Q3
Q3'= -9/8*Q0*Q3 + 1/8*Q0*Q1 + 1/4*Q0*Q2

but when i plug these into mathematica for eigenvalues and eigenvectors they dont result in logical answers

Last edited: Dec 2, 2011
2. Dec 2, 2011

### HallsofIvy

Staff Emeritus
You say "as indicated" but did not include the presumed diagram that "indicates" that. Also,how does the product of the amount of salt in two tanks enter into this? You say you were looking for eigenvalues and eigenvectors but with those products, this is NOT a linear problem.