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?(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Three-tank flow system problem

**Physics Forums | Science Articles, Homework Help, Discussion**