Question

Consider two tanks A (with 45 L of solution) and B (with 55 L of solution) in a dynamic fluid system. Water is flowing into tank A at a rate of 330 L/hr Water is flowing into tank B at a rate of 370 L/hr. Fluid is pumped from tank A to tank B at a rate of 180 L/hr and fluid is pumped from tank B to tank A at a rate of 165 L/hr. Fluid is pumped out of the system from tank A at a rate of 315 L/hr and out of the system from tank B at a rate of 385 L/hr There is initially 28 grams of solvent in tank A There is initially 35 grams of solvent in tank B Set up the matrix equation for the quantities of salt (in grams) in the tanks after t hours: Q'A QA The eigenvalues for this matrix are and =

Answer 1

310 L/hY 330 L/h 45L SS L 385L/hy 315 LIhY I )and a. (t ib amount of ^alt at time t. 2 8 = 3S Now dan dt ) -0 QA QA x 16S SS x180 4S x 3IS 4S and x 18o 4S dt SS S 4 QA 2 euation 0 and can be wri+ten as, QA - 4 -/D Toind eizenvalues -1-A (-1-A) C-10-A) -12 = 0 21A + 38 = o -lo-A 4 14) (A +7) = o (A and 14