Solving two independent ordinary differential equations. Concentrations of solute in flowing from one tank to another.
Response to the following question:
Two tanks A and B, each of volume V, are filled with water at time t = 0. For t > 0, volume v of solution containing mass m of solute flows into tank A per second; mixture flows from tank A to tank B at the same rate and mixture flows away from tank B at the same rate. The differential equations used to model this system are given by
dσA/dt+(u/V)σA=m/V,dσB/dt+(u/V)σB=(u/V)σA
where Q4, g are the concentrations of solute in tanks A and B, respectively. Show that the mass of solute in tank B is given by
mV/u(1-e-ut/V)-mte-ut/V