Mixing Model Problem?
English Brine Initally, 50 lbs of salt is dissolved in a tank containing 300 gallons of water. A salt solution with 2 lb/gal concentration is poured into the tank at 3 gal/min. The mixture, after stirring, flows from the tank at the same rate the brine is entering the tank. In all of the problems below, we measure in minutes.
(a) Find the amount of salt Q (in lbs) in the tank as a function of time .
(b) Determine the concentration C of salt (in lbs/gal) in the tank as a function of time .
(c) Determine the steady-state amount of salt (in lbs) in the tank.
(d) Find the steady-state concentration (in lbs/gal) of the salt in the tank.
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Verified answer
change in salt = incoming salt - outgoing salt
dQ / dt = [2 (lb/gal)] [ 3 (gal/min] - [Q/300 ( lb/gal)] [ 3 (gal/min]
dQ / dt = 6 - Q/100---> [D+1/100} Q = 6 , Q_p = 600 ,
Q_c = c1 e^(-t/100), Q(0) = 50---> c1 = - 550
now you answer the questions