Answer to Question #244047 in Civil and Environmental Engineering for Fernando Matienzo

Question #244047
Situation 2
A tank initially contains 100 gal of brine where there is dissolved 20lb of salt. Starting at time t = 0, a
brine containing 3lb of dissolved salt per gallon flows into the tank at the rate of 6gal/min is kept uniform
by stirring and the well-stirred mixture simultaneously flows out of the tank at a slower rate of 3gal/min.
1. How much salt is present at the end of 15 min?
2. How much salt is present after a long time?
1
Expert's answer
2021-10-03T17:12:02-0400


Let Q be the amount of sait in the tank and dt/dQ

​ be the rate of change of amount in the tank

We get the equation as 

\space dt/ dQ ​ + 1/20 ​ Q=0


It is linear equation and the solution of it is Q=Ce ^{-\frac{t}{20} t} ​


At t=0 , the value of Q is 20 

⇒C=20


Therefore the equation is\space Q=Ce ^{-\frac{t}{20} t}


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