Two tanks each contains 100 liters salt solution (20 gr/lit). A stream of water is feed into the first tank at a rate 5 liters/min. The liquid flows from the tank to the second tank at a rate of 8 liters/min. The liquid flows from second tank at a rate of 8 liters/min where part of it (3 liters/min) is directed to the first tank and the balance flows to some point out of the system. Determine the salt concentration (gr/lt) in the first and second tank as a function of time. Assume ρ is constant in all streams.
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Question 1Two tanks each contains 100 liters salt solution (20
gr/lit). A stream of water is feed into the first tank at a rate 5
liters/min. The liquid flows from the tank to the second tank at a
rate of 8 liters/min. The liquid flows from second tank at a rate
of 8 liters/min where part of it (3 liters/min) is directed to the
first tank and the balance flows to some point out of the system.
Determine the salt concentration (gr/lt) in the first and second
tank as a function of time. Assume is constant in all
streams.Lumped parameter model, Conservation of mass, Mixing
ProcessIllustration2st tank100 liters salt solution(20gr/lit)1st
tank100 liters salt solution(20gr/lit)5 lt/min8 lt/min5 lt/min3
lt/min3SolutionAssumption:Density is constant.Concentration in the
tank is equal to concentration out of the tank.Evaporation is not
occured, and mixing process is completely done.
Substitue eq. (5) and (6) into eq. (2) :Using Laplace
TransformationFrom Tank I component balance, we got eq (1)
From Tank II component balance, we got eq (2)
Search C1(s) and C2(s) from eq (1) and (2)
Transformation Laplace C2(s) so that we can get
C2(t)Transformation Laplace C1(s) so that we can get C1(t)
THANK YOU
