A brine solution flows at a constant rate of 6 L/min into a large tank that init
ID: 1018726 • Letter: A
Question
A brine solution flows at a constant rate of 6 L/min into a large tank that initially held 50 L of brine solution in which was dissolved 0.5 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. if the concentration of salt in the brine entering the tank is 0.05kg/L, determine the mass of the salt in the tank after t time. When will the concentration of salt in the tank reach 0.03 kg/L ? A brine solution flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 3 L/min. If the concentration of salt in the brine entering the tank is 0.2kg/L, determine the mass of the salt in the tank after t time. When will the concentration of salt in the tank reach 0.1 kg/L ?Explanation / Answer
q1
x(0) = 0.5 kg.
Conversion
Input :
rate = 6 L/min · 0.05 kg/L = 0.3 kg/min.
===================
Output :
rate = 6 L/min · xt /50 kg/L = 6x /50 kg/min
===================
Let x(t) denote the amount of salt (in kg) in the tank at time t 0.
Then we have that x(0) = .5 and
dx /dt = 6(.05) 6x(t)/ 50 = .3 (3 /25) x(t).
dx / 3 (3 /25) x = dt
(25/ 3) ln(.3 – (3 /25) x) = t + C
.3 (3 /25) x (t) = Ce 3/ 25 t
x(t) = 2.5 + Ce 3 25 t .
x(0) = .5
C = 2.
Therefore x(t) = 2.5 2 e 3/ 25 t.
concentration of salt = 0.03 kg/L
x(t)/50 = .03 kg
x(t) = 1.5 kg
which gives t = 25 /3 ln(.5) = 5.78 minutes
Answer: The salt conc. in the tank = 0.03 kg/L at 5.78 min
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.