Question

Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank Bat a rate of 4 min and from B into A at a rate of 2 Limin The liquid inside each tank is kept wel stirred. A brine solution with a concentration of 0.2 ko'l of salt flows into tank Aata rate of Limin. The (diluted) solution flows out of the system from tank Aat 6 min and from tank Bat 2 min. If initially, tank A contains pure water and tank B contains 20 kg of salt, determine the mass of salt in each tank at time 120 Limin 020 x ) 100L x(0)=0 kg 100 L yo) - 20 kg 6 min What is the solution to the system? x(t)-

Answer 1

Y(+) X(t) & Umin -0.gigel lool 1X (0)=oke 6 min 7 kg / am 100L 1460) = gorg Hain į kg/L J 2 L/min dx = 02(8) +2 (1) 40 (40) = -10% +27 + 16 00 Let A=(-10 do 21807 **= 7+1 7 , y = (-34 ] and eigenvalue/eigen vector pair

X=Ge *3)*(-248]+56**(7,0) Let tp = {f} (395(3 7C63+[*] o] = [ lot 23 + 14/07 -Auß SA=&=20 Hence &p= [20] Hence Hence Hence 1726,624 vaje P-3+26.-2-waje Put X (0)=0, 7(0) = 20 - 667=41-353 )+5/-3-737+ () -G=-2425, CG= 2.425 Here a) = -2.495 (272) + (-37 V7 ) + 2.425 (2003 - 20 Y(t) = -9.701 e (77012)t + q. 2016 (20) + + 20 Hence

>x(t)= -22774873 - 17.276 27423+ + -7.123t y(t) = -9.70le t 9.70le tao 1.123t