Two large tanks are interconnected by pipes with the l i quid flow i ng fr o m t

Question

Two   large tanks are interconnected by pipes with the liquid flowing from tank A into tank B at a rate of 6 L/min and from tank B into tank A at a rate of 4 L/min. Tank A contains initially 100 L of pure water and tank B contains   initially 100 L of water in which 9 Kg of salt are dissolved. The liquid inside each tank is kept well stirred. Pure water flows into tank A at a rate of   2 L/min. The (diluted) solution flows out of the system from tank B at 2 L/min. Determine the mass of salt in each tank at time t>0

Model the problem into a system of Differential Equations

Explanation / Answer

LET THE AMOUNT OF SALT IN THE TANK A AND B AT ANY TIME T BE X AND Y AND LET IT CHANGE BY AN AMOUNT DX AND DY IN SMALL PERIOD OF TIME DT. TANK A ORIGINAL SOLUTION IN TANK A AT T=0 ......= 100 L QTY OF SALT ORIGINALLY AT T=0............= 0 KG INFLOW RATE = 4 LPM FROM TANK B + 2 LPM PURE WATER OUT FLOW RATE TO TANK B = 6 LPM HENCE ACCUMULATION RATE = 4+2-6 = 0 LPM HENCE SOLUTION AT ANY TIME T=100

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