Chapter 5.2, Problem 33E

In Problem 31, assume that no solution flows out of the system from tank B, only $1\text{L}/\text{min}$ flows from A into tank B, and only $4\text{L}/\text{min}$ of brine flows into the system at tank A, other data being the same. Determine the mass of salt in each tank at time $\text{t}\ge \text{0}$.

31.Two large tanks, each holding $100\text{L}$ of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of $3\text{L}/\text{min}$ and from B into A at a rate of $1\text{L}/\text{min}$ (see Figure $\left(5.2\right)$). The liquid inside each tank is kept well stirred. A brine solution with a concentration of $0.2\text{kg}/\text{L}$ of salt flows into tank A at a rate of $6\text{L}/\text{min}$.The (diluted) solution flows out of the system from tank A at $4\text{L}/\text{min}$ and from tank B at $2\text{L}/\text{min}$.If, initially, tank A contains pure water and tank B contains $20\text{kg}$ of salt, determine the mass of salt in each tank at time $\text{t}\ge \text{0}$.

Figure $\left(5.2\right)$ Mixing problem for interconnected tanks