Consider a tank used in certain hydrodynamic experiments. after one experiment the tankcontains 200 l of a dye solution with a concentration of 1 g/l. to prepare for the next experi-ment, the tank is to be rinsed with fresh water flowing in at a rate of 2 l/min, the well-stirredsolution flowing out at the same rate. find the time that will elapse before the concentrationof dye in the tank reaches 1% of its original value.

Explanation:

1. Set up an expression for the rate of change of dye concentration.

2. Integrate the expression

3. Find the constant of integration

4. Solve for A as a function of time.

5. Calculate time to reach 1 % of original concentration

The initial concentration was 1 g/L, so the new concentration is 0.01 g/L

The diagram shows the concentration starting at 1 g//mL and decreasing asymptotically to 0.01 g/mL after 460 min.

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