Question

10. Two tanks, A and B, each contain 5000 gal of water. To each tank 150 gal of a chemical should be added, but in error the entire 300 gal are poured into the A tank. Pumps are set to work to circulate the liquid through the two Figure 15.14" tanks at the rate of 100 gal/min (Fig. 15.14). (a) How long will it take for tank A to contain 200 gal of the chemical and tank B to contain 100 gal- lons? (b) Is it theoretically possible for each tank to contain 150 gal?

Answer 1

Given that

we have to calculate how long will it take for tank A to contain 200 gal of the chemical and tank B to contain 100 gallons.

Initial conditions: Tanks A: 5000 gal water, 300 gal chemical total volume 5300 gal, concentration of chemical 300/5300 Tank B: 5000 gal water Now 100 gal gets circulated between the two tanks each minute So in one minute 100 gal of the mixture from tank A will go into tank B and vice versa For the first minute 100 gal of pure water goes from Tank B to tank A and 100 gal of mixture of concentration 3/53 goes into Tank B Thus. The concentration of each now changes In order to solve the problem, you need to \r\n calculate the rate of change of concentration and set up a system. If the way the concentration changes is hard to understand try calculating the concentration of the mixture in the tanks for each minute so that you can visualize it.