A tank contains 2500 m3 of salt solution, with a salt concentration of 20 kg/m3. At time zero, salt free water starts to be pumped into the tank at a rate of 20 m3/min. The exit flow from the tank leaves at 18 m3/min, so that the volume of solution in the tank changes. A mixer in the tank keeps the concentration of salt in the tank uniform.
a) What is the concentration as a function of time in this system?
b) The tank can hold a maximum of 3500 m3 of salt solution and a minimum of 500 m3 of salt solution. Which limit will be encountered first in this situation? How long after the pumping starts? Ignore changes in the density of the salt solution.