A soft drink process requires mixing sugar and water continuously in a 250 m³ tank. We have one measurement of the density of sugar: At a concentration of 207.5 kg/m³ the density is 1,083 kg/m³. The process operators measure the concentration of sugar by weighing a fixed volume of solution, and they have a correlation chart that is a straight line passing through zero at a density of 1,000 kg/m³.
a. The plant is being shut down for maintenance, so the tank is flushed with pure water at a rate q = 1 m³/s. The initial concentration of sugar is 100 kg/m³. What are the density and concentration in the tank after 5 minutes, assuming that the operators’ chart is correct?
b. How long should the operators expect to have to wait for the sugar concentration to be below 1 ppm?