Question

6. For the following waste treatment facility, chemical concentration (mg/gal) within the tank can be considered uniform. The initial chemical concentration inside the tank was 5 mg/gal, the concentration of effluent coming in is 20 mg/gal. The volume of the tank is 600 gallons. The fluid coming in rate is equal to fluid going out is equal to 60 gal/min. (a) Establish a dynamic model of how the concentration of chemical inside the tank increases over time. Specify the units for your variables. (Hint: establish a mass balance of the waste chemical. The concentration inside the tank = concentration going out) (b) Find the Laplace transformation of the concentration (transfer function) for this step input of 20 mg/gal.

Answer 1

mass of chemical coming in per minute = 60 × 20 = 1200 mg/min

at a time t(min) , M = mass of chemical = 1200 × t mg

concentration of chemical = 1200t / 600 = 2t mg / gallon

Step-by-step explanation:

Since it is only fluid that is leaving and not chemical.