A tank-based intensive aquaculture system has a tank volume of V m3 . Fresh water is corning in at a rate of F m3 / s, which is also the rate at which water is leaving the tank. The oxygen...

A tank-based intensive aquaculture system has a tank volume of V m3 . Fresh water is corning in at a rate of F m3 / s, which is also the rate at which water is leaving the tank. The oxygen concentration in water at the inlet is c; . Water in the tank is circulating enough such that the oxygen concentration, c [g/ m3], can be assumed uniform throughout the tank. Oxygen is consumed by the fish at a rate of k 1 g per m3 per second. Oxygen is produced by the plants in the tank at a rate of k 2 g per m3 per second. Air is bubbled through the tank and the oxygen transfer from the air to the tank is given by k3 (cb - c ), where k3 is the rate constant in 1/s, and ch is the appropriate concentration of oxygen in air in the bubble (a constant value). 1) Write a mass balance for the tank for change in oxygen concentration, f...c, over a time, f...t. 2) Develop the differential equation for concentration as a function of time. 3) Solve the differential equation, assuming an initial concentration of c; . 4) Plot the concentration versus time. 5) What is the steady-state concentration? 6) What is the steady-state concentration if there is no bubbling of air?