Remember that the density of the feeder goes on the LHS of the equation. Since it is not a constant it also must stay in the differential. A liquid feed is being pumped into a straight-sided cylindrical reactor. There is no flow out of the tank during this time. The flow rate into the reactor changes with time according to the following graph.
Spring water is collected in a concrete rectangular covered reservoir in the mountains.
The area of the orifice is Ao. The springs feed water into the reservoir at a constant flow rate, . Draw a physical picture of this problem. The points are the actual data and the line is the theoretical fit to Torricelli's law. Ao is getting larger with time due to breaks in the concrete.