Water is added to a 300 L tank. when a valve in a discharge line is opened, water flows out at a rate proportional to the height and hence to the volume V of water in the tank. The flow of water into the tank is slowly increased and the level rises in consequence, until at a steady input rate of 60.0 L/min the level just reaches the top but does not spill over. The input rate is then abruptly decreased to 20.0 L/min

write a differential balance on the water in the tank for the period from the moment the input rate is decreased (t=0) to the attainment of steady state (t - inf) in dV/dt.

Question

Water is added to a 300 L tank. when a valve in a discharge line is opened, water flows out at a rate proportional to the height and hence to the volume V of water in the tank. The flow of water into the tank is slowly increased and the level rises in consequence, until at a steady input rate of 60.0 L/min the level just reaches the top but does not spill over. The input rate is then abruptly decreased to 20.0 L/min

write a differential balance on the water in the tank for the period from the moment the input rate is decreased (t=0) to the attainment of steady state (t -> inf) in dV/dt.