A tank with vertical sides has a square cross-section of area $4$ square feet. Water is leaving the tank through an orifice of area $5/3$ square inches. If the water level is initially $2$ feet above the orifice, how to find the time required for the level to drop $1$ foot?
If water also flows into the tank at the rate of $100$ cubic inches per second, then how can we show that the water level above the orifice approaches the value $(25/24)^2$ feet above the orifice, regardless of the initial water level?