# Water is added at varying rates to a 300-liter holding

## Water is added at varying rates to a 300-liter holding 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 60.0L/min the level just reaches the top but does not spill over. The input rate is then abruptly decreased to 20.0L/min.

(a) Write the equation that relates the discharge rate, v out (L/min), to the volume of water in the tank. V (L), and use it to calculate the steady-state volume when the input rate is 20 L/min.

(d) Separate variables arid integrate the balance equation to derive an expression for V (t). Calculate the time in minutes required for the volume to decrease to within 1% of its steady-state value.