A 4-liter sink has a drainage problem which limits its ability to drain water in the sink. Consider a case in which you turn on the sink faucet and the sink is half full of water the instant the sink is turned on. The faucet runs at 1 liter/min and the drain flow depends on the amount of mas in the tank, M, by the following expression: dM Mout 0.002M in g/s dt (a) Develop an expression for the mass of the water in the sink as a function of time.
(b) Convert part a to an expression that has fraction of the sink being full as a function of time.
(c) If there is no overflow protection drain, how many minutes will it take to have an overflow of water?