The liquid storage tank shown in figure has two inlet streams with mass flow rates w1 and w2 and an exit stream with flow rate w3. The cylindrical tank is 2.5 m tall and 2 m in diameter. The liquid has a density of 800 kg/m3. Normal operating procedure is to till the tank until the liquid level reaches a nominal value of 1.75 m using constant flow rates: w = 120 kg/min, w2 = 100 kg/mm, and w3 200 kg/mm. At that point, inlet flow rate wt is adjusted so that the level remains constant. However, on this particular day, corrosion of the tank has opened up a hole in the wail at a height of 1 m, producing a leak whose volumetric flow rate q4 (m3/min) can be approximated by q4 = 0.025vh - 1 where h is height in meters.
(a) If the tank was initially empty, how long did it take for the liquid level to reach the corrosion point?
(b) If mass flow rates w1, w2, and w3 arc kept constant indefinitely, will the tank eventually overflow? Justify your answer.
