The liquid storage tank shown has two inlet streams with mass flow rates w/ and w₂ and an exit stream with flow rate ws. 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 fill the tank until the liquid level reaches a nominal value of 1.75 m using constant flow rates: w/120 kg/min, w2100 kg/min, and w3 -200 kg/min. At that point, inlet flow rate w, is adjusted so that the level remains constant. However, on this particular day, corrosion of the tank has opened up a hole in the wall at a height of 1 m, producing a leak whose volumetric flow rate q4 (m3/min) can be approximated by:

940.025 Vh1

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 wi, wa, and w; are kept constant indefinitely, will the tank eventually. overflow? Justify your answer.