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 = 0.025√h – 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.

w2 w1 94 w3