Answer the questions and show your steps.

The liquid storage tank shown in Figure 1 has two inlet streams with mass flow rates wi and uy 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/m4. Normal operating procedure is to fill the tank until the liquid level reaches a nominal value of 1.75 m using constant flow rates: 1 = 120 kg/min, ug = 100 kg/min, and wg = 200 kg/min. At that point, inlet flow rate way 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 on the side. 1. If the tank was initially empty, how long (in minutes) did it take for the liquid level to reach the corrosion point? 2. If loak volumetric flow rate 474 (m/min) is approximated by 44 = 0.025 - 1, what would be the equation describing the liquid height dynamics in the tank? 3. If mass flow rates, w, and us are kept constant indefinitely, what would be the maximum liquid height Amaz that could be attained in the tank? |Hint: you will need to use the concept of finding marimum or minimum value of a given continuous function, covered in Calculus. 4. Based on the given information, will the tank overflow at any point of operation? 94 Im Es Figure 1: The tank describing the process of Probleml