Q$2.(20$ marks$)$

A liquid storage tank shown in below figure has $2$ inlet streams with mass flow rates $w_1$ and $w_2$ and an exit stream with flow rate $w_3.$ The cylindrical tank has a diameter of $2m.$ The liquid has a density of $800k\frac{g}{m^3}.$ Normal operating procedure is to fill the tank using constant flowrates of $w_l=120k\frac{g}{m}in,w_2=100k\frac{g}{m}in$ and $w_3=200k\frac{g}{m}in.$ Develop a model for this process and mention the controlled variable. If the tank is initially empty, how long did it take for the liquid level to reach a height of $1m?$ Draw a FB an FF controller for this process and mention the manipulated variable and measured variable.