Q$5$: From the control system for mixing$-$process tank shown below. Where: $q$ is volumetric flow rate $(\frac{m^3}{?}$ time$).$ Also, $x$ and $y$ are the concentrations of input and output. respectively $(Kmo\frac{l}{m^3}),v$ is liquid volume in the tank $(m^3).$

L$.$ Derive transfer function of single tank liquid level system. Draw a suitable sketch.

II$.$ Sketch the Block Diagram for the system, which include:

Controller and Final control element $($PI controller $G_1(s)=($:$\frac{K_8(r_{1}s+1)}{s}\}.$

Process of single tank liquid level system derived in part $1$