(Solved): 2. A liquid-level system is shown in Figure below. Two tanks have cross-sectional areas A1 and A ...

2. A liquid-level system is shown in Figure below. Two tanks have cross-sectional areas ${\mathrm{A}}_1$ and ${\mathrm{A}}_2$ where first tank is connected to pump through valve of resistance $R_1$ Liquid flows from tankl to tank 2 through valve of resistance $R_2$ while leaving tank 2 through valve of resistance $R_3$. Consider density is fixed and pressure above water is the same as the atmosphere. Derive the system dynamic equations. Consider the following information $(A_1=2{\mathrm{m}}^2,{\mathrm{A}}_2=3{\mathrm{m}}^2,{\mathrm{R}}_1={\mathrm{R}}_2={\mathrm{R}}_3=40\mathrm{m}/\left({\mathrm{m}}^3/\mathrm{s}\right)$, and initial heads of liquid in tanks are $h_1(0)=1\mathrm{m}$ and $h_2(0)=0\mathrm{m}$, initial pump head (at $=0$ ) is zero and it is $12\mathrm{m}$ after $\mathrm{t}=0)$ then: A. Derive differential equations in terms of liquid heads $h_1$ and $h_2$ B. Construct Simulink block diagram based on the received differential equations C. Draw the system response using MATLAB.