Figure 7.18 shows a liquid-level system in which two tanks have cross-sectional areas A1 and A2, respectively. The volume flow rate into tank 1 is qi. A pump is connected to the bottom of tank 1, and the pressure of the fluid increases by Δp when crossing the pump. Tank 2 is located higher than tank 1, and the vertical distance between the two tanks is H. The liquid is pumped from tank 1 to tank 2 through a valve of linear resistance R1 and leaves tank 2 through a valve of linear resistance R2. The density ρ of the liquid is constant. Derive the differential equations in terms of the liquid heights h1 and h2. Write the equations in second-order matrix form.
