Problem 6. Hydraulic System Consider the two-tank liquid-level system shown in the figure below. The liquid is pumped into tanks 1 and 2 through valves of linear resistances Rị andR2,

respectively. The pressure of the fluid increases by Ap when crossing the pump. The cross-sectional areas of the two tanks are A1 and A2, respectively. The liquid flows from tank 1 to tank 2 through a valve of linear resistance R3 and leaves tank 2 through a valve of linear resistance R4. The density p of the liquid is constant. Derive the differential equations in terms of the liquid heights h, and h2. Write the equations in second-order matrix form.