Consider the single-tank liquid-level system shown in Figure 7.16, where the volume flow rate into the tank through a pipe is \(q_{\mathrm{i}}\). A pump is connected to the bottom of the tank through a valve of linear resistance \(R_{1}\). The pressure of the fluid increases by \(\Delta p\) when crossing the pump. The liquid leaves the tank through a valve of linear resistance \(R_{2}\). Derive the differential equation relating the liquid height \(h\) and the volume flow rate \(q_{\mathrm{i}}\) at the inlet. The tank's cross-sectional area is constant. The density \(ho\) of the liquid is constant.

FIGURE 7.16 Problem 4. giv Pa Ap A R Pa