Consider the rectangular tank in Figure 7.15a and the pyramid tank in Figure 7.15b. The volume flow rate into each tank through a pipe is \(q_{\mathrm{i}}\). The liquid leaves each tank through a valve of linear resistance \(R\). The density \(ho\) of the liquid is constant.

a. Derive the dynamic model of the liquid height \(h\) for each tank.

b. For each tank, write the differential equation in terms of hydraulic capacitance and hydraulic resistance. Compare the models for the two single-tank systems.

Transcribed Image Text:

FIGURE 7.15 Problem 3. b Pa 9i h H h a Pa qi R