Consider the single-tank liquid-level system shown in Figure 7.19, where the volume flow rate into the tank through a pipe is qi. The liquid leaves the tank through an orifice of area Ao. Denote Cd as the discharge coefficient, which is the ratio of the actual mass flow rate to the theoretical one, and lies in the range of 0 <>Cd <>1 because of friction effects. Derive the differential equation relating the liquid height h and the volume flow rate qi at the inlet. The tank’s cross-sectional area is constant. The density ρ of the liquid is constant.
