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….

## Derive the differential equation relating the liquid height h and the volume flow rate qi at the inlet.

Consider the single-tank liquid-level system shown in Figure 7.19, where the volume flow rate into the tank through a pipe is *q*_{i}. The liquid leaves the tank through an orifice of area *A*_{o}. Denote *C*_{d} 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 <>*C*_{d} <>1 because of friction effects. Derive the differential equation relating the liquid height *h *and the volume flow rate *q*i at the inlet. The tank’s cross-sectional area is constant. The density ρ of the liquid is constant.