Problem 5. Hydraulic system Consider the single-tank liquid-level system shown in the figure below, where the volume flow rate into the tank through a pipe is qi. A pump is connected to the bottom of the tank through a valve of linear resistance R1. The pressure of the fluid increases by Ap when crossing the pump. The liquid leaves the tank through a valve of linear resistance R2. Derive the differential equation relating the liquid height hand the volume flow rate q; at the inlet. The tank's cross-sectional area A is constant. The density p of the liquid is constant. Find the transfer function G1(s) = that relates the fluid height, h, to the flow rate into the pipe from above, q; (assuming Ap = 0). Find the transfer function G2(s)Q1(s)H(s)AP(s)that relates the fluid height to the pump pressure increase(assuming qi == 0).

Fig: 1

Fig: 2