Derive the transfer function H(s)/Q(s) for the liquid-level system of Fig. P5-1 when

(a) The tank level operates about the steady-state value of hs = 1 ft

(b) The tank level operates about the steady-state value of hs = 3 ft.

The pump removes water at a constant rate of 10 cfm (cubic feet per minute): this rate is independent of head. The cross-sectional area of the tank is 1.0 ft2, and the resistance R is 0.5 ft/cfm.

q. ft/min h(t) FIGURE P5-1 2 ft