Derive the transfer function H(s)/Q(s) for the liquid-level system of Fig. P51 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 Ris 0.5 ft/cfm. q. ft/min h(1) 2'ft FIGURE P51