Problem 1 (10 points): (Based on Problem B-7-3) At steady state, the flow rate throughout the liquid- level system is and the heads of tanks 1 and 2 are H, and H2, respectively. Att = 0, the inflow ate is changed to +q, where q is small. The resulting changes in the heads (h; and h2) and flow rates (91 and 92) are assumed to be small as well. The capacitance of tanks 1 and 2 are C1 and C2, respectively. The resistance of the outflow valves of tanks 1 and 2 are R, and R2, respectively. (a) Obtain the system equations corresponding to the capacitances C and C2 and the resistances Rand R2. Answer: Cza = q -91, C2h2 = 91 92, R1 = h/91, R2 = h2/92- (b) Obtain the ordinary differential equation for the system as a function of q (input) and q2 (output). Answer: C7C2RR292 + (CR1 + C2R2)92 +92 = 9 C) Obtain the ordinary differential equation for the system as a function of q (input) and hz (output). Answer: C1 C2 R1Rzhz + (GR1 + R2hz + hz = R29 =