1. (100 pts.) Consider the three-tank arrangement as shown in the figure below. The crosssectional areas of the tanks are A1,A2, and A3, respectively. (a) Find the transfer function G1(s) describing the effect of input v1 on output h1. Express the result in terms of the gain and the appropriate time constant. (b) Find the transfer function G2(s) describing the effect of input v2 on output h2. Express the result in terms of the gain and the appropriate time constant. (c) Find the transfer functions G31(s) and G32(s) describing the effect of inputs h1 and h2 on output h3. Express the results in terms of the gains and the appropriate time constants. (d) Sketch the block diagram of the three-tank system. (e) Using the block diagram of part (d) and the results of parts (a)-(c), find the transfer functions G~1(s) and G~2(s) describing the effect of inputs v1 and v2 on output h3. Express the results in terms of the gains and the appropriate time constants