4_2

  In the following figure is a system of two water tanks. Mass flow into the top tank at a fixed rate q0 and exits this tank through an orifice of area A1. This exit water then flows into a second tank which has an orifice of area A2 at its bottom. Each tank has constant cross section of area A, with A>>A1,A2. (a) Determine the ODE model which governs the heights z1 and z2 of water in the system. (b) Determine the equilibrium given a fixed rate q0. (c) Linearize the system model about the equilibrium. (d) Compare the step responses of the nonlinear model and linearized model by choosing reasonable system parameters. ( (b) Plot the flow v.s. pressure drop curve with the estimated c to validate your estimation