2. Three tanks of water are attached in series as shown below. All three tanks have the same constant cross sectional area (A). The flow rate through the valves is a function of the height of water in the tanks; for example the flow rate of water through the first valve, F1, is proportional to the difference in water heights between tanks 1 and 2. The first and the third tanks are initially full (h = ht) and the middle tank is initially empty. a) Perform mass balances on each of the three tanks and develop a model for the rate of change of liquid height in each tank. Do not solve the equations! b) Develop a system of equations for the steady state heights in the tanks. c) Write these three mass balances as a matrix equation A h = b and identify all terms in the vector h and matrix A. Leave them in terms of the variables of the problem. d) Using the data below, solve the system of coupled equations for the steady state h using Gauss Elimination method (hand calculation is sufficient). F h, -h System Data: R A = 5 m, fo = 5 m/hr, h-h Ri= 2 hr/m, R2 = 1 hr/m2, F R3 = 1 hr/m R2 F1 h2 F2 F where R are constants. R Fo FLOH. hi