The following diagram shows a linked water tank system. Cold and hot water streams, with volume flow rates ( and ( in cm'/s respectively, are fed to the first tank where they are mixed, then passes to the second tank, and flows out from the second tank. The cross sectional areas of tanks 1 and 2 are 289 cm' and 144 cm respectively. The water flow rate (O) through a valve is proportional to the square root of the pressure drop across the valve (P), i.c. Q = kvP. If the pressure is measured as height of water in cm, then the unit of k is em /s. The maximum inlet flow rates for both Q. and ( are 120 cm /s. The flow rate Qa is usually at its nominal value 30 cm /s but is subject to variations. H Valve 1 Valve 2 I Tank I Tank 2 The following table shows a set of steady state process operation data. H (cm) H (cm) O. + 0. (em /s) 6.15 2.52 55.6 12.81 5.67 75.3 20.02 8.57 92.5 20.07 10.17 943 27.0 15.4 104.0 Write a report to cover the following 3 parts and upload it along with your SIMULINK file for part 2 to CANVAS. I ). Develop a dynamic model for the tank levels using material balance. Estimate the valve parameters ki and ka using the steady state operation data. Develop a simulation program for the tank levels using MATLAB/Simulink. Using the simulation, obtain the step response of /2 when Or is increased from $5 cm /s to 65 cm /s. Obtain an approximate first order transfer function from the step response