The level and flow through a partially opened restriction (Valve) in the figure below is considered in this example. The system is the liquid in the tank and the important variables are the level and the flow out. The initial steady state conditions are (i) flows=F0 =F1=100m3/h and (ii) Level, L=7.0m. The crosssectional area is 7m2 a) State the assumptions for this system b) Carry out a mass balance on the system. Use. the relationship between the pressure drop across the valve and flow out. c) Perform a degree of freedom analysis for this system d) Linearize the model around the steady state conditions e) Bonus question: Compare the accuracy of the linearization for small (10m3/h) and large (60m3/h) step changes in the inlet flow