A process tank has two input streams—Stream 1 at mass flow rate F1 and Stream 2 at mass flow rate F2. The tank’s effluent stream, at flow rate F, discharges through a fixed valve to atmospheric pressure. Pressure drop across the valve is proportional to the flow rate squared. The cross-sectional area of the tank, A, is 5m2, and the mass density of all streams is 940 kg/m3.
(a) Draw a schematic diagram of the process and write an appropriate dynamic model for the tank level. What is the corresponding steady-state model?

(b) At initial steady-state conditions, with F1 =2.0 kg/s and F2 =1.2 kg/s, the tank level is 2.25 m. What is the value of the valve constant (give units)?