A process tank has two input streams—Stream 1 at mass flow rate w1 and Stream 2 at mass flow rate w2. The tank’s effluent stream, at flow rate w, 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 5 m2, 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 w1 = 2.0 kg/s and w2 = 1.2 kg/s, the tank level is 2.25 m. What is the value of the valve constant (give units)?

(c) A process control engineer decides to use a feed- forward controller to hold the level approximately constant at the set-point value (h = 2.25 m) by measuring w and manipulating w2. What is the mathematical relation that will be used in the controller? If the w1 meseiremer1t is not very accurate and always supplies a value that is 1.1 times the actual flow rate, what can you conclude about the resulting level control?