Question

Problem 2. The concentration of sodium hydroxide is measured in a mixing tank using a conductivity cell (see figure below). The total volume of the tank (7 f3) is constant and the density (p-70 lb/ft3) of the solution can be considered independent of concentration. AT W, C a) Derive the first order transfer function C'(s)/C1?'(s) relating the concentration C of sodium hydroxide in the mixing tank to the concentration C1 entering the tank assuming the flow rates are equal and constant (wi-w2-5 lb/min). What are the values of the gain and time constant? Be sure to clearly show all of the step used to derive the transfer function and include all units b) Let Cm denote the concentration of sodium hydroxide measured by the conductivity cell. The dynamic response of the conductivity cell to a step change (at t-0) of 3 lb/f3 in the actual concentration (passing through the cell) is shown in the figure below. From the graph below, determine the first order transfer function for the process that related Cm to C. What are the values of the gain and time constant? Be sure to clearly show all of the steps used to derive the transfer function and include all units. (lb/ft3) 15 Time (s) 0 30

Answer 1

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