The caustic concentration of the mixing tank shown in figure is measured using a conductivity cell. The total volume of solution in the tank is constant at 7 ft3 and the density (? = 70 lb/ft3) can be considered to be independent of concentration, Let cm denote the caustic concentration measured by the conductivity cell. The dynamic response of the conductivity cell to a step change (at t = 0) of 3 lb/ft3 in the actual concentration (passing through the cell) is also shown in figure.

(a) Determine the transfer function Cm(s)/C1(s) assuming the flow rates arc equal and constant: (w1 = w2 = 5 lb/min):

(b) Find the response for a step change in c1 from 14 to 17 lb/ft3.

(c) If the transfer function C_m(s)/C?(s) were approximated by 1 (unity), what would be the step response of the system for the same input change?

(d) By comparison of (b) and (c), what can you say about the dynamics of the conductivity cell? Plot both responses, if necessary.

(ib/t?) AT 15 Time (s) 30