w2 wi C2 C1 Cm 2 (Ib/ft³) Cm AT 1 15 30 Time (s) 3.
The caustic concentration of the mixing tank shown in Fig is measured using a conductivity cell. The total vol-ume of solution in the tank is constant at 7 ft3 and the density(ρ=70 lb/ft3) can be considered to be independent of concen-tration. 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 concen-tration (passing through the cell) is also shown in Fig. (a)Determine the transfer function C′m(s)∕C′1(s) assuming that the flow rates are equal and constant: (w1=w2=5 lb/min).(b)Find the response for a step change in c1from 14 to17 lb/ft3.(c)If the transfer function C′m(s)∕C′(s) were approximated by1 (unity), what would be the step response of the system forthe 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.
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