Appelpolscher and Arrhenius Quirk, head of IGC?s Chemical Kinetics and Reactor Design Group) are engaged in a dispute concerning the model developed earlier for the inadequately agitated reactor (Exercise 2.7). Quirk, who really likes to beat Appelpolscher at his own game, is attempting to combine the two differential equations in the model into a single equation relating outlet composition (c_T) to inlet tracer composition (c_T1). Quirk wants to analyze the resulting expression to be sure that it makes physical sense in the limiting cases. However1 derivatives always gave Quirk trouble, and he is having a bad time with the calculus. Appelpolscher, in an unusual fit of magnanimity, has offered to help out. He personally is sold on the idea of transfer function analysis, but is having his own troubles with the algebra. After several hours of wrestling with their individual methods, both decide that supervising other people is more productive than working. They dump the problem in your lap with the following specific

(a) Find suitable dynamic relations for both c_T and c_T1 in terms of input en only. (Appelpolscher suggests that, since you report to him, they ought to be transfer functions.)

(b) For the situation V₁ = ?_V (0 ? 1), evaluate the limiting cases of your dynamic relations for

(b) For the situation V1 = ?V (0

(c) For each case (i?iv), explain how the system dynamics are affected in the limit and discuss how this relates to the physical situation.

(d) Determine whether this system is overdamped or underdamped and whether it can exhibit overshoot or inverse response.

(e) Determine mathematical relations for c_T(t) and c_T1(t) it c_Ti(t) is a rectangular pulse of magnitude h and width . Under what circumstances could the pulse response of this system be approximated reasonably well by the impulse response?

Transcribed Image Text:

(i) y-0 (ii) qR -0 (iv) qR co