ASSIGNMENT:

1. The two-tank mixing process shown contains a recirculation loop that transfers solution from tank 2 to tank 1 at a flow rate of qo . (a) Develop a transfer function that relates the concentration c2 in tank 2 to the concentration x in the feed, that is, C2(s)/X(s) where C2 and X are deviation variables. For convenience, assume that the initial concentration c2 = 0. (b) If a unit-step change in X occurs, determine the time needed for c2 to reach 0.60 for the case where =0.

a) C2(s) = 1 X(s) [s2/(1+ )] +2s + 1

b) t = 2 mins.

2. A thermometer having a time constant of 0.1 min is at a steady state temperature of 900F. At time t = 0, the thermometer is placed in a temperature bath maintained at 100F. Determine the time needed for the thermometer to read 980F. (Ans. 0.16 min)

3. A mercury thermometer, which has been on a table for some time, is registering the room temperature, 75F. Suddenly, it is placed in a 400F oil bath. The following data are obtained for the response of the thermometer. Give an estimate of the thermometer time constant. (Ans. 10 s)

Time, s Thermometer Reading, 0F

0 75 1 107

2.5 140 5 205 8 244 10 282 15 328 30 385

(1 + )qo