# The two-tank mixing process shown in Fig. P6.14 contains a recirculation loop that transfers…

The two-tank mixing process shown
in Fig. P6.14 contains a recirculation loop that transfers solution from tank 2
to tank 1 at a flow rate of (;Y q o.

(a) Develop a transfer function that
relates the concentration in tank 2, ~2, to the concentration in the feed, x;
i.e. Cz(s)/X(s) where C2 and X are deviation variables. For convenience, assume
that the initial concentrations are x = Cl = c2 = 0.

(b) If a unit-step change in x occurs,
determine the time needed for c2 to reach 60 percent of its ultimate value for
the cases where (Y = 0, 1, and 00.

(c) Sketch the response for (Y = 00. Assume
The two-tank mixing process shown
in Fig. P6.14 contains a recirculation loop that transfers solution from tank 2
to tank 1 at a flow rate of (;Y q o.

(a) Develop a transfer function that
relates the concentration in tank 2, ~2, to the concentration in the feed, x;
i.e. Cz(s)/X(s) where C2 and X are deviation variables. For convenience, assume
that the initial concentrations are x = Cl = c2 = 0.

(b) If a unit-step change in x occurs,
determine the time needed for c2 to reach 60 percent of its ultimate value for
the cases where (Y = 0, 1, and 00.

(c) Sketch the response for (Y = 00. Assume
that each tank has a constant holdup volume of 1 ft3. Neglect transportation lag
in the line connecting the tanks and the recirculation line. Try to answer parts
(b) and (c) by intuition.

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