CHEMICAL ENGINEERING

LIQUID MIXING 107

and: PD 0. 6 N^3 D^5 D 0. 6 ð 1000 ð 0. 3463 ð 0. 835 

D 9 .8W

c) In the smaller tank:ReDD^2 N/D 0. 12 ð 4. 17 ð 1000 / 1 ð 10 ^3 D 41700

In Equation 7.22, the dimensionless mixing time is:

mDNtmDkRe

or fortmD60s: 4. 17 ð 10 Dkð 41700

and: kD 0. 0060

Thus in the larger tank:NtmD 0. 0060 Re

or: 0. 346 tmD 0. 0060 ð 238 , 360 

and: tmD4140 s or 1.15 min

PROBLEM 7.8

An agitated tank with a standard Rushton impeller is required to disperse gas in a solution
of properties similar to those of water. The tank will be 3 m diameter (1 m diameter
impeller). A power level of 0.8kW/m^3 is chosen. Assuming fully turbulent conditions
and that the presence of the gas does not significantly affect the relation between the
Power and Reynolds numbers:

(a) What power will be required by the impeller?

(b) At what speed should the impeller be driven?

(c) If a small pilot scale tank 0.3 m diameter is to be constructed to test the process,

at what speed should the impeller be driven?

Solution

(a) Assuming that the depth of liquidDtank diameter, then:

volume of liquidDD^2 / 4 H

Dð 32 ð 3 / 4 D 21 .2m^3

With a power input of 0.8kW/m^3 , the power required be the impeller is:

PD 0. 8 ð 21. 2 D 17 .0kW

(b) For fully turbulent conditions andD1mNs/m^2 , and the power number, from

Fig. 7.6 is approximately 0.7. On this basis:

P/N^3 D^5 D 0. 7

or:  17. 0 ð 103 / 1000 N^3 ð 15 D 0. 7

from which: ND 2 .90 Hzor 173 rev/min