CHEMICAL ENGINEERING

106 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

PROBLEM 7.6

A reaction is to be carried out in an agitated vessel. Pilot-plant experiments were performed
under fully turbulent conditions in a tank 0.6 m in diameter, fitted with baffles and
provided with a flat-bladed turbine. It was found that satisfactory mixing was obtained
at a rotor speed of 4 Hz, when the power consumption was 0.15 kW and the Reynolds
number 160,000. What should be the rotor speed in order to retain the same mixing
performance if the linear scale of the equipment is increased 6 times? What will be the
power consumption and the Reynolds number?

Solution

See Volume 1, Example 7.3.

PROBLEM 7.7

Tests on a small scale tank 0.3 m diameter (Rushton impeller, diameter 0.1 m) have
shown that a blending process between two miscible liquids (aqueous solutions, prop-
erties approximately the same as water, i.e. viscosity 1 mN s/m^2 , density 1000 kg/m^3 )
is satisfactorily completed after 1 minute using an impeller speed of 250 rev/min. It is
decided to scale up the process to a tank of 2.5 m diameter using the criterion of constant
tip-speed.

(a) What speed should be chosen for the larger impeller?

(b) What power will be required?

(c) What will be the blend time in the large tank?

Solution

a) In the small scale tank, the 0.1 m diameter impeller is rotated at 250 rev/min or:

 250 / 60 D 4 .17 Hz.

The tip speed is then:DNDð 0. 1 ð 4. 17 D 1 .31 m/s

If this is the same in the large scale tank, whereDD 2. 5 / 3 D 0 .83 m, then:

1. 31 Dð 0. 83 ðN

from which the speed of rotation to the larger impeller,

ND 0 .346 Hzor 20.8 rev/min

b) In the large scale tank: ND 0 .346 Hz, DD 0 .83 m, D1000 kg/m^3

andD 1 ð 10 ^3 Ns/m^2.

Thus, ReDD^2 N/D 0. 832 ð 0. 346 ð 1000 / 1 ð 10 ^3 D 238 , 360.

From Fig. 7.6, for a propeller mixer, the Power number,NpD 0 .6.

Thus: 0. 6 DP/N^3 D^5