Question

The separation of solid particles into different fractions based upon their terminal velocities in a liquid is called hydraulic classification. For example, consider two particles with different settling velocities placed in a rising current of water. If the water velocity is adjusted to a value between the terminal settling velocities of the two particles, a separation will result: the slower- settling particle will move upward with the water while the faster settling particle will settle out to the bottom.

A mixture of ground galena and limestone with specific gravities of 7.5 and 2.7, respectively, is to be separated by hydraulic classification using water at a velocity of 0.01 ms-1 and at a temperature of 20 C. The solid feed contains 20% Galena and 80% limestone on a dry mass basis and the following size analysis is applicable to both solids:

Diameter (um) 20 40 60 80 100 120 140 160 180

CUS (mass)% 33 53 67 77 83 88 91 93 100

Assuming free settling condition and spherical particles, calculate:

a. The size ranges of galena and of limestone particles that will be carried away in the water stream.

b. The mass fractions of galena and limestone in the overhead and bottom streams leaving the classifier.

c. Would it be possible to obtain pure galena in the bottom stream with water as the classifying fluid? If yes, what would be the water velocity required, and the product size range be? Show calculations to support your answers.

Answer 1

solution (A)

To obtain the size range of the gelena and limestone particle we have to calculate the terminal velocity of the both particles

the particle with terminal velocity less than the velocity of the fluid will be carried away

let the fluid be water of density 1000 kg/m³ and the particles are settling in the stokes law regime

V_T = [gD_p²(_p - _l)]/18

where viscosity of water is 1 cp and g = 9.81 ms^-2

calculating D_p of particle for the terminal velocity equal to the velocity of the fluid (0.01 ms^-1)

for gelena D_p = 1.68 x 10^-4 m

above this size gelena particle will settle down and below this size the gelena particle will carried away with water

for limestone D_p = 3.28 x 10^-4 m

above this size limestone particle will settle down and below this size the limestone particle will carried away with water

Solution (B)

more data is required or data is not cleared

Solution (C)

yes we can obtain pure gelena in the bottom by reducing the velocity of the water

the velocity of the water should be choosen as the velocity of the smallest particle of the heaviest (gelena) material shoul be greater than the velocity of the upstream water

smallest particle of gelena 20 x 10^-6 m

V_T = 1.417 x 10^-4 ms^-1  

the velocity of the water should be less than the above value