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[Jack188817]

Hi there.

I have a problem that I cannot figure out why the answer is such.



It is to do with a cuboid shaped particle with dimensions say : 1 cm: 5 cm: 20cm.

I know that the sieve equivalent sphere diameter passing the same sieve aperture is is 4.24 cm, but I am not sure as how to achieve this value.

For spheres and cubes I know that the sieve diameter is equal to the diameter of the cube/sphere, but it is the shape that is confusing me.


Any pointers would be much appreciated.

Thanks,
Jack
Chemical Engineering Student

Edited by Jack188817, 07 November 2011 - 06:47 AM.

[kkala]

"Ideally, a particle would have the greatest chance of passing through the screen if it stuck the surface perpendicularly, if it were so oriented that is minimum dimensions were parallel with the screen surface, if it were unimpeded by any other particles , and if it did not stick to, or wedge into, the screen surface. None of these conditions applies to actual screening, but this ideal situation can be used as a basis for estimating the effect of mesh size and wire dimensions on the performance of screens".
W McCabe, J Smith, P Harriot, "Unit Operations of Chemical Engineering", 5th edition (1993), Mechanical Separators, p. 1001.
An interpretation of the above could say that "equivalent diameter" of 1cm x 5cm x 20cm cuboid particle would be 5 cm, seeing that such a particle in perpendicular position could pass through a 5 cm x 5 cm opening.
The probability of the cuboid to be in perpendicular position is already quite low. If we additionally assume that the cuboid enters the opening diagonally (i.e. its 5 cm edge parallel to the diagonal of the opening), the cuboid can pass through a square opening of 5+2*0.5=6 cm diagonal, thus the side of the opening 6/sqrt(2)=4.24 cm (see attached opening.doc). In this sense equivalent diameter would be 4.24 cm, but probability of the cuboid to meet the proper position to pass from 4.24 cm opening would be close to zero. In practice a larger screen opening (aperture) has to be applied, also taking screening time into account.
The proper screen opening could be determined experimentally; probably a rough estimate could assume that the cuboid has to lift up enough (by screen shaking) to form a slope of 45 o, so the opening has to be 20*cos45o = 14 cm. This depends on the residence time on the screen, on cuboid physical properties, on what sizes are to be separated by screening. Size of 1 cm x 5 cm x 20 cm is supposed to be reported as an example, actual size may be smaller.
Having limited theoretical knowledge plus seen operation of industrial screens, above is only an opinion (hopefully a bit useful), seeing that the query has not received answers.

Note: Examples from other books indicate that "equivalent diameter" of an irregular shaped particle does not always correspond to minimum of maximum dimension.

Attached Files

•  opening.doc   21KB   52 downloads

Edited by kkala, 11 November 2011 - 01:23 PM.