Mechanical Operations

Size-reduction energy is estimated from comminution laws — Kick’s for coarse crushing, Rittinger’s for fine grinding, and Bond’s (via the work index) for the intermediate range that covers most industrial mills.

Screening separates particles by size against an aperture, and classification separates by settling velocity in a fluid; performance is judged by screen efficiency and by the cut size d₅₀ at which a particle has equal chance of reporting to either stream.

Cake filtration is modelled by adding the growing cake resistance to a constant medium resistance; at constant pressure the filtrate volume follows a parabolic law, and plotting t/V against V linearises the data to extract specific cake resistance α and medium resistance R_m.

Gravity settling is governed by Stokes’ terminal velocity (valid only for particle Reynolds number below one), and a centrifuge simply replaces g with the far larger centrifugal acceleration rω², dramatically speeding separation of fine particles.

Fluidization occurs when upward gas velocity is high enough that the bed pressure drop equals the bed weight per unit area; beyond the minimum fluidization velocity the pressure drop stays constant while the bed expands and behaves like a boiling liquid.