As a metallurgist, you are required to sizing hydrocyclones for a ball mill circuit. Target overflow particle size is $80\%$ passing $105\backslash$mu m$.$ The pressure drop across the cyclone is $30$ kPa. Slurry feed rate is $2,000$ m$3$ h$-1.$ Slurry is $56\%$ by weight of solids with the solid specific gravity of $4\mathrm{.}0.$ Using the Arterburn technique,

a$)$ Select the size of Krebs cyclones.

b$)$ Determine the number of cyclones required to meet the capacity.