Q$1$ A grinding mill is required to grind quartz from a feed size of $5cm$ to a product size of $1cm.$ The work index of quartz is $15\mathrm{.}23kW\frac{h}{?}$ ton. Calculate the energy required to grind $50$ tons of quartz per hour.

Q$2$

A crusher is used to crush a material with an average particle size of $20mm$ to a final product with a particle size of $5mm.$ The power required to crush the material is found to be $10kW.$ Calculate the power required to crush the same material to a particle size of $2$ mm$.($Use bond's law$)$

Q$3$

A cylindrical column contains a bed of spherical solid particles with a total bed height of $1\mathrm{.}5$ meters. The density of the solid particles is $1500k\frac{g}{m^3}$ and the diameter of the particles is $0\mathrm{.}05$ meters. Air is used as the fluidizing medium. Determine the minimum fluidization velocity required to fluidize the bed.

Given:

Void fraction $()=0\mathrm{.}4$

Dynamic viscosity of air $()=1\mathrm{.}8{10}^{-5}k\frac{g}{m*s}$

Density of air $({}_0)=1\mathrm{.}2k\frac{g}{m^3}$