$($a$)$ Mention $5$ size separating equipment for solids moving in a fluid and elucidate on any two.

$($b$)$ The screen analysis of crushed quartz was carried out using $14$ mesh increaments. The density of quartz particle is $2,650k\frac{g}{m^3}(0\mathrm{.}00265\frac{g}{m}{m}^3).$ The shape factor, $a=2$ and spericity $\frac{O}{?}=0\mathrm{.}580.$

If the summation of quotient of mass fraction in a given increamem $($Xi$)$ to the average particle diameter $($ Dpi $)$ is $0\mathrm{.}9455m{m}^{-1},$ and the summation of quotient of mass fraction in a given increament $()$ to the cube of average particle diameter $(D{}^3)$ is $10\mathrm{.}2456m{m}^{-3}.10\mathrm{.}2456$ Calculate

$10\mathrm{.}2156m{m}^{-3}$

$($a$)$The specific surface area of the particles in $m\frac{m^2}{g}.($b$)$The number of particles in the m$...$

$($c$)$The volume mean diameter. $($d$)$Did the specific surface area of $($a$)$ meet up with the specification order of $4\mathrm{.}5{10}^{3}m\frac{m^2}{g}$