$($b$)$ A cyclone is used to separate particulate material from air. The cyclone has specifications of: body diameter $=1m,$ height of inlet

$=15cm,$ width of inlet $=15cm,$ length of cone $=1\mathrm{.}2m,$ length of body $=1\mathrm{.}8m.$ Flow rate of air$-$particulate mixture is $200m\frac{3}{m}in.$ Density of the particle is $1800k\frac{g}{m^3}.$ Density and viscosity of air are $1\mathrm{.}204k\frac{g}{m}3$ and $1\mathrm{.}81{10}^{-5}k\frac{g}{m}.s.$

Particle size distributions are as follows:

$\begin{array}{cc}\text{P}\text{a}\text{r}\text{t}\text{i}\text{c}\text{l}\text{e}\text{s}\text{i}\text{z}\text{e}(dp)inm& \%\text{m}\text{a}\text{s}\text{s}in\text{t}\text{h}\text{a}\text{t}\text{s}\text{i}\text{z}\text{e}\text{r}\text{a}\text{n}\text{g}\text{e}(\frac{m}{M})\\ 0-2& 1\\ 2-4& 9\\ 4-6& 10\\ 6-10& 30\\ 10-18& 30\\ 18-30& 14\\ 30-50& 5\\ 50-100& 1\end{array}$

Calculate collection efficiencies and contribution to performances of each particle size range.