Q$2$ A rapid gravity filter is to be filled with three different media, as shown in Table Q$2$:

Table Q$2$

$($a$)$ Indicate which material should be placed in the bottom, middle and top layers. Provide reasons for your choice.

$($b$)$ Determine whether the particles would settle in the correct order after backwash. Show calculations to support your judgement and explain your reasoning clearly.

$($c$)$ Calculate the head loss $($loss of pressure$)$ through the garnet sand layer in the above filter during normal operation at $\backslash (15^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ with a filtration rate of $\backslash (10\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$h$\}\backslash ).$ Assume that the density of water is $\backslash (1000\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ),$ the absolute viscosity of water at $\backslash (15^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ is $\backslash (1\mathrm{.}139\backslash$times $10^\{-3\}\backslash$mathrm$\{$Ns$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash )$ and the dimensionless Kozeny constant may be taken as $6.$ Assume a shape factor $($sphericity$)$ of $0\mathrm{.}73$ and porosity of $0\mathrm{.}5.$

$($d$)$ Explain briefly the importance of head loss in filter operation.

$($e$)$ Name a long$-$established process which could provide a satisfactory alternative to rapid gravity filtration for potable water and explain briefly the main differences in the cleaning methods for the two filter types.