A height$-$time curve is recorded for a Type $2$ batch settling experiment which was carried out in a vertical graduated cylinder. The plot is shown in the following page. The initial concentration of the suspension in the cylinder is $0\mathrm{.}2$ m$^3/$m$^3.$Determine:

$($a$)$ the velocity of the interface between the clear liquid and the suspension concentration of $0\mathrm{.}2$ m$^3/$m$^3$

$($b$)$ the velocity of the interface between the clear liquid and the suspension concentration of $0\mathrm{.}48$ m$^3/$m$^3$

$($c$)$ the velocity of a layer of concentration of $0\mathrm{.}48$ m$^3/$m$^3$ propagates upwards from the base of the cylinder

$($d$)$ the concentration of the final sediment

$($e$)$ the velocity at which the sediment propagates upwards from the base