$3.$ A settling column analysis is performed on a dilute suspension of particles from a water. The suspension exhibited discrete'particle settling characteristics. Data collected from samples taken at a depth of $1\mathrm{.}5$ m are as follows

$(4$ Marks$)$

a$)$ Plot the velocity distribution for the suspension.

b$)$ Find the overall removal if the surface loading rate of a clarifier is designed to be $\backslash (2400\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$m$\}^\{2\}/\backslash$mathrm$\{$d$\}\backslash ).$

c$)$ For a lab settling column with a height of $200$ cm $,$ find the concentration of solids at $25$ cm intervals in the column at $1$ min intervals using the above data. Report only the concentrations between $0$ to $175$ cm $.$ assume the suspension is uniformly distributed throughout the column at the initial time. The initial concentration of suspended solids is $\backslash (160\backslash$mathrm$\{$mg$\}/\backslash$mathrm$\{$h$\}\backslash ).$