Water is flowing unidirectionally through a porous medium with an overall diameter of $0\mathrm{.}25$ m at a constant flow rate of $1$ mL$/$s$.$ If a tracer is introduced at the inlet as a step change, then $($i$)$ calculate the time required $($in hrs up to two decimal place$)$ for the concentration at the outlet to reach $95\%$ of the inlet concentration from the instance the step change was introduced at the inlet. $($ii$)$ plot concentration at the outlet as a function of cumulative flow.

Assume a dispersion coefficient of $10-6$ m$2/$s$,$ length of the porous system as $4$m$,$ porosity of the porous medium as $0\mathrm{.}2.$