A stormwater bioinfiltration system $(1$ m deep, $2$ m wide and $2$ m length$)$ contains filter layer as a mixture of sand and soil with the following properties: porosity $0\mathrm{.}39,$ bulk density $2\mathrm{.}1$ g$/$cm$3,$ and foc $0\mathrm{.}1\%.$ The hydraulic conductivity of the media layer is $1\mathrm{.}5$ cm$/$min$.$ During a rainfall, the filter media becomes quickly saturated and develop a head equal to its depth; that is hydraulic gradient is $1.$

a$)$ Estimate the velocity of water $($Darcy$$s$)$ exiting the bioinfiltration system at the bottom.

b$)$ If it receives a contaminant with Koc of $2\mathrm{.}2$ cm$3/$g$,$ what would be the velocity of the contaminant plume?

c$)$ Calculate the time $($min$)$ required for the contaminant to migrate from the surface to bottom of the bioinfiltration system.

d$)$ To slow down the contaminant migration, you have added a compost layer $(0\mathrm{.}1$ m deep$)$ that has foc $=25\%.$ Assuming the porosity and bulk density of compost layer as $0\mathrm{.}4$ and $1\mathrm{.}3$ g$/$cm$3,$ what would be net travel time $($min$)$ of contaminant in the modified bioinfiltration system? $($assume that hydraulic conductivity of compost is same as that of sand$).$

e$)$ To effectively remove the organic contaminants, the average travel time of contaminant in biofilter must be $4$ h$.$ What should be foc to ensure contaminant travel time is $4$ h$?$