A filter bed has the following properties:

$$ Flow $($Q$)$ of $8,000$ L$/$min

$$ Surface area $($As$)$ of $40$ m$2$

$$ Specific deposit at breakthrough $($sigma B$)$ of $1,000$ mg$/$L

$$ Filter media depth $($L$)$ of $1\mathrm{.}8$ m

$$ Average influent concentration $($Co$)$ of approximately $2\mathrm{.}5$ mg$/$L

$$ Average effluent concentration $($Ce$)$ of approximately $0$ mg$/$L

a$.$ Calculate the filtration rate $($Vf$).$

b$.$ Estimate how long the filter bed can operate before breakthrough occurs $($tB$).$