Particulate is partially removed from a wastewater stream using a Type $1$ rectangular sedimentation basin $($Fig $1),$ with depth of $2\mathrm{.}5$ m$,$ width of $5$ m$,$ and length of $40$ m$.$ The settling velocity and concentration of particulate are as follows:

a$)$ Calculate the efficiency of the sedimentation basin and the concentration of

particles in the treated water.

To improve the efficiency of the separation, you want to analyze the effect of recycling

partially the treated water $($Fig$.2),$ to increase the retention time and to improve the

removal of particulate.

b$)$ Calculate the expected efficiency for a recycle ratio of $0\mathrm{.}5($recycle flowrate$/$inlet

flowrate $=0\mathrm{.}5).$

c$)$ Graph the efficiency versus the recycle ratio $(0$ R

d$)$ Analyze briefly your results considering the effect of increasing the recycle ratio on

the critical velocity.

Tip: Define clearly your nomenclature $($for example, you can identify each stream with a

number$),$ and apply the corresponding mass balances in terms of the recycle ratio.