The sludge used to thicken has a solid concentration equal to C$0=4\%.$ The thickening method is to use a centrifuge to thicken until the output concentration is CE $=10\%.$ However, from the centrifuge process, the solid concentration will increase from $4\%$ to $20\%,$ so engineers designed the system to bypass some Feed Sludge in order to dilute $($Dilute$)$ the concentrated sludge $($Dewatered$)$ to leave the output concentration equal to $10\%.$

Asked what flow rate must be bypassed the sludge?

Assume that the sludge concentration is $1$ g$/$cm$3.$ Wastewater flows in with a flow rate $($Q$0)$ equal to $4$ l$/$min at a solid concentration of $4\%.$ From the Centrifuge process, clear water $($Centrate$)$ with a solid concentration $($CC$)$ will be obtained. at $0\mathrm{.}1\%$ and the cake layer $($Cake$)$ with a high solid concentration $($CK$)$ is at $20\%$