$[10$ points$]$

The owner of a company contacted your ENVE $662$ professor to design a chemostat, and the professor

has confidence in the students' ability to handle the task. As such, you have been tasked with designing

a chemostat for domestic wastewater, with the given kinetics parameters. The design should include

reporting the solid retention time $({}_x),$ outlet concentration of organic matter $(S),$ biomass concentration

$(x_V),$ and chemostat volume $(V).$ The professor is supportive and will provide hints to aid in the problem$-$

solving process.

Please assume that the inlet flow rate is equal to $10\frac{m^3}{d},S^0$ is equal to $500$mgBO$\frac{D}{L},$ Safety factor

$($SF$)$ is equal to $20,$ and there is no biomass in the inlet flow.

Step $1$: Find the amount of the minimum hydraulic retention time $(\{$:$x^{\text{m}\text{i}\text{n}})$ :

Step $2$: Find the amount of $S_{\text{m}\text{i}\text{n}}$

Step $3$: Find ${}_x$ by multiply the ${}_x$min to the SF$.$

Step $4$: Find the effluent substrate concentration $($S$)$

Step $5$: Find the volatile suspended solids concentration $(x_v)$

Step $6$: Find the volume of the chemostat $(V)-$ hint: there is no recycling flow in chemostat.

Well done! You just designed a reactor!