$(20$ pts$)$ Showing all your work and reasoning, find the volume of aeration tank in a water ireatment process. The water treatment plant with a completely mixed activated sludge system needs to meet an effluent standard of $20$ mg L of BOD and $15$ mg L $.$ of suspended solids, Before the activated slodge tank, there is a primary tank which has a flow rate of $0\mathrm{.}9m^{\frac{3}{\frac{?}{?}}s}$ and the effluent has BODs of $85$ mg L$.$ Using the assumptions provided, estimate the required volume of the aeration tank.

BODS of the effluent suspended solits is $80$ petcent of suspended solids concentration.

Growth constants are estimated to be: $Ks=100$mgIL. BOD $Kd=0\mathrm{.}070d-1$;$m=2\mathrm{.}5$ d$-1$; Y $=0\mathrm{.}5mg$ VSS$/$mg BODS remeved.

The design MIVSS is $2,000$ met

$ $=$ BODS allowed $-$ BODS in suspunded sultics