An activated sludge system is operating with the conditions described below. The conditions include the average influent flow, aeration tank volume and MLSS concentration, return activated sludge flow recycle ratio and TSS concentration, and the secondary clarifier effluent TSS concentration. Wasting is from the return activated sludge line leaving the bottom of the secondary clarifier.

$($a$)$ What should be the average daily waste sludge rate in m$3/$d to maintain an SRT of $10$ d$?$

$($b$)$ The plant operator decides to waste $1/10$th of the aeration volume each day to maintain the SRT$.$ What is the waste volume in m$3/$d and what is the actual SRT$?$

Given: Flowrate $=4000$ m$3/$d

Aeration tank volume $=2000$ m$3$

Aeration tank MLSS concentration $=3000$ mg$/$L

Clarifier effluent TSS concentration $=10$ mg$/$L

Return sludge recycle ratio $=0\mathrm{.}5$ unitless

Return sludge TSS concentration $=9000$ mg$/$L