$l\frac{b}{h}r,$ DO in summer $=0\mathrm{.}87m\frac{g}{L}$ per eq $12\mathrm{.}102,$ not ok in summer$)$

$12\mathrm{.}74$ A completely mixed aerated lagoon with a volume of $1\mathrm{.}0$ mil gal treats a daily wastewater flow of $250,000$gal with a BOD of $400m\frac{g}{1}.$ The liquid temperature ranges from $4C$ in the winter to $30C$ in the summer. There are four $5\mathrm{.}0-$ hp surface aerators rated at $2\mathrm{.}0lb$ of oxygen $\frac{?}{hp}*hr.$ The wastewater characteristics are $=1\mathrm{.}035,=0\mathrm{.}9,=0\mathrm{.}9,k=0\mathrm{.}80$ per day at $20C,$ and $a=1\mathrm{.}0lb$ of oxygen utilized$/$lb of BOD removed. The designer states that this system will remove at least $400lb$ of BOD$/$day and maintain a dissolved$-$oxygen concentration greater than $2\mathrm{.}0m\frac{g}{l}.$ Verify or disprove these claims by appropriate calculations.

Example $12\mathrm{.}73$

An aerated lagoon with a $10-ft$ depth and liquid volume of $175,000cu.ft.$ treated an average of $0\mathrm{.}20mgd$ wastewater with a BOD of BOD$/$day$).$ The anticipated temperature extremes the aerating wastewater range from $10C$ in winter to $30C$ in summer. The two $15-$hp surface aerators recommended for adequate mixing and oxygenation have themanufacturer's guarantee to provide an oxygen transfer of $2\mathrm{.}5l\frac{b}{h}p*hr$ under standard conditions. Based on laboratory treatability studies, the wastewater has the following characteristics: $k_{20}=0\mathrm{.}68$ per day, $=1\mathrm{.}047,=0\mathrm{.}9,=0\mathrm{.}8,$ and an oxygen utilization rate of $1\mathrm{.}0lb$ of oxygen to satisfy $0\mathrm{.}8lb$ of BOD removal. Ts the lagoon adequately sized? For a minimum BOD reduction of $75\%,$ is the aeration capacity adequate?

At $10C,B00$ veduction Controls!

$t_{\text{d}\text{e}\text{t}}=\frac{V}{Q}=\frac{175,0007\mathrm{.}48}{200,000}=6\mathrm{.}55$ days

$eq\mathrm{.}12-100K_{10}=0\mathrm{.}68(1\mathrm{.}047{)}^{10-20}=0\mathrm{.}43d^{-1}$

$eq\mathrm{.}12-99\frac{L_e}{L_0}=\frac{1}{1+K_t}=\frac{1}{1+(0\mathrm{.}43)(6\mathrm{.}55)}=0\mathrm{.}26$

BOD reduction $=74\%$~~$75\%$

probably $0.K.$

$]=\frac{36\mathrm{.}416}{h}v>36[$ transich

At $30C,O_2$ transfer controls!

Required removal $=0\mathrm{.}75(920)=690$bBO$\frac{D}{d}ay$

Requived oxygen $=\frac{690\text{l}\text{b}\text{B}\text{O}\frac{D}{d}}{0\mathrm{.}816BO\frac{D}{1}lb.O_2}=862\mathrm{.}5\frac{\text{l}\text{b}\text{O}}{a}2(\frac{1}{24})$

$=()2$

manufacturers Data

$R=R_0\frac{C_s-C_4}{9\mathrm{.}2}{1\mathrm{.}02}^{T-20}$

$R=(2\mathrm{.}5)[\frac{0\mathrm{.}8(7\mathrm{.}6)-2}{9\mathrm{.}2}]{1\mathrm{.}02}^{30-20}0\mathrm{.}9$

$=1\mathrm{.}22l\frac{b}{h}p*hr215$

$R=36\mathrm{.}4l\frac{b}{h}r>R_{\text{m}\text{i}\text{n}}=36oK.$