$12\mathrm{.}74$ 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 dis. solved$-$oxygen concentration greater than $2\mathrm{.}0m\frac{g}{l}.$ Verify or disprove these claims by appropriate calculations.