Q$.1$ Set. $($A$)$

A pond with a single inflow stream has the following characteristics:

Volume $=4{10}^5{m}^3$; Residence time $=9$ days; Inflow BOD concentration in the stream $=10m\frac{g}{L}$

A residential project is planned for $500$ people in pond catchment. Each individual contributes about $0\mathrm{.}5m^3$ per day of wastewater and $120\frac{g}{?}$ day of BOD $($UBOD$).$

a$.$ Write a mass$-$balance equation for BOD for this system.

$[1$ Mark$]$

b$.$ If the BOD decays at a rate of $\frac{0\mathrm{.}23}{?}$ day and settles at a rate of $0\mathrm{.}12\frac{m}{?}$ day, calculate the assimilation factor for the pond prior to the construction of the residential project $($without the sewage contribution from the housing project$)?$ Which of the purging mechanisms $($Flushing$/$ decay$/$settling$)$ is most effective? List them in decreasing order of effectiveness.

$[6$ Marks$]$

c$.$ Calculate the transfer function factor after construction of the residential project?

$[2$ Marks$]$

d$.$ Determine the steady$-$state concentration for the lake with and without the construction of the residential project?

$[3$ Marks$]$