QUESTION $6)$

A river has a heavily$-$polluted discharge of wastewater from industrial area entering it at a flow rate

of $0\mathrm{.}5m\frac{3}{s}$ as shown in Figure $1.$ The $5-$day BOD and DO of this discharge at $18\mathrm{.}70C$ are $168m\frac{g}{L}$

and $1\mathrm{.}9m\frac{g}{L}$ respectively. The river flow upstream of the discharge may be taken as $5\mathrm{.}6m\frac{3}{sec}$ and

have a $5-$day BOD of $2\mathrm{.}4m\frac{g}{L}$ and DO of $7\mathrm{.}4m\frac{g}{L}$ at $15\mathrm{.}60C.$ The river may be taken as having a

width of $11m$ and a depth of flow of $1\mathrm{.}5m$ in a rectangular channel. The following information is

derived from the laboratory results and river field survey: o Deoxygenation constant $(K1)=0\mathrm{.}33$ day$-1$

at $200$ C $($e$-$base$)$ o Reaeration constant $($K$2)=0\mathrm{.}57$ day$-1$ at $200C($e$-$base$)$ o K$1$ and K$2$ at temperature

$T$ can be changed using the following equations:

$K_{1,T}=K_{20}(1\mathrm{.}135{)}^{(T-20)}$

$K_{2,T}=K_{20}(1\mathrm{.}024{)}^{(T-20)}$

Assume there are no other discharges downstream.

Current discharge condition:

a$)$ Calculate DOM, BODM, initial DO deficit $($DO$),$ ultimate BOD, and BOD$5$ loading rate $($kg$/$day$)$ at the

mixing point.

b$)$ Calculate the distance downstream $($xc$)$ where the minimum dissolved oxygen concentration will

occur and show it in the graph of DO concentration against distance downstream.

c$)$ Provide the table for DO concentration against distance downstream $($DO Sag curve$)$ including DO

deficit, Dc$,$ DOmin, Tc$,$ and $x_c$ for the first $220km$ downstream of the mixing point.

d$)$ Construct a clearly$-$labelled DO Sag curve $($plotted with a point and value of DOmin, Dc$,$ and Tc$)$ of

DO concentration against distance $(km)$ downstream from the mixing point for the first $220km$

downstream of the mixing point, making clear the values of all the parameters you have used.