Find the concentration profile $(C$ versus $x)$ for the modeling application example in the book section $2\mathrm{.}3$ considering:

$Q=2832m\frac{3}{}$second

$W=372Ib\frac{s}{d}ay$

$A=93000m2$

$K=0\mathrm{.}1$ day$-1$

Remember:

$C_0=\frac{W}{EA(g-j)}$

$C=\frac{W}{Q}{e}^{gx}$ for $x0$

$C_0=\frac{W}{EA\{[\frac{U}{2E}(1+)]-[\frac{U}{2E}(1-\text{p}\text{r}\text{o}\text{p})]\}}$

$C=\frac{W}{Q}{e}^{jx}$ for $x0$

$C_0=\frac{W}{}Q$

Use Streeter$-$Phelps equation to find DO concentration profiles $(C$ versus $t,C$ versus $x)$ for a river considering:

Upstream BOD value upon mixing $=15\mathrm{.}00m\frac{g}{L}$

Saturated dissolved oxygen $=10\mathrm{.}00m\frac{g}{L}$

Initial oxygen deficit $=2\mathrm{.}2m\frac{g}{L}$

Re$-$aeration coefficient $0\mathrm{.}55$ day $-1$

Deoxygenation coefficient $=0\mathrm{.}4$ day$-1$

Stream velocity $=0\mathrm{.}20\frac{m}{s}$

Find $t_{\text{c}\text{r}\text{i}\text{c}\text{a}\text{l}}$ at DO concentration at the critical $($lowest DO$)$ point downstream.

Both numerical and algebraic solution is acceptable. Show all your calculations.

Hint: The use of an integration factor is needed, see the attached document.

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