Question

A wastewater is to be disinfected with $35mg/L$ of chlorine to obtain 99% kill of micro-organisms. The number of micro-organisms remaining alive $\left(N_t\right)$ at time $t$, is modelled by $N_t=N_0{e}^{-kt}$, where $N_0$ is number of micro-organisms at $t=0$, and $k$ is the rate of kill. The wastewater flow rate is $36m^3/h$, and $k=0.23{min}^{-1}$.
If the depth and width of the chlorination tank are $1.5m$ and $1.0m$, respectively, the length of the tank (in m, round off to 2 decimal places) is

• A. 8.0089

Answer 1

The correct option is A 8.0089
For 99% kill of microorganisms

$\eta =\frac{N_0-N_t}{N_0}=0.99$

$N_T=0.01N_0$

${\mathrm{N/}}_0{e}^{-kt}=0.01{\mathrm{N/}}_0$

$-Kt\ell ne=\ell n0.01$

$0.23t=-4.605$

$t=20.022min$

Volue of tank req. = Q.t

$=36\frac{m^3}{hr}\times 20.02min$

$=\frac{36\times 20.02}{60}{m}^3$

$=12.012m^3$

$\text{length}=\frac{\text{V}}{\text{depth}\times \text{width}}$

$=\frac{12.012}{1.5\times 1}=8.0089m$