Question

A wastewater is to be disinfected with 28 $mg/l$ of chlorine to obtain 99.9% kill of micro-organisms. The number of micro-organisms remaining at the time t is given by mathematical expression. $N_t=N_0{e}^{-0.13t}$ where $N_0$ is initial concentration of micro-organisms and t is time in minutes. The waste water flow rate is 0.015 $m^3/sec$ If the depth of chlorination tank is 1.5 m, the diameter of chlorination tank is 1.5 m, the diameter of chlorination tank is m.

• A. 6.3

Answer 1

The correct option is A 6.3
Efficiency of chlorination tank, $\eta =\frac{N_0-N_t}{N_0}=0.999$

$N_0-N_t=0.999N$

$N_t=0.001N_0$

$N_0{e}^{-0.13t}=0.001N_0$

t=53.14 minutes

Volume of tank= Qt
$=0.015\times 53.14\times 60m^3$
$=47.826m^3$

Let diameter of chlorination tank be d
$\frac{\pi }{4}{d}^2\times 1.5=47.826$
d=6.37 m