Question

$16$ MLD of water is flowing through a $2.5km$ long pipe of diameter $45cm$. The chlorine at the rate of $32kg/d$ is applied at the entry of this pipe so that disinfected water is obtained at the exit. There is a proposal to increase the flow through the pipe to $22$ MLD from $16$ MLD. Assume the dilution co-efficient $n=1$. The minimum amount of chlorine (in kg per day) to be applied to achieve the same degree of disinfection for the enhanced flow.

• A. $44.00$
• B. $60.5$
• C. $23.27$
• D. $38$

Answer 1

The correct option is B $60.5$

In the disinfection process we have the relationship

$t{C}^n=K$

Where
t= time required to kill all organisms.
C= concentration of disinfectant
N = dilution coefficient
K= constant

$\Rightarrow t_1{C}_1^n=t_2{C}_2^n$

In our case n =1

$\Rightarrow t_1{C}_1=t_2{C}_2$

$t_1=\frac{L}{v_1}$

L= length of pipe
$V_1=$Velocity of flow

$t_1=\frac{L}{Q_1/A}$

$t_1=\frac{LA}{Q_1}$

$C_1=\frac{W_1}{Q_1}$

where $W_1$= weight of disinfectant per day

$Q_1$= discharge per day

$\Rightarrow \frac{LA}{Q_1}\times \frac{W_1}{Q_1}=\frac{LA}{Q_2}\times \frac{W_2}{Q_2}$

$\Rightarrow W_2=\frac{Q_2^2}{Q_1^2}\times W_1$

$={\left(\frac{22}{16}\right)}^2\times 32kg/day$

$=60.5kg/day$