Respuesta :
Solution :
According to Chick's law
[tex]$\frac{N_t}{N_0}=e^{-k'C^n t}$[/tex]
where, t = contact time
c = concentration of disinfectant
k' = lethality coefficient = 4.71
n = dilution coefficient = 1
4 log removal = % removal = 99.99
[tex]$\frac{N_t}{N_0}=\frac{\text{bacteria remaining}}{\text{bacteria initailly present}}$[/tex]
= 1 - R
= 1 - 0.9999
Now for plug flow reactor contact time,
[tex]$\tau =\frac{V}{Q} =\frac{75000}{40 \times 10^6}$[/tex]
= 0.01875 days
= 27 minutes
For CSTR, [tex]$\tau =\frac{V}{Q} =\frac{150000}{40 \times 10^6}$[/tex]
[tex]$=3.75 \times 10^{-3}$[/tex] days
= 5.4 minute
There are 3 reactors, hence total contact time = 3 x 5.4
= 16.2 minute
Or [tex]$\frac{N_t}{N_0}=e^{-k'C^n t}$[/tex]
or [tex]$(1-0.9999)=e^{-4.71 \times C \times t}$[/tex]
∴ C x t = 1.955
For PFR, [tex]$t_1 = 27 $[/tex] min
∴ C [tex]$=\frac{1.955}{27}$[/tex] = 0.072 mg/L
For CSIR, [tex]$t_2=16.2$[/tex] min
[tex]$C=\frac{1.955}{16.2} = 0.1206$[/tex] mg/L
∴ Chlorine required for PFR in kg/day
[tex]$=\frac{0.072 \times 40 \times 10^6 \times 3.785}{10^6}$[/tex] (1 gallon = 3.785 L)
= 18.25 kg/day
Therefore we should go for PFR system.
