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Question

A wastewater is to be disinfected with 35 mg/L of chlorine to obtain 99% kill of micro-organisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled by Nt=N0ekt, where N0 is number of micro-organisms at t=0, and k is the rate of kill. The wastewater flow rate is 36 m3/h, and k=0.23min1.
If the depth and width of the chlorination tank are 1.5 m and 1.0 m, respectively, the length of the tank (in m, round off to 2 decimal places) is
  1. 8.0089

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Solution

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

η=N0NtN0=0.99

NT=0.01 N0

N/0ekt=0.01 N/0

Ktne=n0.01

0.23 t=4.605

t=20.022 min

Volue of tank req. = Q.t

=36m3hr×20.02 min

=36×20.0260m3

=12.012 m3

length=Vdepth×width

=12.0121.5×1=8.0089 m

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