Question

A wastewater treatment plant must disinfect its effluent before discharging the wastewater to a near-by stream. The wastewater contains 4x107 fecal coliform colony-forming units (CFU) per 100 mL. The maximum permissible fecal coliform concentration that may be discharged is 2,000 fecal coliform CFU/100mL. It is proposed that a pipe carrying the wastewater be used for disinfection process. Determine the length of pipe required if the linear velocity of the wastewater in the pipe is 0.6 m/sec. Assume that the pipe behaves as a steady-state plug-flow system and that the reaction rate constant for destruction of the fecal coliforms is 0.3 min-1 .

Answer 1

The destruction of coliform follows first order reaction. (Refer unit of rate constant min^-1 which is unit of first order reaction rate constant)

A steady state plug flow first order system can be represented as given below.

K= rate constant = 0.3min^-1=(0.3/60) s^-1= 0.005s^-1

C= outlet concentration=2000 cfu/100mL

C₀= inlet concentration = 4*10⁷ cfu/100mL

v= velocity of waste water in pipe =0.6m/s

L= length of pipe

Substitute the values in above equation and calculate required length L of the reactor.

L=1188.42m