Question

The initial ultimate BOD after mixing of the River is 12.0 mg · L−1. The DO in the River after the wastewater and river have mixed is at saturation. The river temperature is 10◦C. At 10◦C, the deoxygenation rate constant (kd) is 0.30 day−1, and the reaeration rate constant (kr) is 0.40 day−1. Determine the critical point (tc) and the critical DO.

Answer 1

`t_c = 2.87\ DAYS`

Step-by-step explanation:

Given data:

Initial BOD level is
`12 mg l^(-1)`

temperature of river is 10 degree C

Rate constant is
`kd = 0.30 day^(-1)`

Reaeration rate constant is kr
`0.40 day^(-1)`

As DO in river is at saturation hence initial Da is zero

critical temperature is calculated as

`t_c = (1)/(K_r - k_d) ln[ (k_r)/(k_d)(1 -Da(k_r -k_d)/(k_d L_a))]`

`t_c = (1)/(K_r - k_d) ln[ (k_r)/(k_d)(1 -0)]`

`t_c = (1)/(0.40 - 0.30) ln[ (0.40)/(0.30)(1 -0)]`

`t_c = 2.87\ DAYS`