Question

A wastewater treatment plant discharges 1.0 m3/s of effluent having an ultimate BOD of 40.0 mg/ L into a stream flowingat 10.0 m3/s. Just upstream from the discharge point, the stream has an ultimate BOD of 3.0 mg/L The deoxygenationconstant kd is estimated at 0.22/day.(a) Assuming complete and instantaneous mixing. find the ultimate BOD of the mixture of waste and river just downstreamfrom the outfall.(b) Assuming a constant cross-sectional area for the stream equal to 55 m2, what ultimate BOD would you expect to find ata point 10.000 m downstream?

Answer 1

a) 6.4 mg/l

b) 5.6 mg/l

Step-by-step explanation:

Given data:

effluent Discharge Q_w = 1.0 m^3.s

Ultimate BOD L_w = 40 mg/l

Discharge of stream Q_r = 10 m^3.s

Stream ultimate BOD L_r = 3 mg/l

a) Ultimate BOD of mixture
`= (Q_w l_w + Q_r L_r)/(Q_w + Q_r)`

`= (1*40 + 10*3)/(10 +1) = 6.4 mg/l`

b) utlimate BOD at 10,000 m downstream

`t =(distance)/(speed) = (10,000)/((Q_r +Q+w)/(55)) * (hr)/(3600) *  (day)/(24 hr)`

putting
`Q_r + Q_w = 1+ 10 = 11 m^3/s`

t = 0.578 days

we know

`L_t = L_o e^(-kt)`

`L_t = 6.4 * e^(-0.22 * 0.578)`

`L_t = 5.6 mg/l`