Question

A city of 150,000 people discharges sewage, after removing 90% of the total suspended solids (TSS), into a stream with 0 TSS and a flow of 50 m³/min. A newspaper critic stated that what the city is doing is equivalent to discharging untreated sewage from 15,000 people. Is this criticism fair? Assume that each person produces 2.67 x 10^-4 m³/min of wastewater with a TSS concentration of 200 mg/L.

Answer 1

Total quantity of sewage discharged by city into stream = Q₁ = 150000x2.67x10^-4

= 40.05 m³/min

Concentration of total suspended solids in discharged sewage = S₁ = 10% of 200 mg/L

= 20 mg/L

Stream discharge = Q₂ = 50 m³/min

Concentration of TSS in stream = S₂ = 0

Steady state concentration in stream is given by mass balance

S_o = (Q₁S₁ + Q₂S₂)/(Q₁ + Q₂)

= (40.05x20 + 50x0)/(40.05 + 50)

= 8.895 mg/L

Now

Discharge of untreated sewage from 15000 people is given by

Q₃ = 15000x2.67x10^-4

= 4.005 m³/min

Concentration of TSS in untreated sewage = S₂ = 200 mg/L

Steady state concentration in stream is given by mass balance

S_o = (Q₃S₃ + Q₂S₂)/(Q₃ + Q₂)

= (4.005x200 + 50 x0)/(4.005+50)

= 14.832 mg/L

Since S_o in second case is greater than the first case criticism is not fair