Question

The wastewater having an organic concentration of 54 mg/l is flowing at a steady rate of 0.8 m³/day through a detention tank of dimensions 2 m × 4 m × 2 m. If the contents of the tank are well mixed and the decay constant is 0.1 per day, the outlet concentration (in mg/l, up to one decimal place) is ________

Answer 1

Concept:

Outlet concentration L_t = L₀ e- ^Kt

\(Detention\;Time\;\left( {{t_d}} \right) = \frac{{volume}}{{Discharge}} \)

Note that if decay constant is assumed to have been given at base ‘e’

Calculation:

Given ⇒ Initial concentration \(\left( {{L_0}} \right) = 54\frac{{mg}}{l}\)

Q = 0.8 m³/day

V = 2 × 4 × 2 = 16 m³

\(Detention\;Time\;\left( {{t_d}} \right) = \frac{{16}}{{0.8}} = 20\;day\)

Outlet concentration L_t = L₀ e^{- Kt}

L_t = L₀e^-Kt = 54e^{-0.1 × 20} = 7.3 mg/l