Question

A manufacture in Ontario has been fined because it has been releasing 5 L/s effluent having
zinc concentration of 0.1 mg/L into a river. Upstream of the factory, the stream water rate is
100 L/s with zinc concentration of approximately zero. The factory has been forced to
reduce the zinc concentration of the effluent to below 20 μg/L. The engineer that is an
employee of the factory recommends that they divert parts of the stream into the site and
dilute the effluent to bring its zinc concentration to the required level.

a) Calculate the present concentration of zinc several miles downstream of the plant
where the zinc is diluted in stream completely.

b) Compute the amount of water needed to be diverted to the site to achieve the required
zinc concentration of effluent.

c) Determine the concentration of zinc downstream of the plant where the zinc is diluted
in stream completely if the engineer’s plan is put into operation.

Answer 1

a) To calculate the zinc concentration downstream of the plant, we should first calculate the mass flow rate of Zinc knowing that it is released 5 L/s into the river with a zinc concentration of 0.1 mg/L. The mass flow rate of Zinc is calculated as follow:

We have that downstream of the factory, the total volumetric flow rate is 5 L/s (effluent) plus 100 L/s (stream water rate). So, the total volumetric flow rate several miles downstream is 105 L/s.

Knowing the total volumetric flow rate and the mass flow rate of Zinc we can calculate the zinc concentration several miles downstream of the plant as follow:

b) The required Zn concentration of effluent is:

The ratio between the present effluent Zn concentration and the required Zn concentrztion is:

. This ratio means that the required Zinc concentration is 5 times more diluted the current Zn concentration, indicating that the current effluent flow rate need to be increased 5 times. So, the required effluent flow rate is calculated as follow:

Finally, knowing that the required effluent flow rate is 25 L/s and the current effluent flow rate is 5 L/s, we need to divert 20 L/s of water from the river to achieve the required zinc concentration of effluent.

c) Knowing that the Zn mass flow rate of the effluent is 0.5 mg/s (calculted in a), and the new volumetric effluent flow rate is 25 L/s (calculated in b), the Zinc concentration downstream of the plant where the zinc is diluted
in stream completely if the engineer’s plan is put into operation is: