Question

A homeowner accidentally drops 10 kg of pesticide XX into the storm sewer inlet (drain), which flows into a pond with a volume of 1,000 m3. The water in the drain has a flow rate of 5 m3/min and a velocity of 0.20 m/s. The distance from the drop site to the pond is 20 km. Assume that the drop is quick enough to treat the injection of the pesticide as a pulse and that the drain behaves as a plug flow reactor (PFR). Assume the pond behaves as a CMFR and that the pesticide is completely mixed immediately once it enters into the pond. The pesticide is also nonreactive.

From the time the pesticide is dropped, estimate the time (in hours) that it will take to flush 99% of the pesticide out of the pond.

Answer 1

• the total time will be equal to the time taken by 99% of pesticides to reach the pond and the detention time of the pond.
• for 99% of pesticides to flush out the velocity will be calculated as follows-
•   
• where v is the velocity for 99% removal of pesticides.
• & V is velocity for 100% removal i.e.= 0.20m/s
• v=0.99*0.20=0.198m/s
• time taken to reach the pond by 99% of pesticides- = 20000m/0.198m/s =101010.10 seconds

=101010.10/3600 = 28.05 hour

• detention time of pond= volume of pond / flow rate

= 1000m^3/5m^3/min

= 200 min= 3.33 hour.

• total time required to flush out 99% of pesticides

​​​​​​​​​​​​​ =28.05+3.33=31.38 hour.