Question

A waste stabilization pond is used to treat a dilute municipal wastewater before the liquid is discharged into a river. The inflow to the pond has a flow rate of Q = 4,000 m3/day and a BOD1 concentration of Cin = 25 mg/L. The volume of the pond is 20,000 m3. The purpose of the pond is to allow time for the decay of BOD to occur before discharge into the environment. BOD decays in the pond with a first-order rate constant equal to 0.25/day. What is the BOD concentration at the outflow of the pond, in units of mg/L?

Answer 1

BOD concentration at the outflow = 17.83 mg/L

Step-by-step explanation:

given data

flow rate of Q = 4,000 m³/day

BOD1 concentration of Cin = 25 mg/L

volume of the pond = 20,000 m³

first-order rate constant equal = 0.25/day

to find out

What is the BOD concentration at the outflow of the pond

solution

first we find the detention time that is

detention time t =
`(volume)/(flow rate)`

detention time t =
`(20000)/(4000)`

detention time = 5 days

so

BOD concentration at the outflow of pond is express as

BOD concentration at the outflow =
`Cin ( 1 - e^(-kt) )`

here k is first-order rate constant and t is detention time and Cin is BOD1 concentration

so

BOD concentration at the outflow =
`25 ( 1 - e^(-0.25(5)) )`

BOD concentration at the outflow = 17.83 mg/L