BOD Calculation Using Dilution Test Data
This solution explains how to calculate the 5-day Biochemical Oxygen Demand (BOD5) of a wastewater sample using data from a dilution test.
Identify Given Parameters
The following parameters are provided:
- Initial Dissolved Oxygen (DO) of the mixture: $DO_0 = 9.0$ mg/L
- DO of the mixture after 5 days: $DO_5 = 3.0$ mg/L
- Dilution factor (volume fraction of waste in mixture): $p = 0.03$
- Time: $t = 5$ days
- Reaction rate constant: $K = 0.22$ /day (Note: This value is not required for calculating BOD5 from DO depletion data).
Calculate DO Depletion
The depletion in dissolved oxygen over the 5-day period indicates the amount of oxygen consumed by microorganisms in the diluted sample due to the decomposition of organic matter.
DO Depletion = Initial DO - Final DO
$ DO_{depletion} = DO_0 - DO_5 $ $ DO_{depletion} = 9.0 \text{ mg/L} - 3.0 \text{ mg/L} = 6.0 \text{ mg/L} $Apply 5-Day BOD Formula
The 5-day BOD of the original undiluted water sample ($BOD_{5, water}$) is calculated by adjusting the DO depletion observed in the diluted mixture using the dilution factor ($p$).
The formula is:
$ BOD_{5, water} = \frac{DO_{initial\_mix} - DO_{final\_mix}}{p} $Substituting the calculated DO depletion:
$ BOD_{5, water} = \frac{DO_{depletion}}{p} $Compute 5-Day BOD
Now, substitute the values into the formula:
$ BOD_{5, water} = \frac{6.0 \text{ mg/L}}{0.03} $ $ BOD_{5, water} = 200 \text{ mg/L} $Therefore, the five-day BOD of the water sample is 200 mg/L.
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