Understanding BOD Calculation

Biochemical Oxygen Demand (BOD) is a key measure of water quality, specifically indicating the amount of oxygen required by aerobic biological organisms to break down organic material present in a water sample. This process typically occurs over a specific incubation period under controlled conditions.

The calculation involves considering the dilution of the original sample and the amount of oxygen consumed during incubation. Standard BOD tests are performed over 5 days at 20 degrees Celsius, denoted as BOD₅.

BOD Calculation Formula

When a sewage sample is diluted before incubation, the BOD is calculated using the following formula:

$$ \text{BOD} = \frac{(\text{DO}_{\text{initial}} - \text{DO}_{\text{final}}) - (B \times \text{Volume of dilution water})}{\text{Volume of sample}} $$

In cases where the oxygen depletion is directly given for the diluted sample, and the BOD of the dilution water is negligible or accounted for, a simplified formula can be used:

$$ \text{BOD} = \frac{\text{Oxygen Depletion}}{\text{Fraction of Sample}} $$

Here, 'Oxygen Depletion' is the difference in dissolved oxygen before and after incubation in the diluted sample, and 'Fraction of Sample' is the proportion of the original sewage in the diluted mixture.

Given Parameters for BOD Test

• Sample Dilution: 2%
• Incubation Time: 5 days
• Incubation Temperature: 20°C
• Oxygen Depletion: 5 ppm

Step-by-Step BOD Calculation

First, we need to determine the fraction of the sewage sample used in the dilution. The sample concentration is given as 2%.

Fraction of Sample ($ P $) = $ \frac{2}{100} = 0.02 $

The oxygen depletion measured in the diluted sample is 5 ppm.

Now, we apply the simplified BOD formula:

$$ \text{BOD} = \frac{\text{Oxygen Depletion}}{\text{Fraction of Sample}} $$

Substitute the given values:

$$ \text{BOD} = \frac{5 \text{ ppm}}{0.02} $$

Performing the calculation:

$$ \text{BOD} = 250 \text{ ppm} $$

Conclusion

The calculated BOD for the sewage sample under the specified conditions is 250 ppm. This value represents the amount of oxygen required to decompose the organic matter in the sewage over 5 days at 20°C.