If you have an estimate of the BOD likely to be found in your sample water, you can use the two equations below to determine the maximum and minimum amount of sample water to be used in your dilutions.
For example, suppose that the estimated BOD of an influent sample is 400 mg/L. The D.O. of saturated dilution water is approximately 8.0 mg/L. If you want the D.O. depletion to be at least 2.0 mg/L after 5 days of incubation and the residual D.O. to be at least 1.0 mg/L, then you would calculate the dilutions as follows.
First, to calculate the least concentrated dilution, use the minimum allowable depletion:
This means that you will use 1.5 mL of sample water in a 300 mL sample bottle, filling the bottle the rest of the way with dilution water.
Next, to calculate the most concentrated dilution, use the maximum allowable depletion. The maximum allowable depletion can be calculated as follows:
Max. allowable depletion = (Saturated D.O. concentration) - (Min. residual concentration)
Max. allowable depletion = 8.0 mg/L - 1.0 mg/L
Max. allowable depletion = 7.0 mg/LThen the amount of sample water used in the dilution is calculated as follows:
From the calculations above, we can estimate that we should use a 1.5 mL sample and a 5.25 mL sample. Since the BOD value we used was just an approximation, we should probably use slightly lower and slightly higher sample sizes, as well as a few sample sizes in between. We might choose to use samples of 1 mL, 3 mL, 4 mL, 5 mL, and 6 mL.
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