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Ultimate BOD from 5-day BOD at 37°C

Short answer

5-day BOD at 37°C=200 mg/L, k=0.17/day (base 10). Ultimate BOD=232.9 mg/L. BOD remaining after 5 days=32.9 mg/L.

If the 5 day BOD at 37°C is 200 mg/l and if the rate of deoxygenation is 0.17/day, calculate the ultimate BOD and BOD remaining after 5 days.

Given: y5=200y_5=200 mg/L at 37°C and rate of deoxygenation k=0.17k=0.17 day⁻¹ at that temperature (taken as base 10, the usual form yt=L(1−10−kt)y_t=L(1-10^{-kt}), so no temperature correction is needed).

Ultimate BOD

L=y51−10−kt=2001−10−0.17×5=2001−0.1413=232.9 mg/LL=\frac{y_5}{1-10^{-kt}}=\frac{200}{1-10^{-0.17\times5}}=\frac{200}{1-0.1413}=232.9\ \text{mg/L}

BOD remaining after 5 days

L5=L−y5=232.9−200=32.9 mg/L(=L 10−kt)L_5=L-y_5=232.9-200=32.9\ \text{mg/L}\quad\left(=L\,10^{-kt}\right)

Answer: Ultimate BOD = 232.9 mg/L; BOD remaining after 5 days = 32.9 mg/L. (If the constant is taken as base ee, L=200/(1−e−0.85)=349.3L=200/(1-e^{-0.85})=349.3 mg/L.)

✓ Answer checked by Claude Opus 5.5 (high effort)

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