Wastewater math
Food-to-microorganism ratio from the flow in MGD, BOD in mg/L, aeration volume in MG and MLVSS in mg/L.
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The formula
F/M = BOD₅, lb/day ÷ MLVSS, lbWPI Formula/Conversion Table (2023), Printed page 3 of 10, Food/Microorganism Ratio
Loading Rate, lb/day = (Flow, MGD)(Concentration, mg/L)(8.34 lb/gal); Mass, lb = (Volume, MG)(Concentration, mg/L)(8.34 lb/gal)WPI Formula/Conversion Table (2023), Printed page 4 of 10, Loading Rate and Mass
Worked example
A plant sends 2.0 MGD at 200 mg/L BOD to a 0.8 MG aeration basin with 3,000 mg/L MLVSS. What is the F/M ratio?
Find the food: 2.0 MGD × 200 mg/L × 8.34 lb/gal = 3,336 lb/day BOD.
Find the microorganisms: 0.8 MG × 3,000 mg/L × 8.34 lb/gal = 20,016 lb MLVSS.
Divide food by microorganisms: 3,336 lb/day ÷ 20,016 lb = 0.17.
Answer: 0.17 lb BOD/day per lb MLVSS
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