Last verified:
mean cell residence time (MCRT) is the pounds of solids under aeration divided by the pounds of solids leaving the system each day, as waste sludge plus effluent solids. food-to-microorganism ratio (F:M) is the pounds of biochemical oxygen demand (BOD) entering the aeration tank each day divided by the pounds of mixed liquor volatile suspended solids (MLVSS) in it; both quantities come from the pounds formula, flow or volume in million gallons (MG) times milligrams per liter (mg/L) times 8.34.
MCRT (days) = Solids under aeration (lb) ÷ [waste activated sludge (WAS) solids (lb/day) + effluent suspended solids (SS) (lb/day)] · F:M = BOD (lb/day) ÷ MLVSS (lb)
| Term | Meaning | Units |
|---|---|---|
| Solids under aeration | aeration volume (MG) × mixed liquor suspended solids (MLSS) (mg/L) × 8.34 | lb |
| WAS solids | WAS flow (MGD) × WAS concentration (mg/L) × 8.34 | lb/day |
| Effluent SS | effluent flow (MGD) × effluent SS (mg/L) × 8.34 | lb/day |
| F:M | lb BOD per day ÷ lb MLVSS | per day |
Both wastewater sheets list MCRT and F/M. The Version 2 sheet's MCRT also counts solids held in the clarifier; this example uses aeration tank solids only. Official sheets: Equivalents and Formulas Sheet, Version 1 (State Water Resources Control Board, Wastewater Operator Certification Program; Wastewater Treatment Plant Operator exams); Equivalents and Formulas Sheet, Version 2 (State Water Resources Control Board, Wastewater Operator Certification Program; Wastewater Treatment Plant Operator exams).
Activated sludge process control · Original practice item, not a real exam question.
An aeration basin holds 1.75 MG at 2,800 mg/L MLSS and 2,150 mg/L MLVSS. The plant wastes 0.042 MGD of sludge at 7,600 mg/L, and 4.3 MGD leaves in the effluent at 11 mg/L SS. Primary effluent BOD entering aeration is 155 mg/L at 4.3 MGD. Find the MCRT and the F:M.
1.75 MG × 2,800 mg/L × 8.34 = 40,866 lb0.042 MGD × 7,600 mg/L × 8.34 = 2,662 lb/day; 4.3 MGD × 11 mg/L × 8.34 = 394.5 lb/day40,866 lb ÷ (2,662 + 394.5) lb/day = 40,866 ÷ 3,057 = 13.4 days4.3 MGD × 155 mg/L × 8.34 = 5,559 lb BOD/day; 1.75 MG × 2,150 mg/L × 8.34 = 31,379 lb MLVSS5,559 ÷ 31,379 = 0.177 per dayAnswer: MCRT 13.4 days; F:M 0.177
F:M asks how much food each pound of living biomass receives, and the volatile fraction approximates the biomass. MCRT is a solids inventory: every pound of solids, volatile or not, leaves through wasting or the effluent.
Through the wasting rate. Wasting more solids per day shortens MCRT; wasting less lengthens it, provided effluent solids stay steady.
The free study app has a step-by-step lesson on this calculation, with fraction-tile unit cancellation and graded practice problems.
Open the activated sludge process control lessonFormulas follow the official sheets linked above, which are the reference at the exam. The worked example and the mistakes are original practice material written for this page; they are not real exam questions, which are confidential. Written by the site's author.
Questions, flashcards, and explanations are AI-written under a sourcing policy that builds on the exam content outlines and candidate materials each certifying body publishes without restriction and the regulations and technical references they cite, and that excludes actual exam questions, recollections of any exam sat by the author, other study products, and any handbook or document released under a confidentiality agreement. Any item found outside that policy is rewritten from primary sources or removed. Content is then put through repeated review — regulatory values checked against primary sources, every calculation recomputed, and errors corrected — plus spot checks by the author, who holds California water operator certifications and a California civil engineering license. Those spot checks are sampling, not a professional review: nothing here is stamped, sealed, or offered as engineering advice, and not every item has been individually verified, so mistakes can still slip through.
Not affiliated with or endorsed by the State Water Resources Control Board (SWRCB), its Division of Drinking Water (DDW) or Wastewater Operator Certification Program (WWOCP), the California-Nevada American Water Works Association (CA-NV AWWA), the California Water Environment Association (CWEA), the National Council of Examiners for Engineering and Surveying (NCEES), the California Board for Professional Engineers, Land Surveyors, and Geologists (BPELSG), the Contractors State License Board (CSLB), or the American Public Works Association (APWA). All questions, flashcards, and references are independent study aids; verify against the official exam materials.