Wastewater treatment math
The math on the wastewater treatment exam, built on the pounds formula, through process control and the reverse problems that decide Class III.
Wastewater treatment carries the heaviest math of any track. Everything starts from the pounds formula: mg/L times MGD times 8.34. From there you build organic loading, the process-control trio of food to microorganism ratio, mean cell residence time, and sludge volume index, plus settling, clarifier loading, dosage, and pumping horsepower. Class III flips these into reverse problems, given a target residence time or ratio, find the wasting rate or solids needed. Those reverse problems are where most candidates stall. Watch for volatile solids versus total solids, they are not the same number.
You can apply the pounds formula to find loading, solids, and dosage from mg/L and flow. You can calculate the process-control trio: F/M ratio, MCRT, and SVI. You can work Class III reverse problems, solving for wasting rate or required solids. You can tell volatile solids and total solids apart in F/M and MCRT calculations. You can locate the formula sheet, practice problems, and calculator to drill this math.
The math on the wastewater treatment exam
Wastewater treatment carries the most math of any track, because process control is run by the numbers. This page maps what to study. The formulas are on the wastewater treatment formula sheet and the foundations are in operator math fundamentals.
What you calculate
Everything runs on the pounds formula, which sets pounds per day as the milligrams per liter times the MGD times 8.34. From there:
- organic loading, the BOD pounds per day onto a process or a pond
- the process-control trio: the food to microorganism ratio, mean cell residence time, and the sludge volume index, plus the return rate
- settling and solids: percent removal, percent volatile, and the sludge mass
- surface and weir overflow rates and solids loading on a clarifier
- dosage and disinfection, including hypochlorite at a given strength
- pumping horsepower, and at the top, mass balance and the nitrogen stoichiometry
The reverse problems are the hinge
At Class I and II you run these forward: given the numbers, find the food to microorganism ratio or the mean cell residence time. Class III flips them. The exam gives you a target residence time and asks for the wasting rate that holds it, or a target ratio and asks for the solids you need under aeration. These reverse problems are where most candidates stall, so give them the most time. Class IV adds mass balances, the oxygen and alkalinity arithmetic of nitrification, and digester gas.
A couple worked the exam's way
An aeration basin holds 3,200 mg/L of volatile solids in 0.85 million gallons, with 180 mg/L of BOD coming in at 1.2 MGD. The solids under aeration are 3,200 times 0.85 times 8.34, about 22,700 pounds. The BOD load is 180 times 1.2 times 8.34, about 1,800 pounds a day. The food to microorganism ratio is 1,800 over 22,700, which is 0.08.
A plant wants a 10 day residence time and holds 38,000 pounds of solids in the system, losing 40 pounds a day in the effluent. To hit 10 days it needs 3,800 pounds leaving daily, so the wasting rate is 3,800 minus 40, or 3,760 pounds a day. That is the reverse problem the exam loves.
Where operators lose points
The reverse process-control problems, every time. And forgetting that the food to microorganism ratio uses volatile solids while residence time uses total solids, not the same number.
Study this
Live in the wastewater treatment formula sheet, grind the process-control problems in the free practice tool by hand, and check them in the operator calculator. The exam page is wastewater treatment, and your state's specifics are on your state's page.
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