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The pounds formula
What is the pounds formula for water treatment?
Pounds per day equals flow in million gallons per day times dose in milligrams per liter times 8.34. The 8.34 is the weight of a gallon of water in pounds. A 2-MGD plant dosing 8 milligrams per liter of chlorine feeds 2 times 8 times 8.34, or about 133 pounds per day. Keep flow in MGD.
Pounds per day = flow (million gallons per day) x dose (milligrams per liter) x 8.34. The 8.34 is the weight in pounds of one gallon of water, and it converts the concentration-times-flow product into a daily weight. The same formula sizes chemical feed and computes solids and BOD loadings.
The formula, worked
Common slip Dropping the decimal on 8.34, or using flow in gallons per day instead of million gallons per day, which inflates the answer a million-fold. The formula wants MGD. Forgetting 8.34 entirely leaves a nonsense small number.
Where this shows up
The pounds formula is the backbone of chemical feed, solids loading, and BOD loading, so nearly every plant-math word problem folds it in. The chlorine-dosing drill applies it after finding the dose, and the activated-sludge drill uses it for BOD and MLSS pounds. Check any feed rate in the process calculator.
Problem set: 5 worked problems
Each problem is original, authored from the underlying non-copyrightable relationship, with the full worked solution and the exact slip that produces each wrong answer. Work the problem before opening the solution. For a timed, randomized run with a per-topic score, use the free practice test.
Watch for Pounds per day = MGD x mg/L x 8.34. Two errors sink most answers: using flow in gallons per day instead of MGD (which inflates the answer a million times), and dropping the decimal on 8.34. Keep flow in MGD and carry 8.34 to two decimals.
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A 4.0 MGD plant doses fluoride at 12 mg/L. What is the feed rate in pounds per day?
- A 4,003 lb/day
- B 100 lb/day
- C 48 lb/day
- D 400 lb/day
Show the worked solution
Correct answer: D. 400 lb/day
4.0 x 12 x 8.34 = 400.3 lb/day. Forgetting the 8.34 leaves 48; using gallons per day instead of MGD blows the answer up by a million.
Source: Public relationship: lb/day = flow (MGD) x dose (mg/L) x 8.34
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How many pounds per day of alum feed a 1.5 MGD plant dosing 10 mg/L?
- A 15 lb/day
- B 1,251 lb/day
- C 83 lb/day
- D 125 lb/day
Show the worked solution
Correct answer: D. 125 lb/day
1.5 x 10 x 8.34 = 125.1 lb/day. Dropping 8.34 gives 15; slipping a decimal on the flow or the 8.34 gives the order-of-magnitude distractors.
Source: Public relationship: lb/day = flow (MGD) x dose (mg/L) x 8.34
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A plant feeds 200 pounds per day of chemical at a flow of 5.0 MGD. What dose in mg/L does that deliver?
- A 4.0 mg/L
- B 24 mg/L
- C 40 mg/L
- D 4.8 mg/L
Show the worked solution
Correct answer: D. 4.8 mg/L
Rearrange: dose = lb/day / (MGD x 8.34) = 200 / (5.0 x 8.34) = 200 / 41.7 = 4.8 mg/L. Dividing only by the flow and forgetting the 8.34 gives 40.
Source: Public relationship: dose (mg/L) = lb/day / (flow (MGD) x 8.34)
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A 0.5 MGD plant doses polymer at 45 mg/L. Feed rate in pounds per day?
- A 375 lb/day
- B 90 lb/day
- C 23 lb/day
- D 188 lb/day
Show the worked solution
Correct answer: D. 188 lb/day
0.5 x 45 x 8.34 = 187.65, about 188 lb/day. Forgetting the 8.34 leaves 23; using a flow of 1.0 MGD by mistake would give 375.
Source: Public relationship: lb/day = flow (MGD) x dose (mg/L) x 8.34
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A large 10 MGD plant holds a 2.5 mg/L chlorine dose. Pounds per day of chlorine?
- A 2,085 lb/day
- B 21 lb/day
- C 25 lb/day
- D 209 lb/day
Show the worked solution
Correct answer: D. 209 lb/day
10 x 2.5 x 8.34 = 208.5, about 209 lb/day. Forgetting 8.34 gives 25; a decimal slip on the flow gives 2,085 or 21.
Source: Public relationship: lb/day = flow (MGD) x dose (mg/L) x 8.34
Drill the whole exam
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