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Math practice questions

40 questions from the water and wastewater operator practice test.

Math practice test

10 questions, graded as you go, with the reason for every answer. No sign-up.

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Sample questions

A circular clarifier is 40 ft in diameter with a water depth of 16 ft. What is its volume in gallons? Use area = 0.785 × D² and 7.48 gal/ft³.

Answer in gal.

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150320 gal

Surface area = 0.785 × 40² = 0.785 × 1,600 = 1,256 ft². Volume = 1,256 × 16 = 20,096 ft³. Gallons = 20,096 × 7.48 = 150,318 gal, about 150,320 gal.

Reference: Cylinder volume: V = 0.785 × D² × depth; 7.48 gal/ft³

A stream gauge shows 3.0 cfs flowing into a raw water intake. What is this flow in gpm? (1 ft³ = 7.48 gal)

Answer in gpm.

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1346.4 gpm

3.0 ft³/s × 7.48 gal/ft³ = 22.44 gal/s. 22.44 gal/s × 60 s/min = 1,346.4 gpm. (Shortcut: 1 cfs = 448.8 gpm.)

Reference: Flow conversion: 1 cfs = 7.48 gal/s = 448.8 gpm

A wastewater plant's influent flow is 4.0 MGD. What is the flow in cubic feet per second? (1 ft³ = 7.48 gal; 86,400 s/day)

Answer in cfs.

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6.19 cfs

4,000,000 gal/day ÷ 7.48 gal/ft³ = 534,759 ft³/day. 534,759 ÷ 86,400 s/day = 6.19 cfs. (Shortcut: 1 MGD = 1.547 cfs, so 4.0 × 1.547 = 6.19 cfs.)

Reference: Flow conversion: 1 MGD = 1.547 cfs

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