Mathematics, Hydraulics, and Calculations
Calculation items reward clean unit tracking more than memorization. Know the conversions, set up the expression with labeled units, and check that the answer is physically sensible.
Formulas worth memorizing
- 1 ft³ = 7.48 gal; 1 gallon of water weighs 8.34 lb; 1 psi = 2.31 ft of head; 1 MGD = 694 gpm = 1.547 cfs.
- Feed rate: lb/day = mg/L × 8.34 × MGD.
- Detention time = volume ÷ flow, with both in the same units.
- Water horsepower = gpm × ft ÷ 3,960; brake horsepower = water horsepower ÷ efficiency.
- Circle area = 0.785 × D²; cylinder volume = 0.785 × D² × length.
- Affinity laws: Q ∝ speed, H ∝ speed², power ∝ speed³.
- Loading rates: filter gpm/ft², weir gpm/ft, clarifier overflow gpd/ft².
Worked example
A rectangular settling basin is 100 ft long, 40 ft wide, and 12 ft deep, with a flow of 0.5 MGD. Volume = 100 × 40 × 12 = 48,000 ft³ = 48,000 × 7.48 = 359,040 gal. Detention time = 359,040 ÷ 500,000 gal/day = 0.718 day × 24 = 17.2 hours. Sanity check: a basin that size at half a million gallons a day should hold water for most of a day, and it does.
Traps
Mixing gpm with gpd in the same equation. Flipping the 1 psi = 2.31 ft relationship or using 0.433 psi/ft the wrong direction. Dividing by efficiency when the question asks for water horsepower. Reporting theoretical detention time when baffled time is requested. Rounding early and losing the last digit on a multiple-choice choice.