Operator Math and Hydraulic Calculations
Core formulas and worked examples
Most Class I math reduces to a few relationships. Area of a circle = πr²; volume of a cylinder = area × length; 1 cubic foot = 7.48 gallons; 1 mgd = 694.4 gpm; 1 cfs = 448.8 gpm; 1 psi = 2.31 ft of head. Velocity = flow ÷ area, with consistent units. Detention time = volume ÷ flow. The pounds formula is pounds = mg/L × mgd × 8.34. Chlorine dose, demand, and residual: dose = demand + residual. Horsepower = (gpm × head in ft) ÷ (3,960 × efficiency) for water.
Worked example: a 12-in. main carries 1,500 gpm. Radius = 0.5 ft, area = π(0.5)² = 0.785 ft². Convert flow: 1,500 ÷ 448.8 = 3.34 cfs. Velocity = 3.34 ÷ 0.785 ≈ 4.3 fps - within normal design range.
Another: a tank 40 ft in diameter holds water 20 ft deep. Volume = π(20)² × 20 = 25,133 ft³ × 7.48 = 188,000 gal, or about 0.188 mg. At 500 gpm, detention time ≈ 376 minutes, about 6.3 hours.
Traps: mixing gpm and cfs; using diameter instead of radius; forgetting 8.34 in the pounds formula; using brake horsepower where water horsepower is asked. Check units before calculating and sanity-check the answer.
Rule of thumb: convert everything to feet, seconds, and gallons (or cfs) first; then the formula usually takes care of itself.