Math, Hydraulics, and Calculations
What to know
Operators must perform reliable calculations. Core formulas: flow = velocity × area (Q = V × A), detention time = volume ÷ flow, dose = (chemical mass) ÷ volume, pressure = head × 0.433 psi/ft, horsepower (water hp = gpm × ft head ÷ 3960; brake hp = water hp ÷ efficiency), and CT = concentration × time. Know unit conversions: 1 cubic foot = 7.48 gallons, 1 mg/L = 1 ppm, 1 gallon of water ≈ 8.34 lb, and 1 psi ≈ 2.31 ft of head. Understand mass loading (concentration × flow × 8.34) and percent removal. Hydraulics includes velocity, friction loss, and pump affinity laws. Always track units and check whether the answer is dimensionally sensible.
Traps
Questions often mix units - mg/L with lb/day, gpm with cubic feet, or minutes with hours. Watch for detention time calculated with the wrong volume (e.g., total tank vs. actual water depth) and for horsepower formulas that omit efficiency. Another trap: using 8.34 lb/gal for a chemical with a different density.
Worked example / rule of thumb
A tank holds 50,000 gallons and flow is 500 gpm. Detention time = 50,000 ÷ 500 = 100 minutes. If instead you need hours, divide by 60 → 1.67 hours. Rule of thumb: write the units at every step; if units do not cancel to the target, the setup is wrong.
Study tip
Build a formula sheet with units attached; practice converting between gpm, cfs, and MGD (1 MGD ≈ 694 gpm).