Applied Calculations and Unit Conversions
Unit conversions decide most calculation points. Memorize: 1 MGD = 694.4 gpm = 1.547 cfs = 3,785 m3/day; 1 cfs = 448.8 gpm; 1 ft3 = 7.48 gal; 1 psi = 2.31 ft of water; 1 mg/L = 1 ppm in water; and the workhorse lb/day = mg/L x MGD x 8.34.
Core relationships: detention time = volume ÷ flow (units must match); hydraulic loading = flow ÷ area; percent removal = (in − out) ÷ in x 100; dose = demand + residual; mass = concentration x volume x 8.34. Volumes: rectangular = length x width x depth; cylinder = 0.785 x diameter squared x depth; results in ft3, then multiply by 7.48 for gallons. A tank 40 ft in diameter with 12 ft of water holds 0.785 x 1,600 x 12 = 15,072 ft3 = about 112,700 gal.
Traps: mismatched time units (hours versus minutes versus days); using diameter where radius belongs; applying 8.34 when the flow is not in MGD or the concentration is not in mg/L; reporting gpm/ft2 when gpd/ft2 was requested; confusing percent removal with percent recovery; and rounding too early in a chain of steps.
Worked example: a plant feeds 25 mg/L of alum to 3.2 MGD. Alum = 25 x 3.2 x 8.34 = 667 lb/day. If a question gives lb/day and asks for mg/L, divide by (MGD x 8.34) instead.
Habit that prevents errors: write the units into every step. If they do not cancel to the requested unit, the setup is wrong - fix it before doing the arithmetic.