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Exam Math Tips
- Always verify your units cancel correctly before calculating
- Use the pounds formula for 30%+ of water treatment questions
- Know the conversion factors: 8.34 lbs/gal, 1 MGD = 1.547 cfs, 1 acre = 325,872 gallons
- If a question gives you time (minutes, hours), convert to the matching time unit
- Check if flow is in MGD, GPM, or something else - convert before solving
- Practice rearranging formulas: if asked for dose, you may need to solve backwards
Basic Calculations
" Pounds Formula (Lbs/Day)
Lbs/Day = mg/L × MGD × 8.34
Concentration × Flow Rate × Unit Weight
| mg/L | Concentration / Dose | Milligrams per liter (ppm) |
| MGD | Flow Rate | Million gallons per day |
| 8.34 | Unit Weight | Lbs per gallon of water |
| Lbs/Day | Result | Pounds of chemical per day |
Quick Example
A facility treats 1.5 MGD with chlorine at 2 mg/L.
Lbs/Day = 2 - 1.5 - 8.34 = 25 lbs/day
Lbs/Day = 2 - 1.5 - 8.34 = 25 lbs/day
Flow Rate (Velocity Formula)
Q = A × V
Flow = Cross-Sectional Area × Velocity
| Q | Flow Rate | Cubic feet per second (cfs) or gallons per minute |
| A | Cross-Section Area | Square feet (width - depth) |
| V | Velocity | Feet per second (ft/s) |
Quick Example
A channel is 5 ft wide, 3 ft deep, water flows at 1.2 ft/s.
Q = (5 - 3) - 1.2 = 18 cfs
Q = (5 - 3) - 1.2 = 18 cfs
% Percent Concentration
% = (Part / Whole) × 100
What percentage is one value of another?
| Part | Quantity | The smaller or component amount |
| Whole | Total | The total amount |
| % | Result | Percentage of whole |
Quick Example
A tank solution is 50 lbs chemical in 500 lbs total solution.
% = (50 / 500) - 100 = 10%
% = (50 / 500) - 100 = 10%
Water Treatment
Detention Time
DT = Volume / Flow Rate
How long water stays in a tank or basin
| DT | Detention Time | Hours, minutes, or seconds |
| V | Volume | Gallons or cubic feet |
| Q | Flow Rate | GPM or gallons per day |
Quick Example
Clarifier holds 50,000 gallons, flow is 100 GPM.
DT = 50,000 / 100 = 500 minutes = 8.3 hours
DT = 50,000 / 100 = 500 minutes = 8.3 hours
' Dosage (Demand & Residual)
Dose = Demand + Residual
Total chemical needed = What gets used + What remains
| Dose | Total Chemical | mg/L to add to water |
| Demand | Amount Used | mg/L consumed in reaction |
| Residual | Amount Left | mg/L remaining in water |
Quick Example
Chlorine demand is 1.2 mg/L, desired residual is 0.5 mg/L.
Dose = 1.2 + 0.5 = 1.7 mg/L needed
Dose = 1.2 + 0.5 = 1.7 mg/L needed
" Percent Removal (Efficiency)
% Removal = ((Initial - Final) / Initial) × 100
How much contaminant was removed?
| Initial | Before | Concentration before treatment |
| Final | After | Concentration after treatment |
| % | Result | Percentage removed (0-100%) |
Quick Example
Turbidity: 10 NTU in, 0.2 NTU out.
% Removal = ((10 - 0.2) / 10) - 100 = 98% removal
% Removal = ((10 - 0.2) / 10) - 100 = 98% removal
" Advanced Calculations
" Loading Rate
Loading = Flow / Surface Area
Flow per unit area of clarifier or filter
| Loading | Rate | GPM/sq ft or gal/(daysq ft) |
| Flow | Q | GPM or gallons per day |
| Area | A | Square feet of clarifier surface |
Quick Example
500 GPM into clarifier with 200 sq ft surface.
Loading = 500 / 200 = 2.5 GPM/sq ft
Loading = 500 / 200 = 2.5 GPM/sq ft
Basin Volume (Rectangular)
V = Length × Width × Depth
Cubic feet to gallons: - 7.48
| V | Volume | Cubic feet (cu ft) or gallons |
| L, W, D | Dimensions | All in feet |
| 7.48 | Conversion | Cubic feet to gallons |
Quick Example
Tank: 10 ft - 8 ft - 6 ft.
V = 10 - 8 - 6 = 480 cu ft = 480 - 7.48 = 3,590 gallons
V = 10 - 8 - 6 = 480 cu ft = 480 - 7.48 = 3,590 gallons
" Essential Conversion Factors (Memorize These!)
| 8.34 | Lbs per gallon water | Key to pounds formula |
| 7.48 | Gallons per cu ft | Volume conversion |
| 325,872 | Gallons per acre | Large area volumes |
| 1.547 | CFS per MGD | Flow unit conversion |
| 60 | Minutes per hour | Time conversion |
| 1,440 | Minutes per day | Minutes to days |
| 86,400 | Seconds per day | Seconds to days |
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