Learn Water Treatment and Distribution Certification Math

Compute surface area and paint required for a 140 ft fence with 6 ft height, two sides, subtracting 12 ft and 4 ft gates, at 100 ft² per gallon.

Compute roundup by taking fenced area 240×140, subtract the circle area 0.785×50^2, then divide by 4000 to estimate about 7.9 gallons (≈8).

Compute the tank’s side area by using circumference equals pi times diameter; with a 50-ft diameter and 30-ft height, paint 47.1 gallons at 100 ft² per gallon.

Compute volume of a sedimentation basin by multiplying length, width, and height, then convert cubic feet to gallons using 7.48 gallons per cubic foot; for 50×20×15 you get 112,200 gallons.

Compute tank’s volume using V = 0.785 × diameter^2 × height for a 100 ft diameter, 50 ft high tank, then convert with 7.48 gal/ft^3 to about 2.94 million gallons.

Compute the water volume from intake to the treatment plant for a three-mile, 18-inch pipe using the volume formula, convert to cubic feet, and then to gallons.

Calculate the water volume in a 20 ft diameter tank with 19 ft water using V = 0.785 d^2 h to obtain cubic feet, then convert to gallons at 7.48 gal/ft³.

Calculate the pressure at the bottom of a 30 ft water tank using two formulas from the formula sheet; both yield about 13 psi.

Convert the 200 psi pump pressure to water head using 2.31 ft/psi (or 0.433 psi/ft), showing that the well depth is 462 feet.

Convert a flow rate from 800 gallons per minute to million gallons per day using 60 minutes per hour and 24 hours per day, then validate with back-calculation.

In flow problem #2, a 100 ft diameter tank with 30 ft water is pumped at 750 gpm for eight hours. About 6.1 ft is removed, leaving roughly 24 ft.

Calculate detention time for a 35-ft diameter, 10-ft clarifier at 0.3 MGD using cylinder volume and detention time formulas, yielding about 5.75 hours; check shows 8 hours equals 0.216 MGD.

Compute detention time for a basin using volume = length × width × depth; convert to gallons with 7.48 gal/ft^3 and divide by 0.25 million gal/day to get 8.6 hours.

Apply the pounds per day formula from million gallons a day flow, using mg/L dose, water weight per gallon, and purity to calculate chlorine usage.

Calculate chlorine dose in pounds per day for a 4 million gallon per day flow using 3 mg/l, applying the 8.34 conversion factor and 100% purity.

Calculate the aluminum sulfate feed rate for a 5 million gal/day plant at a 12 mg/L dose, using £5 per gallon and £8.34 per gallon, yielding 101 gallons per day.

Calculate pounds per day for a 4 million gallon reservoir using a 0.3 mg/L dose and 8.34 pounds per gallon, then verify with an inverse mg/L calculation.

Calculate the alum dose in mg/L from a 2.2 million gallons per day flow using mg/L = pounds per day divided by million gallons per day × 8.34.

Calculate velocity in feet per second for flow of 1 million gallons per day through an 18-inch pipe using area velocity formulas from the formula sheet, yielding about 0.877 ft/s.

Calculate velocity in a ten-inch pipe with a flow of 5 cfs by dividing flow by area, converting diameter to feet, using area = 0.785 diameter squared, yielding 9.18 ft/s.