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Filtration and removal: California T2 water treatment operator math

Filtration and loading rates, filter production, backwash, UFRV, percent and log removal.

Below are 3 worked examples. Each answer is computed with the formulas and constants on the CA Exam Conversion Sheet (revised 4/30/2026), and the solution names the line it uses.

Formulas from the sheet for this topic

Example 1. A 29 ft × 27 ft filter is backwashed at 17 GPM/ft² for 8 minutes. How many gallons of backwash water are used?

  1. A) 797,000 gal
  2. B) 13,300 gal
  3. C) 106,000 gal
  4. D) 1,770 gal
Show the answer and worked solution

Answer: C) 106,000 gal

1. Filter area = 29 × 27 = 783 ft² [Sheet p.1, Area and Volume: "Area of Rectangle = Length x Width"]. 2. Backwash Volume = Filter Area × Backwash Rate × Time [Sheet p.2, Filtration: "Backwash Volume (Gal) = Filter Area (Ft2) x Backwash Rate (GPM/Ft2) x Time (min)"] = 783 × 17 × 8 = 106,488 gal. 3. Answer: 106,000 gal (rounded to 3 significant figures).

Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Area and Volume: "Area of Rectangle = Length x Width"; p.2, Filtration: "Backwash Volume (Gal) = Filter Area (Ft2) x Backwash Rate (GPM/Ft2) x Time (min)"

Example 2. A filter is backwashed at 22.5 GPM/ft². What is the rate of rise of the water in inches per minute?

  1. A) 36.1 in/min
  2. B) 14.0 in/min
  3. C) 270 in/min
  4. D) 3.01 in/min
Show the answer and worked solution

Answer: A) 36.1 in/min

1. Rate of Rise = Backwash Rate × 12 (in/ft) ÷ 7.48 (gal/ft³) [Sheet p.2, Filtration: "Rate of Rise (Inches/min) = Backwash Rate (GPM/Ft2) x 12 (in/Ft) / 7.48 (gal/Ft3)"]. 2. = 22.5 × 12 ÷ 7.48 = 270 ÷ 7.48 = 36.1 in/min. 3. Answer: 36.1 in/min (rounded to 3 significant figures).

Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.2, Filtration: "Rate of Rise (Inches/min) = Backwash Rate (GPM/Ft2) x 12 (in/Ft) / 7.48 (gal/Ft3)"

Example 3. A filter is backwashed at 23 GPM/ft². What is the rate of rise of the water in inches per minute?

  1. A) 3.07 in/min
  2. B) 276 in/min
  3. C) 36.9 in/min
  4. D) 14.3 in/min
Show the answer and worked solution

Answer: C) 36.9 in/min

1. Rate of Rise = Backwash Rate × 12 (in/ft) ÷ 7.48 (gal/ft³) [Sheet p.2, Filtration: "Rate of Rise (Inches/min) = Backwash Rate (GPM/Ft2) x 12 (in/Ft) / 7.48 (gal/Ft3)"]. 2. = 23 × 12 ÷ 7.48 = 276 ÷ 7.48 = 36.9 in/min. 3. Answer: 36.9 in/min (rounded to 3 significant figures).

Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.2, Filtration: "Rate of Rise (Inches/min) = Backwash Rate (GPM/Ft2) x 12 (in/Ft) / 7.48 (gal/Ft3)"

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