Water operator math tutorial
Filter Backwash Rate
Find the backwash rate from the backwash flow and the filter dimensions.
Backwash rate uses the same idea as loading rate, but the flow is the backwash pump flow and the filter area comes from length and width.
A rate that is too low leaves the media dirty; too high can wash media out. Exams ask you to calculate it and compare it to a target range.
The formula
backwash rate (gpm/ft²) = backwash flow (gpm) ÷ [length (ft) × width (ft)]
| Variable | Unit |
|---|---|
| Backwash flow | gpm |
| Filter length | ft |
| Filter width | ft |
| Result: Backwash rate | gpm/ft² |
Applies to: Water Treatment.
Common exam tip: Both dimensions must be in feet. Convert inches before computing area.
Calculator
Backwash rate
20 gpm/ft²
- 1. 10 ft × 15 ft = 150 ft²
- 2. 3,000 gpm ÷ 150 ft² = 20 gpm/ft²
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Worked examples
Example 1
3,000 gpm backwashes a 10 ft by 15 ft filter.
- 10 ft × 15 ft = 150 ft²
- 3,000 gpm ÷ 150 ft² = 20 gpm/ft²
Answer: 20 gpm/ft²
Example 2
4,200 gpm backwashes a 12 ft by 20 ft filter.
- 12 ft × 20 ft = 240 ft²
- 4,200 gpm ÷ 240 ft² = 17.5 gpm/ft²
Answer: 17.5 gpm/ft²
Common mistakes
Wrong result: 120 gpm/ft²
adding length and width instead of multiplying
Wrong result: 0.05 gpm/ft²
dividing area by flow (upside down)
Practice questions
1. 3,300 gpm, filter 10 ft by 20 ft. Backwash rate?
- A16.5 gpm/ft²
- B110 gpm/ft²
- C0.06 gpm/ft²
- D165 gpm/ft²
Show answer and explanation
Correct answer: A. 10 ft × 20 ft = 200 ft² 3,300 gpm ÷ 200 ft² = 16.5 gpm/ft² Answer: 16.5 gpm/ft². A common slip is adding length and width instead of multiplying, which gives 110 gpm/ft².
2. 5,000 gpm, filter 12 ft by 25 ft. Backwash rate?
- A135.14 gpm/ft²
- B16.67 gpm/ft²
- C0.06 gpm/ft²
- D166.7 gpm/ft²
Show answer and explanation
Correct answer: B. 12 ft × 25 ft = 300 ft² 5,000 gpm ÷ 300 ft² = 16.67 gpm/ft² Answer: 16.67 gpm/ft². A common slip is adding length and width instead of multiplying, which gives 135.14 gpm/ft².
3. 2,520 gpm, filter 12 ft by 12 ft. Backwash rate?
- A105 gpm/ft²
- B0.06 gpm/ft²
- C17.5 gpm/ft²
- D175 gpm/ft²
Show answer and explanation
Correct answer: C. 12 ft × 12 ft = 144 ft² 2,520 gpm ÷ 144 ft² = 17.5 gpm/ft² Answer: 17.5 gpm/ft². A common slip is adding length and width instead of multiplying, which gives 105 gpm/ft².
Where this formula applies
This calculation can appear in the disciplines below. Exact exam coverage depends on your state, certification level, and official exam outline.
Water Treatment
Study guides
Keep going with the full guide
Water Operator Math Made Simple walks through operator math step by step and includes printable references plus a full practice exam.
Water Operator Math Made Simple
A Step-by-Step Guide to the Math Every Water Operator Needs to Know