Water operator math tutorial
Detention Time
Divide basin volume by flow to find how long water stays in the tank.
Detention time tells you how long water is held in a basin, clearwell, or tank. It affects settling, disinfection, and how quickly a change reaches the effluent.
Volume and flow must use the same time base. This version uses gallons and gallons per minute, so the answer comes out in minutes.
The formula
detention time (min) = volume (gal) ÷ flow (gpm)
| Variable | Unit |
|---|---|
| Volume | gal |
| Flow | gpm |
| Result: Detention time | min |
Conversion factors used: 60 minutes per hour.
Applies to: Water Treatment, Water Distribution, Wastewater Treatment, Collection Systems.
Common exam tip: Check the question's units first. If flow is in MGD, convert volume and flow to the same basis.
Calculator
Detention time
300 min
- 1. 150,000 gal ÷ 500 gpm = 300 min
- 2. 300 min ÷ 60 = 5 hr
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
A 150,000 gal basin receives 500 gpm.
- 150,000 gal ÷ 500 gpm = 300 min
- 300 min ÷ 60 = 5 hr
Answer: 300 min
Example 2
A 75,000 gal clearwell runs at 1,250 gpm.
- 75,000 gal ÷ 1,250 gpm = 60 min
- 60 min ÷ 60 = 1 hr
Answer: 60 min
Common mistakes
Wrong result: 0 min
dividing flow by volume (upside down)
Wrong result: 5 min
reporting hours when minutes were asked
Practice questions
1. A 240,000 gal tank at 1,200 gpm. Detention time in minutes?
- A3.3 min
- B2,000 min
- C200 min
- D20 min
Show answer and explanation
Correct answer: C. 240,000 gal ÷ 1,200 gpm = 200 min 200 min ÷ 60 = 3.33 hr Answer: 200 min. A common slip is reporting hours when minutes were asked, which gives 3.3 min.
2. A 96,000 gal basin at 400 gpm. Detention time in minutes?
- A4 min
- B2,400 min
- C24 min
- D240 min
Show answer and explanation
Correct answer: D. 96,000 gal ÷ 400 gpm = 240 min 240 min ÷ 60 = 4 hr Answer: 240 min. A common slip is reporting hours when minutes were asked, which gives 4 min.
3. A 180,000 gal basin at 750 gpm. Detention time in minutes?
- A240 min
- B4 min
- C2,400 min
- D24 min
Show answer and explanation
Correct answer: A. 180,000 gal ÷ 750 gpm = 240 min 240 min ÷ 60 = 4 hr Answer: 240 min. A common slip is reporting hours when minutes were asked, which gives 4 min.
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
Water Distribution
Wastewater Treatment
Collection Systems
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