Exam math · Hydraulics
Pump and horsepower math
The power needed to move water against head, and how motor and pump efficiency inflate it.
The formula
Water horsepower = flow in gallons per minute x total head in feet over 3,960. Brake horsepower divides that by pump efficiency; motor horsepower divides again by motor efficiency.
The unit trap
Efficiencies enter as decimals and always divide. If your answer got smaller after applying an efficiency, it went the wrong way.
Worked practice example
Practice pump moving 500 gpm against 80 feet: 500 x 80 / 3,960 is about 10.1 water horsepower; at 75 percent pump efficiency, brake horsepower is roughly 13.5. (Invented numbers.)
On exam day
A formula and conversion table is provided with the standardized exam; the official version is published by the exam provider at gowpi.org. These pages teach the concepts in our own words so the sheet on the desk reads as a reminder, not a puzzle.
The rest of the math
| Volumes | Tank volume |
| Volumes | Pipe and cylinder volume |
| Flow | Flow and velocity |
| Flow | Detention time |
| Treatment math | Chemical dosage |
| Treatment math | Percent strength and dilution |
| Treatment math | Removal efficiency |
| Hydraulics | Pressure and head |
| Foundations | The conversion backbone |
| Foundations | Averages and loading rates |
| Foundations | The formula-first method |
The operator math sheet
One printable page: the exam format, the formula-first drill method, and the unit-conversion discipline that decides the math questions. Free.
No spam. One useful sheet and occasional notes.