Exam math · Volumes
Pipe and cylinder volume
Water held in a length of pipe: the cylinder formula lying on its side.
The formula
V = 0.785 x diameter squared x length.
The unit trap
Pipe diameters arrive in inches and lengths in feet. Convert the diameter to feet before squaring, because squaring an unconverted number squares the error too.
Worked practice example
A practice main 12 inches across is 1 foot; a 500-ft run holds 0.785 x 1 x 1 x 500, about 393 cubic feet, times 7.48 for roughly 2,937 gallons. (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 |
| 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 |
| Hydraulics | Pump and horsepower math |
| 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.