Water operator math tutorial
Brake and Motor Horsepower
Account for pump and motor efficiency to find the motor horsepower required.
A pump needs more power at the shaft than the water receives, and a motor needs more power than the shaft uses. Each step loses some to inefficiency.
Divide water horsepower by pump efficiency to get brake horsepower, then divide again by motor efficiency for motor horsepower.
The formula
motor hp = [flow (gpm) × head (ft) ÷ 3,960] ÷ pump efficiency ÷ motor efficiency
| Variable | Unit |
|---|---|
| Flow | gpm |
| Total head | ft |
| Pump efficiency | % |
| Motor efficiency | % |
| Result: Motor horsepower | hp |
Conversion factors used: 3,960 for gpm and feet of head.
Applies to: Water Treatment, Water Distribution, Wastewater Treatment, Collection Systems.
Common exam tip: Efficiency always makes the required horsepower go up. If your answer got smaller, you multiplied.
Calculator
Motor horsepower
33.67 hp
- 1. Water hp = 1,000 × 90 ÷ 3,960 = 22.73 hp
- 2. Brake hp = 22.73 ÷ 0.75 = 30.3 hp
- 3. Motor hp = 30.3 ÷ 0.9 = 33.67 hp
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
1,000 gpm at 90 ft; pump 75% efficient, motor 90% efficient.
- Water hp = 1,000 × 90 ÷ 3,960 = 22.73 hp
- Brake hp = 22.73 ÷ 0.75 = 30.3 hp
- Motor hp = 30.3 ÷ 0.9 = 33.67 hp
Answer: 33.67 hp
Example 2
600 gpm at 140 ft; pump 80% efficient, motor 92% efficient.
- Water hp = 600 × 140 ÷ 3,960 = 21.21 hp
- Brake hp = 21.21 ÷ 0.8 = 26.52 hp
- Motor hp = 26.52 ÷ 0.92 = 28.82 hp
Answer: 28.82 hp
Common mistakes
Wrong result: 15.34 hp
multiplying by the efficiencies instead of dividing
Wrong result: 30.3 hp
stopping at brake horsepower
Practice questions
1. 1,500 gpm, 100 ft, pump 78%, motor 91%. Motor horsepower?
- A26.89 hp
- B48.56 hp
- C53.37 hp
- D533.7 hp
Show answer and explanation
Correct answer: C. Water hp = 1,500 × 100 ÷ 3,960 = 37.88 hp Brake hp = 37.88 ÷ 0.78 = 48.56 hp Motor hp = 48.56 ÷ 0.91 = 53.37 hp Answer: 53.37 hp. A common slip is multiplying by the efficiencies instead of dividing, which gives 26.89 hp.
2. 800 gpm, 50 ft, pump 70%, motor 88%. Motor horsepower?
- A6.22 hp
- B14.43 hp
- C164 hp
- D16.4 hp
Show answer and explanation
Correct answer: D. Water hp = 800 × 50 ÷ 3,960 = 10.1 hp Brake hp = 10.1 ÷ 0.7 = 14.43 hp Motor hp = 14.43 ÷ 0.88 = 16.4 hp Answer: 16.4 hp. A common slip is multiplying by the efficiencies instead of dividing, which gives 6.22 hp.
3. 2,200 gpm, 75 ft, pump 82%, motor 93%. Motor horsepower?
- A54.64 hp
- B31.78 hp
- C50.81 hp
- D546.4 hp
Show answer and explanation
Correct answer: A. Water hp = 2,200 × 75 ÷ 3,960 = 41.67 hp Brake hp = 41.67 ÷ 0.82 = 50.81 hp Motor hp = 50.81 ÷ 0.93 = 54.64 hp Answer: 54.64 hp. A common slip is multiplying by the efficiencies instead of dividing, which gives 31.78 hp.
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