Pump Head, Total Dynamic Head, Pressure/Head Conversion, Horsepower, and Efficiency Basics
Key Takeaways
- Total dynamic head is the head a pump must overcome: static lift plus friction losses plus minor velocity and pressure-head requirements.
- Pressure and head are interchangeable for water-style calculations: 1 psi is about 2.31 ft of head, and 1 ft of head is about 0.433 psi.
- Water horsepower equals (gpm x head) / 3,960; brake horsepower divides that result by pump efficiency.
- Efficiency must be entered as a decimal in horsepower formulas, so 70% becomes 0.70.
- Higher flow in a force main increases friction loss sharply, so the pump operating point shifts when system demand changes.
Head Is Energy Per Unit Weight
In pump questions, head is expressed in feet, but it is not the physical length of pipe. It is the energy per pound of liquid that the pump must add to move wastewater from the wet well to the discharge point while overcoming elevation, friction, and any required discharge pressure. Operators think in head because pump curves are plotted as head versus flow.
Components of Total Dynamic Head
Total dynamic head (TDH) is built from these pieces:
| Component | Meaning | Example |
|---|---|---|
| Static head | Elevation difference between suction level and discharge grade | Wet-well surface to force-main discharge elevation |
| Friction head | Energy lost in pipe and fittings | Long force main, elbows, valves, check valve |
| Velocity head | Energy of the moving flow | Usually small on basic exams |
| Pressure head | Required residual pressure at discharge | Pumping into a pressurized main |
Simplified exam setup: TDH = static head + friction head + pressure head + velocity head. Some advanced problems subtract a positive suction head when the suction side is pressurized or flooded, but most collection lift-station questions assume a wet well open to the atmosphere, so they focus on static lift plus force-main losses.
Pressure and Head Conversion
For water and wastewater near ordinary temperatures (specific gravity about 1.0):
| Conversion | Use |
|---|---|
| ft of head = psi x 2.31 | Convert a pressure gauge reading to head |
| psi = ft of head x 0.433 | Convert head to pressure |
Example: A discharge gauge reads 35 psi. Head = 35 x 2.31 = 80.9 ft. Example: A pump must overcome 92 ft of head. Pressure = 92 x 0.433 = 39.8 psi. The two factors are reciprocals (1 / 2.31 = 0.433), so picking the wrong one inverts the answer.
Horsepower Formulas
The WPI wastewater formula sheet lists water, brake, and motor horsepower plus wire-to-water efficiency. The 3,960 constant comes from 1 hp = 33,000 ft-lb/min divided by the 8.34 lb weight of a gallon of water. For collection questions, master these:
- Water hp = (Flow, gpm x Head, ft) / 3,960
- Brake hp = (Flow, gpm x Head, ft) / (3,960 x pump efficiency)
- Motor hp = (Flow, gpm x Head, ft) / (3,960 x pump efficiency x motor efficiency)
Water horsepower is the theoretical minimum power delivered to the liquid. Brake horsepower is the larger shaft power the motor must supply because the pump is not 100% efficient. Always express efficiency as a decimal: use 0.70, never 70.
Worked Example: Brake Horsepower
A pump delivers 500 gpm against 75 ft TDH at 68% pump efficiency. Find brake horsepower.
- Water hp = (500 x 75) / 3,960 = 9.47 hp.
- Brake hp = 9.47 / 0.68 = 13.9 hp.
Brake hp is always larger than water hp because you divide by a number less than one. A selected motor would sit above this value with service factor and design margin; the exam answer is usually just the calculated horsepower.
Worked Example: TDH From Components
A lift station discharges to a gravity manhole 48 ft above the wet-well pumping level. Friction loss at design flow is 22 ft; minor losses and velocity head total 3 ft. TDH = 48 + 22 + 3 = 73 ft. If the problem also requires 10 psi residual pressure at the discharge, convert it: 10 x 2.31 = 23.1 ft, so TDH = 48 + 22 + 3 + 23.1 = 96.1 ft.
Pump and System Curve Concepts in Words
| Term | What It Means |
|---|---|
| Pump curve | Head the pump can produce at each flow |
| System curve | Head the piping requires at each flow |
| Operating point | Where the pump and system curves intersect |
| Added friction | Shifts the operating point to lower flow, higher head |
| Worn impeller or air binding | Pump falls below its rated curve, delivering less flow |
A rising discharge pressure with falling flow often signals a partly closed valve, a blockage, or rags on the impeller, not a healthier pump.
Worked Example: Motor Horsepower
A lift-station pump moves 800 gpm against 60 ft TDH. Pump efficiency is 75% and motor efficiency is 90%. Find the motor horsepower input.
- Water hp = (800 x 60) / 3,960 = 12.1 hp.
- Brake hp = 12.1 / 0.75 = 16.1 hp.
- Motor hp = 16.1 / 0.90 = about 17.9 hp.
The product of the two efficiencies (0.75 x 0.90 = 0.675) is the wire-to-water efficiency, about 67.5%. Wire-to-water efficiency measures how much of the electrical input actually ends up as useful work on the water, so it always falls below either single efficiency alone.
Net Positive Suction Head in Plain Words
Many lift-station wet wells sit below the pumps, but submersible and self-priming setups still depend on having enough pressure at the pump inlet to keep liquid from flashing to vapor. When suction conditions are poor, the pump may cavitate: vapor bubbles form and collapse, causing noise, vibration, lost capacity, and impeller pitting. Operators reduce cavitation risk by keeping the wet-well level above the manufacturer minimum, clearing inlet screens, and avoiding excessive lift on the suction side. The exam may describe rattling, gravel-like noise and lost flow and expect you to identify cavitation.
Common Traps
- Using static head only and ignoring friction in a long force main.
- Multiplying by efficiency instead of dividing when finding brake horsepower.
- Entering 72 instead of 0.72 for 72% efficiency.
- Confusing psi with feet of head (factor of 2.31).
- Assuming a high-pressure reading always means high flow; it may mean a closed valve, blockage, or high friction.
A pump must lift wastewater 38 ft and overcome 17 ft of estimated friction loss. Velocity and minor losses are 2 ft. What is the approximate TDH?
A pressure gauge reads 42 psi on a force main. What is the approximate equivalent head in feet?
A pump delivers 650 gpm against 80 ft of TDH at 65% pump efficiency. What is the approximate brake horsepower?
Compared with water horsepower for the same flow and head, brake horsepower is always: