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 usually increases friction loss sharply, so the pump operating point changes when system demand changes.
Head Is Energy Per Unit Weight
In pump questions, head is usually expressed in feet. It is not the physical length of the pipe. It is the energy the pump must add to move wastewater from the wet well to the discharge point while overcoming elevation, friction, and pressure conditions.
Components of Total Dynamic Head
TDH is commonly built from these pieces:
| Component | Meaning | Example |
|---|---|---|
| Static head | Elevation difference between suction level and discharge hydraulic grade | Wet well water surface to force-main discharge elevation |
| Friction head | Energy lost in pipe and fittings | Long force main, elbows, valves, check valve |
| Velocity head | Energy associated with moving flow | Usually small on basic exams |
| Pressure head | Required pressure at discharge, if any | Pumping into a pressurized main |
Simplified exam setup:
TDH = static head + friction head + pressure head + velocity head
Some advanced pump problems subtract suction pressure head if the suction side is pressurized, but most collection lift station questions use a wet well open to the atmosphere and focus on static lift plus force-main losses.
Pressure and Head Conversion
For water and wastewater math near ordinary conditions:
| Conversion | Use |
|---|---|
| ft of head = psi x 2.31 | Convert pressure gauge readings 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 equivalent = 92 x 0.433 = 39.8 psi.
Horsepower Formulas
The WPI wastewater formula table includes water horsepower, brake horsepower, motor horsepower, and wire-to-water efficiency relationships. For most collection questions, know these two:
Water hp = (Flow, gpm x Head, ft) / 3,960
Brake hp = (Flow, gpm x Head, ft) / (3,960 x pump efficiency)
If motor efficiency is included:
Motor hp = (Flow, gpm x Head, ft) / (3,960 x pump efficiency x motor efficiency)
Efficiency must be a decimal. Use 0.70, not 70.
Worked Example: Brake Horsepower
A pump delivers 500 gpm against 75 ft TDH. Pump efficiency is 68%. Find brake horsepower.
- Water hp = (500 x 75) / 3,960 = 9.47 hp.
- Brake hp = 9.47 / 0.68 = 13.9 hp.
A motor would need to be selected above this brake horsepower with appropriate service factor and design margin. The exam answer may simply be the calculated horsepower.
Worked Example: TDH From Components
A lift station discharges to a gravity manhole. The discharge elevation is 48 ft above the wet-well pumping level. Estimated friction loss at design flow is 22 ft. Minor losses and velocity head total 3 ft. What TDH should be used?
TDH = 48 + 22 + 3 = 73 ft.
If the problem also gives a required 10 psi residual pressure at discharge, convert that pressure to head: 10 psi x 2.31 = 23.1 ft. TDH would become 48 + 22 + 3 + 23.1 = 96.1 ft.
Pump Curve Concepts That Show Up in Words
- A pump curve shows the head a pump can produce at different flows.
- A system curve shows the head the piping system requires at different flows.
- The operating point is where the pump curve and system curve intersect.
- More force-main friction moves the operating point toward lower flow.
- Worn impellers, ragging, air binding, or check-valve problems can reduce actual flow below expected curve performance.
Common Traps
- Using static head only and ignoring friction in a long force main.
- Multiplying by efficiency instead of dividing when calculating brake horsepower.
- Entering 72 instead of 0.72 for 72% efficiency.
- Confusing pressure in psi with head in feet.
- Assuming a high-pressure reading always means high flow; it may mean a closed valve, blockage, or high friction condition.
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?