Every variable frequency drive presentation has the same slide. Slow a pump 20% and the power drops by half, because power follows the cube of speed. It is a real law, it is on the slide for a reason, and on a water well it is usually the wrong number.
The cube law is true for a pump pushing water around a loop of pipe, where every foot of head it makes is spent on friction. A well is not that. Most of the head a well pump makes is static lift — raising water from the pumping level to the surface and then up to system pressure — and static lift does not get smaller when you slow the pump down. It is the same 300-odd feet at 60 Hz or at 50.
That one difference decides whether a drive on a well saves money, costs money, or earns its keep for reasons that have nothing to do with energy. This note is the arithmetic.
What the affinity laws say, and what they assume
For the same pump at a different speed:
flow changes with speed: Q₂ = Q₁ × (n₂ ÷ n₁)
head changes with the square of speed: H₂ = H₁ × (n₂ ÷ n₁)²
power changes with the cube of speed: P₂ = P₁ × (n₂ ÷ n₁)³
Those three relationships describe the pump. They move a point on the pump’s curve to the matching point on its curve at the new speed. What they do not tell you is where the pump will actually run, because that is decided by where the new pump curve crosses the system curve — the head the well and the piping demand at each flow.
On a friction-only system, the system curve is a parabola through zero and the affinity laws happen to land on it, so the cube law works. On a well, the system curve starts hundreds of feet up the y-axis at the static lift. The Hydraulic Institute and Europump’s guide to variable speed pumping says it plainly: in systems with high static head, a small turn-down in speed greatly reduces flow rate and pump efficiency, and using the affinity laws to calculate savings there can lead to major errors.
Slow the drive and see what happens
Take the well from our diagnosis note: 1,000 gpm at 60 Hz, static water level 180 ft, 50 ft of drawdown at full flow, 60 psi at the wellhead. At full speed the pump makes 379 ft of total head, and 319 ft of that is static lift plus system pressure that no speed change can touch.
Now turn the drive down and find where the pump curve meets the system curve at each speed:
| Drive | Speed | Affinity laws predict | The well makes |
|---|---|---|---|
| 60 Hz | 100% | 1,000 gpm | 1,000 gpm |
| 57 Hz | 95% | 950 gpm | 846 gpm |
| 54 Hz | 90% | 900 gpm | 674 gpm |
| 50 Hz | 83% | 833 gpm | 390 gpm |
| 48 Hz | 80% | 800 gpm | 183 gpm |
| 47 Hz | 78% | 783 gpm | nothing |
Read the last row twice. At about 47 Hz the pump’s shutoff head falls to the static lift, and the pump spins, heats the water in the bowls and delivers nothing. Everything between 47 and 60 Hz is this well’s entire working range, and the bottom of it is a place the pump must never be allowed to sit. That is why minimum speed is a design number on a well, not a default in the drive — and why it belongs next to the skip band from our critical speed note in the O&M record.
Three ways to get 700 gpm
Say the district only needs 700 gpm from this well for part of the year. There are three ways to get it, and the arithmetic separates them clearly. We have used an illustrative bowl-efficiency curve peaking at 80% at 1,000 gpm, a 94% motor and a 97% drive; your own pump’s curve will move the numbers, not the order.
| Method | Pump runs at | Input power | kWh per acre-foot |
|---|---|---|---|
| Throttle a valve to 700 gpm | 60 Hz, 451 ft of head | 86.9 kW | 674 |
| Slow the drive to 700 gpm | 54.4 Hz, 359 ft of head | 68.4 kW | 530 |
| Run full speed, fewer hours | 60 Hz, 1,000 gpm | 94.8 kW | 515 |
Three things are going on in that table.
Throttling is the expensive way. Closing a valve makes the pump climb its curve to 451 ft of head and spend the extra 92 ft burning energy across the valve. If a district is throttling a well today, a drive pays: at 700 gpm for 4,000 hours a year, the difference is about 74,000 kWh a year.
The drive is not the cheapest way. Slowing to 54 Hz moves the pump off its best efficiency point, and the drive has losses of its own. Per acre-foot it lands slightly worse than simply running the well at full speed, at its best efficiency point, for fewer hours — and fewer hours is exactly what our time-of-use scheduling note wants, because those hours can be the cheap ones.
The cube law would have promised much more. By the affinity laws, 70% flow should need about a third of the power. The real figure is 72% of full-speed power. Anyone who sized a drive’s payback on the slide would be off by more than a factor of two.
When a drive does pay for itself
None of that makes drives a bad idea on wells. It makes them a tool for specific jobs, and they are very good at these:
- Replacing throttling or bypass. Any well that holds a flow or a pressure by closing a valve is burning energy across that valve. This is where the real energy savings are.
- Feeding a zone with little or no storage. Where the well has to follow demand minute by minute to hold pressure, a drive does it smoothly and a fixed-speed pump cannot do it at all.
- Matching a pump to a well that has changed. A pump sized for a well that has since lost capacity, or for a water table that has since dropped, can over-pump the well — pulling the pumping level toward the screen, pulling sand, cascading water. Trimming speed matches it to the well it has today without pulling the pump to trim impellers.
- Soft starts. A drive ramps the motor up instead of slamming it across the line: lower inrush current, less mechanical shock on the lineshaft and couplings, less water hammer in the discharge. That saves no energy and can still be worth the whole cost on a well with a history of start-up damage.
- Getting the most out of the cheap hours. Some motors and pumps can run a little above 60 Hz. Whether yours can is a question for the motor nameplate and the pump maker, not for the drive’s parameter menu.
What the drive brings with it
A drive changes the machine, not just the speed, and the job is not finished when it is wired:
- New frequencies to avoid. A fixed-speed pump runs at one speed. A pump on a drive can sit at any speed in its range, and the guide on variable speed pumping warns that the chance of meeting a resonance inside that range goes up sharply. Program the skip band before commissioning, not after the first vibration complaint.
- Minimum speed. Set it from the well’s static lift and the pump’s curve, with margin, as above. On this example well it is nowhere near the drive’s factory default.
- The motor. Drive output is hard on insulation and can push current through the bearings. Motors for drive duty are built to NEMA MG 1 Part 31, and long leads to the motor may need a filter at the drive. On a submersible, check the pump maker’s requirements for drive operation before buying.
- The utility side. Drives draw distorted current back from the supply. IEEE 519 sets the limits most utilities expect, and a large drive may need filtering to meet them.
Do the arithmetic before you buy one
A drive is justified by the flow the district actually needs over the year, not by the nameplate. Before buying, get three numbers:
- The flow profile. How many hours a year does this well need to run at less than full flow? If the answer is “none, it runs flat out when it runs”, a drive saves almost nothing on energy.
- The system curve. Static lift, drawdown at the working flows, and the system pressure. That tells you the working speed range and where the pump will actually land at each speed.
- The alternative. Compare the drive against running full speed for fewer hours, not only against throttling. If there is storage, fewer hours usually wins on energy. If there is no storage, the drive may be the only option that works at all.
Then payback is simple: drive cost installed, divided by the kWh saved each year times what a kWh costs in the hours the well runs. The speed calculator will convert between drive frequency and pump speed for any motor.
Quick answers
Does a VFD save energy on a well pump?
It saves a lot compared with throttling a valve. Compared with running the well at full speed for fewer hours, it usually saves little or nothing on a well lifting mostly static head, because the pump moves off its best efficiency point and the drive has losses of its own.
Why do the affinity laws overstate savings on a well?
They assume all of the head is friction, which falls with speed. On a well most of the head is static lift, which does not. A 10% speed cut can remove a third or more of the flow while cutting power by far less than the cube law predicts.
What is the minimum speed for a well pump on a VFD?
The speed below which the pump can no longer lift water to the system, plus a margin. On a high-lift well that can be 45 to 50 Hz, not the drive’s default. It depends on static lift, system pressure and the pump’s shutoff head.
See the working speed range, minimum speed and skip band the record implies for your own wells. Request a walkthrough →
Sources
- Europump, Hydraulic Institute and U.S. Department of Energy. Variable Speed Pumping: A Guide to Successful Applications, Executive Summary. 2004. Source for high static head systems losing flow and efficiency sharply with a small speed reduction, the warning that affinity-law savings estimates in systems with static head can lead to major errors, the increased likelihood of resonance within a variable speed range, and converter losses.
- U.S. Department of Energy. Adjustable Speed Drive Part-Load Efficiency, Motor Systems Tip Sheet #11. 2012. Source for the cube-law relationship as applying to pumps with no static lift, and for drive efficiency near 97% at full load.
- NEMA. ANSI/NEMA MG 1, Motors and Generators, Part 31. Source for definite-purpose inverter-fed motors.
- IEEE. IEEE 519, Standard for Harmonic Control in Electric Power Systems. Source for the harmonic limits applied at the point of common coupling with the utility.
Every link above was retrieved and read on 2026-09-26. Paid standards are named by designation so you can check them against your own copy.