What are the Pump Affinity Laws?
The Affinity Laws are mathematical rules that express the relationship between speed, flow rate, pressure (head), and power consumption for centrifugal pumps and fans.
They demonstrate that flow is directly proportional to speed, pressure is proportional to the square of the speed, and power is proportional to the cube of the speed. These laws apply strictly to centrifugal loads, not positive displacement pumps.
The Cubic Relationship of Power to Speed
The most critical law for energy savings is the power relationship. Because power consumption drops by the cube of the speed reduction, even small decreases in speed yield massive energy savings.
The Formula: P2 = P1 x (N2 / N1)³. Where P is power and N is RPM or flow speed.
For example, if you reduce a pump's speed by just 20% (running at 80% of normal speed), the power requirement is: (0.80)³ = 0.512. That means running at 80% flow requires only 51.2% of the original power—nearly a 50% energy savings.
Calculating Annual VFD Savings
To calculate actual monetary savings, you must compare the energy used by a mechanical throttling method (like a discharge valve) against the energy used by a VFD across your specific operational load profile.
Example: A 50 HP (37 kW) pump runs 4,000 hours a year at $0.10/kWh. If throttled by a valve to 80% flow, it might still draw 90% power (33.3 kW), costing $13,320 annually. With a VFD at 80% flow, it draws 51% power (18.8 kW), costing $7,520 annually. The savings is roughly $5,800 per year just for that one operational state.
Limitations of the Affinity Laws
The Affinity Laws assume a system with purely friction head (resistance from piping). In the real world, many systems have 'static head'—meaning the pump has to lift water vertically or push into a pressurized vessel.
If a system has high static head, a pump must maintain a minimum speed just to overcome gravity. In these cases, slowing the pump too much results in zero flow, and the pure cubic savings calculation must be adjusted against the system curve.
Frequently asked questions
Do the affinity laws apply to positive displacement pumps?
No. Positive displacement pumps (like gear or lobe pumps) have a linear relationship with power and speed. A VFD will still save energy, but the savings will not be cubic.
Can a VFD save energy if the motor always runs at 100% speed?
No. VFDs themselves consume about 3-5% of the power they pass through due to heat loss. If a process truly requires 100% flow 24/7, a VFD will actually consume slightly more energy than an across-the-line starter.
What is the difference between a pump curve and a system curve?
A pump curve shows what the pump is mechanically capable of producing at different speeds. A system curve shows the resistance of the piping network. The pump operates exactly where these two curves intersect.
Will slowing down a fan motor cause it to overheat?
Standard motors rely on a shaft-mounted fan for cooling. If run too slowly for extended periods, they may overheat. When using a VFD, it is best practice to install an 'inverter-duty' motor designed to handle lower speeds and VFD harmonics.