The affinity laws
Turn the speed down a little and the power drops a lot. The three rules behind huge energy savings.
⏱ 6 min
- Everyday comparisonStep 1 of 6
Pedalling faster
Pedal twice as fast on a bike and you go roughly twice as fast. But it doesn’t feel twice as hard — it feels far harder. Wind resistance grows much faster than speed.
Pumps follow similar rules, and they are called the .
- ExplainedStep 2 of 6
The three rules
Flow grows in step with speed: 2× the speed → 2× the flow.
Head grows with speed squared: 2× the speed → 4× the head (remember: the outward push grew with RPM² in Module 1).
Power grows with speed cubed: 2× the speed → 8× the power.
- Try itStep 3 of 6
Slow the pump down
The dashed line is the pump at full speed. Lower the speed and watch the whole curve shrink, the operating point slide down the system curve, and the power fall.
Challenge: Set the speed to about 80% (2300 RPM). How much power do you need compared with full speed?
- ExplainedStep 4 of 6
The cube is the magic
Run at 80% of the speed and, by the cube rule, you need only about 0.8 × 0.8 × 0.8 ≈ 51% of the power. Your flow is still 80%.
In a real system with a height to lift, the operating point also slides along the system curve, so the exact numbers differ a little from the pure rules — the chart shows the real ones. Notice how the flow collapses at low speed: the pump can barely reach the height any more.
- ExplainedStep 5 of 6
Valve or speed?
The old way to get less flow is : partly close a valve. The pump keeps spinning at full speed and the extra pressure is simply burned off in the valve — like driving with the brake on.
A slows the motor instead. Same lower flow, far less electricity. That is why modern heating circulators and building pumps almost all have one.
- The impeller connectionStep 6 of 6
Trimming the impeller
A pump that is always too strong can also be fixed by machining its impeller a little smaller. The tip speed drops, and the curve shrinks — following very similar rules to slowing it down.
📌 Remember this
Change a pump’s speed and flow ∝ speed, head ∝ speed², power ∝ speed³. Slowing a pump with a variable speed drive saves far more energy than closing a valve.