How this instrument works
A fan's flow rate rises and falls in direct proportion to its rotational speed. Picture a centrifugal impeller at a fixed blade angle: it displaces one particular parcel of air with every revolution, so at 1,000 RPM it displaces that parcel a thousand times a minute, and at 1,500 RPM it displaces it fifty percent more often. Nothing about the geometry changes, only how many times per second it happens, so the simplest possible relationship, Q₂ = Q₁ × (N₂ ⁄ N₁), holds exactly as long as the flow pattern around the blades stays geometrically similar.
This is the first of three fan affinity laws, and the mildest. Pressure across the fan rises with the square of the speed ratio, and shaft power rises with the cube, because pressure depends on velocity squared and power on velocity cubed, while flow depends on velocity to the first power alone. The laws rest on dynamic similarity: as long as the system curve downstream — ductwork, dampers, grilles — stays fixed, every operating point at the new speed sits at the same relative spot on a scaled version of the same fan curve, so one ratio predicts flow without needing a chart at all.
The law breaks the moment the system itself changes shape. Close a damper, add a filter, or let a coil ice over, and the resistance curve shifts, so the fan settles at a new point this simple ratio cannot see — that calls for the fan's full performance curve, not one speed ratio. It also assumes air density stays put; a rooftop unit moving hot air in summer and cold air in winter meets slightly different density, which nudges pressure and power more than it nudges flow, since flow is the one quantity here that does not depend on density at all.
- Enter Flow rate at RPM 1 — the fan's known or rated airflow at its current speed, in any consistent volumetric unit.
- Enter RPM 1 — the rotational speed at which that flow rate was measured or rated.
- Enter RPM 2 — the new or target speed you want to evaluate, in the same RPM units.
- Read Flow rate at RPM 2 — the predicted airflow once that speed change is applied.
Worked example — a 2 m³/s fan sped up to 1,500 RPM
An air-handling unit's supply fan is rated at 2 m³/s while its motor turns 1,000 RPM. A comfort complaint means more air is needed, so a technician raises the variable-frequency drive's set point to 1,500 RPM. Flow rate at RPM 2 works out to 2 × (1,500 ⁄ 1,000) = 2 × 1.5 = 3.0 m³/s, a fifty-percent jump in airflow for a fifty-percent jump in speed, exactly as the first affinity law predicts, since flow scales with speed to the first power alone.
The same fifty-percent speed increase does not treat pressure or power so gently. Pressure would climb by 1.5² = 2.25 times, and shaft power by 1.5³ = 3.375 times, so a motor drawing 1.5 kW at 1,000 RPM would need roughly 5.1 kW at 1,500 RPM. That gap is the entire reason variable-speed drives save energy at part load, and it is exactly the mistake that trips up anyone who assumes every fan quantity scales the same way with speed.
Questions
Why does flow rate scale directly with RPM instead of some other power of it?
Because a fixed-geometry impeller sweeps a fixed volume of air with every revolution, provided the flow pattern around the blades stays geometrically similar. Turn it fifty percent faster and it sweeps that same volume fifty percent more times per second, a straight first-power relationship. Pressure and power involve velocity squared and cubed, which is why they climb faster than flow does.
Does this formula still work if I close a damper or add a filter?
Not reliably. Closing a damper or fitting a dirty filter changes the system resistance curve, which moves the fan's actual operating point off the curve this ratio assumes. The first affinity law only predicts flow correctly when the ductwork, dampers, and grilles stay exactly as they were — same system curve, different speed. A changed system needs the fan's full performance curve, not a single ratio.
How is the flow law different from the fan power law?
Flow scales with speed to the first power; shaft power scales with speed cubed. Raise a fan's RPM by fifty percent and flow rises by fifty percent, but the power needed to drive it rises by 1.5³, about 3.4 times the original draw. That cube relationship is why slowing a fan even slightly with a variable-frequency drive saves disproportionately more energy than the airflow reduction alone would suggest.
Does the same law apply to pumps, not just fans?
Yes. Centrifugal pumps obey the identical set of affinity laws, because both machines move a fluid with a rotating impeller inside a casing: flow scales with speed, head scales with speed squared, and power scales with speed cubed. A pump curve behaves the same way a fan curve does, so an engineer estimating a pump's new output after a speed change can reuse this exact formula.
What breaks down at very low fan speeds?
At low speeds the flow inside the fan stops behaving like a scaled-down copy of the flow at higher speed — bearing friction, motor slip, and Reynolds-number effects start to matter more than blade geometry alone. Manufacturers generally consider the affinity laws reliable from roughly thirty to a hundred percent of rated speed; below that, measured performance data is safer than the ratio.
Can I use flow rate at RPM 2 to size a new motor?
Not directly — flow rate alone does not tell you power. Apply the third affinity law, power scaling with the cube of the speed ratio, to the motor's original draw at RPM 1, then add a margin for drive and bearing losses. Sizing a motor from the flow figure alone, while ignoring the cube relationship power actually follows, is a common and costly mistake.