Pump Affinity Laws Calculator
Predict how a centrifugal pump's flow rate, head, and power change when its speed is varied using the pump affinity laws. Essential for engineers evaluating variable-speed drives or re-rating existing pumps for new duty points.
About this calculator
The pump affinity laws describe the proportional relationships between a centrifugal pump's rotational speed and its hydraulic performance. When speed changes from N₁ to N₂, the three laws state: (1) Flow scales linearly: Q₂ = Q₁ × (N₂/N₁); (2) Head scales with the square of speed: H₂ = H₁ × (N₂/N₁)²; (3) Power scales with the cube of speed: P₂ = P₁ × (N₂/N₁)³. The cubic relationship between speed and power is why variable-speed drives (VSDs) offer dramatic energy savings — reducing speed by just 20% cuts power consumption by nearly 50%. These laws assume geometric similarity, the same pump, and that efficiency remains constant, which is approximately true near the best efficiency point (BEP). They apply to both speed changes and geometrically similar (homologous) pumps of different sizes.
How to use
A pump runs at 1450 RPM, delivering 60 m³/h, 25 m of head, and consuming 8 kW. The speed is increased to 1750 RPM. Speed ratio: 1750/1450 = 1.2069. New flow: 60 × 1.2069 = 72.4 m³/h. New head: 25 × (1.2069)² = 25 × 1.4566 = 36.4 m. New power: 8 × (1.2069)³ = 8 × 1.759 = 14.1 kW. So increasing speed by ~21% increases flow by 21%, head by 46%, and power demand by 76% — illustrating how power grows far more steeply than flow with speed increases.
Frequently asked questions
How accurate are the pump affinity laws for predicting real pump performance?
The affinity laws are an approximation that is most accurate when the pump operates near its best efficiency point (BEP) and speed changes are modest, typically within ±30% of the original speed. At larger speed deviations, the actual efficiency curve shifts and the laws can overestimate or underestimate performance. They also assume that system resistance curves are purely quadratic (friction-dominated), which is not true when a significant portion of the head is static (elevation difference). For precise predictions, especially in critical applications, manufacturers' performance curves at the new speed or computational fluid dynamics analysis should be used.
Why do variable speed drives save so much energy on centrifugal pumps?
The third affinity law shows that pump power scales with the cube of speed (P ∝ N³). This means a 10% reduction in speed reduces power by about 27%, and a 20% reduction cuts power by nearly 49%. In systems where flow demand varies (most building HVAC, water supply, and process systems), throttling control with a fixed-speed pump wastes energy as pressure across a control valve. A VSD instead reduces the pump speed to match demand, eliminating throttling losses and delivering the cubic savings of the affinity law. Payback periods for VSDs on large pumps are often under two years through electricity cost savings alone.
Do the pump affinity laws apply when changing impeller diameter as well as speed?
Yes — the affinity laws also apply to changes in impeller diameter D for geometrically similar impellers within the same pump casing, with N simply replaced by D in the ratios: Q ∝ D, H ∝ D², P ∝ D³. This is commonly used when 'trimming' (machining down) a pump impeller to reduce its performance to match a lower-flow duty point, avoiding the purchase of a different pump. However, impeller trimming is less precise than speed reduction because trimming changes the impeller geometry slightly, altering the velocity triangles and reducing efficiency more than a pure speed change would. Most manufacturers recommend limiting impeller trim to no more than 75–80% of the full diameter.