Affinity Laws for Centrifugal Pumps: The Engineer's Guide to Speed, Flow, and Power

If you have ever needed to resize a pump, change its operating speed, or justify a Variable Frequency Drive (VFD) installation, you have encountered the Affinity Laws — whether you knew it or not. These three relationships are among the most powerful tools in a process engineer's toolkit, governing how a centrifugal pump's performance changes when you alter its rotational speed or impeller diameter.

This article walks through all three laws with formulas, a worked numerical example, and practical guidance on how to apply them — including how Weltech pump series are engineered to take full advantage of this operating flexibility.

What Are the Affinity Laws?

The Affinity Laws describe the proportional relationships between a centrifugal pump's operating speed (or impeller diameter) and three key performance parameters: flow rate (Q), total head (H), and shaft power (P). They hold for any geometrically similar pump — meaning the same pump at different speeds, or two pumps of the same design at different scales.

There are two sets of affinity relationships:

• Speed-based: What happens when you change the rotational speed (RPM) of the same pump — the most common application in VFD-equipped systems.

• Impeller diameter-based: What happens when you trim or replace the impeller with a different diameter — used for permanent performance adjustment without changing the pump casing.

This article focuses on the speed-based laws, which are directly applicable to VFD-driven variable-flow systems and day-to-day pump operating decisions.

Law 1 — Flow Rate is Proportional to Speed

Q₂ / Q₁ = N₂ / N₁

Where Q₁ and Q₂ are the flow rates before and after the speed change (m³/hr), and N₁ and N₂ are the corresponding rotational speeds (RPM).

In plain terms: flow changes in direct proportion to speed. Reduce speed to 80% and flow drops to 80%. This is the most intuitive of the three laws — the pump simply moves fluid faster or slower in direct proportion to how fast the impeller spins.

Law 2 — Head is Proportional to Speed Squared

H₂ / H₁ = (N₂ / N₁)²

Where H₁ and H₂ are the total head values before and after the speed change (m).

In plain terms: head changes as the square of the speed ratio. A 20% reduction in speed results in a 36% reduction in head (0.8² = 0.64). This non-linear relationship is frequently underestimated when evaluating pump performance at reduced loads — a pump running at 80% speed cannot develop 80% of its rated pressure.

Law 3 — Power is Proportional to Speed Cubed

P₂ / P₁ = (N₂ / N₁)³

Where P₁ and P₂ are the shaft power values before and after the speed change (kW).

In plain terms: power scales as the cube of the speed ratio. A 20% reduction in speed reduces power consumption to just 51.2% of the original (0.8³ = 0.512). This cubic relationship is the entire economic case for Variable Frequency Drives (VFDs) in pump systems. On variable-load applications — cooling towers, water treatment plants, process recirculation loops — energy savings from even modest speed reductions are commercially significant.

Worked Example

Consider a Weltech CP Series centrifugal process pump running at its design point:

N₁ = 1500 RPM | Q₁ = 300 m³/hr | H₁ = 80 m | P₁ = 90 kW

System demand drops. Speed is reduced via VFD to N₂ = 1200 RPM — 80% of original speed. Applying each law:

New Flow: Q₂ = 300 × (1200/1500) = 240 m³/hr

New Head: H₂ = 80 × (1200/1500)² = 80 × 0.64 = 51.2 m

New Power: P₂ = 90 × (1200/1500)³ = 90 × 0.512 = 46.1 kW

A 20% reduction in speed delivers a 48.8% reduction in power — saving 43.9 kW continuously. Over an 8,000-hour operating year, that equates to approximately 351,000 kWh saved per pump. For multi-pump installations, the cumulative savings justify VFD capital costs within months.

Key Limitations of the Affinity Laws

1. They assume dynamic similarity — pump efficiency is treated as constant across the speed range. In practice, efficiency shifts at off-BEP (Best Efficiency Point) operation, particularly at very low speeds below 50% rated RPM.

2. They do not account for static head — in systems with significant elevation differences, the system resistance curve does not pass through the origin. Affinity Law calculations must be applied alongside a proper system curve analysis in these cases.

3. Impeller trimming has physical limits — diameter reductions beyond approximately 10–15% distort the hydraulic passages and can significantly degrade efficiency, independent of what the scaling laws predict.

4. Motor and VFD efficiency — shaft power savings from Law 3 are calculated at the pump shaft. Actual electrical energy savings also depend on motor efficiency and VFD efficiency at partial load, which must be factored into a complete energy audit.

Weltech Pump Series and Affinity Law Applications

Weltech's centrifugal pump range is designed with broad hydraulic flexibility. The following outlines how the Affinity Laws apply across key series in the portfolio.

CP/CPC Series — Centrifugal Process Pump

Rated to 1,500 m³/hr and 160 m head, the CP/CPC Series is Weltech's largest process pump for industrial recirculation, cooling, and transfer duties. Its wide hydraulic envelope makes it especially suited for VFD-controlled variable-flow systems where Law 3 delivers the largest absolute energy savings on high-horsepower installations.

ACP Series — ANSI Process Pump

With performance reaching 350 m³/hr and 150 m head, the ACP Series is built to ANSI B73.1 standards for chemical and process duty. The ACP's robust impeller geometry maintains hydraulic similarity across a wide speed range, ensuring Affinity Law calculations remain accurate throughout its operating window — critical for precise process control in chemical plants and refineries.

P Series — Solid Handling Industrial Pump

Engineered for flows to 4,000 m³/hr in slurry, effluent, and solids-laden streams, the P Series is Weltech's highest-volume pump. In variable-load process applications — dewatering, effluent handling, washdown circuits — Law 3's cubic savings potential is most significant here, where high-horsepower drives make every percentage point of speed reduction financially meaningful.

VCP Series — Vertical Long Shaft Sump Pump

Installed in sumps and collection pits for chemical and petro-chemical duty, the VCP Series — rated to 325 m³/hr and 60 m head — often serves batch or variable-demand process streams. VFD-driven speed modulation guided by Affinity Law calculations allows the VCP to precisely match pump output to variable inflow rates, preventing energy waste at low demand and eliminating the cavitation risk that arises when over-pumping a shallow sump.

ECHO Series — Polypropylene Centrifugal Pump

Designed for corrosive chemical media at flows to 100 m³/hr, the ECHO Series handles dosing recirculation, acid transfer, and chemical process duties. For variable-demand systems, Law 2 — the head-speed squared relationship — is especially important here: a modest speed increase to recover lost head can overstress the PP/FRP wetted components if not carefully bounded within the pump's rated operating envelope.

Conclusion

The Affinity Laws are not theoretical abstractions — they are the mathematical backbone of every VFD specification, impeller selection decision, and energy optimisation exercise in a centrifugal pump system. For process engineers working with Weltech's pump range, mastering these three relationships provides the tools to right-size operating speeds, validate capital investment in variable-speed drives, and reduce lifecycle energy costs meaningfully.

A pump system running at 80% of design speed consumes less than 52% of design power. Applied consistently across a multi-pump plant, that single principle can transform a facility's energy profile.

For application-specific guidance on operating Weltech pumps at variable speeds or trimmed impeller configurations, contact the Weltech engineering team at airfin.tech.