{"id":2999,"date":"2026-10-18T17:21:00","date_gmt":"2026-10-18T09:21:00","guid":{"rendered":"https:\/\/borrapumps.com\/blog\/centrifugal-pump-affinity-laws\/"},"modified":"2026-10-21T18:15:19","modified_gmt":"2026-10-21T10:15:19","slug":"centrifugal-pump-affinity-laws","status":"publish","type":"post","link":"https:\/\/borrapumps.com\/th\/blog\/centrifugal-pump-affinity-laws\/","title":{"rendered":"\u0e01\u0e0e\u0e1e\u0e31\u0e19\u0e18\u0e30\u0e02\u0e2d\u0e07\u0e1b\u0e31\u0e4a\u0e21\u0e41\u0e23\u0e07\u0e40\u0e2b\u0e27\u0e35\u0e48\u0e22\u0e07: \u0e17\u0e33\u0e19\u0e32\u0e22\u0e01\u0e32\u0e23\u0e40\u0e1b\u0e25\u0e35\u0e48\u0e22\u0e19\u0e41\u0e1b\u0e25\u0e07\u0e04\u0e27\u0e32\u0e21\u0e40\u0e23\u0e47\u0e27\u0e42\u0e14\u0e22\u0e44\u0e21\u0e48\u0e04\u0e32\u0e14\u0e2b\u0e27\u0e31\u0e07\u0e1c\u0e25\u0e1b\u0e23\u0e30\u0e42\u0e22\u0e0a\u0e19\u0e4c\u0e17\u0e35\u0e48\u0e40\u0e01\u0e34\u0e19\u0e08\u0e23\u0e34\u0e07"},"content":{"rendered":"

Centrifugal pump affinity laws estimate how corresponding pump performance points change when rotational speed changes under similar hydraulic conditions. For the same impeller and liquid, flow varies approximately with speed, head with speed squared, and shaft power with speed cubed. These relationships help screen a variable-speed option, but they do not automatically predict the final installed flow or electricity saving. The changed pump curve must still intersect the actual system curve, and pump, motor and drive efficiency can change. Confirm the manufacturer’s permissible speed range and operating limits before turning a calculation into a control setting.<\/p>\n

A speed-ratio calculation is different from an impeller-trimming calculation. Trimming changes geometry and may depart more substantially from ideal similarity. This article focuses on speed changes and identifies the information needed to make the estimate useful for an industrial water installation.<\/p>\n

Establish the unchanged baseline<\/h2>\n

Start with the exact model, impeller diameter, number of stages, original rotational speed and test liquid. Obtain the head, flow, efficiency, shaft power and NPSH information for that configuration. A catalogue family chart is not enough if it combines several impeller sizes or speeds. Record whether the quoted power is hydraulic power, shaft input or electrical input.<\/p>\n

Select a known reference point from the pump curve. The affinity laws relate that point to a corresponding point at another speed. They do not say that every installation will operate at those corresponding points. A water-transfer system with significant static lift can intersect the slower curve at a different relative flow, or fail to deliver water at all if the available pump head is inadequate.<\/p>\n

The pump curve reading guide<\/a> provides a starting checklist for the reference data. Preserve an unmodified copy of the supplier’s chart beside any calculated estimates.<\/p>\n

Apply the speed ratios with clear symbols<\/h2>\n

Let r be the new rotational speed divided by the original rotational speed. With the stated similarity assumptions, Q2 = Q1 \u00d7 r, H2 = H1 \u00d7 r\u00b2, and P2 = P1 \u00d7 r\u00b3. Q denotes flow, H denotes developed head, and P here denotes pump shaft power. Speeds can be in revolutions per minute as long as both use the same unit.<\/p>\n

These are approximate relationships for corresponding points with unchanged diameter and liquid properties. They do not establish motor current, input electricity or guaranteed efficiency. At a substantial speed reduction, motor cooling, drive losses, mechanical resonance and hydraulic operating limits may matter. The supplier should confirm the approved range rather than relying on an arbitrary minimum frequency.<\/p>\n

If density changes, shaft power changes for another reason. If viscosity changes significantly, the assumption of comparable pump performance may no longer hold. Keep liquid changes out of a simple speed-only comparison unless the performance has been corrected through an appropriate method.<\/p>\n

\"ISG
ISG Vertical Inline Booster Pump, Red Original. Illustration based on the original BORRAPUMP product; not an actual installation, performance chart or approval for a particular duty.<\/figcaption><\/figure>\n

Calculate one illustrative comparison<\/h2>\n

Assume a documented reference point of 50 cubic metres per hour, 40 metres head and 8 kilowatts of shaft power. Consider a new speed that is 80 percent of the original. The corresponding estimates are 40 cubic metres per hour, 25.6 metres and 4.096 kilowatts. These numbers describe a hypothetical pump point, not a BORRAPUMP specification or a guaranteed operating condition.<\/p>\n

\n\n\n\n\n\n\n\n\n
Quantity at a corresponding point<\/th>\nCalculation for r = 0.8<\/th>\nIllustrative estimate<\/th>\n<\/tr>\n<\/thead>\n
Flow<\/td>\n50 \u00d7 0.8<\/td>\n40 m\u00b3\/h<\/td>\n<\/tr>\n
Head<\/td>\n40 \u00d7 0.8\u00b2<\/td>\n25.6 m<\/td>\n<\/tr>\n
Shaft power<\/td>\n8 \u00d7 0.8\u00b3<\/td>\n4.096 kW<\/td>\n<\/tr>\n
Electrical input<\/td>\nRequires motor and drive efficiencies at the new load<\/td>\nNot established<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

The apparent reduction in shaft power is about 48.8 percent, but it is not a system energy-saving guarantee. If the installation needs a fixed delivered volume, pumping time may change. If it requires a minimum pressure, this reduced-speed point may not satisfy the service requirement. Use the example only to understand the mathematical relationship.<\/p>\n

Rebuild the curve rather than moving one dot<\/h2>\n

Estimate several points on the new head-flow curve using the same speed ratio. Overlay that curve on the system requirement for the operating case. The intersection predicts an expected steady operating point, subject to the approximation and the manufacturer’s limits. Comparing only one original point with one scaled point can obscure a static-head constraint.<\/p>\n

Consider a transfer line that needs 30 metres of static head before any friction is overcome. A corresponding estimated head of 25.6 metres cannot establish useful delivery in that condition. Increasing operating time does not remove the missing pressure requirement. Conversely, a predominantly friction-controlled circulation system may respond more closely to the simple proportional-flow relationship over a suitable range.<\/p>\n

Compare speed control with throttling fairly<\/h2>\n

Throttling adds system resistance, while a speed reduction changes the pump characteristic. Both can reduce flow, but they need not use the same power. Compare each method at the same delivered duty and over the same annual operating profile. Include the cost of the drive and any changes in instrumentation, protection and commissioning.<\/p>\n

A valve can still be needed for isolation, balancing or a defined control function. A variable-speed drive does not make an unsuitable pump suitable for every demand. The VFD selection discussion<\/a> covers control and equipment considerations that remain separate from hydraulic scaling. Specify the required pressure, flow range and response to abnormal inlet conditions before choosing the control method.<\/p>\n

\"ISW
ISW Horizontal Inline Pump, Blue Original. Illustration based on the original BORRAPUMP product; not an actual installation, performance chart or approval for a particular duty.<\/figcaption><\/figure>\n

Keep hydraulic and electrical power separate<\/h2>\n

Hydraulic power is the rate of useful energy transferred to the liquid. Shaft power is the mechanical input to the pump. Electrical input includes motor losses and, where fitted, drive losses and other equipment inside the measurement boundary. A cube-law shaft-power estimate cannot be directly compared with an electricity meter without accounting for those differences.<\/p>\n

Efficiency may vary as the operating point moves. Motor efficiency can also change with load, and fixed electrical losses become more significant at low output. Measure real kilowatts over a representative operating cycle when evaluating savings. Current alone is insufficient because voltage, power factor, supply quality and drive behaviour affect the relationship between amperes and real power.<\/p>\n

Check the inlet and the mechanical limits<\/h2>\n

Reduced speed may change NPSH requirements, but do not assign a universal exponent to NPSH from this article. Obtain the applicable manufacturer data and compare them with the actual available suction conditions. A change in flow also changes suction friction. Lowest source level, high liquid temperature and atmospheric conditions can remain controlling cases.<\/p>\n

Confirm shaft, bearing, seal and coupling limits, allowed motor operation with the drive, and any prohibited resonance bands. Protection and direction checks remain necessary after electrical work. An ISW horizontal inline pump<\/a> is an example of a product family that may be assessed for a circulation duty; a photograph does not confirm that a particular motor or pump configuration is approved for variable speed.<\/p>\n

Use a demand profile for the business case<\/h2>\n

List the hours spent at each required flow and pressure condition. Calculate or measure input power for each accepted operating point, then multiply by operating time. Include start and stop behaviour, bypass flows and standby equipment if they fall within the energy boundary. Compare annual kilowatt-hours as well as maximum demand.<\/p>\n

Do not claim that reducing speed by a fixed percentage always reduces a site’s bill by the cube-law percentage. Some installations have a large static term, restricted turn-down or substantial auxiliary loads. Others already operate near the desired duty with little throttling loss. State the baseline and the measured result so that a saving can be reproduced rather than inferred from a formula alone.<\/p>\n

Verify the final setting under controlled conditions<\/h2>\n

Commission at several approved speeds while recording flow, suction and discharge pressures, tank levels and real electrical input. Observe temperature, vibration and control stability without exceeding permitted operating limits. Keep instruments synchronized so that a changing demand does not mix unrelated readings.<\/p>\n

The US Department of Energy pump-system sourcebook<\/a> explains variable-speed opportunities and system interactions. The DOE pumping systems resources<\/a> provide additional assessment guidance. Use these principles with manufacturer data, a documented operating envelope and the site’s commissioning procedure. Record the final approved settings and the circumstances requiring reassessment.<\/p>\n

For the low-demand boundary, also check the minimum-flow requirements<\/a> before approving a reduced-speed setting.<\/p>\n

Further learning: NPTEL explains centrifugal pump characteristics. Use this educational background with the model-specific data and method discussed above; the lecture does not certify a BORRAPUMP model.<\/p>\n