Pump performance changes with flow rate and is shown by the pump curve. Pump curves present head, efficiency, net positive suction head required (NPSHR), and power across the operating flow range for a given rotational speed and impeller diameter.
The affinity rules indicate how the pump curve changes as a function of rotational speed. Additionally, impeller trimming alters the pump curve, which is commonly done for centrifugal and mixed flow pumps. Operating multiple pumps in parallel or in series results in a new composite pump curve that is a function of the individual pump curves.
Understanding the pump curve and how it changes with respect to speed, impeller trimming, and parallel and series operation is essential for proper pump selection. The flow rate, pump total head, pump input power and specific gravity of the liquid can be used to calculate pump efficiency. Liquid viscosity will affect the pump total head, flow, efficiency, NPSHR and power, which is not discussed here. Refer to ANSI/HI 9.6.7 for effects of liquid viscosity on rotodynamic pump performance.
The head versus flow curve is the most commonly used curve to describe pump performance. Pump total head (H) is plotted on the y-axis in . This is the measure of energy increase per unit weight of the liquid, imparted to the liquid by the pump, and is the difference between the total discharge head and the total suction head. On the x-axis is the flow rate, typically in .
Using head, the performance of the pump can be shown independent of the density or specific gravity of the fluid pumped.
The Pump efficiency versus flow curve is shown as a percentage on most pump curves. It shows pump efficiency at various flow rates and the flow rate where efficiency is at a maximum is called the pump’s best efficiency point (BEP). BEP is an important operating point that is further described later in this section. Pump efficiency is defined by Eq. 1.B.3 as the ratio of pump output power and pump input power.
$$ η_{p} = {P_{w} \over P_{p}} $$
where:
The pump input power curve shows the amount of input power required for different flow rates. This is the power used to select the driver and can be determined by Eq. 1.B.4.
$$ P_p = {{Q · H· s} \over {3960 · η_{p}}} $$
$$ P_p = {{Q · H · s} \over {366.6 · η_{p}}} $$
Pump input power can also be determined if the amount of power absorbed by the fluid (pump output power, Pw) and pump efficiency (ηp) are known by rearranging the Eq. 1.B.3, as shown in Eq. 1.B.5.
$$ P_p = {P_{w} \over η_{p}} $$
The pump input power curve is important because it is the power required at the pump shaft, which supports proper selection of the pump driver.
The NPSHR curve plots NPSHR for different flow rates. NPSHR is the minimum NPSH needed to achieve the specified performance at the specified flow rate, speed, and pumped liquid. NPSHR in combination with the system's available NPSH is an important considerations in pump selection. NPSHR is further defined in Rotodynamic Pump Principles.
Best Efficiency Point (BEP): A pump’s best efficiency point is defined as the flow rate and head at which the pump efficiency is the maximum at a given speed and impeller diameter. Typically, a pump is specified to have its duty point, or designed operating point, at BEP. At BEP, a pump will have low vibration and noise when compared to other operating points. Also, there is minimum recirculation within the impeller and shockless entry into the impeller. Shockless entry is when the flow entering the impeller matches the angle of the impeller vanes at entry.
Preferred Operating Region (POR): The preferred operating region (POR) is a range of rates of flow to either side of the BEP within which the hydraulic efficiency and the operational reliability of the pump are not substantially degraded. Flow induced vibrations and internal hydraulic loading is low in this region. Depending on the specific speed of the pump, which is further defined in the Rotodynamic Pump Principles section, the POR can be anywhere from 90-110% of BEP flow to 70-120% of BEP flow.
Allowable Operating Region (AOR): The AOR is the flow range at the rated speed with the impeller supplied in which the pump may be allowed to operate, as limited by cavitation, heating, vibration, noise, shaft deflection, fatigue, and other similar criteria. It is the flow range at which the pump can be run with acceptable service life. The pump manufacturer should be consulted to define this region. Typically, operating intermittently within this region does not cause issues over the life of the pump. The graph above shows the various operating regions and the types of issues that can occur when operating outside of the POR and AOR.
Shut-off Head and Pump Runout: These points are important during manufacturer testing to fully define the shape of the pump curve. They are the furthest points to the left and right on the curve. Shut-off is the condition of zero flow rate where no liquid is flowing through the pump, but the pump is primed and running. Operating at this point for more than a few seconds can cause serious mechanical issues. Pump Runout is the point at which flow is at a maximum. Operating at this flow can cause cavitation, vibration and, in some pumps, overloading of the driver. These points are to be avoided when operating pumps.
Read more about the BEP, POR and AOR at HI’s Pump FAQs.
Preferred and Allowable Operating Regions for Rotodynamic Pumps to Maximize Reliability - 1 Part Recorded Webinar
Learn how the Preferred Operating Region (POR) and Allowable Operating Region (AOR) are defined for centrifugal, mixed and axial flow pumps and their impact on efficiency and reliably. Curve shape, hydraulic loading, temperature rise, vibration/noise, suction recirculation, priming, NPSH margin and more will be discussed related to a pumps AOR as well as methods to ensure operating in the AOR will be presented. This webinar is a must for pump end users, application engineers, pump system designers, specifying engineers and pump service providers.
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Two or more pumps in a system can be placed either in parallel or in series. In parallel, a system consists of two or more pumps that are configured such that each draws from the same suction reservoir, wet well, or header, and each discharges to the same discharge reservoir or header. In series, a system consists of two or more pumps that are configured such that the discharge of one pump feeds the suction of a subsequent pump.
Pumps in Parallel
Pumps operating in parallel allow the pumping system to deliver greater flows than is possible with just one such pump. To determine the composite pump curve of two or more pumps operating in parallel, at each head value, the flow rate of each pump must be added together to obtain the composite flow rate.
The amount of increased flow that occurs within the system depends on both the shape of the system curve and the shape of the pump curves. The composite pump curve intersects the system curve at different operating points, yielding different flow rates. As more pumps are called to operate, the flow will increase accordingly, as shown in Fig. 1.B.7.
It should be noted, however, that unless the system curve is completely flat, meaning friction and other dynamic losses are negligible, bringing a second pump on-line does not double the flow rate. The increased flow will be something less than double. How much less depends on the steepness of the system curve.
Pumps in Series
While pumps placed in parallel provide greater flow capabilities at the same head as one pump operating individually, pumps placed in series provide greater head capabilities at the same flow rate.
A composite pump curve representing pumps in series can be generated by adding the individual head values of the pumps for a given flow. Plotting this sum at various flow values will yield a composite pump curve for the group of pumps. Fig. 1.B.8 shows a composite pump curve for two and three identically sized pumps operating in series.
Pumps operating in series allow the pumping system to deliver greater heads than is possible with just one such pump. This allows a pump station to be designed to satisfy systems that require large discharge pressures that may not be practical with one pump. Where certain applications require, it may also allow a pump station to address a wide variation in system pressures by staging the number of operating pumps. Fig. 1.B.9 shows how applying a configuration with pumps in series to a system with a steep system curve may allow the pumps to address different head requirements so long as inter-stage discharge piping is configured to permit it.
Factory Performance Testing: Hydraulic, Mechanical and Hydrostatic – Recorded Webinar
Learn laboratory test standards for rotodynamic pumps, covering test procedures, setups, and arrangements along with data acquisition, acceptance grades, and instrumentation.
Rotodynamic pump performance can be altered to meet a design point by adjusting the pump speed as described by the affinity rules. Pump affinity rules are fundamental principles, based on kinematic, dynamic, and geometric similarity, that govern the relationships of pump scaling and modeling. Application of the affinity rules to pump speed changes are described below, and you can refer to ANSI/HI 14.6 for more information on pump modeling and to ANSI/HI 14.3 regarding limitations in using the affinity rules.
Because the affinity rules are based on similarity, they are applied to determine the pump performance change with respect to rotational speed change. Under the assumption that changing the speed of a pump maintains the same efficiencies, the affinity rule equations show the relationships between pump parameters, flow (Q), head (H), and power (P), as a function of rotational speed (n) change.
$$ {Q_2 \over Q_1} = {n_2 \over n_1} $$
$$ {H_2 \over H_1} = ({n_2 \over n_1})^2 $$
$$ {P_2 \over P_1} = ({n_2 \over n_1})^3 $$
According to the affinity rules (Eq. 1.B.6a through Eq. 1.B.6c), changing speed results in a proportional change in flow rate, a squared change in head, and a cubed change in power consumption. It is important to understand that the affinity rules are applied to a point on the pump performance curve. The affinity rules are applied to both values associated with that point, such as flow rate and head or flow rate and power, to calculate a corresponding point at the new rotational speed, as shown in the worked example below.
Application Guideline for Variable Speed Pumping
This guideline has been created to provide pump industry professionals and the end user operators of pumps with the knowledge required to apply variable speed pumping so that it will result in improved energy efficiency and increased reliability. This intention of this guidebook is to educate the pumping industry and to ensure the safe, reliable, and efficient operation of the pumping equipment we all depend on every day.
Affinity Rules Example - Rotational Speed Change
The following worked example is done in U.S. customary units but can be applied Metric units.
A booster pump is designed to operate at 1800 GPM and 135 ft, with a speed of 1740 RPM. Due to fluctuating flows, the booster pump is equipped with a variable frequency drive (VFD), which reduces the pump speed by 10% during low-flow conditions. Using the pump curve below and the affinity rules, this example generates the pump curve for low-flow conditions at the reduced speed.
Determine the Reduced Speed
During low-flow conditions, the speed of the pump is reduced by 10%.
$$ n_2= n_1 · (1-0.10)= 1740 · (1-0.10)= 1566\,RPM $$
Calculate New Flow Values
Using Eq. 1.B.6a, calculate the new flow values. Repeat the calculation until all points under the flow column are converted.
$$ {Q_2 \over Q_1} = {n_2 \over n_1} $$ $$ Q_2 = (Q_1=0) · ({1566 \over 1740})= 0\,GPM $$
$$ Q_2 = (Q_1=200) · ({1566 \over 1740})= 180\,GPM $$
$$ Q_2 = (Q_1=400) · ({1566 \over 1740})= 360\,GPM $$
Calculate New Total Head Values
Using Eq. 1.B.6b, calculate the new total head values. Repeat the calculation until all points under the total head column are converted.
$$ {H_2 \over H_1} = ({n_2 \over n_1})^2 $$ $$ H_2 = (H_1=213)·({1566 \over 1740})^2= 173\,ft $$
$$ H_2 = (H_1=206)·({1566 \over 1740})^2= 167\,ft $$
$$ H_2 = (H_1=198)·({1566 \over 1740})^2= 160\,ft $$
Plot Pump Curve for Low-Flow Conditions
Comparison of Normal Flow and Low-Flow Conditions
Rotodynamic pump performance can be altered by changing the impeller diameter, and many centrifugal pumps have their performance represented as a function of impeller diameter to support the selection of the appropriate curve for a pump application to fit the desired system conditions. Fig. 1.B.13 illustrates the trimming of a radial flow impeller where it is cut straight across, and Fig. 1.B.14 is a representation of rotodynamic pump performance for a range of impeller diameters.
Trimming the impeller down in diameter will move the pump curve down. The same can be said for selecting a larger impeller; the curve will shift up. When sizing a pump for an application in which the pump is not connected to a variable speed controller, the impeller diameter is selected for the desired duty conditions. Fig. 1.B.14 shows a pump performance curve over an impeller trim range. There is a lot of information presented on this curve, which, when studied carefully, is useful in selecting the correct impeller trim for a rated point and determining other important factors such as required motor size and NPSHR.
The impeller geometry changes with the pump specific speed, which may impact impeller trimming. Impeller trimming is typically applied to radial and mixed flow impellers, and the trimming methods may vary. Refer to ANSI/HI 14.3 for additional information and the impeller trimming section below.
As noted in the preceding section, changing the impeller diameter will change pump performance. It is common to trim an impeller to meet a rated condition that is below the pump curve. Because changes in impeller diameter do not maintain similarity, the affinity rules are not intended to be applied for changes in impeller diameter. The information presented in Fig. 1.B.14 is representative of tested performance, and it can be noted that the efficiency does not remain constant as diameter changes and the relationship between head and flow with diameter change does not exactly match the affinity rules. However, affinity rules can be used for minor impeller diameter changes within 5% with acceptable accuracy. Eq. 1.B.6a through Eq. 1.B.6c can be modified for impeller diameter change by substituting impeller diameter (D) for rotational speed (n), as shown in the worked example below. If the diameter reduction exceeds 5% from the original, correction coefficients should be used for the diameter calculated using affinity rules, such as described in Centrifugal and Axial Flow Pumps by A.J. Stepanoff.
Impeller Trimming Example
The following worked example applies the affinity rules within the 5% impeller diameter limit and is done in U.S. customary units but can be applied to any units.
Given Conditions
A pump designed with a 10-5/8 in diameter impeller will be operating in a chemical process system at 2000 GPM at 80 ft. After installation and startup, it was found that the flow rate was 2100 GPM, and total head was 89 ft. The manufacturer recommends trimming the impeller to bring the flow rate down to the specified value. The following uses the affinity rules to determine the new impeller diameter and operating head.
Calculate the New Impeller Diameter
Substituting impeller diameter (D) for rotational speed (n) into the affinity rule equation for flow rate (Eq. 1.B.6a), we get Eq. 1.B.7a and the new impeller diameter can be calculated as shown in Calc.1.B.7a.
$$ {Q_2 \over Q_1} = {D_2 \over D_1} $$
$$ D_2 = {Q_2 \over Q_1} · D_1 $$
$$ D_2 = {2000 \over 2100} · 10.625 = 10.12\,in $$
Calculate the New Head
Substituting impeller diameter (D) for rotational speed (n) into the affinity rule equation for head (Eq. 1.B.6b), we get Eq. 1.B.7b and the new head can be calculated as shown in Calc.1.B.7b.
$$ {H_2 \over H_1} = ({D_2 \over D_1})^2 $$
$$ H_2 = H_1 · ({D_2 \over D_1})^2 $$
$$ H_2 = 89 · ({10.12 \over 10.625})^2 = 81\,ft $$
With the impeller trimmed down to 10.12 in, the pump parameters, flow rate and head, now satisfy the process requirements. Also, as the trim comprises less than a 5% reduction of the original diameter, no further correction to the calculated diameter is necessary.
It is common to trim a radial or mixed flow impeller to meet performance requirements. The information provided in the preceding Changes in Impeller Diameter section Fig. 1.B.13, provides details on expected performance changes as impeller diameter is changed. However, it should be noted that this is representative of a traditional trim where a radial flow impeller is cut consistently across the vanes and shrouds, as shown in Fig. 1.B.13, or for mixed flow impellers based on mean diameter change while maintaining the original angle.
There are instances where performance requirements are not met for flow, head, efficiency, power, head rise to shutoff, vibration, or curve shape and the curve needs to be adjusted to better meet multiple rated points. Different or alternate impeller trimming methods may be used to achieve performance requirements in these cases. The performance effects of these methods do not follow the affinity rules as similarly or uniformly along the pump performance curve range. The effect of these methods on performance is more empirical and is applied based on experience of the manufacturer.
The following is not a complete list, but it discusses some alternate impeller trimming modifications that may be applied by the manufacturer and are described here qualitatively because there are no consensus rules or relationships for the change in performance. If one of these modifications is made to meet a specification, it is important to precisely document the modification for future replacements.
Impeller vane trimming: An enclosed or semi-open impeller may have its vanes trimmed while leaving one or both shrouds in place. The reason for doing this may be to maintain the radial gap between the impeller shrouds and diffuser, when the shroud has a ring near the full diameter for thrust balance, or to increase the slope of the curve in a volute pump. This may result in slightly lower efficiency compared to trimming both the vanes and shrouds because of increased disk friction.
Impeller shroud trimming: Trimming the back shroud or both the front and back shroud while leaving the vanes at full diameter may be done to limit a pump curve that droops to shutoff. The head at shutoff or zero flow is strongly influenced by the velocity within the volute that is generated by the impeller rotation. Exposing the vane allows a larger component of the impeller tangential velocity to be imparted to the liquid within the volute at low flow, and the stagnation of this velocity at the casing throat within the volute increases the pressure measured at the pump outlet. A slight reduction in efficiency should be expected when the back shroud is trimmed, with a considerably greater reduction if both shrouds are trimmed.
V-cutting the impeller vanes: A V-cut involves machining a V-shaped notch or taper into the trailing edge of the impeller vane. The angle and depth of the V-cut will be carefully determined by the manufacturer based on the pump specific speed and desired hydraulic performance. It may be used on a double suction or end suction impeller when a standard diameter trim does not achieve the desired performance outcome. It results in more aggressively reducing flow and head at higher flow while preserving shutoff head. Additionally, it may be employed to preserve vane overlap to maintain NPSHR.
Angle trimming: Mixed flow impellers have outlets that are angled where the front and rear shrouds are at different diameters, as shown in Fig. 1.B.21. For these impellers, trimming may require the angle to change. Decreasing the angle will flatten the pump curve, and increasing the angle will steepen the pump curve. For these impellers, trimming is done to achieve a mean diameter. Trimming impellers at an angle is typically done on vertical turbine pumps or pumps with Francis-vane impellers, but the angle trim could be applied to radial flow impellers.
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Underfiling is a procedure performed on the impeller vane trailing edge where material is removed from the underside of the vane outlet, as illustrated in Fig. 1.B.23. A manufacturer may employ underfiling as a standard methodology to achieve consistent vane profiles or to achieve a desired performance or operational requirement. The effects of underfiling are presented qualitatively and should only be performed by the pump manufacturer. If underfiling is done to meet a specification, it is important to precisely document the modification for future replacements.
Underfiling helps to achieve uniform vane tip thickness and consistent vane-to-vane spacing, and results in increased area between the vanes, which can be used to adjust tested performance. It is most typically applied to rotodynamic pumps with low to moderate specific speeds, including mixed flow pump impellers. Underfiling flattens the performance curve, shifting BEP to higher flow rates with performance gains most noticeable to the right of BEP. Therefore, this may be employed to increase head and flow to meet a rated flow and total head. The pump input power will increase consistently with the increase in flow rate and total head.
Overfiling is a procedure performed on the impeller vane trailing edge where material is removed from the top side of the vane outlet, as illustrated in Fig. 1.B.25. The effects are discussed qualitatively and should only be performed by the pump manufacturer. If overfiling is done to meet a specification, it is important to precisely document the modification for future replacements.
Overfiling does not increase the distance between vanes or exit area; therefore, it has minimal impact on hydraulic performance. The effect of overfiling thins a blunt trailing edge, which may limit the impeller vane pass pulsation and related vibration.
This summary table is presented qualitatively and the modifications within are recommended to be applied only by the manufacturer with specific knowledge of how each modification will affect pump performance.
Last updated on September 17, 2026