This document presents a numerical model for predicting the performance curves of centrifugal water pumps. The model requires easily obtainable pump geometrical data and empirical coefficients. It was developed to provide a fast approximation of pump characteristic curves, including pressure head, volumetric efficiency, and power required. The model was validated by comparing predictions to experimental data from 30 pumps tested on a pump test rig. On average, the model predicted head within 5.16% error, power within 10.6% error, and efficiency within 7.3% error. The results indicate the method provides a satisfactory approximation of pump performance curves.

1. Applied Engineering in Agriculture
Vol. 24(2): 153‐157 E 2008 American Society of Agricultural and Biological Engineers ISSN 0883-8542 153
A PRACTICAL METHOD TO PREDICT PERFORMANCE
CURVES OF CENTRIFUGAL WATER PUMPS
A. Fatsis, A. Panoutsopoulou, V. Vlachakis, N. Vlachakis
ABSTRACT. A simple numerical model was developed to predict the performance curves of centrifugal water pumps. The model
inputs are easily obtainable pump geometrical data and empirical coefficients experimentally determined or found in the
literature. The predicted pump characteristic curves for pressure head, volumetric efficiency, and power required to drive the
pump were compared to experimental data obtained with a pump test rig. From the cases examined, it was concluded that
the proposed method provides a very fast and satisfactory approximation of centrifugal water pump performance curves to
determine suitability for a particular application or to be used as a potential design tool by water pump manufacturers.
Keywords. Water pump, Centrifugal pump, Performance curve, Characteristic line, Numerical prediction.
esign and production of centrifugal water pump
series involves the testing and experimental
determination of the characteristic performance
curves of the prototypes in the laboratory (Japikse
et al., 1997). This implies an increased cost of the final
product (pump) due to the acquisition and maintenance cost
of the test rig as well as the cost of operation. Additionally,
existing characteristic curves may only partially cover the
operating range of pumps or the performance map of a given
pump is not always available for someone to evaluate its
adequacy for a particular installation (Samani, 1991). Even
if one possesses the pump test rig to measure the performance
of a pump, it might be difficult to transport large diameter
pumps to the location of the rig or the rig may not
accommodate very large or very small pump types.
Alternatively, it would be useful in time and cost savings to
numerically predict the overall pump characteristics with a
reasonable degree of precision as a first approach.
Significant numerical modeling work was done in the past
to estimate the performance characteristics of centrifugal
pumps. A simple method was presented by Amminger and
Bernbaum (1974) to predict pump pressure head. It was
demonstrated by Yedidiah (2003) that predictions based on
the Euler's method and airfoil theory sometimes produce
unrealistic results. A better estimation of the pump
characteristics was obtained by considering the interaction of
impeller and volute. Sophisticated three‐dimensional
unsteady flow analysis methods employed by Fatsis (1993)
Submitted for review in December 2006 as manuscript number PM
6794; approved for publication by the Power & Machinery Division of
ASABE in January 2008.
The authors are Antonios Fatsis, Assistant Professor, Mechanical
Engineering Department, Technological University of Chalkis, Psachna,
Greece; Angeliki Panoutsopoulou, Engineer, Hellenic Defense Systems
S.A., Athens, Greece; Vassilios Vlachakis, Doctoral Student, ESM,
Virginia Polytechnic Institute and State University Blacksburg, Virginia;
and Nikolaos Vlachakis, Professor, Mechanical Engineering Department,
Technological University of Chalkis, Psachna, Greece. Corresponding
author: Antonios Fatsis, Mechanical Engineering Department,
Technological University of Chalkis, 34400 Psachna, Greece; phone:
+302228099662; +302228099660; e‐mail: afatsis@teihal.gr.
and by Kaps (1996) are time consuming, require detailed
three‐dimensional geometrical data of the impeller and
volute, and are not suited for use as an engineering tool for
performance prediction. These methods are preferably used
in the final stage of the pump design process since they can
be used to analyse cavitating flows inside the impeller
(Medvitz et al., 2001) and can calculate the forces exerted on
impeller blades and shaft bearings (Gonzalez et al., 2002).
Nevertheless, when numerical predictions are compared to
experimental data, discrepancies in the impeller head are
observed at the shut‐off and at the maximum discharge flow
areas.
This article presents a series of results of a rapid method
to estimate pressure head, volumetric efficiency and the
required power for centrifugal water pumps, requiring
geometrical data from only a few pumps. Numerical
predictions are compared with experimental data from thirty
pumps and are treated statistically.
PREDICTION METHOD
The present prediction method was based on the
assumption of one‐dimensional flow inside the impeller
accounting for different types of losses using empirical
coefficients determined from experimental measurements
and analysis of previous experimental data for centrifugal
pumps (Vlachakis, 1974).
Two further assumptions were also made. First, the pumps
considered in the present study were centrifugal pumps with
backward‐leaning outlet blade angles. According to Japikse
et al. (1997), each 10° of backward blade angle is worth one
or two points of stage efficiency and for usable stable flow,
the backswept angle should range from 30° to 40° from the
radial direction. As a first approach, the specific influence of
the impeller outlet angle was not considered. According to
Acosta and Bowerman (1957), steep outlet blade angles shift
pump performance to higher flow coefficients. The second
assumption was that the present method was valid for
impellers having more than five blades. For impellers having
backward leaning blades, a further increase of the blade
number has only a small influence on the characteristic
D

2. 154 APPLIED ENGINEERING IN AGRICULTURE
curve. This feature affects the characteristic line throughout
the range of volume flows (Yedidiah, 1966). Pfleiderer
(1961) correlated the blade number with the impeller outlet
blade angle and showed that for all operating points, large
blade number corresponded to large outlet blade angles.
Moreover, in three‐bladed impellers, the deformation of
velocity distribution is very pronounced due to the high
loading. In five‐bladed and in seven‐bladed impellers, the
velocity distributions are similar to a potential flow near the
impeller inlet, but are deformed considerably by a secondary
flow developed in the impeller passage near the impeller exit.
It is known that the maximum head produced by a
centrifugal pump corresponds to throttling conditions, where
the volumetric flow is zero (Gülich, 1988). The maximum
theoretical head is proportional to the square of the product
of the impeller rotational speed and the impeller tip diameter
(Bohl, 1988).
( )2
2
D
n
Htheor[ @ (1)
where Htheor is the theoretical pressure head (m), n is the
rotational impeller speed (rps), and D2 is the impeller exit
diameter (m).
Taking into account that the main centrifugal pump losses
are mechanical losses, impeller losses, disk friction losses,
and leakage losses in the gap between impeller and casing
(Japikse et al., 1997), the maximum available head can be
approximated by:
( )
[ ]
2
2
1
max D
n
K
H = @ @
(2)
where Hmax is the maximum pressure head corresponding to
zero volume flow, and K1 is an empirical loss coefficient at
throttling.
In this work K1 = 0.6, which is similar to the values
attributed to this coefficient by Stepanoff (1957) and Gülich
(1988).
To simulate the pump behavior for all other operating
points up to the maximum volume flow, the methodology of
the non‐dimensional flow rate principle presented by
Grabow (1961) was modified. The non‐dimensional flow
rate coefficient, ξ, was defined by the volume flow at any
operating point and easily obtainable pump engineering data:
2
2
2
)
(
D
n
b
d
Q
K
Q
p
=
c @
@ @ @
(3)
where Q is the pump volume flow (m3/s), dp is the pump
impeller discharge diameter (m), b2 is the pump impeller
width at the impeller outlet (m), and D2 is the pump impeller
exit diameter (m).
The coefficient ξ(Q) should vary from 0 at throttling
conditions (where the pump volume flow is zero) to a value
close to 1 indicating the point of maximum estimated flow
delivered by the pump. The non‐dimensional coefficient K2
was experimentally determined as 0.3 to match maximum
predicted flow rate as close as possible to the value obtained
in the test rig.
Pump manufacturers often use the pump discharge
diameter dP and the impeller tip diameter D2 to group pump
categories, thus these two geometrical data were deliberately
used in equation 3. Samani (1991) also used the discharge
diameter to develop empirical correlations for the
determination of characteristic curves.
Characteristic curves based on experimental data found in
the literature (Japikse et al., 1997) show a slight curvature in
the area of throttling where the volume flow is zero and an
almost linear behavior elsewhere. This behavior was
modelled by using a cosine function raised to an exponent.
The exponent 0.2, experimentally defined according to
studies done with centrifugal pumps by Vlachakis (1974)
guarantees an almost linear and monotonic behaviour of the
head‐volume flow (H‐Q) curve corresponding to stable pump
operation. Bolte (1971) also used a similar flow coefficient
to model stable centrifugal pump performance. For ξ ranging
from 0 to 1, the pump head can be expressed as:
( )
[ ]
2
,
0
2
2
1
2
cos ⎥
⎦
⎤
⎪
⎣
⎡
⎟
⎠
⎞
⎢
⎝
⎛
c
p
= D
n
K
H @
@ @
(4)
Experimental data of the volumetric efficiency
distribution with respect to volume flow resemble a parabola.
Previous researchers attempted to estimate the efficiency
distribution by means of polynomials (Engelberg, 1971). For
this research, the volumetric efficiency was described as a
second order function in terms of ξ.
⎥
⎥
⎦
⎤
⎪
⎪
⎣
⎡
⎟
⎟
⎠
⎞
⎢
⎢
⎝
⎛
c
−
c
=
5
,
0
2
2
3 )
1
(
D
D
K
eff X
@ @ @
(5)
where the non‐dimensional coefficient K3 was
experimentally determined as 2.5 to match as close as
possible the experimental efficiency obtained with the test
rig.
The ratio D2x/D2, used to calculate the volumetric
efficiency of a pump with an impeller tip diameter D2x with
respect to the nominal diameter of the pump category, D2,
accounts for the issue that two pumps with different tip
diameters of the same pump category operating under the
same volume flow have different efficiencies.
The power required to drive the pump was estimated by
the formula:
eff
H
Q
g
N =
1000
@ @ @
@
ò (6)
where the power N is expressed in KW and ρ is the density
of the water expressed in kg/m3.
EXPERIMENTAL FACILITY
The experimental facility used to validate the numerical
results was a model MT1102 pump test rig provided by
TecQuipment, Ltd. (Nottingham, U.K.) and installed in the
pump laboratory at the Technological University of Chalkis.
This facility, allowing the testing of full‐scale industrial
pumps over a wide range of volume flows, was designed
according to British Standards BS‐5316 Part‐2 (1977). In the
facility, water was pumped from and returned to a large
reservoir whereas the flow was regulated by a set of butterfly
valves located close to the reservoir discharge. A direct
current (d.c.) electric motor was used, which allowed
continuous variability of the pump speed permitting the
mechanical energy generated by the motor and absorbed by

3. 155
Vol. 24(2): 153‐157
the pump to be measured. Instrumentation included pressure
gauges for pump suction and discharge pressure, flowmeter,
tachometer, ammeter, and voltmeter for the d.c. motor. The
flow meters used to measure the volume flow were composed
of a glass tube that contained a floating indicator which was
pushed upwards when water passed through. The pressure
difference measured by the pressure gauges upstream and
downstream from the pump provided data for the head
calculation. The ammeter and voltmeter were used to
measure the power that the electric motor transferred to the
pump. The valves' regulation produced diverse operating
points, corresponding to head and volume flow
measurements. The experimental technique was developed
and validated by Sideris (1988).
RESULTS
The numerical model described previously was applied to
30 different pumps evaluated with the test rig. The flow rate
range of the pumps tested was between 10 and 1000 m3/h. In
this section, some cumulative results will be shown to assess
applicability of the method.
Figure 1 presents the comparison of the predicted pump
head versus the experimental head at maximum flow rate
where the error is at maximum. The continuous line has a
slope of 45_ and represents the hypothetical case where
numerical predictions coincide with the experiments. Dots
represent the actual results obtained by plotting the points
that have as abscissa the experimental value and as ordinate
the predicted one. The average error for the head prediction
was 0.0516 (5.16%) the maximum error was 0.0955 (9.55%)
and the variance was 0.0048 (Montgomery and Runger,
2003). Prediction of the pump head for all points except the
one that corresponds to shut‐off conditions was obtained
using equation 4 where the flow rate coefficient ξ was
obtained using equation 3. The higher errors occurred for the
pumps delivering flow rates less than 100 m3/h.
Figure 2 presents the standardized normal (or Gaussian)
distribution of the maximum error for the head prediction.
Practically speaking the two‐sigma limits according to
standard statistical theory (Montgomery and Runger, 2003)
contain about 95% of the pumps' maximum error (illustrated
with dots) corresponding to the abscissa value of ±2.
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
MEASURED HEAD (m)
PREDICTED
HEAD
(m)
Figure 1. Predicted vs. experimental head at maximum flow rate for the
pumps tested.
0
0.02
0.04
0.06
0.08
0.1
0.12
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Figure 2. Density of the normal distribution of maximum error in the head
prediction.
Predicted versus experimentally determined power
absorbed by the pumps at maximum flow rate conditions is
shown in figure 3. The average error of the power prediction
was 0.106 (10.6%), the maximum error was 0.113 (11.3%)
and the variance was 0.0031.
Figure 4 presents the comparison between predicted and
experimentally determined volumetric pump efficiency
corresponding to maximum flow rate conditions. The
average error of the efficiency prediction was 0.073 (7.3%),
the maximum error was 0.11 (11%) and the variance was
0.00227.
0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60 70 80
MEASURED POWER (KW)
PREDICTED
POWER
(KW)
Figure 3. Predicted vs. experimental power at maximum flow rate for the
pumps tested.
10
20
30
40
50
60
10 20 30 40 50 60
% EFFICIENCY MEASURED
%
EFFICIENY
PREDICTED
Figure 4. Predicted vs. experimental volumetric efficiency at maximum
flow rate for the pumps tested.

4. 156 APPLIED ENGINEERING IN AGRICULTURE
Figure 5 shows typical head, efficiency, and power
distributions for a pump delivering less than 100 m3/h with
nominal impeller tip diameter D2 = 315 mm, discharge
diameter dp = 80 mm, running at 1450 rpm. Head and power
predictions show good agreement to experimental data. The
efficiency prediction in figure 5c follows a parabolic
distribution in terms of the coefficient ξ according to
equation 5.
Typical results of pumps that deliver more than 100 m3/h
are shown in figure 6a, comparing the predicted versus
experimental head for a centrifugal pump with nominal
impeller tip diameter D2 = 400 mm, discharge diameter dp =
250 mm, and running at 1480rpm. Two cases were examined:
(a)
10
15
20
25
30
35
40
45
50
0 10 20 30 40 50 60 70 80 90 100
Volume Flow (m3
/h)
HEAD
(m)
(b)
0
5
10
15
20
25
30
0 10 20 30 40 50 60 70 80 90 100
Volume Flow (m3/h)
N
(KW)
(c)
0
20
40
60
80
100
0 10 20 30 40 50 60 70 80 90 100
Volume Flow (m3
/h)
eff
%
Figure 5. Predicted (lines) vs. experimental (points) performance curves
for the centrifugal pump with nominal characteristics D2 = 315 mm, dp =
80 mm, and running at 1450 rpm.
one with D2 = 400 mm and another with D2 = 350 mm. The
comparison between predicted and measured head is again
satisfactory for all the volume flow range. Figure 6b shows
a fair agreement between predicted and measured power
required to drive the pump. Predicted pump volumetric
efficiency shows the same trend with the experimental
points; in some range agrees also quantitatively whereas in
the low flow rates significant differences are marked (fig. 6c).
CONCLUSIONS AND DISCUSSION
A simple and fast method to predict performance curves
of centrifugal water pumps was presented. For all centrifugal
pumps examined, the same empirical coefficients and
equations were used. To validate the model, 30 centrifugal
pumps were tested. Comparison between numerical results
and pump test data showed that the proposed model predicts
the performance characteristics of centrifugal pumps
adequately for the cases examined. The maximum error in
the head, volumetric efficiency and power prediction was
always less than 12%. The maximum error corresponds to the
maximum volume flow, indicating that the present method
(a)
20
30
40
50
60
70
0 100 200 300 400 500 600 700 800 900
Volume Flow (m3/h)
Head
(m)
(b)
0
50
100
150
200
250
0 100 200 300 400 500 600 700 800 900
Volume Flow (m3/h)
Power
(KW)
(c)
0
20
40
60
80
0 100 200 300 400 500 600 700 800 900
Volume Flow (m
3
/h)
efficiency
%
Figure 6. Predicted (lines) and experimental (points) performance curves
for centrifugal pumps with nominal characteristics D2 = 400 mm
(continuous line) and D2 = 350 mm (dashed line), both having dp = 250 mm
and running at 1480 rpm.

5. 157
Vol. 24(2): 153‐157
does not give accurate results under this condition. From the
representative results shown in figures 5 and 6, it can be seen
that the predictions for centrifugal pumps delivering greater
than 100 m3/h fit the experimental data better. Maximum and
average error in efficiency and power predictions were in fair
agreement with the experimental data. The parabolic form of
the predicted efficiency (eq. 5), shows, in some cases, a drop
after a certain value of the volume flow, whereas this trend
was not always observed in experimental data.
This research gives a simple and easy‐to‐apply numerical
tool for estimating pump performance curves. It requires a
minimum amount of pump geometrical data and can be
advantageous to pump designers by providing initial
performance curve estimation before advancing to detailed
design of the pump and its experimental verification on a test
rig. Furthermore, in cases where pump performance data are
not available, the present method works as a quick
assessment tool that can present an approximate answer to the
question of whether a particular pump is well suited to fulfil
an installation's requirements.
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6. 158 APPLIED ENGINEERING IN AGRICULTURE