This document provides an overview of pumps and pumping concepts. It discusses various pump types including centrifugal, axial flow, and regenerative pumps. Key concepts covered include pump head, power, efficiency, net positive suction head, cavitation, and pump characteristics. Impeller design, forces acting on impellers, and shaft seals are examined. The document also explores the theory behind impeller pumps using turbomachine equations and discusses specific speed, hydraulic efficiency, and losses. Pump applications, system curves, and selection are briefly outlined.

1. Lectures „Pumps and pumping“
Prof. T. Koppel
Department of Mechanics
Tallinn Technical University
Contents
1 Pump Types and Definitions.
1.1 Pump Types
1.2 Operating Variables of the Pumps
1.3 Pumping Head
1.4 Pump Power and Efficiency
1.5 Pump Suction Head
2 Impeller Pumps
2.1 Centrifugal Pumps
2.1.1 Single-Stage Centrifugal Pump
2.1.2 Forces on Impeller
2.1.3 Main Types of Centrifugal Pumps
2.2 Axial Flow Pumps
2.3 Regenerative Pumps
2.4 Shaft Seals of the Impeller Pump
3 Theory of Impeller Pumps
3.1 Turbomachine Equation
3.2 Similarity of Pumps
3.3 Specific Speed of Pump
3.4 Pump Characteristics
4 Application of Pumps
4.1 System Curve
4.2 Operating Point
4.3 Operation of Pumps in Parallel
4.4 Operation of Pumps in Series
4.5 Energy Savings with Variable-Speed Centrifugal Pump Drive
4.6 Effect of Liquid Viscosity on Performance of a Pump
4.7 Cavitation
5 Positive-Displacement Pumps
6 Selection of Pump
Literature:
1. R. W. Fox, A. T. McDonald. Introduction to Fluid Mechanics. John Wiley & Sons,
1994, 781 pp.
2. R. Neumaier. Hermetic Pumps. Gulf Publishing Company, 1997, 593 pp.
3. A. Maastik, H. Haldre, T. Koppel, L. Paal. Hüdraulika ja pumbad. Greif, 1995, 467 lk.
4. Bergius, Blomsted, Hedenfalk, Jonsson, Kempe, Nilsson, Pegert, Ullgren,
Wennström. Pumpputekniikka. Nesteiden pumppaus. Insinöörilehdet OY, 1978, s.199.

2. 1
1. Pump Types and Definitions
1.1 Pump Types
Machines that add energy to a fluid stream are called pumps when the flow is liquid or slurry,
and fans, blowers, or compressors for gas or vapor handling units, depending on pressure rise.
Fluid machines may be broadly classified as either positive displacement or dynamic.
A centrifugal pump is a kinetic machine convecting mechanical energy into hydraulic energy
through centrifugal activity.
1.2 Operating Variables of the Pumps
- pump capacity (rate of flow) Q, m3
/s, m3
/h, l/s, l/min – pumpun tilavuusvirta.
- pumping head, discharge head H, m – pumpun nostokorkeus.
- power, P, kW - tehon tarve.
- pump efficiency, η – hyötysuhde.
- net positive suction head, NPSH, m. NPSHA (available) and NPSHR (required) –
NPSH – arvo.
- rotation speed, n – pyörimisnopeus.
1.3 Pumping Head
Hst – static or geodetic head, m
H = Hst + ht – total dynamic pumping head, m
ht – head loss in suction and pressure pipe, m
Total dynamic head H = Ep – Es (1.1)
Es = hs +
g
ps
ρ
+
g
vs
2
2
,
hs – static head on the suction side, m
ps – absolute pressure on the suction side, Pa
vs – inflow velocity , m/s
g
ps
ρ
=
g
patm
ρ
- V - Zv

3. 2
Figure 1. Installation scheme of the pump [3]
V – vacuum, m,
patm – atmospheric pressure, Pa
and
Es = hs +
g
patm
ρ
- V - Zv +
g
vs
2
2
.
Ep = hs +
g
pp
ρ
+
g
vp
2
2
,
pp – absolute pressure on the pressure side, Pa
vp – velocity on the pressure side, m/s.
Specific energy at the pump pressure port
g
pp
ρ
=
g
patm
ρ
+ M + Zm

4. 3
M – gauge head, m
and
Ep = hs +
g
patm
ρ
+ M + Zm +
g
vp
2
2
.
Pumping head is equal
H = M + V + Zm + Zv +
g
vv sp
2
22
−
.
1.4 Pump Power and Efficiency
Pump output power Pw is the power imparted to the liquid by the pump
1000
gQH
Pw
ρ
= , kW
where ρ, kg/m3
; Q, m3
/s and H, m.
Pump input power Pp is the power delivered to the pump shaft at the driver to pump coupling.
Pp > Pw.
Pump efficiency
p
w
p
P
P
=η and
mhvp ηηηη = ,
– volumetric efficiency
qQ
Q
v
+
=η ,
- hydraulic efficiency
thtp
h
H
H
hH
H
=
+
=η ,
- mechanical efficiency
p
h
m
P
P
=η , where
- hydraulic power
1000
)( th
h
HqQg
P
+
=
ρ
, kW.

5. 4
mhvp ηηηη = =
p
w
p
th
th
P
P
P
HqQg
H
H
qQ
Q
=
+
⋅⋅
+ 1000
)(ρ
.
Drive efficiency
motor
p
motor
P
P
=η .
1.5 Pump Suction Head
Static suction lift – hs (Fig. 1)
Head losses in suction pipe – hts
ts
ss
s
atm
h
g
v
g
p
h
g
p
+++=
2
2
ρρ
.
To avoid cavitation the absolute pressure everywhere in the machine is kept above the vapor
pressure of the operating liquid. The NPSHA is the net total head provided by the system at the
inlet cross section (reference cross section) of the pump (not of the impeller) at the centre of
the suction connection. It consists of the absolute pressure ps predominating at this point less
the vapor pressure of the fluid in the inlet cross section, plus the total head from the mean
flow velocity in the reference cross section. NPSHA can be defined as follows on the basis of
the measurements on a running pump.
Av
ss
NPSHh
g
v
g
p
+=+
2
2
ρ
NPSHA – the NPSH produced by the system
NPSHR – the NPSH required for the pump relative to the permitted degree of cavitation
∆NPSH – excess of NPSHA over NPSHR (safety allowance).
The duty point Qopt can be taken as:
NPSHR = (0.3…0.5) n Q ,
with n in s-1
and Q in m3
/s or
NPSHR = σH
with σ = k 3
4
q
n and
4
3
H
Qn
ns = , when n = min-1
, Q = m3
/s and k ≈ 0.0014.

6. 5
Suction lift of the pump hs
)( Rtsv
atm
s NPSHhh
g
p
h ++−=
ρ
.
Measures for the avoidance of cavitation
i) Measures by the operator
- Reduction of geodetic suction lift or increase in suction head
- Short suction line with largest possible cross section
- Valves, bends, curves avoided where possible or the maximum radii used
- The temperature of the fluid to be kept to a minimum
- Application of a gas pressure to the surface of the liquid in closed suction or supply
vessels.
ii) Measures by pump manufacturers
- Impellers with double curvature blades drawn well forward into the suction orifice
- Avoidance of short deflection radii at the blade cover
- Reduction of the thickness of the impeller blades
- Use of a smaller blade inlet angle
- Reduction in speed
- Fitting an inducer
- Aligning the flow to the impeller by fitting a guide vane in the inlet connection.
It must be mentioned that there are no materials which are resistant to cavitation damage.
Figure 2. Cavitation erosion on the impeller of a centrifugal pump

7. 6
2 Impeller Pumps
2.1 Centrifugal Pumps
2.1.1 Single-Stage Centrifugal Pump
Centifugal pumps are machines in which fluids are conveyed in rotors (impellers) fitted with
one or more blades by a moment so that pressure is gained in a continuous flow.
Figure 3. Single stage centrifugal pump
1- impeller, 2- impeller blade (vane), 3- volute or scroll, 4- suction pipe, 5- foot valve, 6-
suction strainer, 7- diffuser, 8- valve, 9- pressure pipe, 10- filling opening, 11- water
pipe for the seal, 12- shaft seal.
Impellers could be enclosed (Fig. 3), semiopen (Fig. 4) or open (vane wheel) (Fig. 5) .
Figure 4. Semiopen impeller for sewage pump
Figure 5. Open impeller

8. 7
a) good b) poor
Figure 6. Air lock in suction pipe
2.1.2 Forces on Impeller
Figure 7. Impeller unbalanced to the axial pressure
4
2
1
1
d
pF s
π
= .
⎟
⎠
⎞
⎜
⎝
⎛
−=
44
22
1
2
dd
pF p
ππ
.

9. 8
After simplifing ( )
4
2
1
d
ppF sp
π
−= .
Figure 8. Balancing of axial pressure
Figure 9. Wear ring collars (a- low-, b- mean- and c- high pressure pumps)
1- pump casing, 2- wear ring, 3- impeller, 4- clearance.
Figure 10. Impeller unbalanced to the radial pressure when flow rate is smaller from the
pump design flow rate (a) and radial pressure in double –volute pump (b)
The radial force occurs on pumps with volute casings due to the uneven pressure distribution
on the circumference of the impeller. Radial force increases considerably in the partial flow
rates and overload ranges as the changes in cross-section of the volute guide (e.g. with

10. 9
circular cross-section) change quadratically via φ, whereas the increase or decrease of the
transport flow is linear.
2.1.3 Main Types of Centrifugal Pumps
i) Single-Stage Pumps
ii) Double-Suction Pump
iii) Multistage Pumps
Figure 11. Multistage pump
Figure 12. Inducer postioned before the impeller [2]
- Submersible Pumps
- Process Pumps
- Pumps for Turbid Water
- Portable Submersible Pumps (Flygt in 1948)
- Sewage Pumps (Fig. 13 - Swirl Type Impeller Pump and Super – Vortex Pump)

11. 10
Figure 13. Impellers of swirl type pump
2.2 Axial Flow Pumps
Scheme of the axial flow pump is given in the Fig. 14 (1- vane, 2-hub, 3- vane of the guide
apparatus). Vanes of the impeller are fixed or reversible.
Figure 14. Axial flow pump
Figure 15. Impeller of the axial flow pump

12. 11
2.3 Regenerative Pumps
Special type of impeller pumps. An impeller with several blades which are always radial and
mounted on one or both sides rotates between two plane - parallel housing surfaces. The
energy of the fluid, which is imparted to the particular liquid particles by impulse exchange,
steadily increases from the inlet into the impeller blades until its exit at the interrupter. High
pressure, low flow rate.
Figure 16. Water path in the impeller of the regenerative pump
2. 4 Shaft Seals of Impeller pump
- Staffing box packing
- Single mechanical seal
- Double mechanical seals
- Dynamic seal (Ahlström)
3 Theory of Impeller Pumps
3.1 Turbomachine Equation
The flow processes in the impeller which lead to formation of the H(Q) line can be
mathematically determined by the theoretical assumption that the impeller has an infinite
number of infinitely thin blades. The flow consists in this case from equal stream filaments.
The energy conversion can be arrived at with the aid of the moment of momentum principle.
The change of moment of momentum in time at the inlet (position 1) and at the oulet (position
2) is equal to the moment of forces to this liquid mass. The loss-free flow is considered (ideal
fluid).
Pump Power (W= Nm/s) thgQHP ρ=

13. 12
Figure 17. Flow velocities at impeller [3]
is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω
(rad/s)
P =M ω.
Theoretical pump head (m)
gQ
M
Hth
ρ
ω
= .
In one second through the pump is flowing liquid mass
m = ρQ . (3.1)
Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1).
When we consider that l =R cos α and for mass (3.1)
M = ρQ (c2R2cos α2 – c1R1cos α1 ).
As ωR1=u1 and ωR2=u2, then
g
ucuc
Hth
)coscos( 111222 αα −
= . (3.2)

14. 13
This formula is Euler’s equation for centrifugal pumps. It represents a theoretical relationship
between the individual values where there is an ideal uniform distribution of all liquid
particles in the particular flow cross-sections. However, it also states:
„The theoretical head of a centrifugal pump is independent of the density and the physical
properties of the fluid flowing through it“.
Figure 18. Inlet and outlet triangles on radial impeller [2]
Modern centrifugal pumps are constructed in this way, that inflow has radial direction. This
means α = 90° and cos α = 0.
g
uc
Hth
222 cosα
= . (3.3)
The vortex torque component
cu = c cos α
and Hth =
g
cu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet.
Figure 19. Flow at the impeller of centrifugal pump ( a- real, b- theoretical, c- vortex) [3]
ns, r.p.m. 40 50 75 100 125 150 175 200 250
k 0.78 0.80 0.81 0.82 0.805 0.77 0.715 0.675 0.55

15. 14
The specific speed ns of a pump is the required speed of one of the present pumps which are
geometrically similar in all parts, which delivers a flow rate of 1 m3
/s at a head of 1 m.
The theoretical head Hth is reduced by the losses which occur due to:
- volumetric internal leakage losses at the radial clearance between the impeller and
casing
- friction losses in the blade channels
- energy conversion losses (velocity in pressure due to changes in direction and cross-
section)
- shock losses where the angle of the approach flow to the impeller blades is not
vertical.
Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
η
ukc
gH
H
H
th
h == .
Finally the turbomachine equation takes form
g
ukc
H h 222 cosαη
= . (3.4)
Figure 20. Different shapes of the impeller [3]
The energy transfer begins at the inlet to the cascade and ends on departure from the blade
channels. The pressure and velocity of the pumped liquid is increased on this path. The
pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in
the impeller channels between the channel inlet and outlet. The strong increase in the absolute
velocity c of the fluid during the flow through the impeller channels is partly converted to
pressure energy in a diffuser, volute guide or stator after leaving the impeller.
A distinction is to be made between movement processes of the absolute velocity c and
relative velocity w. Absolute velocity c is that which liquid particles exibit compared with a
static environment. The relative velocity w is the velocity of a liquid particle, compared with
the rotating blades, when flowing through the blade channel. The peripheral velocity u of the
rotating blades at the particular distance from the axis of rotation is also important. The
pressure path in the impeller is parabolic, corresponding to the laws of dynamics. To

16. 15
determine the flow processes mathematically, however, all that is required is the recording of
the velocities at the blade inlet and outlet.
Real head of the pump is smaller than theoretical. In reality impeller has up to 12 blades. The
flow is different from theoretical between blades. In the convex part of blade the velocity is
smaller than in concave part. The energy used for keeping vortex is decreasing the developed
head by pump.
The head given for an infinite number of blades Hth is reduced due to the incomplete flow
guidance where there is a finite number (mainly 7) of blades. A comparison of the velocity
diagrams for the actual and fictitious flow shows vortex components. The decrease of the
head is considered with the coefficient k, which depends from the construction of the pump. k
is characterized by the specific speed ns of the pump.
Theoretically it is impossible to calulate hydraulic efficiency ηh. It depends from many
factors. Theory is giving qualitative recommendations to get higher efficiency:
- to avioid sudden changes of velocities in pump
- to avoid decrease of velocity on the impeller perimeter
- to give simple shape to the impeller blades
- to avoid sharp corners in the pump.
In Fig. 20 are given three different shapes of blades.
If ω = const and Q = const, for β2 = 90°
g
u
Hth
2
2
= , for β2 < 90°
g
u
Hth
2
2
< , for β2 > 90°
g
u
Hth
2
2
> .
For increasing the pump head, the blades should be directed to the direction of rotation. This
will increase c2, and in diffuser we have to convert high kinetic energy to the potential
energy, and we lost in principal much energy. The angle β2 < 90° is preferred for the pumps,
and β2 > 90° for ventilators.
3.2 Similarity of Pumps
Theoretical considerations are giving only qualitative results. The more realistic results is
possible to get by making pump or pump model tests, especially in designing a new pump.
From the test results the pump similarity rules are used for calculating parameters of the pump
under construction. The theory of similarity is based on the rules of hydraulic modelling.
Geometric similitude – measures and shape of the model and pump should be in scale.
Kinematic similitude – velocities should be in scale.
mmm c
c
w
w
u
u
== etc.

17. 16
The peripheral velocity
60
2nD
u
π
=
and corresponding ratio of velocities (model and pump)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
==
m
l
mmm n
n
m
nD
nD
u
u
2
2
,
where ml is the length scale.
Theoretical flow rate of the pump 2222 sinαπ cbDQth = , (3.5)
where b2 is the width of the outflow of the impeller.
Then ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
==
m
l
mmmm n
n
m
cbD
cbD
Q
Q 3
2222
2222
sin
sin
απ
απ
. (3.6)
The pump head is calculated from (3.4).
2
2
222
222
cos
cos
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
==
m
l
mmmhm
h
m n
n
m
uck
ukc
H
H
αη
αη
, (3.7)
where ηhk= ηhmkm .
Pump power P = ρgQH.
3
5
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
==
m
l
mmm n
n
m
HgQ
gQH
P
P
ρ
ρ
.
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in
the model and pump should be the same. Reynolds number is characterizing the ratio of
frictional and inertial forces
ν
cD
=Re , and Re = Rem.
In case we have the same liquid in model and in pump, ν = νm, then cD = const.
From the experimental research has been appeared that influence of the Re number is not
important when Re ≥ 5· 104
. Different roughness of the pump and model impellers will cause
difference in efficiency. Efficiencies are connected by the formula

18. 17
a
m
m D
D
⎟
⎠
⎞
⎜
⎝
⎛
=
−
−
η
η
1
1
, where a = 0, when the roughness is modelled, and a = 0.2, when the
roughnesses are equal.
Froude number is characterizing the ratio of gravity- and inertial forces:
Fr =
gD
c2
, Fr = Frm.
A special case is ml = 1. Pump characteristics depend from the pump speed.
2
1
2
1
n
n
u
u
= ,
2
1
2
1
n
n
Q
Q
= ,
2
2
1
2
1
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
n
n
H
H
and
3
2
1
2
1
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
n
n
P
P
or
3
2
1
2
1
2
1
2
1
P
P
H
H
Q
Q
n
n
=== .
The rate of pump flow where the operating conditions are equal is therefore proportional to its
speed, the heads behave as the square of its speeds, the requared motor power output changes
with the cube of its speed. In case the pump speed is increasing 2 times, the flow rate is
increasing 2 times, head 4 times and necessary power 8 times. The hydraulic efficiencies are
equal, the pump efficiencies reduce slightly with speed.
3.3 Specific Speed of Pump
Definition: The specific speed ns of a centrifugal pump is the required speed of one of the
present pumps which are geometrically similar in all parts, which delivers a flow rate of 1
m3
/s at a head of 1 m. The term is used for comparing numerically different centrifugal
pumps. This is a variable obtained from the service data which has great practical significance
for the design and choice of pumps. For the working parameters of the model pump we can
use index s. From the equations (3.6) and (3.7) we have next expressions

19. 18
s
l
s n
n
m
Q
Q 3
= ;
2
2
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
s
l
s n
n
m
H
H
,
giving us ml and ns:
sss
s
l
n
n
H
H
nQ
Qn
m == 3 ;
4/32/1
⎟
⎠
⎞
⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
H
H
Q
Q
nn s
s
s .
Considering that Q = 1m3
/s and H = 1 m
4/3
2/1
H
Q
nns = .
From the last equation the specific speed increases with n and Q and decreases with H. The
value of the specific speed is determined at the highest efficiency working condition of the
pump and its value is valid for one impeller.
The specific speed is characterizing the construction of the pump. The value of the height
c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig. 21)
Figure 21. Velocity diagram
( )22
22
222
sin
sinsin
sin
βα
βα
α
+
= uc ,
and
( )22
22
2
sin
sin
βα
β
+
=
u
c . (3.8)
The expression (3.8) will be placed to the centrifugal pump equation (3.3). Then pump head
( )22
22
2
2
sin
sincos
βα
βα
+
=
g
u
H

20. 19
or
( )
2
222
2
2
sin
sincos
β
βαα
g
c
H
+
= (3.9)
and velocities
( )
HAgHu =
+
=
22
22
2
sincos
sin
βα
βα
and
( )
HBgHc =
+
=
222
2
2
sincos
sin
βαα
β
.
Quantities A and B are constants, the values depends from the impeller construction (angles α2
and β2).
Rotation speed
D
un
π
60
2= . (3.10)
Specific speed ns = n, if H = 1 m. The expressions (3.10) and (3.9) are giving
( )
22
22
sincos
sin60
βα
βα
π
+
=
g
D
ns . (3.11)
The specific speed depends from the impeller construction – from diameter D and from
angles α2 and β2.
Figure 22. Impeller of the mixed-flow pump
Dependent from the specific speed and construction the dynamic pumps could be low-,
normal- and high-speed centrifugal pumps, mixed-flow pumps and axial flow pumps. The
pumps with small specific speed have low flow rate but high head, pumps with high specific
speed large flow rate and small head (Fig. 23).

21. 20
Figure 23. Impeller shapes and specific speed

22. 21
3.4 Pump Characteristics
Next parameters as a function from flow rate are used for the pump characteristics:
H(Q), P(Q), η(Q) and NPSH(Q). The characteristics are used for a constant rotation
speed of pump (n = const) and for the fixed density and viscosity of he liquid. The
theoretical head curve Hth(Qth) could be derived from the pump equation (3.3) and from
the expression of theoretical flow rate (3.5). From Fig. 17 (velocity diagram)
( ) 222222 tancossin βαα cuc −= . (3.12)
Substituting in (3.12) c2sinα2 =
22bD
Qth
π
from (3.3) and
2
22 )cos
u
gH
c th
=α from(3.5) the
result will be next
2
2
2
22
tan β
π ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−=
u
gH
u
bD
Q thth
,
and the theoretical pump head
thth Q
bDg
u
g
u
H
22
2
2
2
2
tan
1
πβ
−= .
Dependent from the angle β2 we have three straight lines. If β2 = 90° , horizontal line,
for β2 < 90° declining line and for β2 > 90° rising line (centrifugal ventilators). When
the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero. Line 3 is for
the ideal fluid flowing in the impeller with the infinite number of thin blades. With the
correction k (3.4) we have line 4 for finite number of blades. After reducing the friction
losses in pump we have the characteristic 5. In case we have different flow rate from the
design value, the inflow direction is different from the radial direction and we have the
characteristic 6 (supplementary head losses). Part of the flow is circulating in the pump
(ηv < 1), the final result is curve 7.
In reality it is much more complicated, and the real characteristics of the pump are
evaluated experimentally. The shape of the characteristics depends from the specific
speed of the pump ns. Different pump manufacturers form the characteristis in a different
way.
Many conclusions for application of pumps could be done on the basis of characteristic
curves. The starting of the pump should be done when it needs from the motor low
power. For centrifugal pumps it is on zero flow rate, this means with closed valve on
pressure pipe. The pumps with high specific speed have minimum power on high flow

23. 22
rate . These pumps should be started with open valve on pressure pipe. It is quite
common that axial flow pumps do not have valve on pressure pipe.
Figure 24. The H(Q) curve (constant speed characteristic curve)
Figure 25. The H(Q) curve
The impeller pumps before starting should be filled with the liquid. The axial pumps are big
and as the foot valves have a high local losses the foot valves are not installed normally. It is
impossible to fill the suction pipe in this case. We have to install the pump under the water
level surface in suction side. It is constructive way to have pump filled before the starting.

24. 23
Figure 26. Pump MENBLOC 65-40-200 L/8.5 2
(n =2960 r/min) curve
Figure 27. Ahlström closed impeller pump APP 22-65 (n =2950 r/min) curves

25. 24
Figure 28. Axial flow pump curves
Figure 29. Regenerative pump curves
There is possible to use many impellers in one casing of pump (Fig. 27). The multistage pump
has many impellers. The impeller diameters could be reduced by turning (cut off in some
limits). This way of reducing the impeller diameter has been used quite offenly in the past. The
best or recommended working area of the pump is usually indicated on H(Q) curve. Roughly
saying the pump could work in the area 0.5 Qdesign ≤ Q ≤ 1.2 Qdesign, where design discharge
will correspond to the maximum efficiency ηmax.

26. 25
Figure 30. Sarlin submersible sewage pump with SuperVortex impeller
Figure 31. H(Q) curves relative to speed (shell diagram) [2]
The pump could be characterized by the shell diagram, where the same value curves of
efficiency are drawn. In Fig. 28 the shell digram for the axial flow pump is given. The H(Q)
lines are for five different angle of blades, efficiency curves (full lines) and NPSH curves
(stripe lines). The efficiency of this pump is quite high, up to 84 %. High is also NPSH value,
from 8.5m to 15 m in the upper part of diagram. The recommendable working area is indicated
with the bold line. In starting of the pump the head could not rise over the level of line I.

27. 26
Regenerative pump curves are in Fig. 29. When we compare the curves with the same powerful
centrifugal pump curves, the regenerative pump has low flow rate, but high head. The H(Q)
curve is concave and the P(Q) curve is declining. The Sarlin company SuperVortex swirl type
impeller pump curves are in Fig. 30. The characteristic curves are different from the centrifugal
pump curves. This should be considered in case the pump is working in parallel with some
other type of pump.
4 Application of Pumps
4.1 System Curve
The pump characteristic curves indicate the capability of the pump. Before we are starting to
select a pump we have to calculate the system requirements. For this the system head curve
should be calculated. The task of the pump as a machine is to impart energy to a fluid. In
steady state, the head H of the pump is equal to the head Hs of a system. The necessary head is
equal to
H = Hst + ht
where Hst –static or geodetic head, m and ht is the head loss in suction and pressure pipe,
m. The head loss in pipes consists from friction and minor (local) head losses.
The mean velocity is calculated from the continuity equation
v=
A
Q
.
As the flow rate is not changing on the pipe length, then
gA
Q
d
l
ht 2
2
2
⎟
⎠
⎞
⎜
⎝
⎛
+= ∑ ∑ζλ (4.1)
or
2
kQht = ,
where k is expressing the flow resistance. The system head curve could be expressed by
the next way
2
kQHH st += . (4.2)
This is parabola starting from the point H = Hst +kQ2
(Fig. 32).

28. 27
4.2 Operating Point
The operating point of the centrifugal pump is the intersection point of the pump characteristic
curve and system head curve (Fig. 32 and Fig. 34). A corresponding variable for the power
input, efficiency of the pump and NPSHR value is assigned to each duty point. In the design of
the operating data of a centrifugal pump, care should be taken to ensure that the pump works as
close as possible to the point of best efficiency (Fig. 33).
Figure 32. System and pump head curves [1]
Figure 33. Best efficiency operating point [1]
For changing the operating point of the pump we have to change system head curve or pump
head curve. In Fig. 35 the change in rate of flow with a fluctuating static head are given. The
flat pump curves produce relatively large flow rate fluctuations, and those for steeper ones are
smaller. The system head curve is possible to change by throttling control (Fig. 36). If the
pump does not deliver the required service flow rate, then throttling control (gate valve or
orifice) must be used to set

29. 28
Figure 34. System and pump curves [2]
Figure 35. Change of the flow rate with a fluctuating static head
duty point B at flow rate Q. This means an additional pipe friction loss dynH∆ . The additional
pipe friction loss dynH∆ may however be created only in the pipeline because throttling control
on the inlet side poses the danger of cavitation. Allowance must of course be made for a
deterioration in efficiency because the drop in head is converted to heat in the throttling device.
For this reason pumps with a flat H(Q) curve should be used where possible for throttling
control.

30. 29
Figure 36. Throttling control pump characteristics [2]
The pump characteristic is possible to change by speed control or by reducing mechanically the
impeller diameter. The semiconductor frequency converters are used mainly. The pump
similarity rules are used to calculate a new speed n2 that the pump curve intersects the system
head curve at duty point B2.
( ) ,/
2
1212 nnHH = ( )1212 / nnQQ = , ( )3
1212 / nnPP = etc.
Figure 37. Variable speed control [2]

31. 30
The duty points of equal shock states which lie on the affinity parabolas passing through the
co-ordinates data have the approximately equal efficiency. It is particularly important that the
affinity law is valid only if it does not lie within the range of cavitation. The shell diagram of a
centrifugal pump clearly shows the possible applications of this pump (Fig. 31).
If the impeller characteristic curve does not agree with the required flow characteristics for the
actual operating conditions, this can be corrected by changing the impeller outlet conditions.
The reduction of the impeller diameter depends from the specific speed of the pump
1200
75.0
min
1 sn
D
D
+=⎟
⎠
⎞
⎜
⎝
⎛
,
where D is the nominal diameter of the impeller and D1 reduced diameter, mm. Axial flow and
mixed-flow pump impeller diameters is not possible to reduce.
The new pump characteristic is calculated by next expressions
DDQQ // 11 = , ( )2
11 // DDHH = , ( )3
11 / DDPP =
4.3 Operation of Pumps in Parallel
Figure 38. Parallel operation using two centrifugal pumps with the
same characteristic curves
Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with
the pumped liquid being drawn mainly through separate suction pipes. Where there is an

32. 31
Figure 39. Parallel operation of two centrifugal pumps with unequal
charactersitic curves
Figure 40. Three pumps operating parallel

33. 32
increased demand, one or more pumps are switched in either automatically or manually, thus
producing parallel operations.
With the parallel operation the rate of flow is less than the total of the rates of flow of
centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency
of the pumps under certain circumstances.
III
IIIIII
III
IIIIII
III
Q
QQHgQHgQ
HgQ
+
+
+
=
+
=
ηη
ηη
ηρηρ
ρ
η
//
Figure 41. Optimum parallel operation domain of the centrifugal pumps
with frequency converters
4.4 Operation of Pumps in Series
Pumps operating in series are used for the increase of pressure.
IIIIII HHH +=+ .
The efficiency
III
IIIIII
III
IIIIII
III
H
HHgQHgQH
gQH
+
+
+
=
+
=
ηη
ηη
ηρηρ
ρ
η
//
.

34. 33
4.5 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42. Example of energy saving on centrifugal pumps using
variable speed control (Danfoss-GmbH) [2]
The speed of three-phase induction motors for pump drives can be changed using static
frequency converters. These devices change a constant power supply with its associated
frequency into a converted voltage and frequency. Fig. 42 shows example of possible power
savings on centrifugal pumps. Although frequency converters still represent a considerable
investment cost they are becoming cheaper. If the cost of the converter is set against the annual
saving in energy cost the is recovered very quickly, particularly for pumps with a long service
life.

35. 34
4.6 Effect of Liquid Viscosity on Performance of a Pump
An increase in the viscosity of the pumped fluid changes the characteristic curves of the
pump. Flow rate and head reduce, accompanied by an increase in power input, i.e.
efficiency is lowered (Fig. 43). The characteristic curves for pumping viscous fluid can
only be accurately determined by trial. The correction values kQ, kH and kη relative to the
flow rate, head and efficiency are given in Fig. 44 dependent from Reynolds number.
wQz QkQ = , wHz
HkH = , wz k ηη η= .
Figure 43. Reduction in performance when handling viscous liquids [2]
Figure 44. Correction factors for pumping viscous fluids [3]

36. 35
4.7 Cavitation
Figure 45. NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46. Cavitation [2]
Cavitation can occur in any machine handling liquid whenever the local static pressure
falls below the vapor pressure of the liquid. When this occurs, the liquid can flash to
vapor locally, forming a vapor cavity and changing the flow pattern from the non-
cavitating condition. The vapor cavity changes the effective shape of the flow passage,
thus altering the local pressure field. Since the size and shape of the vapor cavity are
influenced by the local pressure field, the flow may become unsteady. The unsteadiness
may cause the entire flow to oscillate and the machine to vibrate. As cavitation
commences, the effect is to reduce the performance of a pump rapidly. Thus cavitation

37. 36
must be avoided to maintain stable and efficient operation. In addition, local surface
pressures may become high when the vapor cavity collapses, causing erosion damage or
surface pitting. The damage may be severe enough to destroy a machine made from a
brittle low-strength material. Obviously cavitation must be avoided to assure long
machine life.
Figure 47. NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48. Regenerative impeller with a radial impeller mounted in front [2]
Common regenerative pumps have quite frequently unsatisfactory NPSHR values. A
design such shown in Fig. 48 is based on a radial impeller with good, normal flow

38. 37
characteristics being positioned before the regenerative impeller as a booster pump. In
this way the comparatively good NPSHR values for this type of impeller can be used and
combined at the same time with the advantages which the regenerative impeller has in
achieving large pressures at low capacity coefficients.
Figure 49. NPSHR values of a centrifugal pump specified according to various criteria
[2]
Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump, the inducer also
performs a further task that it ensures the inlet conditions to the cascade are such that
positive pre-rotation conditions are produced thus improving the NPSHR.

39. 38
Figure 50. Impact of an inducer on NPSHR [2]
Figure 51. NPSHR curve of inducer and impeller [2]
Due to the severely throttled delivery, recirculation flows out of and into the impeller
occur at the impeller inlet and outlet in the partial load range and severe pre-rotation
occurs (Fig. 52). This produces shear layers between the normal and reverse flow thus
forming vortices and these in turn form vapor bubbles which implode at the pressure side
of the impeller blade.

40. 39
Figure 52. Pre-rotation and recirculation in an impeller operating in the partial load
range [2]
5 Positive-Displacement Pumps
Main types of positive-displacement pumps are:
- piston pumps
- single-acting piston pump
- double-acting piston pump
- differential piston pump
- diaphragm pump
- wing pump
- rotary pump
- gear pump
- screw pump
- vane pump
- rotary-piston pump
- peristaltic pump (hose pump)
- liquid ring pump
- pumping devices (water wheel, Archimedian screw etc.)

41. 40
6 Selection of Pump