AP2002_01.vp


1 Introduction
Screw agitators rotating in tubes are very efficient tools for

mixing and pumping viscous liquids. They are also suitable
for cases where the viscosity changes during operation. The
effect of Reynolds number on pumping characteristics was
shown in [1]. The influence of geometry on pumping
characteristics of screw agitators was presented in [2]. Paper
[3] was devoted to the effect of Reynolds number on power
characteristics. Both the pumping and the power character-
istics enable us to calculate pumping efficiency, defined as the
ratio of fluid power to power input. The aim of this paper is to
show the effect of Reynolds number on pumping efficiency.

2 Theoretical background
The pumping characteristic is the dependence of specific

energy e (transferred to the unit mass of fluid by the agitator)
on pumping capacity Q. As shown in [4] it is advantageous to
express this in a dimensionless form as

� �e Q* *, Re� f . (1)

As can be seen from [1] and [2] for screw agitators, the
dependence of e* on Q*, for a given Re, can be approximated
by a straight line

� �e e Q Q* * * *max max� �1 . (2)

The values e *max and Q *max are independent of
the Reynolds number in the creeping flow region. In the
turbulent region, the value e * Remax � and Eq. (2) trans-
forms to the form

� �e e Q Q
� �
� �max max* *1 (3)

independent of the Reynolds number.
The power characteristic is a dependence of power con-

sumption P on specific energy e. After an inspection analysis
of the governing equations, the following relationship for the
dimensionless power characteristic was proposed in [4]

� �P P e* * *, Re� . (4)

As was shown in [3], the dimensionless power character-
istic can be approximated by a linear relation

P c ae* *� � . (5)

The values of coefficients c and a are independent of
the Reynolds number in the creeping flow region. In the
turbulent region, the values of a and c / Re are independent

of Re, and the power characteristic can be approximated by
the following equation

Po c ae� � �Re . (6)

Pumping efficiency � (defined as the ratio of fluid power
to power input) can be calculated by the following relation
(see e.g. [5])

� �� e Q P (7)
or in dimensionless form

� � �
�Q e P Q e Po* * * * . (8)

3 Effect of Reynolds number on
pumping efficiency
The procedure for calculating pumping efficiency will

be illustrated on a screw agitator characterized by the fol-
lowing dimensionless geometrical parameters: s / d � 2,
d1 / d � 0.2, L / d � 1.4, Dt / d � 1.1 (see Fig. 3 in [3]). With refer-
ence to [1] the plot of parameters Q *max and e *max on the
Reynolds number shown in Figs. 1 and 2 can be obtained
using the values presented in [2]. Inserting these values into
Eq. (2) we receive the pumping characteristics depicted in
Fig. 3. Dimensionless specific energy e+ instead of e* is rec-
ommended for regions with high Reynolds number values.
The dependence of e max

� on Reynolds number is depicted
in Fig. 4. Inserting values from Figs. 1 and 4 into Eq. (3), the
pumping characteristics shown in Fig. 5 are obtained. The
dependencies of c and a on the Reynolds number and power
characteristics of a given screw agitator were presented in [3].

©  Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 37

Acta Polytechnica Vol. 42  No. 1/2002

Pumping Efficiency of Screw Agitators
in a Tube

F. Rieger

Most information on pumping efficiency that is available in the literature is limited to the turbulent region (centrifugal pumps). The aim of
this paper is to show the effect of the Reynolds number on the pumping efficiency of screw agitators for a wide range of Reynolds number
values from creeping to the turbulent flow region. The dependence of pumping efficiency on Reynolds number extends our knowledge about
the efficiency of classical impeller pumps restricted usually to the turbulent region.

Keywords: Pumping efficiency, screw agitator.

0.1

1

1 10 100 1000 10000 100000

Re

Q
*
m

a
x

Fig. 1: Dependence of maximum dimensionless pumping capa-
city on Reynolds number



Using pumping and power characteristics, the values of
pumping efficiency can be calculated from Eq. (8). The de-
pendence of efficiency on dimensionless pumping capacity
calculated for selected Reynolds number values is shown in
Fig. 6. From this figure it can be seen that efficiency is very low
in the creeping flow region (Re < 10). This is due to the
fact that most of the energy is spent for viscous friction in
the screw at low Reynolds number values. It can also be seen
that with increasing Reynolds number values the efficiency
increases. The dependence of maximum efficiency on the
Reynolds number is shown in Fig. 7. From this figure it can be
seen that maximum efficiency increases from 4.7 % in the

creeping flow region to 50 % in the turbulent region. This
means that only 4.7 % of the power is transferred to the fluid
near the maximum in the creeping flow region, and 50 % in
the turbulent region. The relation between efficiency and
Reynolds number presented in Fig. 6 extends our knowledge
about the efficiency of classical impeller pumps, for which
valid results have until now been restricted mostly to the
turbulent flow region.

Acknowledgement
This research was supported by GA ČR grant No.

101/99/0638.

38 ©  Czech Technical University Publishing House http://ctn.cvut.cz/ap/

Acta Polytechnica Vol. 42  No. 1/2002

100

1000

10000

100000

1000000

1 10 100 1000 10000 100000

Re

e
*

m
a

x

Fig. 2: Dependence of maximum dimensionless specific energy
on Reynolds number

0

50

100

150

200

250

300

350

400

450

500

0 0.1 0.2 0.3 0.4 0.5

Q*

e
*

Re 10�

Re 100�

Fig. 3: Dimensionless pumping characteristics at low Reynolds
number values

1

10

100

1000

1 10 100 1000 10000 100000

Re

e
+
m

a
x

Fig. 4: Dependence of maximum dimensionless specific energy
on Reynolds number

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8

Q*

e
+

Re = 1000

Re > 10000

Fig. 5: Dimensionless pumping characteristics at high Reynolds
number values

0

0.1

0.2

0.3

0,4

0.5

0.6

0 0.2 0.4 0.6 0.8

Q*

�

Re < 10

Re = 100

Re = 1000

Re > 10 000

Fig. 6: Plots of pumping efficiency on dimensionless pumping
capacity at different Reynolds number values

0.01

0.1

1

1 10 100 1000 10000 100000

Re

Fig. 7: Dependence of maximum efficiency on Reynolds number



Symbols
a, c coefficients in Eq. (5)
d agitator diameter [m]
d1 root diameter [m]
Dt tube diameter [m]
e specific energy [J kg�1]
e* dimensionless specific energy, e* � e/�n
e *max maximum dimensionless specific energy
e+ dimensionless specific energy, e+� e / n2d2

e max
� maximum dimensionless specific energy

L length [m]
n agitator speed [s�1]
P power [W]
P* dimensionless power, P* � P/ � n2d3

Po power number, Po � P/ � n3d5

Q volumetric flow rate [m3 s�1]
Q* dimensionless pumping capacity, Q* � Q / nd3

Q*max maximum dimensionless pumping capacity
Re Reynolds number, Re � nd2/�
s pitch [m]
� efficiency
� dynamic viscosity [Pa s]

� kinematic viscosity [m2 s�1]
� density [kg m�3]

References

[1] Rieger, F.: Pumping Characteristics of a Screw Agitator in a
Tube. Chem. Eng. J. 66, 1997, pp. 73–77

[2] Sedláček, L., Rieger, F.: Influence of Geometry on Pumping
Characteristics of Screw Agitators. Collect. Czech. Chem.
Commun. 62, 1997, pp. 1871–1878

[3] Rieger, F.: Power characteristics of a screw agitator in a tube.
Acta Polytechnica, Vol. 41, No. 6/2001, pp. 3–6

[4] Rieger, F., Weiserová, H.: Determination of Operating
Characteristics of Agitators in Tubes. Chem. Eng. Technol.
16, 1993, pp. 172–179

[5] McCabe, W. L., Smith, J. C., Harriott, P.: Unit Operations
of Chemical Engineering. McGraw-Hill, N.Y. 1993

Prof. Ing. František Rieger, DrSc.
e-mail: rieger@fsid.cvut.cz

Department of Process Engineering
Czech Technical University in Prague
Faculty of Mechanical Engineering
Technická 4, 166 07 Prague 6, Czech Republic

©  Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 39

Acta Polytechnica Vol. 42  No. 1/2002