AP1_01.vp


1 Introduction
An axially located standard Rushton turbine impeller in

a cylindrical vessel with radial baffles exhibits the main force
effects – radial and peripheral [1]. The distribution of the

peripheral (tangential) components of dynamic pressure af-
fecting a radial baffle at the wall of a cylindrical pilot plant
vessel with an axially located axial or radial flow rotary im-
peller under turbulent regime of flow of agitated liquid was
determined experimentally [2, 3, 4]. The experiments [3, 4]
were carried out in a flat-bottomed cylindrical pilot plant
mixing vessel with four baffles at its wall (see Fig. 1) of
diameter T = 0.3 m filled with water ( � = 1 mPa�s) or a
water-glycerol solution of dynamic viscosity � = 3 mPa�s and
� = 6 mPa�s, respectively. The impeller was a standard Rush-
ton turbine disk impeller (see Fig. 2) with six flat plane blades
[5]. The range of impeller frequency of revolution was chosen
in the interval N = 3.11–5.83 s�1.

The originally developed technique for measuring the pe-
ripheral component of dynamic pressure affecting the baffle
[4] is illustrated in Fig. 1. One of the baffles was equipped with
a trailing target of height hT and width B enabling it to be
rotated along the axis parallel to the vessel axis with a small
eccentricity and balanced by a couple of springs. Eleven

Acta Polytechnica Vol. 41  No.1/2001

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

Dynamic Effect of Discharge Flow of
a Rushton Turbine Impeller
on a Radial Baffle
J. Kratěna, I. Fořt, O. Brůha

This paper presents an analysis of the mutual dynamic relation between the impeller discharge flow of a standard
Rushton turbine impeller and a standard radial baffle at the wall of a cylindrical mixing vessel under turbulent regime
of flow of an agitated liquid. A portion of the torsional moment of the baffle corresponding to the region of the force
interaction of the impeller discharge stream and the baffle is calculated under the assumption of constant angular
momentum in the flow region between the impeller and the baffles. This theoretically obtained quantity is compared
with the torsional moment of the baffles calculated from the experimentally determined distribution of the peripheral
(tangential) component of dynamic pressure along the height of the radial baffle in pilot plant mixing equipment. It
follows from the results of our calculations that for both investigated impeller off-bottom clearances the theoretically
determined transferred torsional moment of the baffles in the area of interference between the impeller discharge flow
and the baffles agrees fairly well with experimentally determined data and, moreover, that more than 2/3 of the
transferred torsional moment of the baffles as a whole is located in the above mentioned interference area.

Keywords: Rushton turbine impeller, impeller discharge stream, dynamic pressure.

Fig. 1: Sketch of a flat-bottomed agitated pilot plant mixing ves-
sel with four radial baffles at the wall and axially located
standard Rushton turbine impeller and sketch of mea-
surement of local peripheral force affecting the trailing
target (H/T = 1, h/T = 0.33, 0.48, b/T = 0.1, hT = 10 mm,
B = 28 mm)

Fig. 2: Standard Rushton turbine disk impeller
(D/T = 1/3, w/D = 0.2, D1/D = 0.75, l/D = 0.25)



positions of the target along the height of the baffle were
examined, above all in the region of the interference of the
baffle and the impeller discharge flow. The angular dis-
placement of the target � is directly proportional to the
peripheral force F affecting the balancing springs (see Fig. 3).
The flexibility of the springs was selected in such a way that

the maximum target displacement was reasonably small com-
pared with the vessel dimensions (no more than 5 % of
the vessel perimeter). By means of a small photo-electronic
device, composed of two photo diodes, the angular displace-
ment was scanned and the output signal was treated, stored
and analysed by the computer.

The vertical (axial) distribution of the peripheral compo-
nent of dynamic pressure along the height of the radial baffle
coincides with the flow pattern in an agitated system with a
standard Rushton turbine impeller [5]. The aim of this study
was to analyse the force interaction of the impeller discharge
stream and the corresponding part of the radial baffle and to
compare the results of such an analysis with available experi-
mental data.

2 Theoretical
Let us consider a flat-bottomed cylindrical vessel filled

with a Newtonian liquid and provided with four radial baffles
at its wall. At the axis of vessel symmetry a standard Rushton
turbine rotates in such a way that the flow regime of the
agitated liquid can be considered turbulent. In such a system

the radially-tangential impeller discharge stream leaves the
rotating impeller and reaches the baffles (see Fig. 4). For the
balance region considered between the impeller and baffles
we can assume that the angular momentum flow is constant
[6], i.e.,

� � � � �Q w const R D Tt ., ,2 2 . (1)

Eq. (1) can also be used for the relation between the values
of the angular momentum in the impeller discharge stream
and around the baffles

w

w
T
D

Q
Q

t p

t b

b

p

,

,
� � , (2)

where index “b” characterises the baffle area and index “p”
the flow leaving the rotating impeller (impeller discharge
flow). Eq. (2) can be rearranged into the form

� �� � � � �Q T w Mb t b b d th2 , , , , (3)

where quantity Mb d th, , represents a theoretically considered
portion of the time averaged (mean) torsional moment of the
baffles corresponding to the area of the force interaction of
the force action of the impeller discharge stream and the baf-
fle (see shaded area below the curves in Figs. 6 and 7).

By combining Eqs. (2) and (3) we can eliminate the
unknown value of the tangential component of the mean
velocity wt b, in the baffle area, and so we have finally

� �M D w Qb d th t p p, , ,� � � �2 � . (4)

Eq. (4) can be used for estimating the torsional moment of
the baffles transferred via the impeller discharge flow. The
tangential component of the mean velocity in the impeller
discharge stream w t p, is related with the radial component
w r p, by the equation

� �w wt p r p, , tan� � � , (5)

where � is the angle between the horizontal velocity compo-
nent in the impeller discharge stream and its radial compo-
nent [7]. It can be calculated from the equation

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Acta Polytechnica Vol. 41  No.1/2001

–0.25

–0.13

0.00

0.13

0.25

–500 –250 0 250 500

PC indicated displacement

F
[N

]

–0.25

–0.13

0.00

0.13

0.25

–0.2 –0.1 0 0.1 0.21
b [rad]

Fig. 3: Results of mechanical calibration of balancing springs

Fig. 4: Vertical cross section of the turbine impeller discharge
stream region Fig. 5: Turbine impeller as a cylindrical tangential jet



� �� �� � arcsin a D 2 , (6)
where parameter a is the radius of the cylindrical jet, i.e., the
virtual cylindrical source of the impeller discharge stream
(see Fig. 5). Considering the relation between the impeller
pumping capacity Qp and the average value of the radial
component of the mean velocity over the cross section of the
impeller discharge flow

Q w D wp r p� � � �, � , (7)
where D and w are the diameter of the impeller and the width
of the impeller blade, respectively, we can rearrange Eq. (4)
into the form

� �� �� 	
M Q

a D

w
b d th p, ,

tan arcsin
� �

�
�

�

2 2

2
. (8)

Let us consider the flow rate number [8, 9] expressing the
quantity Qp in dimensionless form

N
Q

N D
Q

p
p
�

� 3
. (9)

After substitution into Eq. (8) we have after a simple rear-
rangement

� �� �
� �

M
M

N D
N

a D

w D
b d th

b d th
Q p, ,

* , , tan arcsin�
� �

� �
�

�� �2 5
2 2

2
, (10)

where N is the impeller frequency of revolution.

3 Results and discussion
It follows from the experimental data that the radius of

the virtual cylindrical jet [8] is

� �a D D T h T� � � 
0 34 1 3 1 3 1 2. , , , , (11)
and the Rushton turbine impeller flow rate number [8, 9]

� �N D T h TQ p � � 
0 80 1 3 1 3 1 2. , , , . (12)
The ratio of the impeller blade width according to the

impeller geometry (see Fig. 2) corresponds to the relation [5]

w D � 1 5 . (13)
Now, we can substitute all the numerical values into

Eq. (10), and have finally in dimensionless form the theoreti-
cally considered portion of the impeller torque transferred by
the baffles via the impeller discharge stream

� �M D T h Tb d th, ,* . , , ,� � 
0 472 1 3 1 3 1 2 . (14)
The mean dimensionless pressure affecting the part of the

baffle of dimensionless height Hd
* can be calculated from the

known experimental dependence (see Figs. 6 and 7)

� �p p H Tk av k av T,* ,*� . (15)
Eq. 15 consists of the dimensionless axial position of the

target centre of gravity HT related to the vessel diameter T as
an independent variable and the dimensionless peripheral
component of the local mean dynamic pressure affecting the
baffle

p
p

N D
k av

k av
,

* ,�
� �� 2 2

, (16)

considered as a dependent variable. Then the average mean
dynamic pressure corresponding to the hatched surface
in Figs. 6 and 7, i.e., the region along the baffle between
the lower and upper intersections of the curve

� �p p H Tk av k av T,* ,*� and zero quantity pk av,* below and
above its peak, is

� �p
H

p H Td av
d

k av T
H

H

b

b

,
*

* ,
*

*

*

� �
1

1

2

d , (17)

where

H H Hd b b
* * *� �2 1 . (18)

Dimensionless coordinates Hb1
* and Hb2

* depict the above

mentioned intersections of the curve � �p p H Tk av k av T,* ,*�

with the zero values of the quantity pk av,
* (see Figs. 6 and 7).

The total dimensionless mean peripheral force affecting the
baffle along its interference region with the impeller dis-
charge stream can be calculated from the relation

� �F
F

N D
T D b H pd av

d av
d d av,

* , * *
,

*�
� �

� � � �
�

2 4
2 , (19)

where the dimensionless width of the radial baffle

b b T* � . (20)

Similarly the total mean dimensionless peripheral force
affecting the whole baffle can be calculated from the relation

� �F
F
N D

T D b H pav
av

d av
* * * *�

� �
� � � �

�
2 4

2 , (21)

where the dimensionless total liquid depth in the mixing
vessel

H H T* � (22)

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

Acta Polytechnica Vol. 41  No.1/2001

�

Fig. 6: Axial profile of the dimensionless peripheral component
of dynamic pressure affecting a radial baffle along its
height (h/T = 0.33)

�

Fig. 7: Axial profile of the dimensionless peripheral component
of dynamic pressure affecting a radial baffle along its
height (h/T= 0.48)

p k
av,*

p k
av,*



The average mean dynamic pressure over the whole baffle
can be calculated by integration

� �p
H

p H Tav k av T
H

*
* ,

*
*

� �
1

0
d . (23)

From the momentum balance of the mechanically agi-
tated system [1] it follows that the mean impeller torque

M
P

N
�

�2�
, (24)

where P is the impeller power input, should correspond to
the sum of the mean reaction moments of the baffles, bottom
and walls. The mean impeller torque can be expressed in the
dimensionless form

M
M

N D
P
N D

Po* �
� �

�
� � �

�
� � � �

2 5 3 52 2
, (25)

where the standard Rushton turbine impeller power number
under conditions Re > 104 and D/T 	 
0.25, 0.70� can be
expressed by means of the equation [8, 10]

� � � �Po
P

N D
x D T T�

� �
�

�

�
3 5 1

0 2
0

0 0652 5. . . , (26)

where x1 is the thickness of the turbine disk and T0 = 1 m.

From knowledge of the quantity Fav
* , the mean dimension-

less torsional moment of the baffle can be calculated. We only
need to know the arm corresponding to the centre of gravity
of the linear dynamic pressure along the width of the baffle
(see Fig. 8) from the axis of symmetry of the cylindrical mix-
ing vessel:

� � � �R T bb � �2 2 3 . (27)

If we consider the total number of baffles nb, the moment
transferred by the baffles is

M F R nb av b b� � � , (28)

and finally in dimensionless form

M
F R n

N D
n F

R
D

b
av b b

b av
b*

*
*�

� �

� �
� � �

�
3 5

. (29)

Similarly the portion of the reaction moment of the baffles
corresponding to the mutual interference of nb baffles and
the impeller discharge stream can be expressed in dimen-
sionless form as

M n F
R
D

b d b d av
b

,
*

,
*� � � , (30)

where the quantity Fd av,
* was calculated according to Eq. (19).

Table 1 contains a comparison of the impeller torque and
the calculated reaction moment of the baffles, and a com-
parison of the experimentally determined quantity Mb d,

* and

the theoretically found quantity Mb d th, ,
* [see Eq. (14)]. The

power number Po was calculated for the impeller tested from
Eq. (26).

It follows from Table 1 that theoretical considerations
about the character of the discharge flow leaving a standard
turbine impeller were fairly well confirmed experimentally.
Theoretically and experimentally determined values of the
reaction moments of the baffles corresponding to the mutual
interference of the baffles and the impeller discharge stream
practically coincide. From the results summarised in Table 1 it
also follows that most of the turbine impeller torque is trans-
ferred via the agitated liquid by the radial baffles: more than
3/4 of the impeller torque is indicated as a reaction moment of
the baffles. Moreover, this reaction moment is concentrated
mainly in the impinging region of the impeller discharge
stream and the vessel wall: more than 2/3 of the total baffles
reaction moment affects this narrow part of the baffles, i.e.,
more than 2/3 of the reaction moment takes place along
one third of the height of the baffle. This knowledge plays
a significantly role in the design of industrial mixing units
with a standard Rushton turbine impeller and baffles, where
the maximum of fatigue stress can be considered in the above
mentioned region with consequences for the baffle fixing
using the corresponding welding technique.

Fig. 9 illustrates the axial profiles of the dimensionless
peripheral component of dynamic pressure affecting a radial
baffle for a pitched blade impeller and for a standard
Rushton turbine impeller at the same off-bottom clearances
when the pitched blade impeller is pumping liquid down
towards the bottoms. We can clearly distinguish between the
distribution of the force effect of the agitated liquid on the
radial baffles: the pitched blade impeller exhibits the main

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Acta Polytechnica Vol. 41  No.1/2001

h/T Po M * Mb
* Mb d,

* Mb d th, ,
* Hd

* M Mb
* * M Mb d,

* *

0.33 5.289 0.842 0.713 0.464 0.472 0.33 0.847 0.651

0.48 5.289 0.842 0.641 0.475 0.472 0.30 0.762 0.741

Table 1: Transfer of the impeller torque by radial baffles in an agitated system with a standard Rushton turbine disk impeller (thickness
of the impeller separating disk x1 = 0.55 mm)

Fig. 8: Radial profile of baffle loading



effect at the bottom while the turbine impeller effects mainly
the region around the horizontal plane of its separating disk.

4 Conclusions
• More than 3/4 of the turbine impeller torque is transferred

via agitated liquid by the baffles.
• More than 2/3 of the baffle reaction moment is located in

the impinging region of the turbine impeller discharge
stream and the vessel wall.

• The mean flow characteristics of the turbine impeller
discharge stream allow us to estimate the mutual force
interference of the baffles and the impeller discharge
stream.

This research was conducted at the Faculty of Mechanical
Engineering, CTU in Prague and was supported by grant
No. OK316/2001 of the Czech Ministry of Education, and by
an internal grant of CTU in Prague.

List of symbols
a radius of the virtual cylindrical jet, m
B target width, m
b baffle width, m
D impeller diameter, m
D1 diameter of the impeller separating disk, m
F peripheral component of the force affecting the radial

baffle, N
H total liquid depth, m
Hd height of the area of the impeller discharge stream

interference region with the baffles, m
HT height of the target above the bottom, m
H impeller off-bottom clearance, m
M mean impeller torque, N�m
Mb mean reaction moment of the baffles, N�m

Mb d, mean torsional moment of the baffles transferred via
impeller discharge flow, N�m

N impeller speed, s�1

NQp flow rate number
nb number of baffles
P impeller power input, W
Po power number
p peripheral component of the dynamic pressure af-

fecting the radial baffle, Pa

Qp impeller pumping capacity, m
3
�s�1

R radial coordinate, m
Re impeller Reynolds number
Rb radial coordinate of the dynamic pressure linear

profile centre of gravity, m
T vessel diameter, m
T0 diameter of the standard cylindrical vessel, 1m
x1 thickness of the impeller separating disk, m
z number of impeller blades
w width of the impeller blade, m
� angle between the horizontal velocity component in

the impeller discharge stream and its radial
component, °

� target angular displacement, °
� dynamic viscosity of agitated liquid, Pa�s
� density of agitated liquid, kg�m–3

Subscripts and superscripts
av average value
b related to the baffle
k related to the position of the target
th theoretically calculated value
* dimensionless value

mean (time average) value

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

Acta Polytechnica Vol. 41  No.1/2001

Fig. 9: Comparison of axial profiles of the dimensionless peripheral component of dynamic pressure affecting radial baffle along its
height for down pumping pitched blade impeller and standard Rushton turbine impeller (D/T = 1/3, h/T = 1/2, pitched blade
impeller z = 4: p avmax,

* = 0.195, z = 6 : p avmax,
* = 0.230, Rushton turbine impeller: p avmax,

* = 0.716)

p
p

k
av

av
,*

m
ax

,
*



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Acta Polytechnica Vol. 41  No.1/2001

References
[1] Standart, G.: General Relations Concerning Forces and

Torques in Mixing Vessel. Collect. Czech. Chem.
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[2] Kipke, H. D.: Mechanische Belastung von strömungs-
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[3] Kratěna, J., Fořt, I., Brůha, O., Pavel, J.: Local Dynamic
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[7] Drbohlav, J., Fořt, I., Krátky, J.: Turbine Impeller as a Tan-
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[8] Rutherford, K., Mahmoudi, S. M. S., Lee, K. C., Yian-
neskis, M.: The Influence of Rushton Impeller Blade
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[9] Stoots, C. M., Calabrese, R. V.: Mean Velocity Field Relative
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[10] Bujalski, W., Nienow, A. W., Chatwin, S., Cooke, M.: The
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Ing. Jiří Kratěna
Doc. Ing. Ivan Fořt, DrSc.
Dept. of Process Engineering
Doc. Ing. Oldřich Brůha, CSc.
Dept. of Physics
phone: +420 2 2435 2716
fax.: +420 2 2431 0292
e-mail: kratena@student.fsid.cvut.cz
Czech Technical University in Prague
Faculty of Mechanical Enginering
Technická 4, 166 07 Praha 6, Czech Republic