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(number 9) ENGINEERING EQUIPMENT USERS ASSOCIATION - AGITATOR SELECTION AND DESIGN. 9 (1963)

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© 1963 Engineering Equipment Users Association
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I
THE ENGINEERING EQUIPMENT USERS ASSOCIATION
The Engineering Equipment Users Association is an association of
industrial users of engineering equipment, materials and stores. It was
founded in 1949 by a number of large companies who realised the
important role that would be played in the future by standardisation
and simplification of engineering products, and by the free exchange of
technical information on engineering matters.
The principal objects of E.E.U.A. are to assist its members to promote a common policy for the standardisation of engineering materials,
equipment and stores, through the British Standards Institution or
otherwise; to foster the preparation and adoption of national standards
for such products, and to collate and summarise information in order
to give guidance on their nature and use. Membership is restricted to
companies and other bodies who are predominantly users rather than
manufacturers of engineering products.
The work of the Association is entirely complementary to that of
the B.S.I. with whom close liaison and collaboration are always maintained; it does not duplicate the activity of that Institution in any
way. Everything possible is done to enlist the early support of manufacturing interests in standardisation work which E.E.U.A. considers
should be promoted in the national interest.
This particular handbook was prepared by a Panel drawn from
member organisations interested in the problems of agitator selection
and design for various duties, and was first issued to members in 1957.
The Council of E.E.U.A. decided that this was a case where the results
of the Panel's work ought to be made known outside the Association;
consequently the handbook has been reviewed, amended where necessary, and published for general sale. The Council hopes that it will
prove a useful guide to all responsible for the selection and use of
agitator equipment, and will welcome any information on the results
obtained by following the recommendations given.
This Handbook was prepared by E.E.U.A. Panel M/16, Agitating
and Mixing Equipment, which was constituted from representatives of
the ~ollowing E.E.U.A. organisations:
Courtaulds Limited.
Distillers Company Limited.
Dunlop Rubber Company Limited.
Imperial Chemical Industries Limited.
Monsanto Chemicals Limited.
Unilever Limited.
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AGITATOR SELECTION AND DESIGN
(E.E.U.A. Handbook No. 9.
Revised 1962)
CONTENTS
Page
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FOREWORD
I
SECTION ONE-SCOPE AND DEFINITIONS
3
SECTION Two-RECOMMENDATIONS ON PLANT
5
(a) Types and General Features
(i) Mixing or Agitation Vessels
(ii) Impeller Diameters and Clearances
(iii) Vessel Fittings (including Baffles)
SECTION THREE-GUIDE TO THE CHOICE OF IMPELLER TYPES
AND SPEEDS
12
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(a) Factors Influencing Agitation
(b)
(c)
Selection of Impeller Type and Speed
(i) General Considerations
(ii) Basis of Impeller Selection
(iii) Impeller Type and Speed
"Scaling-up" from Given Data
\./"" SECTION. FOUR-CHOICE OF DRIVE
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9
9
12
13
13
15
16
19
22
(a) General
22
(b) Type of Gearbox
22
(c) Mounting the Drive
22
vii
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10
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Sizes, Proportions and Speeds
(i) Mixing Vessels
(ii) Impellers (Paddles, Turbines and Anchors)
(iii) Baffles
(b)
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5
Page
23
SECTION FIVE-POWER ASSESSMENT
(a) Factors Affecting Power Consumption
23
(b) Methods of Computing Power Consumption
(i) Power Absorbed by the Impeller
(ii) Power Absorbed by Baffles and Vessel Fittings
(iii) Transmission and Gland Losses
(iv) HP of Driving Motor
23
25
26
27
(c) Tables Giving Horse-Power Requirements of Impellers
(Tables 4 to 23)
28
45
SECTION Six-MECHANICAL DESIGN OF AGITATORS
45
45
46
(a) Materials of Construction
(i) The Impeller
(ii) The Vessel
(b)
24
47
47
47
Type of Service
(i) Continuity of Operation
(ii) Possibility of Modification
(iii) Stepwise Processes
(iv) Corrosive Service
47
48
(c) The Design ·of Shafts and Bearings (see also Appendix D)
(i) Assumptions Made
(ii) Application of the Assumptions Made
48
48
49
(d) Glands, Bushes, and Bearings Inside Vessels
50
(e) Drive and Bearing Arrangements (see also Section Four)
52
APPENDIX
A-RECOMMENDED
DIMENSIONS
FOR
VERTICAL
CYLINDRICAL VESSELS, BAFFLES, AND IMPELLERS
54
(a) Proposed Standard Diameters for Vertical Cylindrical
Vessels
54
(b) Recommended Baffle Dimensions
55
(c) Recommended Dimensions for:
(i) Paddle Impellers
(ii) Turbine Impellers
(iii) Anchor Impellers
viii
56
57
58
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Page
APPENDIX B-ASSESSMENT OF THE POWER LOST IN STUFFING
59
BOXES
APPENDIX C-FORMULAE FOR HEAT TRANSFER IN AGITATION
61
VESSELS
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APPENDIX D-THEORY AND CALCULATIONS FOR THE DESIGN
OF IMPELLERS, SHAFTS, AND BEARINGS
64
(a) General Requirements Relating to Design of Impeller
Shaft
64
(b) Calculations for Shaft Diameter
64
(c) Gear Selection when an Impeller is Supported by the
Gear Output Shaft (or Bearing Load Calculations)
67
(d) Calculation of Critical Speeds
69
(e) Calculation of Deflections
71
(/) Design of I111peller Blades
72
(g) Stresses in Shafts and Bearings where a Subsidiary
Bearing is Fitted
(i) Bearing Loads
(ii) Bending Moments
(iii) Critical Speeds
73
73
74
74
(h) Suggested Working Stresses for Shaft Materials
74
(i) Worked Examples
75
APPENDIX E-A NOTE ON SOURCES OF INFORMATION' WITH
SOME LITERATURE REFERENCES
81
(a) Brief Guide to the References Cited
81
(b) Derivation of Individual Sections of this Handbook
83
(c) Some Literature References
86
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FOREWORD
'
This E.E.U.A. Handbook has been prepared to give some guidance to
those responsible for the selection or design of agitation or mixing
equipment for various duties.
j
At present many types of mixers with widely differing character- istics are used industrially, even for similar or identical applications;
performances and costs vary correspondingly. Examination of published data and the experience of member firms strongly suggests that
such variety is unnecessary, except perhaps for certain highly specialised
processes.
Many design methods have been evolved for predicting power
requirements and mixing characteristics. Some methods seem reasonably satisfactory in that the resulting designs prove to be effective and
economical over a limited range of conditions and for a few specific
types of mixers. Because of these limitations, however, the results
obtained cannot readily be woven into a single reliable theory, and
there are many agitation problems which cannot be solved without
further investigation or even specific research.
Nevertheless, it is believed that the majority of agitation problems
can be tackled by methods or recommendations given in this Handbook, though it is not claimed that they will always prove the most
suitable or give the best reusults.
Much of the information given in this Handbook is derived from
experience within the E.E.U.A. Some, however, has of necessity been
taken from the published technical literature briefly discussed in
Appendix E.
It is considered that the proper use of the Handbook will help to
solve or clarify some outstanding problems and will also contribute to
a fuller understanding or a later review of the subject.
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SECTION ONE-SCOPE AND DEFINITIONS
(a) SCOPE
This E.E.U.A. Handbook gives guidance on the selection and design
of agitation equipment for liquid media in vertical cylindrical vessels
or tanks with impellers on vertical shafts.
While the use of other impellers is briefly discussed, the recommendations given are based on the use of paddle, turbine and anchor-type
impellers in vessels having "standardised" diameters ranging from
2 ft 3 in. to 15 ft. Within these limitations the Handbook will help to
solve agitation design problems involving liquids with liquids, solids or
gases over a mixture viscosity range of l ·Oto 1 million cp., and specific
gravity range of 0·6 to 1.4.
The information given is believed to be the best available at the time
of publication; much of the data referred to, however, has not yet
been checked against results obtained in practice, and special care
should be taken when using the Handbook for the design of agitators
where the agitation requirements are or may be critical.
Recommendations regarding the use of the marine type propeller
have been omitted, not because this type of impeller is considered
unsuitable or inefficient, but because of the difficulty of specifying its
shape, on which its performance so largely depends.
(b) DEFINITIONS
For the purposes of this Handbook the following definitions are
employed:
Agitator:
The total assembly of impeller, impeller shaft and
drive; including any gland, bearing, etc., used in
conjunction with these.
Impeller:
J
The actual element which imparts movement to the
liquid.
Impeller Types (see also Table 1 in Section Three-page 14)
Anchor:
An impeller which is profiled to sweep the wall of
the containing vessel with a small clearance.
Paddle:
An impeller having four or fewer blades, which is
not a propeller.
Plate:
A paddle impeller having a blade depth greater
than the blade radius.
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.A.GIT.ATOR SELECTION .AN°~~GN
Propeller:
An impeller imparting essentially an axial thrust to
the liquid, and whose pitch does not vary with
radius.
Turbine:
An impeller with more than four blades, all on the
same boss.
Baffie:
': t
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An element fixed inside the vessel to impede swirl-
1ng.
Draught Tube: A tubular fitting which is arranged to direct the
liquid flow produced by the impelfur:Gland, stuffing box, mechanical seal: Devices to prevent the passage
. of liquid or gas through the :point of entry of a
shaft into a vessel.
Filling Ratio:
(Vertical cylindrical tanks only):
.
Liquid Depth
The rat10 of: Vesse1 D'1amet er
(See Section Two (b) (i), page 9).
The continuous rotation of liquid about a fixed
axis.
Vortex:
A depression in the surface of a liquid produced by
swirling.
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SECTION TWO-RECOMMENDATIONS ON PLANT
(a)
TYPES AND GENERAL FEATURES
(i) Mixin~ or A~itation Vessels
Vertical cylindrical vessels or tanks with dished bottoms are
usually chosen for fluid mixing operations (4),* and in this section
of the Handbook the recommendations made relate to vertical
cylindrical vessels with flat, dished or shallow coned bottoms. Some
generalisations are also made, however, concerning vessels of other
shapes, such as horizontal cylindrical tanks, and rectangular tanks
of various proportions.
The following factors are significant when considering vertical
cylindrical vessels:
1. Ratio of Liquid Depth to Tank Diameter (filling ratio)
The value of this ratio, termed the filling ratio, is normally
between 0·5 an~ l ·5 (16), and a value approximately equal to l ·O
is recommended for most purposes. When dispersing gas in a
liquid, however, a filling ratio of about 2·0 is recommended in
order to maintain a sufficiently long period of contact between the
gas and the liquid. In this connection it should be noted that for
the same agjtating effect, the power consumption per unit volume
increases as the filling ratio departs from unity.
2. Shape of the Bottom of the Vessel
The importance of this factor increases as the filling ratio is
reduced. Other things being equal, vessels with dished, bottoms ,
tend to be most economical in power consumption.
Flat-bottomed and coned-bottomed vessels have the disadvantage of low agitation efficiency in the corners formed between
the walls and the bottom, as well as in the apex of the cone in the
case of coned bottoms. This is particularly significant wheri mixing
involves the suspension of heavy solids in a liquid. In such cases,
fillets should be inserted in the corners between the bottoms and
t~walls of flat-bottomed or coned-bottomed tanks (4).
3. Roughness of Vessel Walls
A rough-walled vessel consumes more power in agitation than a
smooth-walled vessel because of increase in local turbulence at
• Throughout this Handbook the numbers given in parentheses refer to the corresponding literature references listed in Appendix E-A Note on Sources of Information
with Some Literature References.
5
6
AGITATOR SELECTION AND DESIGN
the wall. If mass flow rather than turbulence is the primary objective of the agitator then local increase in turbulence is of litt' .e
value; if, however, an increase in turbulence is definitely required,
it is best achieved by inserting baffles. (See Section Two {b) (iii).)
Hence vessel surfaces should be as smooth as possible.
For similar reasons structural features should not project inside
the vessel more than necessary.
4. Vessel or Tank (dimensions)
In general, vessel proportions should accord with the values of
the filling ratio mentioned above. If, however, it is necessary to
use long vessels, then one impeller should be installed for each
vessel width or diameter of length.
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Details of vessel sizes are discussed in Section Two (b) and a
table of recommended dimensions is given in Appendix A-Recommended Dimensions for Vertical Cylindrical Vessels, Baffles, and
Impellers.
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(ii) Impeller Diameters and Clearances
Essentially most agitating operations can be effected with most
types of impeller. An unsuitable impeller for a particular service or
duty may, however, involve an unnecessarily high power consumption and/or be slow to achieve the required result.
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Fig. 1.
Fig. 2.
Fig. 3.
Any impeller which rotates on the axis of a vertical cylindrical
unbaffied tank produces a flow pattern which is essentially a swirl
with a central vortex (4). (See Fig. 1.) Superimposed on this is a
second flow pattern, depending on the impeller shape, and this is
shown in Fig. 2 for a downthrusting axial-flow impeller such as a
propeller, and in Fig. 3 for a turbine.
RECOMMENDATIONS OF PLANT
7
Many impeller shapes have been used for industrial agitation work.
In view of the complexity of these applications and the limited
knowledge of the subject, it is considered unwise to recommend
more than a few basic types. The recommendations given below
therefore relate only to:
Paddles,
· Turbines, and
Anchors.
_/,,
Recommendations concerning plate impellers, inclined paddl~s,
and swept-back turbines, etc., are not given as it is considered that
too little is known about their applications. This unfortunately also
applies to impellers of the marine propeller type. That type of
impeller is widely used, especially for the agitation of thin liquids,
and some data have been published on_ such applications. Marine
propeller shapes and contours vary so widely however that reliable
generalisations cannot be made.
Some general considerations regarding the three types of ~mpeller
dealt with in this Handbook (paddle, turbine and anchor'"types) are
set out below:
..
1. Clearance between the Impeller and the Bottom of the V e.!sel
For pad.die -and turbine impellers it is recommended that the
ratio of the bottom clearance to the vessel diameter should be
between O·l and 0·4 for a filling ratio of l ·O. This condition
becomes of greater importance as the filling ratio is reduced and
is of special significance for filling ratios below 0·8 (16).
For an anchor impeller the clearance between the vessel and the
impeller is largely ·determined by mechanical considerations; a
clearance of between 1 in. or l½ in. is recommended.
2. Impeller Diameter
With paddle impellers, somewhat similar effects can be achieved
by a large diameter paddle rotating slowly, or by a smaller
diameter paddle rotating more rapidly. It is considered good practice, however, for the diameter of the paddle to be greater than,
or equal to, one-half of the vessel diameter.
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The turbine is essentially a moderate-speed impeller and consequently has a smaller diameter than a paddle-type impeller in a
vessel of similar size. It is recommended that tlie turbine diameter
should not exceed one-half of the tank diameter.
The diameter of an anchor is, of course, equal to the tank
diameter less twice the clearance between the anchor and the tank.
2
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AGITATOR SELECTION AND DESIGN
Further details regarding impeller sizes, etc., are given in subsection Two (b) and in the tables in Appendix A.
;\ (iii) Vessel Fittin~s (including Ba.ffies)
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As already indicated (see item 3 of Section Two (a) (i)), if mass
flow is more important than turbulence for the application under
consideration, then agitation should take place in a smooth-walled,
unbaffled vessel. In many cases, however, turbulence is a primary
requisite, and to promote this it is often necessary to insert baffles
in the vessel. Other process considerations such as heat transfer and
temperature measurement may require the insertion of fittings such
as temperature control coils, thermowells, and dip pipes, etc. Such
fittings distort the flow pattern and hence also function as baffles.
Published work on agitation in tanks containing baffles makes use
of the concept of "fully baffled" condition. This is defined as the
condition when any further increase in baffling causes no significant
increase in power consumption (53); this condition may be considered as a state where the liquid swirl in the tank has become
negligibly small and when nearly all the power input to the impeller
shaft goes to the production of turbulence (53). This "fully baffled"
state may be achieved with four vertical baffles mounted radially
on the vessel wall, each equal in width to one-tenth of the vessel
diameter.
It is often convenient to mount baffles with a small clearance
between their outside edge and the vessel wall; this reduces any
tendency for solid deposits to form in the corners between the wall
and the baffles, and also facilitates cleaning of the vessel. Alternatively.so-called "streamlined-baffles" (i.e. baffles with smooth surfaces and rounded edges) may be used to achieve these two objectives.
Where heat transfer coils have to be inserted and baffled conditions are also required, it is sometimes necessary to mount the baffles
on the inside of the coils ; otherwise there is a tendency for a closepitched coil to function as an apparent wall (57). For such cases,
baffle widths each equal to O·08 of the vessel diameter suffice.
It is considered good practice to open out a coil in the horizontal
plane through the agitator so as to facilitate or increase the flow of
liquid to the space between the coil and the vessel wall. This arrangement also reduces the erosion tendency caused by solid particles in
the liquid impinging on the coil (which tendency is greatest in or
near this plane). 1
Further details relating to baffles and vessel fittings are given in
Section Two (b) (iii) on page 10 and in the tables in Appendix A.
RECOMMENDATIONS OF PLANT
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(b) SIZES, PROPORTIONS AND SPEEDS
(i) Mixing Vessels
For the purposes of making the calculations and preparing the
power tables given later in this Handbook, eight vessels, designated
as Tl to TS in Appendix A, have been chosen. Their diameters have.
been selected from those given in a Draft British Standard (98).
The vessels vary in nominal capacity from 50 to 16,000 gallons and
are of the vertical cylindrical type with flat, dished or coned bottoms.
In all cases the capacity is based on a filling ratio approximately
equal to unity~
It should be noted that in the case of flat and coried bottoms the
liquid depth is measured along the straight side of the vessel, but
for the dished bottoms, to the centre of the dish: Hence for a given
filling ratio, dished bottoms result in slightly smaller capacities, and
coned bottoms in slightly larger capacities than those of vessels of
the same diameter with flat bottoms.
Further details of the vessel dimensions and capacities selected
are given in Appendix A.
(ii) Impellers (Paddles, Turbines and Anchors)
I. Paddles
For the purposes of this Handbook a set of 8 paddle diameters
has been selected for use in the vessels mentioned in preceding
sub-section. The corresponding paddles are coded AI to AS in
Appendix A (see Table 28). The paddle blades therein specified
are of the flat radial type, and are set in the plane through the shaft.
-All shafts arc assumed to be centrally disposed and vertical.
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The diameters of shafts and hubs, and the thicknesses of the
impeller blades have little effect on the agitation efficiency or
power requirements and may the refore be determined by the
strength and rigidity needed for the service. Ribs may be fitted
to stiffen the blades if necessary, although in such cases some effect
on the flow characteristics may result.
The paddles recommended are suitable for use with or without
baffles without change in their dimensions.
Paddle speeds may vary from 10 to 500 rev/min according to
the size of the tank and the vigour of the agitation required. In
practice mechanical difficulties arise in the construction of agitators to operate faster than 100 rev/min in vessels 6-ft diameter or
over. In most circumstances a paddle tip speed of 700 ft/min may
be considered reasonable.
Furt_!ier details relating to paddles are also given in Appendix A.
10
AGITATOR SELECTION AND DESIGN
2. Turbines
A set of 6 turbines has similarly been selected for use in the
vessels mentioned in Section Two (b) (i); they are coded Bl to
B6 in Appendix A (see Table 29), and remarks similar to those
for paddles also apply.
Turbines may run at 30 to 5~0 rev/min according to their
dimensions and the vigour of agitation required. In most circumstances a tip speed of 700 ft/min may be considered reasonable.
Further details relating to these recommended turbines, are also
given in Appendix A.
3. Anchors
A set of six anchors has similarly been accepted for use in the
vessels specified in Section Two (b) (i). These anchors are coded
Cl to C6 in Appendix A (see Table 30), as they are shaped to follow
the profile of the vessel bottom, their individual shapes will 'differ
for flat, dished, and coned-bottomed vessels.
The cross section of an anchor arm is rectangular (with rounded
edges if constructed of cast iron or enamelled iron), but if required,
the arms may be tapered in thickness and width; internal bracing
may also be inserted to increase mechanical strength.
,, Anchors are not recommended for vessels of diameters greater
than 9 ft. Neither should they operate at speeds greater than
l 60 rev/min in vessels of 6-ft diameter or larger; liquid depth should
be between 0·7 and 2·0 times the vessel diameter.
Apart fron1 the limitations just mentioned, anchors should
operate at speeds from 5 to 300 rev/min according to the di~ensions and the vigour of agitation required. In most cases, however,
the tip speed of the agitator will be considerably less than that of
the paddle in a tank of corresponding dianieter.
Further details concerning these recommended anchors are also
given in Appendix A.
(iii) Baffles
Appropriate sets of baffles have likewise been selected for use in
the vessels specified in Section Two (b) (i).
The baffles are flat, vertical and radial, and· may be mounted in
contact with the tank wall or at a small distance from it. They should
extend at least to the surface of the liquid but may have a small
clearance from the bottom of the vessel.
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RECOMMENDATIONS OF PLANT
11
The thickness of the baffles as well as the method of supporting
them should accord with mechJ1,nical requirements of design. Care
should be taken, however, to see th.a~ any strengthening ribs, etc.,
do not significantly alter the desired flow °pattern.
t
Further details of these recommended baffles are also given in
Appendix A.
Notes on the power absorbed by baffles and vessel fittings are
given in Section Five (b) (ii), on page 25.
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SECTION THREE-GUIDE TO THE CHOICE OF
IMPELLER TYPES AND SPEEDS
The factors and considerations which help to determine the most
suitable and economical type of impeller for a given duty are often
interrelated and mutually dependent and in this Handbook are dealt
with under three main headings (a}, (b) and (c) as set out below:
(a) FACTORS INFLUENCING AGITATION
In all applications of agitation the primary effects are concerned with
one or more of the following physical processes:
Mass transfer at an interface.
Heat transfer at an interface.
Dispersion of solids, liquids or gases.
It should be understood that agitation does not directly affect
chemical reaction ; the rate of chemical reaction taking place can be
influenced by the agitation only if the reaction itself is controlled by
one or more of the abov-e primary effects. The factors which influence
the rate and degree of mixing as well as the efficiency may, however, be
classified as follows:
Characteristics concerned with the rotating impeller, e.g its shape,
speed, dimensions and position in the vessel.
·
Physical properties of the materials concerned, e.g. their densities,
viscosities and physical states.
Shape and dimensions of the containing vessel and of any fittings
which may be immersed in the fluid.
Although agitation is concerned with obtaining the primary effects
mentioned above, it is not easy to specify the exact circumstances
needed to achieve them efficiently. This is because the physical properties of the materials being processed are themselves the main factors
which determine the choice of impeller and because these properties
vary widely.
As mentioned in Section Two, the application of any of the common
types of impeller to a given problem will provide a partial solution.
For equipment of low cost and power consumption, efficiency is often
of secondary importance provided the required effect is produced. In
this case, choice of the best impeller is not critical.
There is, moreover, little published information concerning the
selection of agitators for economical operation, nor has much been
publishedr egarding research work directed towards this end.·
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GUIDE TO THE CHOICE OF IMPELLER TYPES AND SPEEDS
13
This section of the Handbook therefore provides only some immediate answers to the simpler problems. Those which are likely to
require much power or equipment, or to be specially difficult or critical
for any reason, should be investigated on an appropriate experimental
scale. The "scaling-up" of such experimental work is discussed later.
Heat transfer is probably the only effect which has been experimentally
closely related to agitation sufficiently well to enable results to be
accurately forecast, and a summary of the relevant formulae is given
in Appendix C.
(b) SELECTION OF IMPELLER TYPE AND SPEED
(i) General Considerations
The general considerations or factors which should first be taken
into account or noted before proceeding to select a given type of
impeller and its speed for a specific duty are summarised under the
following four sub-headings, 1, 2, 3,· and 4.
1. Types of Impeller
Table 1 on page 14 lists those impellers in common use and
briefly describes the situations or conditions under which they are
commonly found to be most suitable.
2. Bajftes
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Baffies have the effect of reducing mass fl.ow and increasing
turbulence. The formation of a vortex is prevented, as circumferential fl.ow is almost completely suppressed. They are useful
where the application requires high turbulence and power, and for
their ability to produce high power absorption with relatively low
speeds of rotation.
3. Speeds of Rotation
;
.
The tip speeds of all impellers will be found to be much the same
for the same agitating effects, except in the case of propellers
(where the speed is much higher) and anchors (where it is slightly
lower). Consequently for a given effect, smaller agitators need to
run at higher speeds; if small agitators are desired the effects of
higher speeds on erosion, bearing wear, gland difficulties, vibration
and allied effects must be tolerated.
4. Impeller Size and Number of Impellers
.,
For the same vessel a "large" agitator operating at "low speed"
produces relatively more mass fl.ow and less turbulence than a
smaller but geometrically similar agitator which operates at
"high speed" and transmits the same power.
14
AGITATOR SELECTION AND DESIGN
TABLE 1. Impellers in Common Use and their Main Characteristics
1
2
8
Impeller
Description
Characteristics
Flat paddle
Single flat blade (two arms)
usually about f of vessei diameter long.
Usually large low-speed agitators, but capable of
producing high intensities of agitation, especially
when baffled. Cheap to make, and suitable for
construction in timber,
plastics,
etc ....,
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Turbine
Flat disc with blades attached
to periphery. Similar effects are
produced with the same nuniber
of blades attached directly to a
boss (often called multi-blade
paddle). Usually about t diameter of vessel (overall).
Generally moderately fast running agitators.
Particularly suitable for high intensities of
agitation and high power inputs. Somewhat more
expensive · to fabricate than a simple paddle.
Very versatile.
Recommended for applications where gas
dispersion combined with intense agitation ts
required.
Propeller
Marine type propellers, usually
less than ¼ of vessel diameter
overall. Wide variety in form
possible, from paddles with
. twisted arms to properly formed
marine propellers~No standardisation of pitch or number of
blades between manufacturers.
Usually snall high-speed. agitators. Cheap to
make, but limited to duties where agitation ls not
very intense, and unsuitable for high viscosities.
Much used'for relatively small-scale blending
operations .
Propeller and
draft tubes
Propeller fitted below, or just
inside the lower end of a cylinder
of slightly larger diameter than
the propeller.,.. Baflles may be
fitted in the draft tube. Top of
tube may be just above or below
standing liquor level, and may
be castellated.
Applications similar to those of simple propellers,
but more positive turnover of liquid and its
passage through the impeller is ensured; this is
of advantage in wetting out some solids and
mixing some immiscible liquids.
By suitable location of the topj eve! of the draft
tube, a pouring action which will drown floating
solids can be achieved.
Anchor
Agitator following closely the
contour of the vessel.
A large low-speed agitator, useful where the wall
film must be disturbed (e.g. heat transfer to
viscous liquids from a jacket), or where build-up
of solids on the walls ls'Ukely (as in crystalllslng).
At low speeds has a very gentle action and will
prevent caking in the bottom of vessels without
vigorous agitation elsewhere.
Wldeley used in enamelled equipment.
Plate
.11- square or rectangular plate
bisected by the shaft on which
it is mounted. Diameter q/!ually
¼-½ that of vessel.
Similar applications .tq those of flat paddles, but
allows more clearance for heating coils, fittings,
etc., in the vessel.
Where the depth of the plate is large relative to
the liauor depth, vertical movement of the
liquor is less than with a paddle of equivalent
power.
Gate
An assembly of horizontal and
vertical bars, sometimes with
diagonal bracing, of length approaching the vessel 'diameter,
and depth about ½-¾ of overall
length.
A large, low-speed agitator, of simllar applications to those of anchors, but allows more
clearance for fittings and coils in the vessel.
Is suitable for fabrication in wood, and can be
made in larger sizes than an anchor. It has not
the close sweeping effect of an anchor on the
vessel walls and base.
Vaned disc
A circular disc, usually !-¼ of
vessel ' diameter with radial
vanes, ¼-~ of diso diameter
deep on its underside.
A small or moderately sized high-speed agitator;
limited usually to gas dispersion work. The gas
ls fed under the centre of the disc. It is an
effective agitator with or without gas flow, but
can be "loaded" if·· excessive gas flow is
applied, when its agitating effect falls abruptly.
The power consumption without gas flow will be
much higher than when- gas is on, and drives
should be adequate to cover the gasless
condition.
!'itched paddles
and turbines
!'addles or turbines with blades
twisted to deflect flow upwards
or downwards.
Similar applcatilons to those of plain paddles and
turbines, but larger vertical flow is produced.
Power consumption drops with increasing twist,
but relatively slightly unless the cant exceeds
45 degrees from the vertical.
GUIDE TO THE CHOICE OF IMPELLER TYPES AND SPEEDS
15
Vessels having a large ratio of height (or length) to diameter are
not recommended, but where used should in general have one
impeller for each vessel diameter of depth (or length). See also
Section Two (a) (i), page 5.
f
(ii) Basis of Impeller Selection
Table 2 on page 16 classifies various agitation operations and the
conditions required in the liquid to achieve them. The table is based
upon the conception that all agitators impart kinetic energy to the
liquid in the form either of general mass flow or of turbulence.
Different mixing problems require different proportions of these
two forms of. kinetic energy as well as different general levels of
intensity. The question of the power input per unit volume has also
to be considered.
'
1.
I
General consideration of most mixing problems suggests, however,
that an approximate estimate can be made of the input power
required, and of the ratio of mass flow to turbulence. Table 2 has
been compiled on this basis, and enables levels of mass flow, turbulence and power, and direction...of mass flow for a given operation to
be established.
It is realised that certain mixing processes involving very high
viscosity liquids are carried out successfully at very low Reynolds
numbers at which turbulence can hardly occur. In these processes
the required action often results from high shear forces close to the
impeller and Table 2 should not be used for viscosities above
100,000 cp.
In using Table 2 it should be noted that:
1. Power levels required increase with viscosity of liquid for
the ,same mixing effect. Viscosities above 100,000 cp often need
very high powers, above 20 hp per 1,000 gals.
2. In general it is better to use larger impellers at lower speeds
as viscosity increases.
3. In agitating immiscible liquids initially in two layers the
impeller must be near the interface.
4. Gases to be dispersed in liquids by mechanical agitation must
be fed from underneath the centre of the impeller.
5. The terms "light", "medium", and "heavy", as applied to
suspended solids, should take into account particle size as well as
density.
6. Solids to be suspended are assumed not to float. If the solids
float, an impeller which produces a deep vortex should be used.
16
AGITATOR SELECTION AND DESIGN
TABLE 2. Characteristics Required for Specific Operations
This table should be considered in conjunction with the preceding text and the following definitions of
the term "Power".
"Low" indicates powers of less than 1 hp/1000 gal.
"Moderate" indicates powers of the order of 3 hp/1000 gal.
"High" indicates powers of the order of 10 hp/1000 gal.
"Very high" indicates powers greater than 20 hp/1000 gal.
2
1
I
3
4
Power
Quantity
Turbulence
Circumferential
Circumferential,
little vertical
Large
Large
Low
Low
Moderate
Moderate
or High
Constant tlp
speed (for
constant
heat transfer
coefficient)
6
6
Mass flow
Duty
Direction
..
Heat transfer to jacket
..
Heat transfer to coil
(F r heat transfer calculations-see Appendix C)
Recommended
Basis for
Scale-up
Suspend light solids
Suspend medium solids
Suspend heavy solids
..
..
..
Vertical
Vertical
Vertical
Small
Moderate
Large
Low
Moderate
Moderate
Low
Moderate
Moderate
or High
Constant
tip speed
Blend miscible liquids:
(a) thin . .
..
..
Ver tical, little
circumferential
Vertical, little
circumferential
Vertical, little
circumferential
Small
Moderate
Low
Constant
tip speed
Small
Moderate
Moderate
Moderate
Moderate
Moderate
or High
Vertical
Moderate
High
Vertical
Vertical
Moderate
Small
High
High
Moderate
or High
High
High
Constant
power per
unit volume
Vertical
Large
High
..
Vertical
Vertical
Large
Moderate
High to
V. High
High
High
Constant
power per
unit volume
..
Vertical
Large
(b) medium
..
(c) viscous
..
..
..
Mix immiscible liquids:
(a) thin . .
..
(b) medium
(c) viscous
..
..
•
Emulsify liquid mixtures:
(a} thin . .
..
(b) medium
(c) viscous
..
..
Disperse gases in liquids
..
..
..
;
..
..
I High
I
V. High
V. High
High or
V. High
I
Mix pastes
..
..
..
Disperse agglomerated solids
Cosnant
I power per
unit volume
I
Vertical and
circumferential
Moderate
Moderate
V. High
Constant
power per
unit volume
Vertical and
circumferential
Large
Moderate
or High
Moderate
or High
Constant
power per
unit volume
.,
(iii) Impeller Type and Speed
Having selected the required. conditions from Table 2, Table 3
(on page 17) can then be used to relate these to impellers and speeds·
for a 6-ft diameter vessel (1000-gal vessel).
Table 3 itself gives the speeds recommended for an impeller in a
6-ft diameter vessel for given levels of mass flow and turbulence; from
the requirements of the duty, the impeller speed appropriate to this
vessel size can therefore be determined. (In many cases it will be
found that the required level of one effect cannot be obtained without
exceeding the required level of the other, and in this case the speed
appropriate to the more difficult agitation should be selected.)
... 1·
17
GUIDE TO THE CHOICE OF IMPELLER TYPES AND SPEEDS
Having found the impeller speed required for the 6-ft diameter
vessel, that required in the vessel size under consideration can be
obtained by scaling up or down on the basis given for the particular
operation (see Table 2, col. 6).
TABLE 3. Choice of Impeller Speed for a Six-Foot Diameter Vessel
The figures represent impeller speeds in rev/min for liquid of a viscosity of 1 cp and a density of 10 lb/gal.
Factors for other viscosities are given on page 18.
,.,.
1
2
3
4
Direction of
flow
Baffles
Impeller
TurbuJenee
5
I
6
I
7
I
8
Mass flow
Small Moderate
I
Vertical
Yes
PaddleA5
(Flat paddle, 4-ft dia)
Moderate
High
Very high
25
Turbine B4
(2-ft dia)
Moderate
High
Very high
50
Propeller
(Dia = Pitch = 1 ft)
70
80
)20
110
140
180
180
230
High
550
700
Propeller and draft tube
(Dia = Pitch = 1 ft)
High
550
700
Plate
(Dia = Height
Moderate
High
Very high
30
65
85
110
(Dia = 2-ft vanes,
12 off, 1-in deep)
Moderate
High
Very high
70
Propeller
(Dia = Pitch
Low
Moderate
300
= 3 ft)
=
1 ft)
110
150
No
Paddle A5
(Flat paddle, 4-ft dia)
Low
Moderate
25
Turbine B4
(2-ft dia)
Low
Moderate
50
Low
Moderate
30
Anchor C5
(See Table 22)
Low
Moderate
15
Gate
(Dia = 4 ft 6 in
Depth= 3 ft)
Low
Moderate
20
Plate
(Dia = Height
Circumferential
180
240
110
---
450
700
1200
450
700
1200
60
100
120
200
75
120
170
55
80
70
100
No
Propeller and draft tube Low
Moderate
(Dia = Pitch = 1 ft)
Vertical and
circumferential
Very
Large
55
! Vaned disc
Vertical,
and a little
circumferential
Large
=
8 ft)
150
25 ·
No
Note on Limiting Viscosities
The various impellers referred to in Table 3 should not be used
below:
Flat paddle
Turbine
Propener
Plate ..
Vaned disc
Anchor
Gate
35
40
with viscosities exceeding those listed
1 X 10 8
2x 10 5
3 X 10 3
5x 10 5
5X 10 3
7 xl0 5
1 X 10 5
cp
cp
cp
cp
cp
cp
cp
18
AGITATOR SELECTION AND DESIGN
If, for example, the operation should be scaled on constant tip
speed, then. the required speed can be calculated from that for the
6-ft diameter vessel (being in inverse ratio to the diameter); the
power required for the appropriate diameter and speed can then be
taken from the power tables given at the end of Section FivePower Assessment-see Tables 4-23, pages 28-44.
If, on the other hand, the basis for scale-up is to be constant power
input per unit volume, then the power for the chosen type of impeller in a 6-ft diameter vessel at the speedJfound from Table 3,
can be obtained from the appropriate Power Table (i.e. for paddle
A5, turbine B4, or anchor C5; see pages 32, 39, and 44). Dividing
this by 1000 (the nominal capacity in gallons of the 6-ft diameter
tank; see Appendix A, page 54) gives the power input per unit
volume. This input, multiplied by the volume in gallons of the
desired vessel gives the design impeller power.
The impeller speed which will absorb this power may be deduced
from the "power table" (see Tables 4-23) appropriate to the desired
vessel size and impeller.
In the simpler agitation problems it may be economically desirable
to use impellers of less than the optimum diameter for agitation to
save material (see Section Two (a) (ii), Item 2 on page 7). Change to a
smaller diameter should be accompanied by an increase in speed at
least sufficient to maintain the tip speed at the level which the
diameter and speed of rotation given in Table 3 implies. Even then
the smaller agitator may not produce the desired effect, and the
optimum impeller size should be retained in any critical applications
or where high intensities of agitation are required.
In general the speeds given in Table 3 should be increased by some
25 per cent for viscosities of the order of 5 x 103cp and 50 per cent for
viscosities above 5 x 104cp. Impeller speeds also should not exceed
about 600 rev/min for _viscosities of 5 x I03cp or 300 rev/min for viscosities of 5 x I0 4cp. Whilst the increases suggested above will not in
general give the same mass flow and turbulence in the viscous liquid,
equal effect can usually be achieved in viscous liquids with a lower
level of mass flow and turbulence due to the high shear forces close
to the impeller. The increases of speed suggested are considered to be
a reasonable guide for many cases, but much greater increases will
sometimes be necessary.
There are certain practical limitations regarding impellers which
should not be overlooked:
I. It is difficult to construct anchors to operate at high speeds
(greater than about 60 rev/min in a 6-ft diameter vessel, i.e. a tip
speed of about 1000 ft/min), or to make anchors for vessels exceeding 9-ft diameter.
t
GUIDE TO THE CHOICE OF IMPELLER TYPES AND SPEEDS
19
2. Gate-type impellers are not usually desirable for mixing vessels
of less than 6-ft diameter. The extra complication compared with an
anchor or fl.at paddle is not worth while.
3. Propellers and other high-speed impellers should not be used
in high viscosity liquids for general agitation, since their effect
rapidly falls with distance from the impeller.
(c) "SCALING-UP" FROM GIVEN DATA
The method of "scaling-up" put forward in this sub-section assumes
that the same liquid is used in the small and the large scale vessels,
and that the vessels and impellers are geometrically similar. This is a
reasonable assumption because if a small or an experimental mixer has
been found satisfactory and a larger mixer has to be designed, then the
"scaling-up" process is normally carried out on a basis of geometrical
similarity.
Typical bases used for scaling-up purposes are:
(I) Allowing the Reynolds number to increase proportionally
with the linear dimensions.
(2) Keeping the agitator tip speed constant.
(3) Maintaining a constant power input per unit volume.
'
.
-
The Froude number is ignored for the moment (see below), as it is
assumed that no appreciable vortex is formed. Other dimensionless
numbers referring to special cases, e.g. mixing of thixotropic fluids, are
also ign9red for the sake of simplicity. Scaling-up at a constant
Reynolds* number is incorrect for reasons given later in this subsection.
Let N = The speed of rotation of the-impeller
L = The length of the typical dimension .
p = The fluid density
µ, = The fluid viscosity
g = Acceleration due to gravity
Re = The Reynolds number= ( N~2p)*
r
Fr - The Froude number
- ( Ng2L)
• Reynolds number in this connection is not the same as Reynolds number for flow
in pipelines. It is however a term which shows similar characteristics-that is, a sharp
change in the gradient of the curve of power input/ Re at a specific value of Re for most
agitator systems similar to the change in the pressure drop/Re curve for fluid flow in
pipes where flow changes from strea,mlined to turbulent.
20
AGITATOR SELECTION AND DESIGN
Hence basis (1) implies that (NL 2 ) oc L (i.e. implies that
NL = constant)
and basis (2) implies that (NL) =
basis (1).
constant, as for
According to Biiche (Refs. 15 and 16), basis (3) implies that:
For laminar fl.ow,
N
= constant.
For "transition" fl.ow, N(L 6 111 ) _:_ constant.
For turbulent fl.ow,
N(L 2 13 ) = constant.
(Biiche's relations apply to plate-type impellers. Other types of
impeller will give slightly different relationships.)
It can be directly deduced from the above (since power per unit
volume is usually proportional to (L 2N 3 ) for turbulent fl.ow, and -to
N2 for laminar fl.ow) that if the Reynolds number is proportional to L,
i.e. to constant tip speed, then the power per unit volume is:
1
proportional to -
L
for turbulent fl.ow.
and
1
proportional to -
L2
for laminar flow.
From these relationships it follows that if scaling-up is carried out
on the assumption of constant Reynolds number then power per unit
volume is proportional to 1/L4 for both laminar and_ turbulent fl.ow.
Hence a result is obtained which indicates that less total power is
required on the large scale than the small scale. This is obviously
ridiculous, and the basis of a constant Reynolds number cannot
therefore be valid.
The question therefore arises as to which basis to use for scaling-up.
In practice many scaling-up problems are tackled on the basis of constant tip speed, and, from the above, it will be noted that the power
input per unit volume will be much smaller for the larger scale. This
indicates that the "degree of agitation" is less on the larger scale. In
some problems it is found that this does not matter,'particularly if
longer mixing times _are allowed for the larger scale as is often the case.
- For a constant heat transfer coefficient Chilton, Dr~w and Jebens
(19) recommend that constant tip speed (i.e. Re oc L), fs the best basis
for scaling-up. It should be noted, however, that-since the ratio of
heat transfer area to volume will be less favourable on the large scale
(if geometrically identical) the time cycle will have to be adjusted
accordingly.
On general grounds, however, it would seem reasonable to assume
that equal power per unit volume is a basis for a true scale-up for
!
j
,:
GUIDE TO THE CHOICE OF IMPELLER TYPES AND SPEEDS
.
21
many applications. This basis is recommended by Biiche, although some
other authors (notably Rushton) disagree. If this basis is accepted,
however, it must be assumed that the same type of agitation, i.e. the
same ratio of energy in the form of mass flow to energy in the form of
turbulence, prevails on the larger scale. With geometrically similar
equipment this seems a reasonable assumption.
If the power per unit volume is to be maintained constant, then the
speed of rotation of the agitator necessary to provide this power can
be taken from the power tables given in Section Five.
It is considered, however, that no general choice can be made
between the above two bases of,.., scaling-up (i.e.
.. between 2 and 3), and
that each type of duty should be dealt with individually. The duties
have, however, been divided between these two methods (see Table 2,
column-6) on the following general principles:
,,.
(1) Where the duty demands a similar flow pattern, with similar
velocities, constant tip speed is recommended.
(2) Where the duty requires vigorous liquid movement ·(e.g. in
the suspension of heavy solids), constant power per unit
volume is recommended.
All agitation problems, however, must necessarily be a combination·
of these two cases, but some will fall fairly definitely into one group or
the other. If the category cannot be clearly decided, it is safer to use
the basis of constant power per unit volume.
It ·should be noted that scaling-up is more certain in the case of
baffled mixers since the Froude number can then be ignored, there
being no vortex problem. It is impossible to scale-up on the basis of
either constant tip speed or constant power per unit volume and at
the same time keep the Froude number constant if the same liquid is
used in both scales. In an unbaffied system therefore different vortex
conditions will normally occur on the two scales.
With gentle agitation at low impeller speeds, there is no vortex
problem and the Froude number can be ignored even in unbaffied
systems.
SECTION FOUR-CHOICE OF DRIVE
(see also Section Six (e))
(a) GENERAL
All impellers should be independently driven by a standard electric
motor of the vertically or horizontally mounted type.
As speed reduction will be necessary in almost all the cases covered
by this Handbook dir~ct drive will not be possible. A V -rope drive from
the motor to the gearbox is recommended to enabl~ standara gearbox
ratios to be used, a:r:id to give some degree of flexibility in impeller
speeds after installation. For impellers opera~ing at high speeds the
required speed reduction required may be obtained by a V-rope drive
alone.
(b) TYPE OF GEARBOX
In most cases it will be found that the best arrangement is to use a
gearbox of the right-angle drive type carrying bearings to accommodate the bending and thrust loads of the impeller shaft, the latter being
rigidly attached to the output shaft of the gearbox. This arrangement
is quite suitable for use with a shaft passing through a stuffing box
designed for low pressure duties, or where a "steady" bearing is fitted ·
inside the vessel.
·
'" For installations with long impeller shafts, or where the load is such
that bearings are required on the shaft, or where deep stuffing boxes
have to be used (e.g. as in autoclaves) it is generally preferable to fit
bearings on the shaft immediately above the stuffing box and a steady
bearing inside the vessel below the stuffing box. In· such cases the
impeller would be connected to the gearbox bya flexible coupling.
~ e size of the gearbox should be at least equivalent t~ the hp of
the motor being used, a 24-hour rating being specified. In computing
the hp rating of the required motor (see Section Five '(b) (iv)) a 20 per
cent power loss through -the drive, based on the maximum rated input
power of the gearbox, should be allowed.
(c) MOUNTING THE -DRIVE
-•·'.
Where the agitator shaft passes through a stuffing box or a seal, the
drive should be mounted on a rigid stool fixed to the top of the vessel
to minimise differential movement. Where this is not practicable, as in
the case of plastic vessels, care should be taken to see that the drive
mounting is rigidly fixed in relation to the vessel.
The driving motor itself should be mounted on slide rails so that
adjustments can be made to the V-rope drive when this is used. Some
right-angle drive gearboxes are fitted with a hinged-motor mounting
on top for this purpose. Jockey pulleys are not recommended.
22
SECTION FIVE-POWER ASSESSMENT
(a) FACTORS AFFECTING POWER CONSUMPTION
The power required for agitation should be considered and calculated from two standpoints:
(1) That needed from the installed driving motor (e.g. to cover
start-up conditions and peak loads).
(2) That required under normal operating conditions.
The first mentioned may be affected by factors which apply only
during starting or during unusual operating conditions, as may be
caused for example by the presence of cold lubricant in the gearbox,
the possibility of solid settling out, or the presence of wash-water in a
vessel designed for the mixing of light solvents. Allowance for such
factors as well as for other additional loads with which the driving
motor may have to cope during "start-up" periods can seldom be estimated accurately. The calculated power needed during "start-up"
should therefore be augmented by some empirical amount to ensure
that the resultant design is capable of dealing with the heaviest loads
likely to occur in practice.
The total power required under normal running conditions may be
considered as the sum of the following three items :The power taken by the impeller itself.
Transmission and gland losses.
Losses in the driving motor.
The first two of these should be determined separately; methods of
so doing and of estimating the power required from the driving motor
during normal operating conditions are described below. (The losses
in the driving motor must, of course, be taken into account when estimating the total power with which it must be supplied-see Section Five
(b) (iv) on page 27.)
(b) METHODS OF COMPUTING POWER CONSUMPTION
For the purposes of this Handbook it is assumed that the following
are known, or can be readily determined:
Size and shape of vessel.
Nature of the fittings (if any) in the vessel.
Type, size and speed of the impeller.
Density and viscosity of the liquid.
Knowledge of these factors enables the power required by the
impeller to be computed, and from that the power lost in transmission.
The total power needed under normal operating conditions can thus
be obtained.
3
23
24
AGITATOR SELECTION AND DESIGN
(i) Power Absorbed by the Impeller
The power required by the impeller itself may be deduced from
the hp figures in Tables 4 to 23 of Section Five (c) beginning on
page 28. These Tables give for both "fully baffled" and "unbafiled"
conditions, the hp required by paddle, turbine, and anchor-type
impellers operating at various speeds in liquids of given densities
and viscosities in vessels corresponding broadly to those recommended in Section Two (b) and in Appendix A.
The hp values given were computed after examining the methods
of calculating power consumption described in the relevant literature referred to in Ap~ndix E. As indicated in the Foreword to this
Handbook, it is not claimed that the values in the Tables will
always produce the best or even give satisfactory results. The
figures need checking against known cases, and until work on such
lines has been done they cannot be regarded as more than provisional. In the present state of knowledge, however, they are as
reliable as can reasonably be expected.
/
,
To determine the power absorbed by the impeller proceed as
follows:
(1) Select the Table for the required impeller type and size
(Tables 4-23).
(2) Read off the hp figure for the relevant speed, liquid density and
viscosity, after converting where necessary into the uni.ts
shown in the tables (i.e. rpm, lb/gal, and centipoises). Use
that part of the table corresponding to "fully baffled" or "unbafiled" conditions, whichever may apply. If there is doubt
about the baffling effects of coils, dip pipes, etc., use· the
"fully baffled" condition as this will ensure a safe design (see
Section Five (b) (ii) page 25).
(3) If two phases are present (e.g. oil and water) use a density
value corresponding to the arithmetic mean (68).
(4) It should be noted that the viscosity of a mixture to be stirred
may vary between wide li1pits. For example, an emulsion of
water in kerosene is much ·thinner than one of kerosine in
water. In the absence of reliable data for such cases, use the
geometric mean(µ) value of the two viscosities (68), i.e.:
µ = µ1Xµ2Y
where µ = Viscosity of liquid mixture ,
µ1
1i
= Viscosity of component
1
= Viscosity of component 2
x = Volume fraction of component 1
y = Volume fraction of component 2
µ, 2
25
POWER ASSESSMENT
In many cases some interpolation will be necessary to calculate
the power. All the variables, other than impeller type and size may
be interpolated graphically. For density, the relationship is arithmetical; for all other factors, logarithmic paper must be used. The
intervals in the tables are sufficiently small for a straight line relationship to be assumed, although this may not be the case over wider
ranges. If several factors are to be interpolated they may be applied
consecutively.
The range of the Tables will generally render extrapolation
unnecessary.
(ii) Power Absorbed by Baffles and Vessel Fittings
The tables of computed hp in Section Five (c) to which reference
has already been made give figures for both "unbaflled" and" fully
baflled" conditions, The use of the figures for "fully baflled" conditions will of course ensure a "safe" design, but it may be quite unnecessary to use them especially when it is known that the baflling
effects will be small. It has therefore been thought worth while to
include in this Handbook some remarks concerning the power
absorbed by baflles and vessel fittings.
Ei
Published information (see Appendix
sugges~s that allowances
for tank baflles and fittings are best made by adding to the power
required for "unbaflled'' conditions, a percentage of the difference
between the power needed for "fully baflled" and "unbaflled" condi~
tions. The percentage to be added will naturally increase with the
number and the size of ~he baflles and fittings under consideration,
as well as with the intensity of agitation. It is difficult to be precise
over this matter, but the following notes and recommendations are
made for the specific cases set out below:
I. D-ip P-ipes and Thermo Wells, etc.
Assuming that the power required by the impeller has been computed for both the "unbaflled" and "fully baflled" conditions,
then about 10 to 20 per cent of the differen-0e between these two
power figures should be added to the "unbaflled" figures to allow
. for the effects of a narrow dip pipe or thermo well ..
For a wide dip pipe or thermo well, a percentage of 20 to 40 is
recommended.
These percentages, however, are recommended on the assumption that the fittings are close to the tank wall. As fittings are
moved further from the tank wall towards the centre of the vessel,
the power absorbed by the fittings becomes progressively less until
a condition is reached where fittings close to the shaft make no
appreciable difference to the power consumption. This may not
be the case however where fittings are placed very close to the
26
AGITATOR SELECTION AND DESIGN
impeller, in which instance some increase in power above that
absorbed by a fitting near the tank wall is to be expected. Fittings should not in general be placed so close to the impeller as
to have this effect, since the beating as each blade of the impeller
passes the fitting creates very high stresses and may lead to the
fracture of dip pipes and thermo wells.
From the standpoint of computing the power absorbed by a
number of fittings, the use of 2, 3, or even 4 spaced uniformly
around the perimeter of the vessel may be taken as the arithmetical sum of their individual effects; less power is absorbed
however if the fittings are close together.
2. Coils
The extra power absorbed by the inclusion of coils in a mixing
tank will naturally vary with the type and size of coil (see Appendix
E). Coil supports also exercise baffling effects, which in some cases
may be greater than those due to the coils themselves. It is almost
impossible to give any percentage power consumption figure to
cover the many different sizes and arrangements of coils and
supports which may occur in practice. In the absence of reliable
information it can only be reiterated that from the standpoint of
adequate design it will be wise to assume "fully baffled" conditions when it is known that coils are to be used. Some information on coils is given in literature references 4 and 16.
(iii) Transmission and Gland Losses
Having computed the hp required by the impeller under normal
operating conditions, the next step is to estimate the value of the
corresponding transmission and gland losses. The hp rating of an
electric motor for driving the impeller can then be assessed, making
due allowance for the output required during normal conditions
and during the start-up periods or periods of heavy duty referred to
in Section Five (a).
Notes on the estimation of gland losses and drive losses are given
below.
1. Gland Loss
I
The power loss in glands seems to vary from less than a half hp
for the smaller impeller shafts, up to 5 hp for the larger. No
reliable method for calculating this loss can be given, and it is
therefore usual to estimate a value based on experience. One
method of calculating this loss is given in Appendix B; it seems
to produce reasonable results, and is therefore suggested where no
relevant experience is available. As a very rough approximation, .
however, the gland loss may be taken as 10 per cent of the agitator power consumption, or 0·5 hp, whichever is the greater.
THE POV/Ef-GAS CORPORA TlO? ~TO. -
\
l
l
254-D,
on.
~u'2¥·
ANNIE BESAi~T
WORLI, BOMBAY - 25 DU.
POWER ASSESSMENT
2. Drive Losses
The efficiency of a V-belt drive is approximately 97 per cent,
and where no gearbox is used 5 per cent of the hp required by the
agitator should be allowed for the loss in the drive. The power
loss in a gearbox is a function of the rated hp capacity of that
gearbox; operation at low loads causes a considerable drop in
efficiency due to lower working temperatures. It is therefore
usual to allow 20 per cent of the maximum input rating as the
gearbox and V-rope drive loss.
It should be noted that gearbox standardisation carried out for
example to reduce the number of varieties in a given organisation
or factory may involve the use of a gearbox of higher rating than
is strictly necessary. In such cases the power lost in the gearbox
may be high.
(iv) HP of Driving Motor
For normal operating conditions the required hp output of an
electric motor installed to drive the agitator is obtained by adding:
hp required by the impeller
to the
hp lost. in the glaD:ds and the drive.
-
In practice a motor with the next higher standard hp rating should
be selected; reference should be made to·the relevant British Standards such as BS. 229 (Flameproof enclosure of electrical apparatus),
B.S. 2048 (Dimensions of fractional horse power motors),* B.S. 2960
(Dimensions of 3-phase electric motors, Parts I and 2) and B.S. 2613
(Electrical performance of rotating electrical machinery) and any
associated amendments or revisions.
As previously stressed in Section Five (a), due allowance must also
be made for the possible occurrence of extra heavy loads during
start-up periods or during some stage of the process. Such loads
may necessitate the installation of a motor of higher rated _hp than
· that deduced from the "normal operating conditions", and, as pre- viously stated, some empirical allowance may have to be made.
Neither should the possible occurrence of high ambient temperatures, corrosive fumes or inflammable vapours be overlooked when
deciding upon the type of motor and associated switching and
wiring. Losses in the motor at various loads can be determined from
output efficiency curves, about which the manufacturer should be
consulted if necessary. (As previously indicated these losses will be
needed for estimating the total power a.bsorbed under various running
conditions.)
* B.S. 2048 may lapse and be superseded by B.S. 2960 as from 1963.
r-
28
AGITATOR SELECTION AND DESIGN
(c) TABLES GIVING THE HORSE-POWER REQUIREMENTS
OF IMPELLERS (TABLES 4-23)
The tables (4-23) given in this sub-section of the Handbook give
the computed hp requirements of p~ddle, turbine and anchor-type
impellers rotating in vessels of specified diameters under "unbaffied"
and "fully baffled" conditions.
As previously n1entioned, these hp requirements were computed
after examining various methods of calculating or estimating power
consumption; it is considered that they are the most reliable that can
TABLE 4. Paddle Type Impeller Al
(Vessel Diameter 2 ft 3 in.)
\
'\
2
1
4
3
8
9
10
11
103
104
10•
lQ8
<0·01
<0·01
<0·01
0·013
0·013
0·013
0·13
0·13
0·13
1·3
1·3
1·8
0·05
0·05
0·05
0·5
0·6
0·5
6
6
6
\ 7
'I
Viscosity
centipoises
Tip
speed
ft/min
Speed
rev/min
6
5
\I
102
10
1
Density
lb/gal
80
141
6
10
14
60
282
6
10
14
I
i
UNBAFFLED
240
480
II
I
<0·01
<0·01
0·01
I
;
120
<0·01
<0·01
0·01
'1
564
I
i
1128
2256
6
10
14
Ii
!
0·041
0·06
0·04
0·06
,...
r. Ar,
r.r.
~
6
10
14
0·3
0·5
6
2·4
n.,
U"I
U"Vtl'
0·3
0·5
"·"
VI
10
4
2·4
4
14
6
6
<0·01
0·01
0·02
i
I
I
0·06
0·09
n
v·
1 O
.J....,
0·4
0·7
0·9
0·013
0·02
0·03
i
--~·--
0·09 I 0·2
0·14
0·2
{\ 1 Q
0·3
v· ~v
0·7
1·0
1·3
2·1
2·1
2·1
l·O
1·5
2·0
3
6
6
0·013
0·013
0·013
0·13
0·13
0·18
1·8
1·3
1·3
0·03
0·05
0·07
0·05
0·05
0·05
0·5
0·5
0·6
6
0·2
0·4
0·5
0·2
0·4
0·5
0·2
0·4
0·6
2·1
2·1
2·1
1·8
3
4
80
141
6
10
14
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
60
282
6
10
14
0·03
0·05
0·07
0·08
0·06
0·07
0·03
0·05
0·07
FULLY
BAFFLED
120
564
6
10
14
0·2
0·4
0·5
0·2
0·4
0·5
1·8
s
1·8
s
1·8
1128
6
10
14
1·8
240
4
4
4
4
s
s
.Absence of a decimal point in thiB Table indicates a whole number
6
6
29
POWER .ASSESSMENT
be put forward in the prese;nt state of knowledge, but they need checking against practical experience and against results obtained by the
use of this Handbook.
, The figures given represent the total hp absorbed by impellers operating
,in vessels with a filling ratio of 1-;Q,-the dimensions of_the vessels and
,impellers being those specified in Appendix A; they relate to the text
\
lin Section Five (b) from pages 23-27.
TABLE 5. Paddle Type Impeller A2
(Vessel Diameter 3 ft 3 in.)
1
2
3
Speed
rev/min
Tip
speed
ft/min
4
5
6
7
8
9
10
11
1
10
10a
10s
104
10s
10e
0·01
0·013
0·018
0·03
0·03
0·03
0·8
0·3
0·3
n
18
13
18
Viscosity
centi•
poises
Density
lb/gal
80
60
UNBAFFLED
120
240
204
409
818
1635
6
10
14
14
0·03
0·04
0·06
0·03
0·04
0·06
0·04
0·06
0·08
0·06
0·10
0·12
0·18
0·14
0·19
1·3
1·3
1·8
6
10
14
0·2
0·4
0·5
0·2
0·4
0·6
0·8
0·45
0·6
0·45
0·7
0·9
0·7
1·0
1·3
6·5
5·5
6
10
14
1·7
3
4
1·7
3
4
2
3
4
3
5
6
10
6
480
3270
10
14
60
204
409
FULLY
BAFFLED
818
6
14
22
30
0·02
0·08
0·05
0·02
0·03
0·05
0·035
0·035
0·05
0·3
0·3
0·3
8
8
6
10
14
0·16
0·3
0·4
0·16
0·8
0·4
0·16
0·3
0·4
0·16
0·3
0·4
0·16
0·3
0·4
1·3
1·3
1·3
13
13
1·2
2
3
1·2
2
3
1·2
2
3
1·2
2
3
1·2
2
3
5·5
5·5
5·5
10
6
1635
5
7
9
0·02
0·03
0·05
14
240
5·5
0·02
0·03
0·05
6
120
18
22
30
8
10
14
6
80
13
22
80
8
10
14
10
17
25
10
17
25
10
17
25
10
17
25
10
17
25
.Absence of a decimal poim in thit TabZ, indicates a whole number
8
18
30
AGITATOR SELECTION AND DESIGN
TABLE 6. Paddle Type Impeller A3
(Vessel Diameter 4 ft)
1
2
Speed
rev/min
4
3
Tip
speed
ft/min
6
6
7
8
9
10
11
1
10
101
lQS
104.
1Q5
10 8
0·016
0·02
0·08
0·02
0·04
0·05
0·07
0·07
0·07
0·7
0·7
0·7
6·6
6·6
6·6
2·5
2·5
2·5
25
25
25
Viscosity
centipoises
Density
lb/gal
80
262
6
10
14
60
503
6
10
14
0·08
0·13
0·18
0·08
0·18
0·18
0·11
0·17 ,
0·25
0·17
0·25.
0·4
0·3
0·4
0·5
120
1005
6
10
14
0·6
1·0
1·4
0·6
1·0
1·4
0·8
1·2
1·6
1·2
1·8
1·8
8
4
6
10
14
6
8·6
12
5
8·5
12
5·5
8·5
12
8·5
13
17
UNBAFFLED
240
I
I
FULLY
BAFFLED
30
2010
252
2·5
13
20
25
1
6
10
14
0·06
0·10
0·14
0·06
0·10
0·14
0·06
0·10
0·14
0·06
0·10
0·14
0·07
0·10
0·14
0·65
0·65
0·65
2·5
2·6
2·6
60
503
6
10
14
0·45
0·8
1·1
0·45
0·8
1·1
0·45
0·8
1·1
0·45
0·8
1·1
0·45
0·8
1·1
8·5
6
8·5
8·6
6
8·6
8·5
6
8·5
3·5
1005
6
10
14
3·6
120
6
6
8·5
8·5
I
11
11
11
6·6
6'6
6·5
25
25
26
I
!
,;
11
11
11
,,
I
Absence of a decimal point in this Table indicates a whole number.
I
31
POWER ASSESSMENT
TABLE 7. Paddle Type Impeller A4
(Vessel Diameter 4 ft 9 in.)
'i
I
'I
1
2
3
Speed
rev/min
Tip
speed
ft/min
'1
I
4
5
6
7
8
9
10
11
1
10
101
103
mt
105
108
0·04
- 0·04
0·04
0·4
0·4
0·4
4
4
4
IViscosity
centipoises
Density
lb/gal
6
149
15
10
14
6
30
i
298
10
14
.!
0·035
0·06
0·08
0·035
0·06
0·08
0·055
0·08
0·11
0·08
0·12
0·16
0·16
0·19
0·25
1·6
1·6
1·6
16
16
16
0·25
0·45
0·65
0·25
0·45
0·65
0·4
0·6
0·75
0·6
0·9
0·85
1·3
1·7
6·5
6·5
6·5
65
65
65
2
3·5
5
2
3·5
5
2·5
4
5·5
4
6
8
I
6
UNBAFFLED
595
60
10
14
6
1190
120
10
14
6
2380
240
10
14
17
30
40
17
30
40
20
30
40
l·l
149
10
14
6
30
298
10
14
FULLY
BAFFLED
6
595
60
10
14
,.
I
,
6
120
1190
10
14
25
25
25
30
45
55
6
15
6
9
12
0·04
0·04
0·04
0·4
0·4
0·4
4
4
4
0·2
0·35
0·5
0·2
0·35
0·5
0·2
0·35
0·5
0·2
0·35
0·5
0·2
0·35
0·5
1·6
1·6
1·6
16
16
16
1·6
2·5
4
1·0
2·5
4
1·6
2·5
1·6
2·5
4
4
1·6
2·5
4
6·5
6·5
6·5
65
65
65
13
13
13
22
30
22
80
22
30
13
22
30
13
22
30
Absence o~ a decimal point in this Table indicates a whole number.
25
25
30
I
32
AGITATOR SELECTION AND DESIGN
TABLE 8. Paddle Type Impeller A5
(Vessel Diameter 6 ft)
1
3
2
Tip
speed
ft/min
Speed
rev/min
UNBAFFLED
4
6
7
8
9
1
10
10 2
10 9
104
l
10
11
10 5
1Q6
0·06
0·06
0·07
0·6
0·6
0·6
6
6
6
Viscosity
centipoises
Density
lb/gal
15
189
6
10
14
30
378
6
10
14
0·08
0·13
0·18
0·08
0,13
0·18
0·11
0·16
0·2
0·16
0·25
0·35
0·25
0·4
0·5
2·5
2·5
2·5
25
25
25
6
755
10
0·6
l·0
1·4
0·6
1·0
1·4
0·75
1·2
1·5
1·2
1·8
2·5
1·7
2·5
3·5
9
60
9
90
90
90
5
8
5
8
5·5
8
11
11
40
65
90
40
65
90
14
120
6
10
14
1510
240
6
10
3020
14
I
I
I
15
I
I
189 .
I
--
11
8
12
16
12
20
25
40
65
90
60
90
110
90
130
170
6
10
14
---
9
35
35
40
0·06
0·06
0·08
0·6
0·6
0·6
6
6
6
. 25
25
25
30
878
6
10
14
0·45
0·75
l·l
0·45
0·75
1·1
0·45
0·75
l·l
0·45
0·75
l·l
0·45
0·75
l·l
2·5
2·5
2·5
755
6
10
14
3·5
6 '
8·5
3·5
6
8·5
8·5
6
8·5
3·5
6
8·5
3·5
6
8·5
9
60;
120
1510
FULLY
BAFFLED
.-
•
5
6
10
14
30
50
70
30
50
70
80
50
70
30
50
70
30
60
70
Absence of a decimal point in this Table indicates a whole number.
9
9
35
60
70
90
90
90
I
i
33
- POWER ASSESSMENT
TABLE 9. Paddle Type Impeller A6
(Vessel Diameter 8 ft 6 in.)
1
3
2
l
4
~jv~ooUy
5
6
7
8
9
10
11
1
10
102
10s
104
lQ5
106
centipoises
Speed
rev/min
speed
ft/min
Density
lb/gal
133
6
10
14
15
267
6
10
14
30
535
10
7½
I
~
0·04
0·04
0·04
0·4
0·4
0·4
4
4
4
0·17
0·25
0·35
1·6
1·6
1·6
16
16
1·2
1·9
2·5
6·5
6·5 ·
6·5
65
65
16
UNBAFFLED
6
14
6
60
1070
10
14
6
0·4
0·7
1·0
0·4
0·7
1·0
0·55
0·8
3·5
5·5
8
3·5
5·5
8
4
6
8
30
50
65
25
45
65
25
45
65
120
2140
10
14
7½
133
10
14
0·3
0·3
267
10
0·55
0·55
14
0·75
0·75
6
2·5
2·5
4
6
l·l
0·8
1·2
1·6
11
9
13
18
25
25
30
40
60
80
60
95
120
100
140
190
6
9
6
I
6
15
FULLY
BAFFLED
30
60
535
1070
10
4
14
6
6
20
35'
60
10
14
6
120
2140
10
14
160
300
400
I
250
250
250
0·041
0·04
0·055
0·4
0·4
0·4
4
4
4
0·3
0·55
0·75
0·3
0·55
0·75
0·3
0·55
0·75
1·6
1·6
1·6
16
16
16
2·5
2·5
4
6
2·5
4
6
6·5
6·5
6·5
65
65
65
4
6
20
35
50
20
35
60
20
35
60
20
35
60
25
35
50
160
800
400
160
300
400
160
300
400
160
300
400
160
300
400
Absence of a decimal point in this Table indicates a whole number
J
5~
250
250
250
.fi
34
AGITATOR SELECTION AND DESIGN
TABLE 10. Paddle Type Impeller A7
(Vessel Diameter 12 ft 3 in.)
.j
1
2
3
Speed
rev/min
Tip
speed
ft/min
4
5
192
1
Density
10
102
1540
120
3080
10
0·65
0·95
1·2
2·5
4·6
6
6
10
14
20
85
50
6
170
300
400
10
14
2·5
4·5
6
3·
5
7
4·5
7
9
192
10
14
FULLY
BAFFLED
6
30
770
10
14
60
1549
I
11
1
6
10
14
10e
2
3·5
4·5
0·13
0·2
0·25
1·2
1·2
1·2
12
12
12
0·95
1·4
1·9
5
5
5
60
50
60
19
19
19
190
190
190
750
750
750
6·5
10,
13
50
45
70
95
75
110
140
170
800
400
170
300
400
200
350
450
350
500
650
600
750
1000
14
385
1Q5
80
45
60
10
6
15
104
25
85
50
20
85
6
7½
10
I
/
6
10
14
60
lQ3
6
10
6
770
30
9
I
14
UNBAFFLED
8
14
385
15
7
· Viscosity
centipoises
lb/gal
7½
6
2 '
3·5
4·5
2
3·5
4·5
2
8·5
4·5
16
25
35
16
25
85
16
25
35
25
35
130
200
800
130
200
800
130
200
300
130
200
300
16
0·14
0·25
0·35
1·2
1·2
1·2
12
12
12
2
8·5
4·5
5
5
5
50
50
50
16.,,
25
35
19
25
35
190
190
190
130
200
800
750
750
750
130
200
300
Absence of a decimal point in this Table indicates a whole number.
I
35
POWER ASS ESSMENT
TABLE 11. Paddle Type Impeller AS
(Vessel Diameter 15 ft)
1
2
8
Speed
rev/min
Tip
speed
ft/min
I
r
4
5
6
7
8
9
10
11
1
10
102
103
104
1Q5
lQB
Viscosity
centipoises
Density
lb/gal
6
7t
286
10
14
6
471
15
10
14
0·9
1·5
2
0·9
1·5
2
1·0
1·5
2
1·6
2·5
8
0·85
0·5
0·65
2
2
2
20
20
20
2·5
8·5
8·5
8·5
8·5
85
85
5
85
UNBAFFLED
6
80
941
10
14
6
1882
60
10
14
7!
60
95
180
16
17
20
17
' 25
85
85
40
50
850
850
850
60
95
180
80
120
160
120
180
250
180
250
850
1400
1400
1400
2
2
2
20
20
20
11
5·5
5·5
5·5
471
10
9
i)
9
14
12
12
12
6
40
70
100
40
70
100
40
70
100
40
70
100
850
550
800
850
550
800
850
550
800
850
550
800
941
10
14
6
60
60
95
180
7·5
12
6
10
14
FULLY
BAFFLED
80
7
12
16
286
6
15
7
12
16
1882
10
14
0·4
0·65
0·9
5·5
9
12
5·5
9
12
8·5
85
9
12
85
85
40
70
100
40
70
100
850
850
850
850
550
800
850
550
800
1400
1400
1400
.Absence of a decimal point in this Table indicates a whole number.
36
AGITATOR SELECTION AN:0 DESIGN
TABLE 12. Turbine Type Impeller Bl
(Vessel Diameter 2 ft 3 in. to 4 ft)
1
2
3
Tip
speed
ft/min
Speed
rev/min
;'
4
5
6
7
8
9
10
11
1
10
10 2
103
104
105
10e
0·017
0·025
0·035
0·05
0·055
0·065
0·5
0·5
5
5
5
Viscosity
centipoises
Density
lb/gal
120
283
425
180
UNBA.FFLED
6
10
14
0·5
6
10
14
0·02
0·03
0·04
0·02 0·04
0·035 0·06
0·045 0·075
0·055
0·085
0·12
0·11
0·14
0·16
1·1
l·l
l·l
11
11
11
240
566
6
10
14
0·04
0·065
0·09
0·045 0·085
0·07 0·12
0·10 0·14
0·12
0·2
0·3
0·2
0·25
0·35
1·8
1·8
1·8
18
18
18
860
849
6
10
14
0·12
0·2
0·25
0·13
0·2
0·3
0·25
0·3
0·4.
0·4
0·65
0·85
0·6
0·8
1·1
4
4
4
40
40
40
1132
6
10
14
0·25
0·45
0·6
0·3
0·45
0·65
0·45
0·6
0·8
0·9
1·4
7·5
7·5
1·7
1·2
1'8
2·5
75
480
7·5
75
0·025
0·04
0·06
0·025 0·025
0·04 0·04
0·06 0·06
0·025
0·04
0·06
0·05
0·05
0·06
0·5
5
5
5
0·085
0·14
0·2
0·085 0·085
0·14 0·14
0·2
0·2
0.085
0·14
0·2
0·11
0·14
0·16
1·1
l·l
1·1
11
11
11
10
14
0·2
0·35
0·45
0·2
0·35
0·45
0·2
0·35
0·45
0·2
0·35
0·45
0·2
0·35
0·45
1·8
1·8
1·8
18
18
18
120
l
6
283
10
14
6
180
425
10
14
FULLY
BAFFLED
<0·01 <0·01 0·016
0·01
0·01 0·02
0·014
0·015 0·03
6
0·5
0·5
75
240
566
360
849
6
10
14
0·7
1·1
1·6
0·7
1·1
1·6
0·7
1·1
1·6
0·7
1·1
1·6
0·7
l·l
1·6
4
4
4
40
40
40
480
1132
6
10
14
1·6
2·5
4
1·6
2·5
4
1·6
2·5
4
1·6
2·5
4
1·6
2·5
4
7·5
7·5
75
75
75
.Absence of a decimal point in this Table indicates a whole number.
7·5
I
37
POWER ASSESSMENT
TABLE 13. Turbine Type Impeller Bl
(Vessel Diameter 2 ft 3 in. to 6 ft)
j'
2
1
5
6
7
8
9
10
11
1
10
10 2
10s
104
105
10s
0·01
0·017
0·025
0·012
0·02
0·025
0·025
0·035
0·045
0·025
0·045
0·06
0·065
0·08
0·09
0·6
0·6
0·6
6
6
6
0·025
0·04
0·055
0·05
0·075
0·085
0·06
0·10
0·14
0·12
0·16
0·19
1·1
1·1
14
0·025
0·04
0·055
l·l
11
11
11
4
Viscosity
centipoises
Speed
rev/min
speed
ft/min
Density
lb/gal
6
90
283
IO
14
6
120
UNBAFFLED
377
180
565
6
10
14
0·075
0·12
0·16
0·08
0·13
0·17
0·14
0·19
0·25
0·2
0·35
0·55
0·35
0·45
0·55
2·5
2·5
2·5
25
25
25
753
6
10
14
0·16
0·25
0·35
0·17
0·3
0·4
0·8
0·35
0·5
0·5
0·85
l·l
0·65
240
4·5
4·5
4·5
45
45
45
l·0
1·3
1180
6
10
14
0·5
0·8
1·1
0·5
0·85
1·2
0·7
1·1
1·4
1·6
2·5
8
2
3
4
90
283
6
10
14
0·045
0·075
0·045
0·075
0·ll
0·ll
0·045
0·075
0·11
0·045
0·075
0·11
0·065
0·08
0·11
0·6
0·6
0·6
6
6
6
10
10
100
100
100
0·11
0·18
0·25
0·11
0·18
0·25
0·11
0·18
0·25
0·11
0·18
0·25
0·12
0·18
0·25
11
377
6
10
14
l·l
120
1·1
l·l
11
11
180
565
6
10
14
0·85
0·6
0·85
0·35
0·6
0·85
0·35
0·6
0·85
0·85
0·6
0·85
0·35
0·6
0·85
2·5
2·5
2·5
25
25
25
240
753
6
10
14
0·85
1·4
2
0·85
1·4
2
0·85
1·4
2
0·85
1·4
2
0·85
1·4
2
4·5
4·5
4·5
45
45
45
360
1180
6
10
14
8
5
6·5
8
5
6·5
8
5
6·5
8
5
6·5
8
5
6·5
.Absence of a decimal point in this Table indicates a whole number.
l1
10
860
/
FULLY
BAFFLED
IO
10
10
10
100
100
100
38
AGITATOR SELECTION AND DESIGN
TABLE 14. Turbine Type Impeller B3
(Vessel Diameter 3 ft 3 in. to 8 ft 6 in.
1
2
3
Speed
rev/min
Tip
speed
ft/min
'
4
6
6
7
8
9
10
11
1
10
102
10s
104
10s
10e
6
10
14
0·026
0·04
0·066
0·03
0·046
0·06
0·066
0·076
0·086
0·06
0·10
0·13
0·11
0·14
0·17
0·9
0·9
0·9
9
9
6
10
14
0·076
0·13
0·17
0·086
0·13
0·18
0·14
0·18
0·25
0·2
0·4
0·55
0·3
0·4
0·56
2
2
2
20
20
20
6
10
14
0·17
0·3
0·4
0·18
0·3
0·4
0·3
0·4
0·5
0·45
0·9
1·1
0·6
0·9
1·2
4
4
4
40
40
40
rJ
0·5
0·85
1·1
0·55
0·9
1·2
0·76
1·1
1·5
1·7
2·5
3
1-ll
8·5
8·5
8·5
85
85
85
'
1·1
1·8
2·5
1·2
2
2·5
1·5
2·5
3
3·5
5
6
4
6·5
9
0·10
0·17
0·26
0·10
0·17
0·26
0·10
0·17
0·26
0·10
0·17
0·26
0·11
0·17
0·26
0·9
0·9
0·9
0·35
0·55
0·8
0·35
0·55
0·8
0·35
0·55
0·8
0·35
0·55
0·8
0·35
0·55
0·8
2
2
20
20
20
Viscosity
centipoises
Density
lb/gal
283
60
424
90
UNB.A.FFLED
120
666
6
180
849
10
14
240
1130
10
14
60
283
10
6
6
14
6
90
424
10
14
FULLY
BAFFLED
3
4
15
15
15
2
9
150
150
150
9
9
9
120
566
10
14
0·8
1·4
1·9
0·8
1·4
1·9
0·8
1·4
1·9
0·8
1·4
1·9
0·8
1·4
1·9
4
4
4
40
40
40
180
849
6
10
14
2·5
4·6
6·5
2·5
4·6
6·5
2·5
4·6
6·5
2·6
4·6
6·5
2·5
4·5
6·5
8·5
8·5
8·5
85
85
85
1130
6
10
14
6·5
240
6·5
11
15
6
-
6·5
11
11
15
15
6·5
6·5
11
11
15
15
Absence of a decimal in this Table ind-icates a whole number.
15
15
17
150
150
150
:·I
39
POWER ASSESSMENT
TABLE 15. Turbine Type ImpellerB 4
(Vessel Diameter 4 ft to 12 ft 3 in.)
l
1
2
3
Speed
rev/min
Tip
speed
ft/min
4
5
6
7
8
9
10
11
1
10
10a
10s
104
10'
me
Viscosity
centipoises
Density
lb/gal
UNB.A.FFLED
45
283
6
10
14
0·055
0·09
0·13
0·06
0·10
0·13
0·11
0·14
0·18
0·13
0·2
0·4
0·2
0·25
0·35
1·5
1·5
1·5
15
15
15
6
60
377
10
14
0·13
0·2
0·3
0·13
0·2
0·3
0·2
0·3
0·4
0·3
0·65
0·85
0·4
0·6
0·8
2·5
2·5
2·5
25
25
25
90
565
6
10
14
0·4
0·6
0·85
0·4
0·65
0·9
0·55
0·85
1·1
1·2
1·8
2·5
1·2
1·9
2·5
6
6
6
60
60
60
120
753
.6
10
14
0·85
1·3
1·8
0·9
1·5
2
1·2
1·8
2·5
2·5
3·5
4·5
3
4·5
5·5
11
11
12
110
110
110
6
10
14
2·5
4
5·5
2·5
4·5
6
3·5
5
7
25
25
30
250
250
250
180
1130
7
9
10
14
12
19
'
0·2
0·35
0·5
0·2
0·35
0·5
0·2
0·35
0·5
0·2
0·35
0·5
14
0·5
0·85
1·2
0·5
0·85
1·2
0·5
0·85
1·2
6
10
14
1·8
3
4
1·8
3
4
1·8
8
4
6
10
4
7
14
6
6
45
283
10
14
0·2
0·35
0·5
1·5
1·5
1·5
15
15
15
0·5
0·85
1·2
0·5
0·85
1·2
2·5
2·5
2·5
25
25
25
1·8
3
4
1·8
8
6
6
6
60
60
60
. .-
6
60
377
FULLY
BAFFLED
90
120
180
565
753
1130
10
10
14
10
4
7
10
14
25
35
14
25
85
4
4
7
10
11
10
4
7
10
11
12
110
110
110
14
25
35
14
25
35
14
25
25
85
250
250
250
4
7
25
35
Absence of a decimal point in this Table indfrates a whole number.
4
40
AGITATOR SELECTION AND DESIGN
TABLE 16. Turbine Type Impeller B5
(Vessel Dia.meter 6 ft to 15 ft)
I
1
2
8
Speed
rev/min
Tip
speed
ft/min
!
4
5
6
7
8
9
10
11
1
10
10•
108
104
10 5
108
Viscosity
centipoises
Density
lb/gal
UNB.AFFLED
80
288
6
10
14
0·18
0·8
0·4
0·19
0·3
0·4
0·8
0·4
0·55
0·4
0·9
l·l
0·5
0·7
1·0
8
8
8
80
30
80
424
6
10
14
0·55
0·85
1·2
0·55
0·05
1·3
0·75
1·2
1·5
l'7
45
2·5
3
1·5
2·5
8
7
7
7
70
70
70
60
566
6
10
14
1·2
1•9
2·5
1·3
2
8
1·6
2·5
3·5
3·5
5
6·6
8·5
5·5
7
12
12
14
120
120
120
8'.6
6
8
4
6·6
9
4·6
7
9·6
9·6
14
17
80
848
6
10
14
11
90
17
25
so
40
260
260
250
6
7·6
13
18
8·5
14
20
l!)
25
40
65
50
65
76
600
600
500
8
8
8
30
30
120
1130
10
14
30
283
6
10
0·65
l·l
1·5
0·65
l·l
1·5
0·65
l·l
15
0·65
l·l
1·6
2
3·5
6
2
10
14
6
10
14
5·5
9
12
6
FULLY
BAFFLED
424
60
666
25
35
0·65
l·l
1·5
14
45
10
15
20
6
90
848
10
14
120
1130
10
14
6
2
3·5
2
2
7
3·5
5
8·5
3·5
7
5
5
5
7
70
70
70
6·5
6·5
6·5
6·6
9
9
9
9
12
12
12
12
12
12
14
120
120
120
18
30
40
18
30
40
18
30
40
18
30
40
18
30
40
30
30
40
250
250
250
40
70
100
40
70
100
40
70
100
40
70
100
40
70
100
50
70
100
500
600
600
..Absence of a decimal point in thiB Tabw indicateB a whow number.
I
r
so
41
POWER ASSESSMENT
TABLE 17. Turbine Type Impeller B6
(Vessel Diameter 8 ft 6 in. to 15 ft)
I
1
3
2
Speed
rev/min
Tip
speed
ft/min
30
377
4
5
6
7
8
9
10
11
1
10
10a
10 9
10'
105
10e
2
Viscosity
centi•
poises
Density
lb/gal
14
0·7
1·1
1·6
0·75
1·2
1·7
1·0
1·5
2
3
4
3
3
4
6
8·5
11
6
9
13
16
18
20
160
160
160
13
6
10
7
7·5
8
70
70
70
45
565
6
10
14
2
3.5
5
2·5
4
5·5
3
4·5
6
60
754
6
10
14
4·5
7·5
11
5
8·5
12
6
9·5
13
12
17
20
20
30
30
85
40
800
300
300
6
10
14
14
25
85
16
25
35
18
25
40
30
45
50
45
70
120
80
100
130
650
650
650
UNB.A.FFLED
90
1130
30
877
45
565
6
FULLY
B.A.FFI;ED
60
754
10
14
8
4·5
6·5
3
4·5
6·5
3
4·5
6·5
3
4·5
6·5
3
4·5
6·5
6
10
9·5
16
9·5
16
14
20
20
9·5
16
20
9·5
16
20
9·5
16
20
16
18
20
100
100
100
6
20
35
50
20
35
50
20
35
60
20
35
50
20
35
50
80
85
50
800
300
800
75
180
180
75
130
180
75
130
180
75
130
180
75
130
180
80
130
180
650
650
650
10
14
6
90
1130
10
14
.Absence of a decimal point in this Table indicates a whole number.
7
7·5
8
70
70
70
42
AGITATOR SELECTION AND DESIGN
TABLE 18. Anchor Type Impeller Cl
(Vessel Diameter 2 ft 3 in.)
2
1
3
Speed
rev/min
6
6
7
8
9
10
11
1
10
102
10a
104
lQ5
10•
6
10
14
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
<0·01
0·01
0·05
0·05
0·05
0·09
0·14
0·19
6
10
14
0·02
0·03
0·04
0·02
0·04
0·05
0·035
0·045
0·06
0·09
0·12
0·13
0·13
0·19
0·25
0·45
0·45
0·5
8
2
2·5
2·5
4
Viscosity
centipoises
Ti~
speed
ft/min
Density
lb/gal
18
118
I
64
UNBAFFLED
354
108
708
6
10
14
0·15
0·25
0·35
0'.18
0·3'
0·4
0·2
0·35
0·46
0·5
0·7
0·75
0·85
1·2
1·6
162
1062
6
10
14
0·6
0·85
l·l
0·6
1·0
1·3
0·7
1·1
1·5
1·4
1·8
2·6
2·5
4
5
216
1416
6
10
14
1·2
1·9
2·5
1·4
2
8
1·6
2·6
3·5
3
4
5
'
✓
2
4
Absence of a decimal point in this Table indicates a whole number.
TABLE 19. Anchor Type Impeller Cl
. (Vessel Diameter 3 ft 3 in.)
\
l
1
2
3
Speed
rev/min
Tip
speed
ft/min
i
- -I
'
Viscosity
i
5
6
1
10
7
116
9
10
11
108
104
10 5
10 8
0·01
0·01
0·02
0·01
0·02
0·02
0·05
0·07
0·08
0·18
0·35
0·36
4
5·5
6
centipoises
10 2
Density
lb/gal
12
8
I
I
6
10
14
·.
349
6
10
14
0·04
0·07.
0·09
0·05
0·08
0·11
0·06
0·09
0·12
0·16
0·2
0·25
0·25
0·35
0·45
0·7
0·75
0·85
72
698
6
10
14
0·3
0·5
0·7
0·4
0·6
0·8
0·4
0·7
0·9
0·85
l·l
1·5
1·6
2·5
3
3
4
5·5
108
1048
6
10
14
1·0
1·8
2·5
1·2
1·9
2·5
1·4
2·5
3
2·5
3·5
4·5
5
7·5
10
8·5
13
17
144
1396
6
10
14
2·5
4
5·5
3
4·5
6
3
5
7
5
7·5
9·5
36
UNBAFFLED
Absence of a decimal point in this Table indicates a whole number.
I
l
41
POWER ASSESSMENT
TABLE 17. Turbine Type Impeller B6
(Vessel Diameter 8 ft 6 in. to 15 ft)
I
1
2
8
Speed
rev/min
80
45
Tip
speed
ft/min
877
565
4
5
6
7
8
9
10
11
1
10
10 2
108
10'
105
10 5
8
8
4
Viscosity
centipoises
Density
lb/gal
14
0·7
1·1
1·6
0·75
1·2
1·7
1·0
1·5
2
2
8
4
6
10
14
2
8·5
5
2·5
4
5·5
8
4·5
6
6
8·5
6
10
7
7·5
8
11
6
9
18
18
20
16
70
70
70
160
160
160
UNBAFFLED
60
754
6
10
14
4·5
7·5
11
5
8·5
12
6
9·5
13
12
17
20
13
20
80
35
40
300
:Svv
300
90
1130
6
10
14
14
25
35
16
25
85
18
25
40
80
45
50
45
70
120
80
100
130
650
650
650
80
377
6
10
14
3
4·5
6·5
3
4·5
6·5
3
4·5
6·5
565
6
10
9·5
16
20
9·5
16
20
14
20
35
50
6
10
14
75
130
180
45
14
FULLY
BAFFLED
60
90
754
1130
6
10
30
3
4·5
6·5
8
4·5
6·5
9·5
16
20
9·5
16
20
9·5
16
20
16
18
20
100
100
100
20
85
60
20
35
60
20
85
50
20
35
50
30
35
60
300
300
300
75
130
180
75
130
180
75
180
180
75
180
180
80
130
180
650
650
650
---
.Absence of a decimal point in this Table indicates a whole number.
7
7·5
8
70
70
70
43
POWER ASSESSMENT
TABLE 20. Anchor Type Impeller C3
(Vessel Diameter 4 ft)
I
3
2
1
---::-1
5
6
7
8
9
10
11
1
10
10a
103
104
lQ5
10 5
0·01
0·02
0·03
0·08
0·08
0·085
0·25
0·35
0·45
5
6·5
6·5
Vi,oosity
centi- ,
poises
speed
ft/min
Speed
rev/min
4
Density
lb/gal _
9
108
6
10
14
27
325
6
10
14
6
54
UNBAFFLED
650
81
.
10
14
6
10 •.
14
975
"r
'.
•
108
6
1300
10
14
0·05
0·08
0·11
0·06
0·10
0·13
0·075
0·11
0·15
0·19
0·25
0·3
0·3
0·4
0·55
0·75
0·85
0·4
0·65
0·9
0·45
0·75
0·95
0·5
0·8
1·2
l·0
1·4
1·7
2
3
3·5
5
6·5
1·3
3
1·5
2·5
3
1·7
2·5
4
3
4
5·5
3
5
7
3·5
6·5
7·5
4
6·5
9
6·5
2
9
11
4
l·0
6
10
9
1:('
1§...
14
20
25
25
35
45
25
30
30
20
.Absence of a decimal point in this Table indicates a whole number.
TABLE 21. Anchor Type Impeller C4
(Vessel Diameter 4 ft 9 in.)
I
l
I
2
3
Speed
rev/min
Tip
speed
ft/min
i
I
4
_--o
6
7
8
9
10
11
1
10
10 2
10 8
104-
1Q5
1Q6
Viscosity
centipoises
Density
lb/gal
6
8
113
10
14
339
48
72
96
678
1018
1356
0·11
0·35
0·5
0·65
7
8·5
8·5
0·09
0·15
0·2
0·11
0·17
0·25
0·25
0·35·
0·4
0·45
0·65
0·8
1·0
1·2
1·4
0·7
1·5
0·8.
1·3
1·8 .
1·4
2.
2·5
3
4·5
5·5
5
7·5
14
0·6
1·0
1·4
6
10
14
2
3·5
4·6
2·5
8·5
6
2·5
4·6
6
4
6 .
7·5
6
10
5
10
14
UNBAFFLED
0·1
0·l
0·08
0·13
0·18
6
24
0·02
0·03
0·04
6
10
14
7·5
11
l·l
6
8
12
6
10
14
6
13
16
10
9
15
14
18
25
30
20
30
40
35
60
65
.Ab,ence of a decimal point in this Table indicates a whole number.
25
35
40
I
44
AGITATOR SELECTION AND DESIGN
TABLE 22. Anchor Type Impeller C5
(Vessel Diameter 6 ft)
1
3
2
Speed
rev/min
Tip
speed
ft/min
I
4
5
6
7
8
9
10
11
1
10
10 2
103
10'
10 5
10 6
0·03
0·04
0·055
0·12
0·13
0·13
0·45
0·7
0·9
1·1
1·5
1·9·
Viscosity
centipoises
Density
lb/gal
6
108
6
10
14
18
325
6
10
14
0·11
0·18
0·25
0·13
0·2
0·3
0·15
0·25
0·35
0·3
0·4
0·55
0·6
0·85
1·1
36
650
6
10
14
0·9
1·4
2
1·0
1·5
2
1·1
1·8
2·5
1·9
3
3·5
4
6
8
6
8·5
10
12
19
25
20
30
40
13
18
20
30
40
50
50
70
90
UNBAFFLED
8·5
11
14
9
9·5
10·5
40
45
45
~
54
975
6
10
14
72
1300
6
10
14
3
5
6·5
7
11
15
3
5
7
4
6
8·5
7
12
17
8·5
14
20
.Absence of a decimal point in this Table indicates a whole number.
TABLE 23. Anchor Type Impeller C6
(Vessel Diameter 8 ft~ 6' in.)
1
2
Speed
rev/min
3
4
Tip
!Viscosity
centij poises
speed
ft/min
Density
5
6
7
1
10
10 2
8
9
10
11
103
104
10 5
10e
lb/gal
UNBAFFLED
5
130
6
10
14
15
389
6
10
14
0·4
0·65
0·9
0·45
0·7
0·9
0·5
0·8
1·2
3
6
7·5
4
6·6
9
0·25
0·25
0·3
-30
777
6
10
14
3
5
7
46
1165
6
10
14
10
16
20
11
18
25
60
1554
6
10
14
25
40
50
25
40
60
0·85
1·3
1·6
1·8
s
3·5
3
4·5
5
1·5
2
2·5
20
20
20
6
8
10
19
25
20
30
40
90
95
95
13
20
30
18
25
35
40
60
75
65
100
120
200
220
250
30
50
70
35
55
75
85
130
170
150
200
280
13
I
.Absence of a decimal point in this Table indicates a whole number.
SECTION SIX-MECHANICAL DESIGN
OF AGITATORS
f
I
!
I
This Section is divided into five sub-sections thus:
(a) Materials of Construction.
(b) Type of Service (and its influence on agitator selection and
design).
.
(c) The Design of Shafts and Bearings.
(d) Glands, Gland Bushe'"s and Bearings Inside Vessels.
(e) Drive and Bearing, Arrangements.
(a) MATERIALS OF CONSTRUCTION
Points to be considered in the use of various constructional materials
for the impeller, and the agitating vessel or tank itself may be summarised as follows :
(i) The Impeller
Whilst almost any type of agitator can be fabricated in high
strength metals, there are certain materials which limit the type of
agitator which can be ·used:
1. Wood
Wood is useful only for relatively large low speed agitators.
Wooden agitators are difficult to balance and tend not to remain
in balance due to warping and absorption of moisture. Complicated shapes cannot readily be fabricated and the wooden components used must be heavy, since glued or bolted connections are
unlikely to resist the conditions under which wood is a chosen
material of construction. Simple paddles or gates can be satisfactorily made, however.
Surface softening which would be tolerable in a wooden vat is
frequently not acceptable in wooden agitators, as erosion is likely
to be serious. Moreover, the end grain of the wood must be exposed; this facilitates penetration into the timber and so helps to
cause early failure.
I
\
'
Wood is successfully used, however, in many aqueous processes
where no suitable metals are available, or where exposed metal
cannot be allowed (e.g. in azo colour vats and vessels or effluent
treatment tanks) or where the size of the equipment is large and
the cost of other materials would be excessive (e.g. copperas
dissolving).
2. Lead and Lead-Covered
Loose-lead covered impellers, or impellers fabricated from solid ·
45
46
AGITATOR SELECTION AND DESIGN
lead are suitable only for low speeds, and are largely restricted
therefore to low power/unit volume applications. Creep of the
lead under centrifugal force can produce rapid failure, and erosion
from suspended solids can be extensive. The weight of lead-covered
impellers is also a difficulty, since it tends to produce low critical
speeds.
Homogeneous lead covering is of wider application, but here
agairi erosion or creep can cause rapid failure. The effect of any
unbalance due to uneven erosion or creep should also be considered, especially for impellers intended to operate at relatively
high speeds.
)
1
I
3. Enamel or Glass-Covered
Enamelled cast-iron, or enamelled mild-steel impellers can be
made in a variety of forms, but the outer contours must be
smoothly rounded, and, if the enamel is to be sound, there should
be no large changes of section or masses of metal. Generally the
simpler the shape the better, and the enamellers should be consulted before design is finalised. While relatively high-speed
impellers are made in enamelled construction, they must be such
that no vibration or high stress is set up during operation; otherwise the enamel will flake off.
Enamelled impellers cannot be balanced after completion; some
warping usually occurs in the enamelling process and their design
cannot therefore rely on fine limits to ensure stability.
A completed enamelled impeller and shaft must be in one piece
and must be capable of being inserted through the manhole pro-'
vided in the cover of a "closed" vessel; alternatively the vessel
mav
., be fitted with a removable cover .
4. Rubber or Ebonite Covered
Provided the design ·of the impeller is suitable for applying
rubber or ebonite covering, little trouble or difficulty is likely to
occur with the larger rubber-covered typ~s. In smaller sizes the
rounding off of external outlines may affect impeller performance ..
Rubber-covered impellers can ·be assembled in the vessel and
the assembly joints covered on site; this practice, however, is
likely to cause trouble in maintenance, and in general such agitators should be inserted through the manhole in one piece or used
in vessels with removable covers.
Soft rubber coverings offer high resistance to erosion.
(ii) The Vessel
One of the main features to be considered in the design of the agitator tank or vessel is the possibility of providing bearings in the
)
1
l
MECHANICAL DESIGN OF AGITATORS
r\
1
47
vessel itself. It is difficult to provide satisfactory bearing arrangements in any lined vessel without leaving weak spots for the attack
of corrosion, even though suitable materials are available for fabricating the bearing brackets which have to be fixed through the tank
lining. For this reason tiled or enamelled vessels should be fitted
with impellers which do not need bottom bearings, and it is preferable to avoid bottom bearings in rubber or lead-lined vessels.
Consideration should also be given to the possible effects of
erosion by liquor from the impeller impinging on lead or tile linings.
(b) TYPE OF SERVICE
Impeller selection should take into account the following points
concerning the type of service for which the unit is required:
(i) Continuity of Operation
Slow speed types of agitator are more suited to continuous operation than high speed ·types; they are likely to have longer life
between overhauls, but involve a greater first cost.
(ii) Possibility of Modification
Unless the process is well established and such that the agitator
can be defined firmly with little possibility of later modifications, it is
desirable to arrange for changes of power and speed to be made
relatively simple in vessels where agitation is believed to be critical •.
Auxiliary vessels in a process plant (e.g. blendling and storage tanks,
solution preparation, effluent treatment, filter feed vessels) can often
be fitted with agitators and forgotten. On the other hand agitators
fitted to vessels where critical operations performed are likely to be
subjected to experimental alterations should be arranged so that
changes can be readily made.
(iii) Stepwise Processes
t
Mixing vessels are often used for several stages ·of a process. For
example, a solution may be made up, a further solution be run in
and a reaction occur, the batch be cooled whilst the product precipitates, and the product be maintained in suspension whilst the vessel
is emptied to a filter press.,
The agitation suitable for the dissolving and the reaction would
probably be unsuitable for the precipitation and excessive for maintaining the suspension. Simple agitators with a range of speeds
should be considered for such applications, and it should be borne
in mind that the power and -torque characteristics of a "change
pole" electric motor are such that if the motor is capable of driving
48
AGITATOR SELECTION AND DESIGN
the impeller at its highest speed, it will also provide adequate power
at the lower speeds, provided there is no large change in the viscosity
of the liquor.
(iv) Corrosive Service
In lined vessels it is often both practicable and economical to use
special alloys for impellers and shafts under conditions where enamel
or rubLer or other lining is the most economical lining material for
the vessel itself. This possibility should always be investigated where
high intensity agitation is required in lined vessels, since covered
agitators at high speeds are likely to be troublesome (see Section
Six (a) (i)).
(c) THE DESIGN OF SHAFTS AND BEARINGS (see also
Appendix D)
The design of an impeller shaft is based on certain reasonable
assumptions which are set out and applied as indicated in the following sub-sections:
(i) - Assumptions Made ·
The stresses resisted by agitator shafts are considerably greater
than the design torque would indicate, particularly when high powers
per unit volume are being used. Loads are to some extent alternating,
since agitators tend to rotate in the centre of rotation of the m~in
mass of liquor in the vessel, and this centre rotates round the vessel
centre. Furthermore, during start-up periods the shaft must handle
· the peak motor torque (less the small amount absorbed in accelerating the drive gears and pulleys); there is also the possibility of the
impeller being checked when material is added to vessels by tipping
bags or other containers.
During starting with the conventional types of electric motor, the
shafts must therefore be capable of resisting about 2½ x full load
rated motor torque, and during steady running, some rather illdefined variable torque depending largely on the power absorbed,
which it is assume<:! is closely related to motor power·. It is desirable
that impellers should run steadily in any state· of loading of the
vessel from empty to full, and, except for small units this means
they must run at least 30 per cent slower than the first critical speed.
Small agitators can run above the "first critical", as they accelerate
through the dangerous range very rapidly. (Dynamic balancing can
reduce the 30 per cent margin to 15 per cent.)
Shaft design must therefore be based on some assumed relation
between the stresses occurring under normal operating conditions
and those capable of being induced by the maximum driving power
available. ·
\
i
1·
4
:;
~
...;
,_'\...-
49
MECHANICAL DESIGN OF AGITATORS
A method of design which has proved successful in practice is to
make the shaft sufficiently strong to withstand (without exceeding
the yield stress of the material) the stresses which would be set up if
an agitator blade were jammed at a point 75 per cent of its length
from the shaft. This method assumes two levels of applied torque as
set out in Table 24.
.
Assumed Applied Shaft Torque
TABLE 24. Ratio of: T orque D eveI ope d m
· Shaft by Motor at its
· Rate d Load
I
2
For Low-Speed Impellers well clear of
vessel walls and in vessels where no
solids are charged or precipitated.
(So called "light duty''.)
For High-Speed Impellers and High
Power per Unit Volume, for impellers
which pass close to the vessel wall or
baffles, where solids may settle out or
may be charged from containers.
(So called "severe duty".)
1·5
2·5
Shafts designed in accordance with col. (I) will not fail even if the
motor is overloaded to a point where the motor overload protection
cuts off the power supply, nor are they likely to fail under fatigue
stresses if speed is under about 60 rev/min. Shafts designed to
col. (2) will not fail if the agitator suddenly jams and the motor
stalls before the overload protection op~rates, nor are they likely to
fail by fatigue unless made of materials not commonly used in this
type of work (e.g. certain high strength steel alloys).
l
If corrosion, particula1ly of the type which leads to cracking or
pitting, is expected in the vessel, higher safety factors than those
indicated in Table 24 should be used, as the highly stressed portions
of impeller shafts are somewhat susceptible to failure by corrosion
cracking and fatigue combined (stainl~ss steel is more susceptible to
this than ·mild steel).
(ii). Application of the Assumptions Made
The method of applying these principles to agitators without bottom bearings is indicated in the Appendix D. Shafts with bottom
bearings are very similarly designed, but the mathematics involved
for these cases are adequately treated in most mechanical engineering text books. (Refs. 2 and' 26.)
Ir
1
The calculations i:q. Appendix D also give values of bearing loads
and of the loads produced in the support structure by the agitator.
Once the shaft size has been calculated, the detailed design and
fabrication of agitators offers few unusual problems; it should be
borne in mind that whilst quite rough work will serve at low speeds
and powers, toleranc~s on straightness of shafts, symmetry of the
f
1
50
AGITATOR SELECTION AND DESIGN
impeller itself, and general accuracy need to be progressively
tightened as speeds and powers increase. It is probably worthwhile
statically balancing shaft and impeller assemblies over say 8-ft long
operating at over 100 rev/min and dynamically balancing really
large high·-speed impellers (say over 12-ft long operating at 150
rev/min). Dynamically balanced impellers can operate smoothly
n1uch nearer their critical speeds than unbalanced ones. (If covered
impellers are to be balanced extra thickness of lead or rubber should
be applied near the tips of the blades, to be carved off as necessary to
achieve a balance.)
I
j
'
(d) GLANDS, BUSHES AND BEARINGS INSIDE VESSELS
No particular features need be introduced in agitator glands beyond
what would be expected from the service conditions in which they are
to be used. Design features which should be examined are:
Ease of access f 9r removal of packing and repacking.
Provision of lantern rings, where necessary for the operating conditions, dimensioned so that the ring will not operate as a bearing.
Sufficient clearance in the assembly to enable the gland to be
centred on the shaft, or alternatively the provision of the necessary
spigots or other locating devices to ensure that the gland is central
on the shaft.
In high temperature service the gland should rise from (as opposed
to projecting into) the vessel for ease of cooling.
Provided the impeller shaft is robust, and its bearings sufficiently
~!g!lUl
..Jly -~
--.-~~;i
n~,;i
A....-.r.,,r,h +,-,. +l--.o 0+11-f'firirr hr.v
hf'n-rinrr hll<;!h
lllUUlllJVU, cti.lJ.U .lJ.'Ci<l>J.
p,J'-"""~,
is unnecessary in the pressure range up to 300 lb/in 2 working, even
with shafts with no bottom bearing.
·
Ll
...-.An-
C,J..J.VUC)J..1.
\JV
\/J...1.V
l,:1\/U. .L.L.J..J..l.6
!\
iv
rvvVII.L..a..a...-o
,...... ............, .......
!
l
I
l
When shafts may deflect or where a particularly high standard of performance is demanded from the gland, a bush in the base of the stuffing
box is desirable, with provision for lubrication. Various clearances are
used for these bushes, but a free running fit (to B.S. 1916, Limits and
fits for engineering) seems to perform reasonably well.
Corrosion of gland and bush and the shaft near the gland is usually
slight, probably because of the protection offered by the grease us~d as
lubricant. Consequently, for low pressures or occasional pressure only,
cast iron or plastic impregnated asbestos or cotton bushes running on
bare mild steel are very often satisfactory even under conditions where
lead,-enamel or rubber are demanded for the rest of the vessel Thus it
has become conventional for the lead, rubber or enamel covering of
agitator shafts to be stopped just below the bearing bush leaving unprotected steel in the gland and bearing. For really severe duties, however, it is possible to shoulder the shafts, stopping the covering on the
l•
51
MECHANIC.AL DESIGN OF AGITATORS
shoulder and pulling down a wearing sleeve of resistant material to joint
on the shoulder and run through the gland.
Sleeves have been used in Hastelloy, Langalloy or Stelcalloy, high
silicon iron, phosphor bronze, plastic impregnated asbestos or cotton,
amongst other materials.
The question of bearings which must run unlubricated inside a vessel,
and bearings at the stuffing box where lubrication is not fully effective
due to the action of solvents or high temperatures is difficult and no
fully successful solution can be suggested. Further difficulty arises
because agitators are sometimes run with the vessel empty and a
bearing which relies on the vessel contents for lubrication may then fail
rapidly. Internal bearings are, however, sometimes unavoidable. Qne
palliative with low-speed shafts is to use a combination of materials
which will not seize, and a large clearance.
TABLE 25. Some Combinations of Bush and Bearing Materials for Bearings
Inside Vessels
I
2
3
Bush Material
Shaft Material
Remarks
Cast iron.
Cast iron.
Mild steel.
Stainless steel.
Phenol formaldehyde.
Impregnated asbestos.
Cast iron.
Mild steel.
Stainless steel.
Phosphor bronze.
Mild steel.
Stainless steel.
Porous bronze impregnated Stainless steel.
with ~.T.F.E. (Fluon).
(Chromium plated and
ground.)
Free running, fit.
Carbon (as a bush or as
plugs in 'a cast iron bush).
Mild steel.
Stainless "'teel.
Small clearances are essential as a large clearance
causes disintegration.
Rubber.
Mild steel.
Excellent if always kept
submerged.
Lignum vitae.
Mild steel.
Stainless steel.
Hardwoods.
Mild steel.
Useful in wet conditions.
Stainless steel.
Mild steel.
Useful so long as impregnation remains.
I
Oil-impregnated
bronze.
porous
In choosing materials for these bearings it should be remembered
that under rubbing conditions, materials which rely on a surface film
.
/
52
AGITATOR SELECTION AND DESIGN
to resist corrosion may fail rapidly (e.g. mild steel in concentrated
sulphuric acid). The combinations shown in Table 25 have been used
with some success.
There is a considerable scope for the application of mechanical seals
in place of the glands on agitated vessels. There appears to be no difficulty in applying seals to agitator shafts if sufficient care is taken to
achieve and maintain correct alignment and rigidity in the shaft. The
makers of the seals should be ccn.sulted regarding permissible misalignment and "run out".
'
(e) DRIVE AND BEARING ARRANGEMENTS (see also
Section Four)
Unit drives from individual electric motors are generally accepted as
the best method of driving agitators.
Their disadvantages of "single speed" and tendency to stall under
heavy loads are recognised, but no alternatives are available with fewer
drawbacks. Variable speeds can be achieved by special motors or by
variable speed gears of many types, though as indicated in Section Six
(b) (iii) on page 47 a change-pole motor with speeds in ratios of 1 : 2 : 3
or 1 : 2 : 4 is often more suitable.
Where stalling is a serious problem, torque limiting clutches offer
short-term protection, as do torque-limiting couplings of either the
electric or hydraulic types, especially where overloads are likely to
persist. Generally -agitator motors up to 20 hp will start quite easily
with "direct on" switching, and at higher powers "high starting
torque" motors can be used. Where starting loads are exceptionaJly
high (e.g. the rousing of heavy sediment) clutches should be introduced
in the drives.
Pneumatic motors have been used for small agitators where stiffening of the batch would stall an electric motor; the speed of these
machines varies with the stiffness of the batch, and there seems to be
no reason why hydraulic or steam motors should not be applied to
larger agitators on a similar basis. Overspeed protection may be
necessary with steam or air drive.
.
The loads transmitted to the bearings by the shaft, as well as the
weight of whatever other items are attached to it must be carried by
the bearing support structure; these loads are live and to some extent
alternating. Support structures should thus be "stressed" on this basis
and designed generously to ensure adequate rigidity and the maintenance of shaft alignment in the gland where one is fitted.
Probably the most economical method of supporting an impeller
and.shaft is to couple the shaft rigidly to the shaft of the gearbox and
let the reduction gear bearings take the loads. This arrangement offers
MECHANICAL DESIGN OF AGITATORS
53
no problem with small impellers; with the larger types conventional
reduction gears are mostly made so that adequate capacity bearings
and higher tensile steel shafts can be fitted with no basic alteration to
the gear unit. The loads to be carried, as well as the power and speed,
should be specified to the gear manufacturer.
i:
\!
l
t
~'
In order to ensure alignment when a gland is used, the shaft bearing ~
housing whether part of the gearbox or a separate assembly, should be \
spigotted into a branch or support on the vessel cover, The branch or \
support can then be machined at the same time as the facing which is (\
to carry the gland.
Couplings between the gear output and impeller shafts can be of any
conventional design. For corrosive service couplings between drive and
impeller shafts are much better arranged outside the vessel, even
though this entails longer shafts and may necessitate the use of bearings below the coupling or in the stuffing box.
·
C
The drive arrangements most commonly used fo~ impellers which
operate well below the driving motor speed comprises a worm-reduction
gearbox mounted on the vessel, directly driven by a flange-mounted
motor, or through V-belts from a motor attached to the gearbox. A
V-belt connection offers advantages in that it provides a very simple
method of adjusting the impeller speed to match process requirements
or the available power. Small changes of speed can make appreciable
changes in motor load, since over small ranges the power absorbed by
an impeller varies as the cube of the speed.
Gearboxes are relatively expensive, and absorb considerable power
especially if a unit larger than is really necessary is installed. Vertically mounted motors driving the impeller Ahaft through a V-belt
should be considered for speeds above about 120 rev/min, this being
about the lowest speed which can be satisfactorily obtained in a single
V-belt reduction step from a '750 rev/min motor.
Bearings outside the vessel are nearly always of the ball or roller
type in modern designs. There seems to be no reason, however, why
plain bearings should not be equally satisfactory for the slower shaft
speeds, although somewhat more difficult to instal. Grease lubrication
is normal and protection against entry of condensation, dust or fumes
from the vessel should be provided. From the mechanical standpoint,
greasing is probably necessary only at long intervals; in practice more
frequent regular greasing is desirable in order to flush out any contaminants which may creep into the bearings.
i'
!
I
\I
APPENDIX A-RECOMMENDED DIMENSIONS FOR
VERTICAL CYLINDRICAL VESSELS, BAFFLES, AND
IMPELLERS
\
\
In this Appendix are given the leading dimensions which have been
accepted as "standard" in this Handbook for:
(a) Vertical Cylindrical Type Vessels,
(b) Baffles,
(c) Paddle, Turbine, and Anchor-Type Impellers.
I.
I,
\:'
(a) PROPOSED STANDARD DIAMETERS FOR VERTICAL
CYLINDRICAL VESSELS
\
(These diameters are in accordance with those given in Ref. 98)
RADIUS NOT
LESS THAN 'T'
-
-
l
LI'
~
H
H
H
\
--1■--T----•1
,____________ T _ : ]
ANGLE NOT
LESS
Fm. 5.
Fm. 4.
THAN 140°
FIG. 6.
TABLE26
2
3
4
5
6
7
8
9
Tl
T2
T3
T4
T5
T6
T7
TS
ft in
ft in
ft in
ft in
ft in
3 3
4 0
4
9
ft in
6 0
ft in
2 3
Nominal capacity, gal•
50
150
300
500
1000
3000
9000
16000
Actual capacity, gal•
66
168
314
525
1059
3010
9010
16540
1
Vessel No.
..
..
Diameter, T
..
..
8 6 12
a
ft
• Capacities are calculated for a liquid height H equal to T, and a fl.at bottom.
54
in
15 0
'·
55
APPENDIX A
Under all conditions the liquid height (H) should lie between the
limits of 0·57! and 2T.
Dished bottoms may be fitted, the main radius being not less than T;
a small corner ("knuckle") radius may be used. The overall height is
unchanged by dishing the bottom; the capacity of the tank is reduced
by some 4 per cent.
Conical bottoms may be fitted, the wall being inclined at not less
than 70° to the vertical (i.e. the cone angle is 140°). The overall height
and the capacity are increased by about 18 per cent and 6 per cent
respectively.
(b) RECOMMENDED BAFFLE DIMENSIONS
:,-
-
....
7J
-
-
r-_,.... r
~~ f_-1
l..- _,
,_ -
.J
I 1
I 1
-
I
;-~
r------1
r-------1
'-- - -- -- _,_J.._ - _____ _,
I
I
r-~,- - - - - - - - - ~
I
T
1
,,_____ _ _ _ T - - - - -
FIG. 7.
FIG. 8.
TABLE 27
1
2
Vessel
Tl
T
I
I
ft in
2 3
4
5
T2
T3
T4
ft in
3 3
ft in
4 0
ft in
4 9
J
2¾
4
4!
IX
!
I
l½
2
3
f3
I
T
J
5
3
= Tank diameter.
= Baffle width.
1
5¾
--2
3½
• IX
f3
6
7
8
9
T5
T6
T7
TS
ft in
6 0
ft in
8 6
ft in
3
ft in
15 0
12
1
0
I
0
7¼
10½
3
3
3
3
4
4
4
4
= Wall clearance.
= Bottom clearance.
56
AGITATOR SELECTION AND DESIGN
Four baffles are fitted for tanks Tl-T6; six baffles are used for the
two largest tanks, T7 and TS.
•
(X
Baffles are flat, vertical, radial and mounted not more than a distance
from the vessel wall.
Baffles should extend at least to the surface of the liquid; they may
have a clearance from the bottom of not more than {3.
The clearances (X and f3 are decided by the requirements of the application (subject to the limits given); they are mainly useful for keeping
the tank surfaces free of solids.
(c) RECOMMENDED DIMENSIONS FOR PADDLE, TURBINE
AND ANCHOR-TYPE IMPELLERS
(i) Paddle Impellers
,..
-
l
t
w
r-1
i
I
I
I
17
D
C
l
11
,,,,
T
i
'.t
FIG. 9.
I
I~ I '
TABLE 28
I
1
2
3
4
5
6
7
8
9
Code
Al
A2
A3
A4
A5
A6
A7
AS
ft in
6 0
ft in
8 6
12
ft in
3
15 0
0
5 8
8
2
10 0
5
7
10
1 0
2 4½
2 11
ft in
ft in
T
2 3
3 3
ft in
4 0
ft in
4 9 '
D
1 6
2 2
2 8
3
w
2
2½
3¼
a
5¼
7½
9¼
2
,\
4
3¾
1 ·2
11
1 7¾
,
T
D
= Tank diameter.
= Paddle diameter.
W
0
ft in
= Paddle width.
= Bottom clearance.
r
57
APPENDIX A
Paddle blades are flat, radial and straight; they lie in a plane through
the shaft.
•
Shafts are central and vertical.
Sizes of shafts and hubs and thickness of impeller blades are determined by the strength and rigidity required; they have little effect on
agitation or power requirements. Ribs, etc., for stiffening blades may
be fitted; due account should be taken of their effect on the flow
characteristics.
The liquid depth should lie between the limits O·5 T and 2 T.
(ii) Turbine Impellers
-
r
r-,
w
L
/
0
.Fm. 10.
TABLE29
I
2
3
4
5
6
7
Code
Bl
B2
B3
B4
B5
B6
ft in
9
ft in
ft in
I 6
ft in
ft in
ft in
D
2
0
3 0
4 0
1 0
L
2¼
3
4½
6
9
W·
If;
2½
3½
4!
7¼
B
6
D
L
I
6
= Impeller diameter.
= Blade length.
6
8
W
B
I
12
0
9½
12
= Blade width.
= Number of blades.
Instead of a disc being used as indicated in Fig. 10, the impeller
blades may be attached directly to the hub.
For notes regarding thickness of blades, etc., see preceding notes
on "Paddle Impellers".
.. -
AGITATOR SELECTION AND DESIGN
58
(iii) Anchor Impellers
----- T ----~
FIG. 11.
TABLE 30
2
3
4
I
5
6
7
Code
Cl
02
03
I
04
05
06
T
ft in
2 3
ft in
3 3
ft in
4 0
ft in
4 9
ft in,
6 0
D
2
I
3 10,
I
,
I
I
3
I'
ft in
8 6."'
I
4
6
5
9
8
3
w
2
3
4
4t
[>
7
0
I
I
1
I½
l½
l½·
T
D
= Tank diameter.
= Anchor diameter.
W
0
= Width of blades.
= Clearance (walls and bottom).
Cross-section of the anchor arms is rectangular, probably with
rounded edges when of cast iron or enamelled iron. Arms may be
tapered in thickness and in width W, in which case W should be taken
at the mean value. Internal bracing may be added for additional mechanical strength.
Where dished bottoms are used the clearance O is maintained constant, the anchor following the contours of the vessel.
Anchors are not recommended above 9-ft diameter.
The depth of liquid should lie in the range 0·7 T to l ·5 T.
For_ notes on shaft diameter, etc., see preceding notes on "Paddle
Impellers" on page 57.
APPENDIX B-ASSESSMENT OF THE POWER LOST
IN STUFFING BOXES
(See Note in in Section (b) of Appendix E regarding derivation of these calculations)
Various methods of calculating the power loss in stuffing boxes have
been suggested from time to time; most possess difficulties due to
absence of data concerning friction factors and the pressure exerted
by the packing on the rotating shaft.
The following method assumes that a stuffing box is merely a bushing with means for adjusting the clearance between bushing and shaft.
In other words, the packing is assumed to be plastic, so that pressure
on the gland causes it to deform and so reduce the clearance between
packing and shaft. The packing will not actually touch the shaft unless
too much pressure is exerted on the gland, and the clearance will fill
with either grease from the packing or with the sealing liquid. Under
these conditions the power lost in the stuffing box will be a function cf
the viscous drag in the liquid between shaft and packing. If too much
pressure is applied to the gland, the film of sealing liquid or grease will
be broken, and seizing will occur causing high power losses, the evolution of.much heat, and scoring of the shaft.
The axial flow of a liquid or gas through the clearance between a
shaft and packing can be estimated in cubic inches per minute as
follows (59):
q=
Where q =
and
c =
d =
p =
l =
µ =
0· l 08( 1000c )3dp
µl
Axial flow (in3/min)
Radial clearance (in.)
Dif;tmeter of shaft (in.)
Pressure drop across stuffing box (lb/in 2 )
Length of the packed section (in.)
Viscosity of liquid in centipoises (cp).
The leakage rate which can be tolerated is usually known or can be
fixed, and is often about 0·006 in3/min, equivalent to two drops per
minute.
The permissible clearance (c) for this rate of leakage (q) will thus be
given by:
C -
3 /(
A/
µql
)
1·08 x l0Bpd
The viscous drag in the fluid between the rotating shaft and the
packing is given by:
. <·
µVS
F=---2·16
X
59
105cg
60
AGITATOR SELECTION AND DESIGN
where F = Force (lb)
µ, = Viscosity of sealing liquid in centipoises (cp)
V = Peripheral shaft speed (in./sec)
S = Surface area of the shaft covered by the packing (in 2)
c = Radial clearance (as above)
g = 32·2 ft/sec.
Now
S
= 1r ld (in2)
and V =
Hence F =
1rnd
in.fsec for a shaft rotating at (n) rev/min.
60
µ,1r 2 nl
· lb.
1·29 x 107cg
The horsepower required to rotate the shaft under these conditions
is given by:
hp= Fx
,
1rnd
.
60 X 550 X 12
µ, 1r2nd2 l
1rnd
1·29 X 107cg
60 X 550 X 12
- -----x-----
-
µ,1r3n2d3 l
5·14 l012cg
Substituting for (c):
n2
a / µ,2dl0l2p
hp=---✓
1·12xl010
'rhP. nppli~at,inn
nf
q
t,hiR form11 l~. t.n
n
pnrtfo11 far ~Sl.RP. iR Rhnwn in thP.
following example.
What is the power lost in a 7-in. long stuffing box of an impeller
shaft 3-in. dia., rotating at 180 rev/min, assuming that the pressure
in the vessel is 800 lb/in 2, that the packing is sealed with an oil of
1000 centipoise viscosity, and that a leakage rate of 0·006 in3/min may
be tolerated1
·
The hp needed to rotate the shaft under these conditions will be
given by:
(180) 2 3 /(1000)2(3)10(7)2(800)
hp=---✓
l · 12 X 1010
= 2·1.
(0·006)
APPENDIX C-FORMULAE FOR HEAT TRANSFER
IN AGITATION VESSELS
(Note.-Self-consistent units are assumed throughout this Appendix-see also Notes in
Section (b) of Appendix E)
Heat transfer i~ related to agitation by the following formula:
hd _
( n D2p)0·67, ( Opµ
--Y-x-~'- ('lf,)
µ,
A
)z ( )0·14
µ
xJ.tc
=
=
,\ =
Y and Z =
where h
d
n
D
p
µ,
µ,c
Op
Heat transfer coefficient, surface to bulk of liquid
Outside diameter of the tubes in the coil
Thermal·conductivity of the liquid
Constants relating to geometrical arrangements,
values of which are given in Tables 31 and 32
= Impeller speed""'
= Impeller diameter
= Liquid density
= Viscosity*
= Viscosity at the temperature of the coil surface*
= Specific heat of liquid.
!'
In general for a given speed and diameter the type of impeller has
little effect on the heat transfer (Kraussald (49)) even for types as
widely different as paddles and propellers; anchors, however, may be
an exception to this.
The figures for the constant Y put forward by Chilton, Drew and
Jebens (19) and by Oldshue and Gretton (66) relate to vessels which are
geometrically generally similar to those recommended in Section 2.
For vessels of those proportions, values of Y equal to 0·87 for coils, and
equal to 0·36 for jackets therefore seem appropriate for unbaffied
conditions-except in the case of anchors.
According to Oldshue and Gretton (66} baffling or the use of heavy
coil support structures can reduce the heat transfer coefficient by a
factor as high as 10.
The values of Yin Table 31 as put forward by Pratt (69) do not in
general agree with the others given for unbaffied conditions.
* 1 cp
= 2·42 lb/ft h.
61
TABLE 31. Values of the Constant Yin Formulae for Heat Transfer in Agitation Vessels
1
2
3
Type of impeller
Type of
mixing vessel
Baffled or
unbaffled
6
4
5
Transfer surface
VALUE OF Y
(See Note below)
7
0:,
~
AUTHORITY
Paddle
Paddle
Anchor
Propeller
Turbine
Wide variety of
paddles and plates
ditto
Two turbines on
one shaft
Two turbines on
one shaft
Turbine
Wide variety of types
ditto
Unbaffled
Helical coil
0·87
Unbaffled
Jacket
0·36
Unbaffled
,Jacket
0·55
Unbaffled
Jacket
0·54
Vertical cylindrical
(flat bottom)
Baffled
Helical coil
Vertical cylindrical
(flat bottom)
Unbaffled
Vertical cylindrical
(dished bottom)
Vertical cylindrical
(dished bottom)
Vertical cylindrical
(hemispherical
bottom)
-
34 ( dg
dp
Vertical square
(flat bottom)
Unbafflecl
Vertical cylindrical
(dished bottom)
Vertical cylindrical
(dished bottom)
Vertical cylindrical
(flat bottom)
Unbaffled
Tubes act as Vertical tubes
as baffles
Vertical cylindrical
idtto
Unbaffled
ditto
39 (du
dp
Unbaffled
- -,c~
__ .....,
~-·
------
---:-
W)
De
D
Helical coil
Helical coil
Jacket
(
(fr r·33 X(;lr·2
0·87
0·36
'
dp
Brown, Scott and
Toyne
Oldshue, Gretton
13
66
Pratt
69
19
13
>
Q
Pratt
69
Cummings and
West
Cummings and
West
Dunlap and
Rushton
21
= Overall height of coil.
= Diameter of coil.
~
>
8
0
C
0·40
0•09
19
D2T
1·01
.Tacket
Chilton, Drew and
Jebens
Chilton, Drew and
Jebens
Brown, Scott and
Toyne
D2T
25
Helical coil
NOTE-Regarding Column 5:
D = Impeller tip diameter.
T = Vessel diameter (or length of side for square-shaped vessels).
d = Outside diameter of the tubes in the temperature control coils.
d11 = Gap between coil turns ( = coil pitch, less d).
---.---,..--
r·l ( r·
0
r·8x { ·25 x ( d3 r·l
8
r· X(wr· X d3r·l
Reference in
Appendix E
x Td
0·17 (D
T
Helical coil
5
Name(s)
21
ttj
t'1
ttj
23
Kraussold
I Kraussold
~
U).
I
49
49
De
W = Width of stirrer (impeller) blade (or sum of widths where
several paddles are on the same shaft).
B 1 = Number of baffles involved.
0
8
H
0
z
~
t:::1
t:::1
ttj
U).
H
Q
z
~=:::.--:=---=----~
---
---==--====--~..._.;_..:..........,._ _ _ _ _ _ _ _ _ _ _-..i.,,_____ __
~
""d
t.":l
TABLE 32. Values of the Constant Zin Formulae for Heat Transfer in Agitation Vessels
I
2
4
3
6
5
7
-
8
Type of impeller
. Baffled or
unbaffled
Transfer surface
VALUE
OF
z
0
Reference in
Appendix E
Oldshue and
Gretton
66
Pratt
69
0;25
Brown, Scott and
Toyne
13
Helical coil
and Jacket
0·33 (but the
values for
higher viscosities will correlate well on a
value of 0·25)
Chilton, Drew and
Jebens
19
Turbine
Vertical cylindrical
(flat bottom)
Baffled
Helical coils
0·37
Wide ranges of
paddles, anchors and
plates
Circular and
square
(flat bottom)
Unbaffled
Helical coils
0·33 (but the
values will correlate well on
a value of O· 28)
Anchors and propeller
Vertical cylindrical
(hemispherical
bottom)
Vertical cylindrical
(flat bottom)
Unbaffled
Jacket
Unbaffled
Paddles
Name(s)
t::1
~
AUTHORITY
Type of
mixing vessel
z
~
Turbines
Vertical cylindrical
(flat bottom)
Unbaffled
Helical coil
and Jacket
0·33
Cummings and
West
21
Turbine
Vertical cylindrical
(flat bottom)
Vertical tubes
act as Baffles
Vertical tubes
0·33
Dunlap and
Rushton
23
Wide range of types
Vertical cylindrical
(flat bottom)
Unbaffied
Helical coil
and Jacket
0·33
Kraussold
49
Remarks
Correlation of
other investigators' results
included
NOTE-The values of Z given-in-this table fall between 0·25 ariiro-37 tnclusive, and it is suggested that the acceptanceoTZequal to 0.33 in all cases except anchors will not lead to serious errors.
0)
~
APPENDIX D-THEORY AND CALCULATIONS FOR
THE DESIGN OF IMPELLERS, SHAFTS, AND
BEARINGS
(See Notes in Section (b) of Appendix E concerning the derivation of these calculationB)
(a) GENERAL REQUIREMENTS RELATING TO DESIGN OF
IMPELLER SHAFT
The general requirements relating to an impeller shaft and associated
blading may be set out as follows:
(1) The shaft should be sufficiently strong to resist:
For Severe Duty: 2½ times the rated motor
torque without the yield stress of the when an impeller
material being exceeded (or 0·2 per cent blade is jammed at
proof stress);
75 per cent of its
or
maximum radius,
For Light Duty: l½ times the rated motor measured from the
torque without the yield stress of the centre of the shaft.
material being exceeded (or 0·2 per cent
proof stress) ;
J(2) The shaft should resist 2½ times the motor rated torque as pure
torque.
v-(3) The shaft should~ run within 30 per cent of its first (lower)
critical speed, or within 15 per cent of that speed if dynamically
balanced.
---{4) Neither should the shaft deflect to an extent as to cause fouling
of the vessel wall or fittings when jammed as i~jl).
(5) The impeller blades should not fail in the jammed condition set
out in (1).
The relevant design calculations given in this Appendix assume
that the shaft is carried entirely by two bearings with sufficient flexibility to have the effect of simple supports. These could be the bearings
of the associated reduction gear, the agitator 'b~ing attached to _the
gear output shaft by a rigid coupling.
·
All stresses in these calculations are expressed in terms of apparent
simple tensile stress.
I
(b) CALCULATIONS FOR SHAFT DIAMETER (See Fig. 12)
Assume that the following are known:
Nominal hp of_g.riving motor
Agitator speed (rev /14in)
Overall dia of agitator (ft.)·
Length of agitator below bottom
bearing !ft). See Fig. 12.
,A,' v1 ..
64
=n
=Dor 2r
= l
APPENDIX D
Distance between centre lines of the two
bearings referred to in (a) (ft)
=S
Yield stress of shaft material in terms of
apparent simple tensile stress (ton/in 2 ) = fy
Safe working stress in terms of apparent
simple tensile stress (ton/in 2 )
= fs
'"'-'-PP.,_;;;..,
......................
,.
I
s
...__............. ·······················+
.
I
f'
''
'
----·--•---t-++--·--·---·_j_
,.
FIG. 12.
••j
and that it is required to find the diameter of the impeller shaft needed
to sustain the loads developed if the agitator becomes jammed by one
or more impeller blades and that the driving motor is capable of developing l½ or 2½ times the normal full load torque .
As indicated under (a) (1), it is assumed that the point of jamming
is at 0·75 of the maximum agitator radius from the axis of the impeller shaft, as this point corresponds approximately to the centre of
pressure on a blade rotating through a liquid. If there is reason to
believe that the agitator may be jammed at a point closer to the axis
(e.g. in a paste mixer the charge might be dumped from a paste bogy
near to the agitator shaft), then this fraction of the radius may be
suitably decrease~. It is, however, unwise to increase it.
·~.·
--·: ,I.
If Tc is the maximuirt:~oii.tinuous rated torque on~~~;~
33000 X 12 X p
-=-=~"
Then Ti; =
. ),:
·1 1(1)
-21rn x 2240
~ 2.S ·if
f
·
If Tm is the torque to be resisted under jammed conditiono,
Then Tm = 2·5__;1c or 1·5 Teton in.
=·7 c,. :::>.J~ _£_>
7
•'1--\,
es-Y-
.
,
L
itz.,. 2-./ ·n
66
AGITATOR SELECTION AND DESIGN
This torque Tm is to be resisted by a force Fm tons acting at a radius
of 0·75r from the axis of the impeller shaft, and hence,
The greatest bending moment Mm to be resisted by the impeller
shaft occurs immediately below the bottom bearing, and
Mm = Fmlton in.·
Using the maximum elastic shear strain energy theory the bending
moment (M em) equivalent to the combination of Tm and Mt!m is given
by:
Under these conditions the stress (fy) in the impeller shaft is then
given by
fy
(3)
where dt = diameter of the shaft (in.)
The theoretical diameter of the shaft can thus be calculated from
expression (3), and a diameter (din.) of some commercially available
size of bar, close to dt can then be selected.
Having determined a shaft diameter in the manner just o-gtlined, it
is then necessary to check that the shaft will not be stressed above its
safe working stress Us) by the torque developed as the driving motor
accelerates through its peak torque during starting. This start-up
torque is here coh-sidered as a pure torque load, and· is seriously large
only with agitators having an unusually large ratio of radius to shaft
length.
If (fq) represents the maximum shear stress developed in the impeller
shaft during start-up
=
Then fq
16 x 2·5
·
T.J,
ton/in 2 •
1rd3
(4)
Again using the maximum elastic shear strain energy theory, the
maximum permissible value offq is equal to fs•
~
. Therefore fr
16 x 2·5
{: .__ 1rd3 ..
Te
ton/in2 ,,
(4a)
If this condition is not met, then a shaft diameter greater than -d
· must be selected.
J
(
67
APPENDIX D
(c) GEAR SELECTION WHEN AN IMPELLER IS SUP-
PORTED BY THE GEAR OUTPUT SHAFT (or Bearing
Load Calculations)
First calculate the value of an equivalent bending moment (say
MEM) at which the selected diameter of shaft will yield:
i
. . ?Td3Jv
.
(5)
Thus MEM = --ton 1n.
32
Then determine the bending moment (MM) which in combination
with the maximum torque (Tm) produces the equivalent bending
moment (MEM), thus:
--=-.,,,-----=----=___,,,.
MM=
y
(MEM) 2 -0·75(Tm) 2 ton in.
·
(6)
This value of bending moment represents the maximum shock
moment which the gear shaft should withstand. The output shafts of
nearly all gear units will withstand a shock bending moment of 2·5
times their rated continuous bending moment. A gear is therefore
required which will withstand a continuous bending moment of:
MM
--ton in.
2·5
The gear unit can then be selected from the maker's data on the
basis of hp output, speed, and a maximum continuous bending moment
· equal to the above value .
•
A check should then be made to ensure that the bearings will not be
overloaded by the side thrusts imposed:
Load developed by shock bending moment on:l-S
S)
tons
(l+ S) tons
~ottom bea:ring = Fm S
.
Top bearing = Fm (
i
(7)
/
(8)
These loads are respectively equivalent to continuous loads on the
top and bottom bearings as under :
l-S)
Fm (2·5S
l- s)
Fm ( -
or
I·5S
(l+ S)
.
s)
.-
and Fm ·- ton1/'J..,
ii,(for severe duty
2·5S
(z
and Fm -+- ton itjor light_ duty
.
I·5S
T."
(but see Notes I, 2, 3 and 4 at the end of this sub-section).
If the impeller is carried. by the gear unit, these total loads should
not exceed that available on t¼e gear bearings for withstanding continii1ms external loads. When: bearings are being provided for the·
(
/
.
i /
68
AGITATOR SELECTION AND DESIGN
agitator separately, the relevant one of these two loads should be taken as the working side thrust for selection purposes.
It is inherent in the design of almost all gears and bearings that if
the bearings will withstand this level of continuous load, then they are
capable of withstanding 2½ times that load under shock conditions:
In order to reduce expense with costly materials, or to reduce weight
and increase the critical speed, it is sometimes convenient to use
hollow shafts. Using suffixes (i) and (o) to denote internal and external
dimensions, the formulae previously given and referenced as (3), (4)
and (5), respectively, become:
32 Mem do
= ----ton/in2
4
4
1r
Is
Mem
=
(do -dt
(9)
)
16 X 2 ·5 Tc do
·
4
1r
(do -dt 4 )
1r
(do 4 -dt4 )fv
.
ton/1n2
.
= -----tonm.
32do
(10)
(11)
It should be remembered that if a shaft is hollow only over the
lower section of its length (where bending moments are small), then
the hollow section should still be capable of transmitting a torque of
2·5 Tc ton in. without a stress of Fa ton/in 2 being exceeded.
Notes Regarding Above Calculations
(I) It may be found that the value of the shaft diameter (d)
selected is sufficiently larger than the required diameter as to
make a larger size of gear nec~sary. If so, a portion of the
shaft immediately below the coupling should be turned down
to (d') in diameter, and the smaller gear used.
(2) If the gear shaft and bearings are likely to be overloaded
whilst the torque is well within the rated output of the gear,
it may be advisable to fit a subsidiary bearing plate beneath
the coupling in preference to the use of a larger size of gear.
The calculations involved are outlined in sub-section (g) of
this Appendix.
In vessels where a bearing bush is used in the gland, such
bush may be regarded as a subsidiary bearing; where this is
done, however, care should be taken to ensure that the impeller
shaft below the coupling will not withstand a shock bending
moment
c::y )
greater than that on the gear shaft, as
otherwise wear on the neck b_ush may damage the gear.
(3) The calculations in this suH;-sP,ction assume that short output
shaft gears are used. I(-4lie •coupling is more than a few inches
/"
·l
!I
69
APPENDIX D
·below the lower bearing of the gear, then the shaft should be
designed to reach its yield point below the coupling before the
applied loads attain values which stress the gear shaft above
its CTaximum shock bending moment at the lower bearing.
(4) If very heavy agitators are used, the end thrust on the bearings may become a serious factor, and should be quoted when
ordering gear units or included as a further load in selecting
bearings.
(d) CALCULATION OF CRITICAL SPEEDS
The method of calculation given in this sub-section has been developed from that given in Ref. 70.
Having selected the impeller shaft diameter (d) as explained in the
previous sections of this Appendix it is necessary to ensure that the
agitator speed is not within ± 30 per cent of the critical speed of the·
shaft as the agitator is unlikely to· run steadily within that range.
The following calculations consider transverse and not torsional
vibration conditions, as the latter very rarely occur with impeller
shafts:
Lets = Distance between centre lines of shaft bearings (in.)
l = Length of overhung portion (in.)
.l
TJ
=-
s
n 8 = Critical speed of shaft alone (rev/min)
K1 = A constant depending upon the value of the ratio TJ,
which can be obtained from Fig.
...., 13
I = Moment of inertia of shaft about an aixs through its
centre of cross-section (in4 )
Ws = Weight of shaft (lb/in.)
E = Youngs Modulus of the shaft material (lb/in 2 ).
Then the critical speed of the shaft itself is given by:
ET
J
ns = K1
..
.
(12)
~w 4 rev/min
81' .
Considering the agitator as a whole:
Let
8a = l\Iaximum deflection (in.)
. Wa = Weight of impeller (lb)
n1 = Critical speed of light shaft with impeller (rev/min)
nc = Critical speed of the whole impeller system (rev/min)
·I
8a and
n1
-
Wal 2 (l+ S).
Ill.
·3EJ
188
_rev/min.
\f(8a)
I
,_i;~..
__. ., i
J
I
I
-,,.,.,
,._
-.
-
"
.....
I
,.
.:.,:
/
,,,:j
'
~'---
·t- ---··
70
AGITATOR SELECTION AND DESIGN
and nc may therefore be calculated from the relationship:
I
I
I
nc2
n1
n8
- = -2+ -2
(13)
700 ,-
WHEN 77--..00
600
.
l
~
1/
V
~
..
K ,___...650
!~'!CRITICAL SPEED.
i
II
400
'
I
300
200
100
~·
0
0
2
3
4
5
6
7
8
10
9
II
12
FIG. 13. Curve showing relationship between 71 and the constant K 1
(see item (d) of Appendix D) ·
·
The critical speed of any couplin6• or other concentrated weight
should also be determined and allowed for if necessary.
71
APPENDIX D
Thus if:
n2
= Critical speed of a coupling or concentrated weight
and
l2 =
and
w,
=
Then S, Hencen2 -
on a light shaft (rev/min)
Distance of coupling or concentrated weight from
centre line of bearing (in.)
Weight of coupling (lb).
Wc"2 2(l2+S)
3El
188
y.(8c)
I.e. 1i2
188
= ------
(14)
J[w.z.:~+8)]
The critical speed of the whole system may therefore be found from
the relationship:
I
nl·
1
1
1
n1
ns
n2
-=-+
-2+ -2
2
The critical range of speed will lie within the range (nc ± 0·3nc)If the calculated critical speed range overlaps the operating speed
the most helpful modifications available are usually to reduce the
weight of th~ agitator blades, and replace solid by hollow shafts. If
further alterations are still necessary a subsidiary bearing plate can be
used or the agitation modified. Minor alterations to impeller dimensions
sufficient to avoid critical speeds can be made on the basis of constant
power by keeping the value (r5 x n3) constant.
(e) CALCULATION OF DEFLECTIONS
If a paddle becomes jammed, the agitator will tend to turn about
th~ point of jamming, thus causing the shaft to deflect.
The stiffness of the shaft (which is governed by the diameter) will
determine its deflection and so the possible rotation of the paddle
about its jamming point.
Consider the shaft as a cantilever which tends to deflect below the
lower bearing.
Then, using the nomenclature previously defined, the force causing
the shaft to deflect is Pm, tons.
.
For a cantilever the shaft deflection s, is given by:
Pml3
3EJ
S=--
(16)
6
/
72
AGITATOR SELECTION AND DESIGJII'
Fig. 14.
From the diagram in Fig. 14:
(fr)
B.
-=-78
:. X
= -3
.
lll.
.
.f •
Relating this deflection to the diameter of the shaft,
448
Pml3
X=-X-9
-rrd4~
(17)
t
Having determined this deflection an inspectton of the relevant
drawings will then help to ascertain whether the paddle is likely to
foul the walls of the vessel when the agitator becomes jammed.
(f) DESIGN OF IMPELLER BLADES
The bending moment at the root of the impeller blades should be
checked by considering the blades as cantilevers. The force to be
resisted is a bending moment of Tm ton in., i.e. the force to be resisted
under shock bending conditions. Owing to the tendency for blades to
vibrate, the maximum stress developed in the material by these loads
should not exceed fy ton/in2 •
Shear stress is negligibly smal1 in all normal shapes of impeller
hlade.
I )
73
APPENDIX D
(g) STRESSES IN SHAFTS AND
BEARINGS WHERE A
SUBSIDIARY BEARING IS FITTED
The shaft is considered as a beam loaded at one end simply supported at the three bearings, K, L, and M, and withstanding a side
thrust at N as indicated in Fig. 15.
F
a
b
-----------------
______________ c ------------
----------------
K
L
M
N
FIG. 15.
(i} Bearin~ Loads
By Macaulay's Method* (Ref. 17):
d2y
EI dx 2
:. Ely
= R1x+R2lx-al+R3 lx-(a+b)I
R1x3 R2lx-al 3 R31x-(a+b)l3
= --+---+-----+A1x+B1
6
6
When x
=
O;
y = 0,
Whenx
=
a;
y
:.
0
(18)
6
and hence B 1 = 0.
= 0..,
R1a3
= - - + A1a, and hence A1 =
6
6
~
Whenx
'
=
(a+b);
y = 0
R1(a+b) 3 R 2b3
+--+A1(a+b)
6
6
R1(a+b) 3 R2b3 R1a2 (a+b)
:.
0
=
:.
0
=---+------6
6
6
Also -Fe = R 1(a+b)+R 2b.
:. -Fcb2 = R 1b2(a+b)+R2b3
(19)
(20)
Multiplying equation (19) by 6, and subtracting equation (20)
from the result:
Fcb 2 = R1(a+b) 8 -R1b2 (a+b)-R 1a2 (a+b)
= R1(a+b){(a+b) 2-b2 -a2} = 2R1ab(a+b)
* In this method, expressions written as [x-a] become zero when xis less than a.
6*
74
AGITATOR SELECTION AND DESIGN
R1
-
Feb
(21)
2a(a+ b)
Similarly:
R2b
- -Fe-R1(a+b)
R2
-
R2
-
· -Fe(2a+b)
2ab
R3
=
F-R1-R2
=
Fbe
-Fe-2a
Fe Fe
b 2a
----
(22)
and:
=
F-
Fbe
2a(a+b)
Fe Fe
+-+b
2a
. I
Fe
Fe
(23)
=F+-+
b 2(a+b)
(ii) Bending Moments
The greatest bending moment is developed at the point M (Fig.
15). It can be determined as set out below and combined with stresses
due to torsion by the method previously used for shafts without
subsidiary bearings. The bending moment at the bottom bearing of
the gear (i.e. in the gear output shaft) should be checked against the
gear capacity.
Bending Moment at M = Fe ton in.
Bending Moment at L = R 1a ton in.
R3
(iii) Critical Speeds
These should be calcnlated as previously explained~ but considering a total shaft length of (b +e) carried in bearings L and JJf..
(h) SUGGESTED WORKING STRESSES FOR SHAFT
MATERIALS
The v~lues of stresses suggested in this Section of the Appendix are
for normal temperatures, and should be reduced for operation at higher
temperatures.
Where steel shafts have failed after fairly long periods of service by
bending without being jammed or otherwise mechanically abused,
blind replacement by higher tensile strength material will not necessarily always give a better result. The higher tensile steels may fatigue
under the conditions of alternating load to which impeller shafts are
subjected.
A check calculation of the stresses developed should be made by the
methods set out in this Appendix, using a permitted stress for fy,
which bears some relation to the yield stress of the selected material
and its resistance to fatigue. No practical information is available on
I
t
l
j
t
I
75
APPENDIX D
such relationship, but the figures given in Table 34 as used by a gear
manufacturer may provide some guide.
TABLE 33; Suggested Working Stresses for Shaft Materials
(tons/in2)
1
2
3
4
Material
Yield stress
or 0·2 % proof
strt:)ss
Safe working
stress
Young's
modulus
(fy)
Us)
(E)
Mild steel . .
..
.. ..
18/8 chrome-nickel steel with or
without additions
. . ..
Monel metal
Hot rolled
..
..
Fully annealed . .
. . ..
..
Cast iron
..
..
6
14
8
---
12,500
6
4
11,500
11,500
3*
6,500
14
'9
..
..
.
17 .
-
7·5*
13,500
-
• .As cast iron has neither a yield nor a proof stress, these values are based on an uUimate tensile strength
of 12 ton/in2 for grey cast iron to B.S. 1452. Grey Iron Castings-grade 12
TABLE 34. Showing Suggested Relationships between Ultimate
Tensile Strength, etc., and the Permitted Stress f y•
- 1
2
3
4
5
Steel
U.T.S.
ton/in2
Yield
ton/in 2
Value
equiv. to
fs ton/in 2
Value
equiv. to
fv ton/in 2
Nickel-chrome B.S. 970, * En 24
50-60
38-48
10·6
25·8
Normalised 0·4 per cent C to
...
B.S. 970, * En 8
..
35
17.
6·6
16·5
'
• B.S. 970, Wrought Steels in the form of Bars, Billets and Forgings, up to 6-in. Ruling Section,for .Automobile
and General Engineering Purposes.
En series.
·
(i) WORKED EXAMPLES
The following calculations relate to the agitation in two imaginary
vessels, A and B. The leading dimensions given below in Table 35 have
been selected so that the calculations for vessel A is a straightforward
example, that for vessel B illustrates a more difficult case.
TABLE 35. Features of the
two "Imaginary" Vessels
1
l
'
i
Vessel depth . .
.. . . . . ..
Paddle length (2r) . .
.. . . . .
Paddle speed (n)
..
..
..
..
Horse power (hp)
..
..
. . ....
Paddle blade depth . .
..
. . . ...
Normafheight of bottom gear bearing above
vessel cover
..
. . ..
..
Length of agitator shaft below bottom gear
bearing (L)
..
. . ..
..
2
3
Vessel A
Vessel B
7 ft
6 ft 8 in.
22 rev/min
15
9 in.
5 ft 6 in .
4 ft 0 in .
40 rev/min
15
9 in .
Approx. 2 ft
Approx. 2 ft
Say 78 in.
Say 78 in.
-
76
AGITATOR SELECTION AND DESIGN
1. Calculation of Shaft Diameters
Vessel B
Vessel A
From eq. (1) Tc
· Tm
Fm
-
33,000 X 12 X 15
27T
X
22
X
33,000 X 12 X 15
21r X 40
2,240
X
= 19·2 ton in.
10·5 ton in.
= 2·5xl9·2
2 X 10·5
= 48 ton in.
26·4ton in.
48
- ---0·75 X 40
= 1·6tons
:. Mm = 1·6x 78
= 125 ton in.
2,240
26·4
0·75 X 24
1·47 tons
1·47x78
115ton in.
· From eq. (2)
Mem = y[(l25) 2 +0·75 (48)2]
= 121 ·5 ton in.
y[(l 15)2 + 0·75(26·4)2]
117 ton.in.
Fron1 Table 33,
fy for mild steel = 17 ton/in2
32 X 121·5
· From eq. (3), 17,= - - 1rd~
= 4·29 in.
· de
. d
4·5 in.
17 ton/in2
117 X 32
1rd:
4· 12 in.
4·25 in.
=---
2. Check for Continuous Working Stress
Vessel A
From eq. (4), Jq
-
Vessel B
16 X 48
16 X 26·4
1r (4·5) 3
. 7T
= 2·68 ton/in2
(4·25)3
l ·76 ton/in2
which values are well below the
maximum permissible continuous
working shear stress.
77
APPENDIX D
3. Gear Selection
Vessel A
From eq. (5)
MEM
Vessel B
1r( 4·5)317
n (4·25)317
32
32
= 152·5 ton in.
127 ·5 ton in.
= v[(l52·5) 2 - o-75(48) 2
= 146·5 ton in.
vr(121•5)2 _ o-75(26·4)2J
-
From eq. (6)
MM
MM
· - - = 58·5 ton in.
125·5 ton in.
50·2 ton in.
2·5
A gear unit has now to be selected on the basis of 15 hp, an agitator
speed of 22 rev/min, and a maximum continuous heh.ding moment
of 58·o ton in. for Vessel A and 15 hp, 40 rev/min, and 50·.2 toa in. fo~·
Vessel B.
·
A study of a gear data sheet shows that a 12-in. gear will be satisfactory for Vessel A, provided that the bearings are not overloaded.
For Vessel B, a 10-in. gear has the necessary power capacity but the
maximum allowable continuous B.M. is, only 42 ton in. Consideration will have to be given therefore to the use of a subsidiary bearing
plate.
From this point, the calculations will proceed separately.
VESSEL A
Check on, Gear Bearing Loads
Wheelshaft bearing span for a 12-in. gear = 12·75 in.
From eq. (8):
(78 + 12·75)
Shock load on bottom bearing = l ·6 - - - 12·75
==. 11 ·4 tons
11·4
· Equivalent continuous load = - 2·5
= 4·55tons
From gear data sheet, the margin on bearings available for withstanding continuous external load lies between 7 · l and 7 ·42 tons.
Also f!OID .the same sheet, the margin on bearing for external end
thrust load lies between 5·31 and 5·12 tons which is sufficient for the
agitator weight.
Hence the bearing loads are satisfactory.
.,
,
78
AGITATOR SELECTION AND DESIGN··
Design of Impeller Blades
The bending moment to be resisted by the root of the blade is
Tm, i.e. 48 ton in. Now fy for mild steel is 17 ton/in 2 (Table 33}.
If tis the blade thickness (in.) then:
48
17=--
•
In practice, 1 ·5 in would be
rather thick; use instead a ½-in.
thick plate with stiffening ribs
on each side, say ½-in. by 2¼-in.
section at the boss, tapering to
nil at the end of the paddle arm.
_
· t - l ·37 in., say l ·5 in.
Critical Speed
For the shaft :
78
'YJ
12·75
=
6·1
From Fig. 13:
K1 = 600
.7t{4·5)4
I
= --- =
Ws
= 4·51 lb/in.
E
=
:. Crit. speed n 8
20·6 in.
64
f
13,500 ton/in2
= 600
J[
13,500
·
20·6 X 2,240]
X
4·51
X
(78)4
, from eq. (12)
:. n 8 = 1,155 rev/min
For the agitator, Wa = 300 lb
188
:. n1
-
-~~~~~~~~~~~~~~~~~~~=rev/min
J[
30q(78) 2 (78 + 12·75)
3 X 13,500
:. n1
since
X
]
20·6 X 2,240
= 630 rev/min
1
1
nc
= 554 rev/min
1
- = - - -2+ - nc2
(1,155) (630)2
This critical speed of 554 rev /min is very high, so that an agitator
running at 22 rev/min is well outside the critical range.
79
APPENDIX D
Shaft Deflection
If x is the deflection of the end of -the -....paddle
----- remote from the
point of jamming, then from equation (17):
X
l ·6(78)3
= -448 X _ _
______,_ __
9,
1r(4·5) 4 (13,500)
= 2·16 in:
Using the above calculated deflection of 2·16 in., the agitator can be.
drawn in its deflected position to show whether or not the paddle is
likely to foul the vessel wall or other fittings (see Fig. 16).
POINT OF JAMMING.
Fm.16.
Position of agitator at maximum deflection
VESSELB
In the case of a 10-in. gear, the wheelshaft bearing span is
ll ·375 in.
Assume in this example that the subsidiary bearing can be accommodated 15 in. below the bottom gear bearing.
Using the previous notation:
a = ll ·375 in.
b = 15 in.
C = 63 in.
(a+b) = 26·375 in.
F = l ·47 tons.
Then from eqs. (21), (22} and (24:), respectively:
1·47x63xl5
R1 - - - - - - - - = 2·32 tons
2 X 11·375
f
X
26·375'
R2
-
1·47x63)-( 1·47x63) =
----(- -15- 2x11·375
R3
-
l ·4 7 X 63) ( l ·4 7 X 63 )
1·47+ ( - - - + - - - - = 9·39tons
15
.2 X 26·375
-
10·24 tons
•
\
\
80
AGITATOR SELECTION AND DESIGN
Equivalent continuous loads ..... ~:
10·24
On bottom gear bearing, - - = 4· l ton
2·5
On subsidiary bearing,
9·39
2·5
- 3·75 ton
· Max. bending moment at
bottom gear bearing
- 2·32 x 11·375 = 26·4ton in.
·•
Max. bending moment at
subsidiary bearing
- 1·47 x 63
= 92·5 ton in.
The shaft diameter has now to be recalculated on the basis of a
maximum bending moment of 92·5 ton in. instead of 115 ton in. as
previously, combined with a maximum torque of 26·4 ton in. The
calculation proceeds exactly as before and gives 2dt = 3 ·96 in.
:. d = 4 in.
26·4
Continuous bending moment at bottom gear bearing= - - = 10· 5 ton in.
2½
Load on bottom bearing = 4 · l ton.
Both these are well within the maximum permissible values for a
10-in. gear. The thrust loads are also satisfactory.
A suitable subsidiary bearing to take a continuous journal load
of 3·75 tons can be selected from any of the manufacturer's tables.
The calculations for paddle design, critical speed and deflection are
similar to those shown for Vessel A.
i•
APPENDIX E-A NOTE ON SOURCES OF INFORMATION, WITH SOME LITERATURE REFERENCES
In compiling a Handbook of this nature, the data used must necessarily be drawn from a large number of sources, and a given item of
information cannot always be allocated to a single source. For example,
in many cases the available technical literature suggests only how a
particular problem may be tackled, so that practical experience has
to be applied in an attempt to solve it.
It is considered however that comments on the principal sources of
information consulted will enable adequate technical criticism of the
Handbook to be raised, and that without such comments further
investigation on specific aspects of agitating problems will be hampered.
A list of the literature references found useful (many of which are
referred to in the text) is therefore included at the end of this Appendix,
which also includes a short guide to the references cited as well as a
section indicating how the individual Sections of this Handbook have
been built up from the information and literature references available.
A few copies of a classified bibliography of some 400 papers published
up to 1953 is also available and may be borrowed on application to the
E.E.U.A. offices.
(a) BRIEF GUIDE TO THE REFERENCES CITED
Many papers in the available literature deal to some degree at least
with several subjects, and the classic work of Btiche (16) could logically
be placed under each of the following headings. Against each of these
headings are given the number(s) of the appropriate literature
reference(s) which deal in some manner with the suhject(s) covered by
the heading. Reference to these papers should be made for more
detailed information than may be given in the relevant Section of this
Handbook.
(i) Literature Surveys and Bibliographies (29, 71-74, 76-78,
80, 81 and 83)
Reference 29 reviews the subject up to 1945; the remainder are
annual surveys by J. H. Rushton, which are still being issued.
(ii) General Discussions (3, 4, 6, 16, 29, 64, 68, 82 and 86)
Useful generalisations will be found in (4, 16, 29, 64, 68 and 86);
algebraic errors invalidate some of the reasoning in (64). Emulsions
are covered by (6).
81
t
82
AGITATOR SELECTION AND DESIGN
(iii) Theory and Efficiency of Agitation (1, 7, 8, 11, 12, 22, 48,
57, 61, 62 and 86)
Mathematical definitions of agitation efficiency are given in ( 1 and
22); theory and data on mixing rate are the subjects of (43, 48 and
61).
Some useful ideas on fl.ow patterns are presented in (51, 62
and 84).
(iv) Practical Considerations and Applications (5, 14, ·1s, 28, 51,
52 and 62)
Suggestions for selecting impellers for specific applications are
given in (18, 28, 51 and 62). Practical hints for installation and operation are given in (5, 14 and 52); the last mentioned dealing only with
turbines.
(v) Scale-up (57, 75 and 79)
These three papers are useful but scarcely adequate; they discuss
the inherent difficulties, rather than usable methods of extrapolation.
(vi) Agitators in Series (9-12 and 58)
The classical paper by MacMullin and Weber (58) is rather long,
but presents a practical design method; chemical reactions in a
series of agitation vessels are also covered.
(vii) Power Consumption
From the wide range of papers-on this subject a selection has been
made Bond classified as follows:
General:
(15, 16, 28, 45, 47, 50, 60, 61, 68, 84 and 86).
Propellers: (87).
Paddles:
(89-94).
Turbines:
(20, 25, 33, 41, 55 and 61 ).
Baffles, etc.: (4 and 53).
The papers found most useful for assessment of power were (16,
47 and 84); it should be noted that parts of two columns have been
transposed in the main table of (84).
Useful summaries of several papers are given in (50, 60, 68 and 86).
(viii) Heat Transfer
General surveys of available data are presented in (49 and 68).
Heat transfer coefficients for jacketed vessels with agitators will be
found in (13, 19, 21 and 56); helical coils are dealt with in (13, 19,
21, 46, 66 and 69).
An unusual arrangement in which vertical tubes are used as baffles
at the tank wall is the subject of (23 and 85).
Heat transfer in the "Votator" is covered in (46).
~
I
!
'
I
-I
I
83
APPENDIX E
(ix) Suspension of Solids (89-94)
The group of six papers in the cfo,ssical work of A. McLaren White
and his collaborators. More recent papers indicate that the power
consumptions recorded are rather high; probably due to the use of
rough wooden tanks.
(x) Solution and Crystallisation (30-32, 34-38, 40, 44, 54 and
56)
The majority of these papers is the work of A. W. Hixson and
various co-workers, who measured power requirements and mass
transfer rates, mainly for the dissolution of tablets of organic acid in
dilute alkaline solutions.
(xi) Miscellaneous
I. Gas dispersion (20, 25, 39 and 55). This is a small selection from
the rather wide range of literature on the subject.
·
2. Liquid-liquid extraction (42 and 67).
3. Mixing with liquid jets (24}.
4. Mixing with air-lifts (27).
(b) DERIVATION OF INDIVIDUAL SECTIONS OF
THIS
HANDBOOK
The following notes briefly indicate the sources of information which
have been used to prepare the various Sections of this Handbook. As
before, the figures in parentheses refer to the literature references given
at the end of this Appendix.
Section Two
Papers (4, 16, 51, 53 and 68} are referred to in the text; other data
are available in (32, 48, 61 and 62).
The more important points raised (e.g. vessel shape) represent
general practice; those factors (such as bottom clearance) regarding
which opinions differ are less critical to the operation.
Section Three (a)
The subject matter covered in this sub-section is treated in a
number of references. Suggested papers for general considerations
are the reviews of mixing literature now published annually in
Ind. and Eng. Chem. (29, 71-74, 76-78, 80, 81 and 83), and the
appropriate sections of (16, _64 and 68).
Section Three (b)
This Section suggests a way of regarding the problem which is
implicit in much experimental work (e.g. 29-44 and 82).
A similar approach is given in (52). That particular paper, however, is aimed at emphasising the versatility of the turbine or multiblade paddle, rather than specifying the best impeller for a particular application.
84
AGITATOR SELECTION AND DESIGN
Section Three (c)
The initial assumption that geometrical similarity and changes in
speed represent a basis for scaling-up seems to be generally accepted
by a number of authorities (e.g. Biiche, Hixson and Rushton).
There is no published information which fully proves or disproves
this assumption.
·
Section Three (d)
The tables in this section are based on n1embers' experience, and
the published descriptions of impellers used for particular operations.
Section Four
This section is based entirely on current practice.
Section Five (b) (i)
The power tables given in this section were calculated as follows:
A. Paddles: the data and methods of Biiche (16, 47) were used
where applicable. As the range of conditions considered was
much wider than that of the original, various assumptions were
required:
(1) For unbaffled conditions Biiche's power factor c was
assumed to vary smoothly over the range given in ( 16);
at higher viscosities c was taken as proportional to viscosity
(cf. 68 and 84); at lower viscosities c was assumed constant
(16, 47, 68 and 84).
(2) Under baffled conditions a factor was applied to the above
figures (4 7).
B. The tables for turbines were calculated directly from the data
-- -- L - Vl.
-C D,rnh~A.,,..
,,f r,] {!;Lj_ \
ana IrU.llllUli:;1,ti
J._\,UDHliV.LJ.,
wv. , ~ ~ , .
c. The tables for anchor agitators (detailed in Section Five (c))
were calculated from (16), with modifications and extensions as
indicated by the operating experiences of member firms (e.g.
( 16) does not deal with highly viscous liquids).
The methods of taking means for two-phase liquids will be
found in (68).
l
C,1/
Section Five (b) (ii)
Most of the allowances for baffles and vessel fittings given were
taken from Biiche (16); further information is available in (4, 53
and 84).
Section Five (b) (iii)
Much of the data given on transmission and gland losses is based
on conventional practice and is verified by member firms' experience.
Section Five (c)
See remarks under Section Five (b) (i) above.
!
!
APPENDIX E
85
Section Five (a) and (b)
The information in these Sections represents the common e,xperience of those who have to design mechanical devices in exotic
materials.
Section Five (c)
The design procedure set out in this Section is based on "a method
which has been found successful in practice", and outlines common
engineering experience and its application to impeller shafts in
particular.
Section Six (d} and (e)
The information and recommendations given are based on n1ember firms' experience and standard engineering practice.
Appendix A
A British Standard on process vessels is in course of preparation,
but has not yet been issued. Accordingly, the tank diameters chosen
have been taken from the Draft Standard {98), but may require
subsequent revision. The tank shapes, etc., found most economical
for mixing are not given in (98), and dimensions based on common
experience have therefore been taken.
The dimensions of other plant referred to represent current practice.
Appendix B
This assessment of the power lost in stuffing boxes is theoretical;
(59) is the appropriate reference.
i
ll
I
I
I
Appendix 0
Eight references relating to heat transfer are given in the text.
Further information is given on jackets (68), vertical pipes (85), and
the "Votator" (46); great reliance is not placed in the general
methods given in (56). The accuracy of the methods of Chilton, et al.
(19) on the large scale has been proved by at least one member
firm.
The validity of results where the heat transfer was measured
overall, and the liquor side calculated by estimating the coefficient
for the heating or cooling medium from standard formulae, is considered doubtful; calculation methods for heat transfer in curved
pipes are known to be unreliable. Those papers in which wall temperatures were actually measured by thermocouples buried in the
metal are believed to be more reliable.
Appendix D
The design calculations given in this Appendix are straightforward
engineering calculations based on {63 and 68), and are sufficiently
elaborated to bring out all the points which experience has shown it
necessary to consider. The choice of the maximum elastic strain
energy theorem as the basis of combining the stresses is debatable;
86
AGITATOR SELECTION AND DESIGN
it is, however, generally accepted as one of the more suitable of the
available formulae for handling combined stresses of this type.
Stress values similar to those given in the tables of suggested permitted stress have been found reliable under a wide range of conditions
FOR IMPELLER SHAFTS DESIGNED BY THIS METHOD OF
CALCULATION. Obviously, if impeller shafts were to be designed
to withstand design stresses of the magnitude commonly used
when considering alternating loads, a method of calculation with
a much lower inherent factor of safety would need to be used.
(c) SOME LITERATURE REFERENCES
Beaudry, J. P. Ohem. Eng., 1948, 55, (7), II2-3.
Bevan, T. "Theory of Machines," Longmans Green & Co. Ltd., 1950.
Bissell, E. S. Ind. Eng. Ohem., 1944, 36, 497-8.
Bissell, E. S., Hesse, H. C., Everett, H.J. and Rushton, J. H. Ohem. Eng. Progress,
1947,43, 649-58.
.
5. Boutros, R. D. Ohem. Eng. Progress, 1952, 48, 2ll -9.
6. Brothman, A. Ohem. Met. Eng., 1939, 46, 263-5.
7. Brothman, A., and Kaplan, H. Ohem. Met. Eng., 1939, 46, 633-6.
8. Brothman, A., and Kaplan, H. Natl. Paint Bull., 1939, (Oct.), 3, 18-21.
9. Brothman, A., Weber, A. P., and Barish, E. Z. Ohem. Met. Eng., 1943, 50, (7),
111-4.
10. Brothman, A., Weber, A. P., and Barish, E. Z. Ohem. Met. Eng., 1943, 50, (8),
107-10 and (9), II3-6.
II. Brothman, A., Wollan, G. N., and Feldman, S. M. Ohem. Met. Eng., 1945, 52, (4),
102-6.
12. Brothman, A., Wollan, G. N., and Feldman, S. M. Ohem. Met. Eng., 1945, 52,( 5),
126-31.
13. Brown, R. W., Scott, R., and Toyne, C. Trans. Inst. Ohem. Engs., 1947, 25, 181-8.
14. Brumagin, I. S. Ohem. Met Eng., 1946, 53, (4), II0-4.
15. Btiche, W. Z. Ver. deut. Ing. (V.D.I.), 1937, 81, (37), 1065-9.
16. Btiche, W. I.G., Ludwigshafen Report "Agitation Research Review of Existing
Information." Board of Trade Microfilm B.I.O.S./D.O.C.S./2714/2466.
17. Case, J. "The Strength of Materials," London; Edward Arnold & Co., 2nd ed. 1932,
p. 226.
18. Chaddock, R. E. Ohem. Eng., 1946, 55, (II), 151-3.
19. Chilton, T. H., Drew, F. B. and Jebens, R.H. Ind. Eng. Ohem. 1944, 36, 510-6.
20. Cooper, C. M., Fernstrom, G. A., and Miller, S. A. Ind. Eng. Ohem., 1944, 36, 504-9.
21. Cummings, G. H., and West, A. S. Ind. Eng. Ohem., 1950, 42, 2303-13.
22. Danckwerts, P. V. Chem. Eng. Sci., 1953, 2, 1-13.
23. Dunlap, I. R., and Rushton, J. H. Ohem. Eng. Progress Symposium Series No. 5,
1953, 49, 137-51.
24. Fossett, H., and Prosser, L. E. J. Inst. Mech. Eng., 1949, 160, (2), 224,240 and 245.
25. Foust, H. C., Mack, D. E., and Rushton, J. H. Ind. Eng. Ohem., 1944, 36, 517-22.
26. Hartog, J. P. DEN. "Mechanical Vibrations," 3rd ed. 1947.
27. Heiser, H. W. Ohem. Eng., 1948, 55, (1), 135.
28. Helmbold, P.A. Ohim. et Ind., 1950, 64, 147-59.
29. Hixson, A. W. Ind. Eng. Ohem., 1944, 36, 488-96.
30. Hixson, A. W., and Baum, S. J. Ind. Eng. Ohem., 1941, 33, 478-85.
31. Hixson, A. W., and Baum, S. J. Ind. Eng. Chem., 1941, 33, 1433-9.
32. Hixson, A. W., and Baum, S. J. Ind. Eng. Ohem., 1942, 34, 120-5.
33. Hixson, A. W., and Baum, S. J. Ind. Eng. Chem., 1942, 34, 194-208.
34. Hixson, A. W., and Baum, S. J. Ind. Eng. Ohem., 1944, 36, 528-31.
35. Hixson, A. W., and Crowell, J. H. Ind. Eng. Ohem., 1931, 23, 923-31.
36. Hixson, A. W., and Crowell, J. H. Ind. Eng. Ohem., 1931, 23, 1003-9.
37. Hixson, A. W., and Crowell, J. H. Ind. Eng. Ohem., 1931, 23, II60-9.
38. Hixson, A. W., Drew, T. B., and Knox, K. L. Chem. Eng. Progress, 1954, 50,
592-6.
I.
2.
3.
4.
APPENDIX E
87
Hixson, A. W., and Gaden, E. L. Ind. Eng. Chem., 1950, 42, 1792-1801.
Hixson, A. W., and Knox, K. L. Ind. Eng. Chem., 1951, 43, 2144-51.
Hixson, A. W., and Luedeke, V. D. Ind. Eng. Chem., 1937, 29, 927-33.
Hixson, A. W., and Smith, M. I. Ind. Eng. Chem., 1949, 41, 973-8.
Hixson, A. W., and Tenney, A.H. Trans. Am. Inst. Chem. Engs., 1935, 31, 113-27.
Hixson, A. W., and Wilkens, G. A. Ind. Eng. Chem., 1933, 25, 1196-1203.
Hooker, T. Chem. Eng. Progress, 1948, 44, 833.
Houlton, H. G. Ind. Eng. Chem., 1944, 36, 522-8.
Imperial Chemical Industries Ltd. Memo. on Ref. 16; circulated to E.E.U.A.,
Panel P(M)/16 in Dec. 1953.
48. Kramers, H., Baars, G. M., and Knoll, W. H. Chem. Eng. Sci., 1953, 2, 35-42.
49. Kraussold, H. Chem. Ing. Tech., 1951, 23, 177-83.
50. Krevelen, D. W. van, and Huiskamp, J. Ingenieur, 1949, 61, Ch. 6-12 and 15-22.
51. Lyons, E. J. Chem. Eng. Progress, 1948, 44, 341-6.
52. Lyons, E. J., and Parker, N. H. Chem. Eng. Progress, 1954, 50, 629-32.
53. Mack, D. E., and Kroll, A. E. Chem. Eng. Progress, 1948, 44, 189-93.
54. Mack, D. E., and Marriner, R. E. Chem. Eng. Progress, 1949, 45, 545-52.
55. Mack, D. E., and Uhl, V. W. Chem. Eng., 1947, 54, (9), 119-21.
56. Mack, D. E., and Ubl, V. W. Chem. Eng., 1947, 54, (10), 115-6.
57. MacLean, G., and Lyons, E. J. Ind. Eng. Chem., 1938, 30, 489-92.
58. MacMullin, R. B., and Weber, M. Trans. Am. Inst. Chem. Eng., 1935, 31, 409-58.
59. Marks L. S. (ed.). "Mechanical Engineers' Handbook," London; McGraw-Hill
Book Co., 4th ed. 1941.
60. Martin, J. J. Trans. Am. Inst. Chem. Eng., 1946, 42, 777-81.
61. Miller, S. A., and Mann, C. A. Trans. Am. Inst. Chem. Eng., 1944, 40, 709-45.
62. Miller, F. D., and Rushton, J. H. Ind. Eng. Chem., 1944, 36, 499-503.
63. Morley, A. "Strength of Materials," London; Longmans, Green & Co., 9th ed. 1940,
p. 330.
64. Newitt, D. H., Shipp, G. C., and Black, C. R. Trans. Inst. Chem. Eng., 1951, 29,
278-89.
65. Olney, R. B., and Carlson, G. J. Chem. Eng. Progress, 1947, 43, 473-80.
66. Oldshue, J. Y., and Gratton, A. T. Chem. Eng. Progress, 1954, 50, 615-21.
67. Oldshue, J. Y., and Rushton, J. H. Chem. Eng. Progress, 1952, 48, 297-306.
68. Perry, J. H. (ed.). "Chemical Engineers' Handbook," London; McGraw-Hill
Book Co., 3rd ed. 1950.
69. Pratt, N. H. Trans. Inst. Chem. Engs., 1947; 25, 163-80.
70. Prescott, J. "Applied Elasticity."
71. Rushton, J. H. Ind. Eng. Chem., 1946, 38, 12-13.
72. Rushton, J. H. Ind. Eng. Chem., 1947, 39, 30-1.
73. Rushton, J. H. Ind. Eng. Chem., 1948, 40, 49-50.
74. Rushton, J. H. Ind. Eng. Chem., 1949, 41, 61-4.
75. Rushton, J. H. Proc. Natl. Conj. Ind. Hydraulics, Illinois, 1949, p. 119.
76. Rushton, J. H. Ind. Eng. Chem. 1950, 42, 74-6.
77. Rushton, J. H. Ind. Eng. Chem., 1951, 43, 111-4.
78. Rushton, J. H. Ind. Eng. Chem., 1952, 44, 88-91.
79. Rushton, J. H. Chem. Eng. Progress, 1952, 48, 33-8 and 95-102.
80. Rushton, J. H. Ind. Eng. Chem., 1953, 45, 93-5.
81. Rushton, J. H. Ind. Eng. Chem., 1954, 46, 133-7.
82. Rushton, J. H. Chem. Eng. Progress, 1954, 50, 587-9.
83. Rushton, J. H. Ind. Eng. Chem., 1955, 47, 582-5.
84. Rushton, J. H., Costich, E. W., and Everett, H. J. Chem. Eng. Progress, 1950,
46, 395-404 and 467-76.
85. Rushton, J. H., Lichtmann, R. S., and Mahoney, L. H. Ind. Eng. Chem., 1948, 40,
1082-7.
86. Rushton, J. H., and Oldshue, J. Y. Chem. Eng. Progress, 1953, 49, 161-8 and
267-75.
87. Stoops, C. E., and Lovell, C. L. Ind. Eng. Chem., 1943, 35, 845-50.
88. Valentine, K. S., and MacLean, G. (See 68.)
89. White, A. McL., and Brenner, E. Trans. Am. Inst. Chem. Eng. 1934, 30, 585-96.
90. White, A. McL., Brenner, E., Phillips, G. A., and Morrison, M. S. Trans. Am. Inst.
Chem. Eng., 1934, 30, 570-84.
91. White, A. McL., and Sumerford, S. D. Ind. Eng. Chem., 1933, 25, 1025-7.
39.
40.
41.
42.
43.
44.
45.
46.
47.
88
AGITATOR SELECTION AND DESIGN
92. White, A. McL., and Sumerford, S. D. Ind. Eng. Chem., 1934, 26, 82-3.
93. White, A. McL., and Sumerford, S. D. Chem. Met. Eng., 1936, 43, 370-1.
94. White, A. McL., Sumerford, S. D., Bryant, E. 0., and Lukens, B. E. Ind. Eng.
Chem., 1932, 24, 1160-2.
95. B.S. 1916, Limits and fits for engineering.
96. B.S. 970: 1947, Wrought steels for use up to 6-in. ruling section for automobile
and general engineering purposes.
97. B.S. 1452: 1948, Grey iron castings.
98. Draft B.S., for Sizes of Process Vessels, issued to industry for comment in 1950 as
CM(CHE)2961; under discussion (1962) as D62/1488 in B.S.l Committee CHE/8.
99. B.S. 229, Flameproof enclosure of electrical apparatus.
100. B.S. 2048, Dimensions of fractional horse power motors.
* 101. B.S. 2083, Dimensions of 3-phase electric motors totally-enclosed fan-cooled.
102. B.S. 2613, The electrical performances of rotating electrical machinery.
* 103. B.S. 2960, Dimensions of 3-phase electric motors (Parts 1 and 2).
* B.S. 2083 may lapse and be superseded by B.S. 2960 as from 1960.
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