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Changes shown by ➧

CONTENTS
Section Page

SCOPE ............................................................................................................................................................3

REFERENCES.................................................................................................................................................3

BACKGROUND...............................................................................................................................................4

DEFINITIONS ..................................................................................................................................................4

EQUIPMENT TYPES AND APPLICATIONS...................................................................................................6

MECHANICAL AGITATORS ...................................................................................................................6
INLINE MOTIONLESS MIXERS..............................................................................................................6
TANK JET MIXERS.................................................................................................................................6

BASIC DESIGN CONSIDERATIONS..............................................................................................................6

(1) MECHANICAL AGITATORS ..............................................................................................................6
TANK GEOMETRY .................................................................................................................................6
PUMPING, VELOCITY HEAD AND POWER ..........................................................................................7
NON-NEWTONIAN FLUIDS....................................................................................................................8
STANDARD DRIVER SIZES ...................................................................................................................8
INVESTMENT AND OPERATING CONSIDERATIONS..........................................................................8
SCALING-UP FROM LABORATORY AND PILOT PLANT STUDIES.....................................................8
(2) IN-LINE MOTIONLESS MIXERS .......................................................................................................8
(3) JET MIXERS ......................................................................................................................................9

DESIGN PROCEDURE ...................................................................................................................................9

MECHANICAL AGITATORS ...................................................................................................................9
IN-LINE MOTIONLESS AND TANK JET MIXERS ................................................................................11

SAMPLE PROBLEMS...................................................................................................................................11

NOMENCLATURE.........................................................................................................................................14

TABLES
Table 1 Selection Guide For Mixing Equipment..........................................................................15
Table 2 Agma Gear Drive Standard Output Speeds...................................................................16
Table 3 Standard Power Ratings Of Induction Motors In HP ......................................................16
Table 4 Quick Guide For Size Estimation Of Pitched Blade Turbine ..........................................17
Table 5 Np And Nq Values at High NRe For Some Hydrofoil Impellers........................................17

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CONTENTS (Cont)
Section Page

FIGURES
Figure 1 Standard Tank Geometry And Nomenclature................................................................18
Figure 2 Common Impeller Types................................................................................................19
Figure 3A Axial Flow Pattern In Baffled Tank With A Pitched Blade Turbine .................................20
Figure 3B Radial Flow Pattern In Baffled Tank With A Flat Blade Turbine.....................................20
Figure 4 Vendor Proprietary Static Mixers ...................................................................................21
Figure 5 Jet Nozzle For Tank Mixing ...........................................................................................22
Figure 6 Liquid Jet Eductor..........................................................................................................22
Figure 7 Flow Patterns In Unbaffled Tank With A Side Entering Propeller ..................................23
Figure 8 Pumping Number For 45° Pitched Blade Turbine Vs. Impeller Reynolds Number ........24
Figure 9 Correlations For Mixing Power Number Vs. Reynolds Number .....................................25
Figure 10 Power Number Correlations For Propellers ...................................................................26
Figure 11 Effect Of Dual Impeller Spacing On Power Number ......................................................26
Figure 12 Dual Propeller Power Effect...........................................................................................27
Figure 13 Effect Of Baffling And D/T On Power Number ...............................................................28
Figure 14 Effect Of Gas Addition On Power ..................................................................................28
Figure 15 Scale-Up By Power Per Unit Volume ............................................................................29

Revision Memo
12/01 Minor changes in the text and definitions.

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SCOPE
Described in this subsection are fundamental mixing concepts and various types of equipment commonly used for carrying out
mixing operations. Emphasis is placed on mechanical agitators since these have the broadest range of applications. Also
included, however, are descriptions of jet, pump, eductor, orifice, and proprietary inline mixing devices. Suitability of these
devices for specific mixing duties is also discussed where possible.
Specifying a mixing device is a two-stage process. Mixing needs of the application first have to be quantified and then these
needs have to be translated to an equipment design. Included in this base subsection is the translation from mixing need to
specified equipment design. General scale-up principles for mechanical agitators are described. The following Sections XIII-B
through XIII-E cover how to quantify the mixing need for blending of miscible liquids, dispersion of gas in liquid, emulsification of
immiscible liquids, suspension of sinking and floating solids. Heat transfer in agitated vessels is covered in Section XIII-F.

REFERENCES
DESIGN PRACTICES
Section X Pumps
Section XI-L Compressors (Electric Motors)
Section XIV Fluid Flow, Perforated Distributor Design

OFFSITES DESIGN PRACTICES

Section XXII Tank Mixing Guidelines
Section XXIV Blending Facilities

GLOBAL PRACTICES
GP 10-9-1 Mechanical Agitators
GP 10-11-1 Sizing of Drivers and Transmissions

OTHER REFERENCES
Handbook of Mixing Technology by Ekato Ruhr-und Mischtechnic GmbH. 1991.
Harnby, N., Edwards, M. F., and Nienow, A. W., Mixing in the Process Industries, Butterworths, 1985.
Harnby, N., Fluid Mixing III, Chem E Symp. Series No. 108, Hemisphere Pub, 1988.
Holland, F. A. and Chapman, F. S., Liquid Mixing and Processing in Stirred Tanks, Reinhold, 1966.
Nagata, S., Mixing Principles and Applications, John Wiley, 1975.
Oldshue, J. Y., Fluid Mixing Technology, McGraw-Hill, NY, 1983.
Hemrajani, R. R., Mixing and Blending, ECT 4th ed., Vol. 16, pp. 844 - 887.
Sterbacek, Z. and Tausk, P., translated by K. Mayer, Mixing in the Chemical Industry, Pergamon Press, NY, 1965.
Tatterson, G. B., Fluid Mixing and Gas Dispersion in Agitated Tanks, McGraw-Hill, 1991.
Uhl, V. W. and Gray, J. B. Mixing-Theory and Practice, Vols. I & II, Academic Press, 1966-7, V. W. Uhl and J. A. VonEssen,
Vol. III, 1986.
Ulbrecht, J. J. and Patterson, G. K., Mixing of Liquids by Mechanical Agitation, Gordon & Breach Sci. Pub., NY, 1985.

GENERAL CONCEPTS
Corpstein, R. R., Dove, R. A. and Dickey, D. S., CEP, 75 (2), 66 (1979).
Dickey, D. S., CEP, 87 (12), 22 (1991).
Dickey, D. S. and Hemrajani, R. R., Chem. Eng., 99 (3), 82 (1992).
Joshi, J. B., Pandit, A. B. and Sharma, M. M., CES, 37 (6), 813 (1982).
Kawase, Y. and Moo-Young, M., the Chem. Eng. J. 43, B19 (1990).
Leng, D. E., CEP, 87 (6), 23 (1991).
Norwood, K. W. and Metzner, A. B., AIChE J. 6 (3), 432 (1960).
Rushton, J. H., Costich, E. W. and Everett, H. J., CEP, 46 (8), 395 (1950).
Tatterson, G. B., Brodkey, R. S. and Calabrese, R. V., CEP, 87 (6), 45 (1991).
Uhl, V. W., Chemical Processing, 47 (July), 26 (1984).

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BACKGROUND
Fluid mixing is one of the most important basic operations of process technology. It is carried out to homogenize fluids in terms
of concentration of components, physical properties and temperature; and create dispersions of mutually insoluble phases. It is
frequently encountered in the process industry using various physical operations and mass transfer/reaction systems. The
fundamental mechanism involves physical movement of material between various parts of the whole mass. This is achieved by
transmitting mechanical energy to force the fluid motion.
Mixing systems are broadly divided into single-phase systems involving miscible liquids; and multi-phase systems such as
solid-liquid, mutually insoluble liquids, and gas-liquid. These mixing systems offer high flexibility because they can be operated
in batch, semi-batch or continuous modes. Adequate mixing is a pre-requisite for the success of chemical processes in terms
of minimizing investment and operating costs. In addition, chemical reactions with mass transfer limitation can be enhanced to
provide high yields.
The desired mixing in a commercial process is achieved with different types of equipment, e.g., agitators, jets, static mixers,
etc. The design approach requires defining process mixing requirements, selecting suitable mixer type, sizing the mixer,
specifying tank internals such as baffles, and designing mechanical components such as shaft and drive assembly.

DEFINITIONS

Agitator
A general term used to describe a device which imparts motion to a fluid. Agitator is commonly used as a synonym for the
more specific term impeller.

Baffle
Generally a flat plate attached to and perpendicular to the wall of a mixing vessel to alter the fluid circulation pattern and
prevent excessive swirl of the fluid in the vessel.

Critical speed
The mixer shaft speed which matches the first lateral natural frequency of the shaft and impeller system. Excessive vibrations
and shaft deflections can occur at this speed.

Driver
The motor and gearbox combination used to rotate the agitator shaft.

Draft tube
A centrally located open-ended tube in a mixing vessel which confines the impeller discharge or suction to produce a vertical
flow in the vessel.

Geometric similarity
The sizing of the components of a mixing system in such a way that the ratio of linear dimensions of the components (impeller
diameter, vessel diameter, vessel height, etc.) remains the same for differing overall system sizes.

Impeller
A physical device which rotates to impart motion to a fluid. Examples are turbines and propellers.

Impeller Reynolds number

A dimensionless number used to characterize the flow regime of a mixing system and which is given in any consistent units by:
60 ρ N D2 ρ N D2
NRe = Customary NRe = Metric
µ µ

where: ρ = fluid density, lb/ft3 (kg/m3)

N = impeller rotational speed, rpm (rps)
D = impeller diameter, ft (m)
µ = fluid viscosity, lb/ft hr (kg/ms)
➧ The flow is normally laminar for NRe < 10, turbulent for NRe > 104, and transitional in between.

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DEFINITIONS (Cont)

Jet
A fluid stream having a velocity greater than the surrounding fluid which discharged from a nozzle or impeller.

Mixer
➧ A device for carrying out a mixing operation and which generally inclusively refers to an impeller, shaft, driver, baffles, and
vessel combination.

Power number
A dimensionless number used to describe the power dissipation of an impeller and which with any consistent units is given by:
Np = P / 2.62 x 10 −10 ρ N3 D5 Customary Np = 1000 P / ρ N3 D5 Metric

where: P = impeller power dissipation HP (kW)

Propeller pitch
Pitch is the advance of the fluid per revolution on the basis that a propeller is a segment of a screw. Normally “square" pitch is
used; i.e., a pitch value equal to the propeller diameter.

Pumping capacity
The amount of discharge flow from an impeller. It is frequently correlated on the basis of the dimensionless impeller pumping
number Nq = Q/ND3, where Q = volumetric discharge rate.

Side entering
Describes a mixer design which has a horizontal shaft entering through the side of a mixing vessel.

Solidity ratio
Ratio of projected blade area to the area swept by the impeller.

Standard geometry
Describes a vessel and mixer design based on a fluid depth equal to vessel diameter and a top-entering impeller having a
diameter equal to 1/3 of vessel diameter and located with a clearance of 1/3 of vessel diameter above the bottom of the vessel.

Steady bearing
A bearing located at the bottom of the shaft of a top entering impeller to minimize shaft deflection and vibration. It is immersed
in the fluid being mixed.

Tip speed

The peripheral speed of an impeller tip which is equal to π ND.

Top entering
Describes a mixer design which has a vertical shaft entering through the top of a mixing vessel.

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EQUIPMENT TYPES AND APPLICATIONS

The commonly used types of mixing equipment can be placed in the broad categories: (1) mechanical agitators, (2) inline
motionless mixers, and (3) tank jet mixers. The nature and type of agitator used depends upon the scale and type of mixing
and upon the fluids being mixed. Table 1 provides a general basis for selection of impeller type and other mixing equipment.

MECHANICAL AGITATORS
➧ Agitated tanks are equipped with a single or multiple impellers attached to a shaft which is rotated by a motor/gear box drive. A
standard geometry of a top entering agitated tank is shown in Figure 1. There are literally hundreds of impeller types in
commercial use, only the most common and general types are shown in Figure 2. Their classification is based on shear level
and flow patterns. Turbines provide high shear levels while close-clearance impellers (Figure 2D) such as anchors and helical
ribbons produce low shear. Turbines are further classified based on flow direction as axial flow (Figure 2A) and radial flow
(Figure 2B) impellers. Recent developments in the impeller technology have been focused on increasing axial flow at reduced
shear. These impellers use hydrofoil profile of blades for efficient and more streamlined pumping (Figure 2C). Turbine
impellers have the widest use in low and medium viscosity liquid applications, solids suspension, liquid dispersion, and gas-
liquid contacting.
The oldest axial flow impeller design is the marine propeller which is used as a side-entering mixer in large tanks and top
entering in small tanks. Top-entering mixers also use pitched blade turbine (PBT) for axial flow (Figure 3B) and disk flat blade
turbine (FBT) for radial flow (Figure 3A). Some hydrofoil impellers, such as Lightnin A315 and Prochem Maxflo, are designed
with high solidity ratio for gas dispersion and blending of non-Newtonian liquids. Radial flow impellers provide higher shear and
lower discharge flow compared to axial flow impellers. DFBT and Chemineer CD6 impellers are efficient for gas dispersion
applications.

INLINE MOTIONLESS MIXERS

Inline motionless mixers derive the fluid motion or energy dissipation needed for mixing from the flowing fluid itself. These
mixers include:
Orifice Mixing Column - An orifice-mixing column consists of a series of orifice plates contained in a pipe. The pipe normally
is fabricated of two vertical legs connected by a return bend at the bottom with the orifice plates installed between flanges in the
vertical legs. Typical use is for cocurrent contacting in caustic and water washing operations. It is generally designed at mixing
energy of 1100 to 4400 ft-lbs/ft3 (50 to 200 kJ/m3) and contact times of 10 to 50 seconds. Typical pressure drop per orifice is in
the range of 1 to 3 psi (7 to 20 kPa).
Mixing Valve - This type of mixing device is normally a manually operated globe valve operated at 3 to 50 psi (20 to 340 kPa)
pressure drop. Common use is for water and crude oil mixing before a desalter and in caustic scrubbing operations.
Static Mixers - These motionless mixers consist of repeated structures called mixing elements attached inside a pipe. These
mixing elements alternately divide and recombine fluids passing through. As a result, they create shearing action at a cost of
pressure drop. Static mixers provide complete transverse uniformity and minimize longitudinal mixing, therefore, their
performance approaches perfect plug flow conditions. There are many proprietary designs marketed, but only a few are shown
in Figure 4. These mixers are used for continuous in-line blending and for cocurrent contacting operations.

TANK JET MIXERS

As an alternate to mechanical agitators, storage and blending tanks can be agitated by jet mixers. Jet mixers can be used for
continuously blending miscible liquids as they enter a tank or batchwise by recirculating a portion of the tank contents through
the jet. They are commonly used to prevent stratification in product and intermediate tankage.
The jet mixer is a streamlined nozzle installed in the side of a tank near the bottom. It points diametrically across the tank and
discharges at an angle above the horizontal. A typical jet nozzle design is shown in Figure 5. A jet eductor, shown in
Figure 6, is sometimes used for higher entrainment of the surrounding liquid.

BASIC DESIGN CONSIDERATIONS

(1) MECHANICAL AGITATORS

TANK GEOMETRY
For large (> 30 ft or 9 m diameter) storage and blending tanks, a side entering propeller agitator is normally used. The agitator
shaft is set at an angle to a tank diameter as shown in Figure 7. No tank baffles are used. For very large (> 120 ft or 36 m
diameter) storage tanks having high mixing power requirements, multiple mixers can be used. Details concerning mixer design
for miscible liquid blending are given in Section XIII-B.

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BASIC DESIGN CONSIDERATIONS (Cont)

➧ Most mechanically agitated mixing operations normally use vertical mixer shafts in vessels equipped with wall baffles. Unless
process requirements dictate otherwise, “standard" tank geometry illustrated in Figure 1 is used. Standard geometry utilizes
only one impeller on the mixer shaft. If an application such as gas absorption requires that the fluid depth, Z, be greater than
1.2 times tank diameter, T, an additional impeller spaced at least an agitator diameter, D, above the standard bottom agitator
should be used. Standard geometry normally implies a top-entering shaft. However, from a flow pattern and power dissipation
standpoint, a bottom-entering shaft is equivalent. If shaft seal problems are handleable, bottom entry can reduce the required
shaft length in vessels which are designed with tall vapor spaces for foam disengagement, etc.

PUMPING, VELOCITY HEAD AND POWER

Mechanical mixers can be compared with pumps because they produce circulating capacity Q and velocity head H. Q in a
mixing tank represents internal recirculation and can be calculated by:
Q = Nq N D 3 Eq. (1)

where: Q = pumping rate, ft3/min (m3/s)

Nq = pumping number, dimensionless - depends on impeller type and NRe
N = impeller rotational speed, rpm (rps)
D = impeller diameter, ft (m)
The velocity head H from kinetic energy generates shear through the pulsating motion of the fluid and is proportional to square
of impeller tip speed (ND).
H α (N D)2

The power consumed by a mixer can be obtained by multiplying Q and H and is given by
P = 2.62 x 10 −10 x N p ρ N 3 D 5 P = N p ρ N 3 D 5 / 1000 Eq. (2)

where: P = mixer power, HP (kW)

Np = power number, dimensionless - depends on impeller type and NRe
➧ Figure 8 shows the relationship between Nq and NRe for a 45 pitched blade turbine (PBT) with various impeller to tank diameter
ratios. For propellers operating at NRe > 3000, Nq can be assumed to be 0.5. Figure 9 shows relationship between Np and
NRe for seven commonly used impellers. Similar plots for propellers with different pitch are given in Figure 10.
Values of the Np and Nq under turbulent flow conditions for some of the hydrofoil impellers are given in Table 5.
The power numbers given in Figures 9 and 10 apply to the impeller types indicated and specifically when these impellers are
employed in a tank of standard geometry which includes wall baffles (except Curve 7 of Figure 9 specifically applies for the
finger baffles shown). For side-entering propeller agitators which are offset from or set at an angle to a tank diameter, Figure
10 is still applicable. For mixing liquids having viscosities greater than 5000 centipoises, baffles can also be eliminated in other
vessels without altering the power number relationship.
Impeller power dissipation can be estimated for a number of departures from the standard geometries. For turbine blade
width / diameter ratios other than shown in Figure 9, power number can be calculated as being proportional to this ratio. For
installations having multiple impellers on the same shaft, the power dissipation is a function of impeller spacing as shown in
Figure 11 for turbines and Figure 12 for propellers. Changes in baffle width from the standard T/12 to T/10 affect power
number as shown in Figure 13. The sparging of a gas into a mixing vessel reduces power dissipation as indicated in Figure
14. Figures 11 through 14 give the ratio of power number for the non-standard geometry (or gas sparging situation) to the
power number for standard geometry (or no gas flow). Thus, the power number for the non-standard situation is the product of
the appropriate standard value times the ratios from the figures.
➧ The power rating of the driver for the impeller has to exceed the power dissipation to the fluid because of driver, seal, and
bearing losses. Unless specific data are available, these losses can be estimated as 20% of the calculated dissipation. This
20% also provides a safety allowance for uncertainties in the correlations and fluid properties used in calculating the dissipation
to the fluid. For specification this power is rounded up to one of the available standard electric motor sizes listed in Table 3.

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BASIC DESIGN CONSIDERATIONS (Cont)

NON-NEWTONIAN FLUIDS
The power dissipation correlations discussed above are specifically applicable to the mixing of fluids having Newtonian
viscosity behavior. A Newtonian fluid has a viscosity independent of the shear to which the fluid is subjected. Thus, although
the shear rates vary greatly throughout the fluid in an agitated vessel, the viscosity of a Newtonian fluid will be the same at all
points in the vessel. In contrast, the apparent viscosity of a non-Newtonian fluid at any point in the vessel depends on the
magnitude of either the shear stress or the shear rate at that point and may also depend upon the previous history of the fluid.
If the apparent viscosity decreases with increasing shear rate, the fluid is called pseudoplastic. If the apparent viscosity
increases with shear rate, the fluid is termed dilatant. If the apparent viscosity of a pseudoplastic fluid decreases with the time
a particular rate of shear is applied, the fluid is termed thixotropic.
The Newtonian/non-Newtonian behavior of a fluid or fluid mixture is known only from prior experience or by viscometry. Most
non-Newtonian fluids encountered are pseudoplastic. For these fluids, studies have established that the power number versus
impeller Reynolds number behavior is such that the power number is always equal to or less than the value for a Newtonian
fluid. Thus, for pseudoplastic fluids, Figures 9 and 10 can still be used and will be conservative. If the agitation conditions are
known to be turbulent and result in operation on the flat portion of the power number-Reynolds number curve, a precise
knowledge of apparent viscosity is not needed. However, in the laminar range, a knowledge of average shear and thus
apparent viscosity is needed to calculate the appropriate Reynolds number. In a stirred tank the average shear rate is equal to
approximately 10 times the rotational speed of the impeller. Experimental measurements are required to determine apparent
viscosities at this shear rate. Chapter 10 of the Holland and Chapman reference or EMRE’s Chemical Engineering Technology
(CET) section should be consulted.

STANDARD DRIVER SIZES

➧ Drivers for mixers are produced with gear reducers having standard output shaft speeds and powered by electric motors having
standard horsepower ratings. The standard output speeds of the American Gear Manufacturers Association (AGMA) are given
in Table 2. For side-entering and portable propeller agitators, the 280, 350, and 420 rpm speeds are the only ones in general
use. Most vendors of mixer drivers provide gearboxes which make possible the changing of gears to produce other standard
output speeds. However, making such changes requires consideration of the horsepower rating of the motor, the torque rating
and service factor of the gearbox and motor, and the critical speed of the shaft and impeller assembly. The mixer vendor or
CET section should be consulted.
Standard motor horsepower ratings are given in Table 3.

INVESTMENT AND OPERATING CONSIDERATIONS

In selecting among mixing system designs, both investment and operating costs must be considered. With turbine agitators,
process requirements can frequently be satisfied by mixers having different horsepower and speed combinations. Because of
the high cost of gear speed reducers, a higher horsepower-higher speed unit will sometimes cost less than a lower
horsepower-lower speed unit. In many continuous operations, the lower cost of the higher horsepower unit is negated by the
higher power costs.

SCALING-UP FROM LABORATORY AND PILOT PLANT STUDIES

The main objective of scale-up is to achieve the same quality of mixing in a commercial size mixing tank as in a laboratory test
tank. Unfortunately, it is not possible to maintain the same combination of flow and shear distributions in commercial mixers as
in small-scale tanks. Several scale-up methods have been developed depending on the process type and mixing
requirements, but all methods emphasize geometric similarity. Geometric similarity refers to maintaining the same impeller
type; and relative dimensions of impeller, liquid height and baffles.
The most commonly used scale-up criterion uses constant P / V, which is usually conservative. Depending on the process
requirement, P / V should be increased or decreased (Figure 15) with increase in volume according to P / V = constant (Vy).
The scale-up exponent ‘y’ can be negative or positive and should be determined either through pilot plant testing or from
recommended values in Figure 15.

(2) IN-LINE MOTIONLESS MIXERS

These mixers are generally suitable for continuous mixing operations where low and high viscosity miscible liquids are blended,
immiscible liquids are contacted, or gas is dispersed in a liquid. These mixers are inexpensive when short mixing time is
acceptable and the system is not limited by pressure drop. Detailed design considerations for in-line mixers are discussed in
the subsequent subsections on individual application types.

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BASIC DESIGN CONSIDERATIONS (Cont)

(3) JET MIXERS

These mixers are commonly used in product blending and storage tanks equipped with a pumparound system with sufficient
pumping capacity and head. They may be preferred to side-entering propellers because of their lower cost and lower
maintenance requirements, and possibly lower cost if a suitable pump is available.

DESIGN PROCEDURE

MECHANICAL AGITATORS
Set Vessel Geometry - For large storage and blending tanks which use side-entering propeller agitators, the vessel geometry
is set by process needs rather than mixing considerations. The mixer design is adapted to a tank of specified geometry and is
discussed in Section XIII-B.
For vessels to be mixed with top-entering agitators, “standard geometry" (Figure 1) should normally be used. Vessel diameter,
T, can be estimated from:
1/ 3
é4 ù
T = ê Vú Eq. (3)
ëπ û

where V is the maximum fluid volume to be mixed in the vessel. This diameter is then rounded to the nearest larger standard
drum and head diameter. Liquid depth in the vessel can then be calculated. Depth and volume in the bottom head are
included. The head can be any of the standard types available for the pressure rating of the vessel. Vessel volume above the
fluid must be added in many installations to provide for the increase in liquid volume due to gas holdup during sparging or to
accommodate foaming. In all cases, space is left between the top of the liquid and the top of the vessel, thus the liquid has a
free interface. Normally for vessels with top-dished heads, the space above the upper tangent line is left unfilled. With flat
heads or open tops, the vertical space left unfilled should be at least 1/10 of vessel diameter.
For mixing fluids having viscosities less than 5000 cP, 4 full length wall baffles spaced 90 apart are used. In vessels having
dished heads, the baffles are only used on the straight side. Except when mixing buoyant particle slurries, baffle width is set at
1/10 to 1/12 of vessel diameter. For buoyant solids, baffle width is reduced to 1/50 of vessel diameter. The baffles are set out
from the vessel wall by 1/72 of vessel diameter, especially when solids are present. If the fluids in the vessel will always have a
viscosity greater than 5000 cP, wall baffles should be narrower than conventional baffles. For very high viscosity liquids, wall
baffles may not be needed.
Pick Impeller Type and Approximate Diameter - Impeller type should be selected in accordance with the discussion in
EQUIPMENT TYPES AND APPLICATIONS. Table 1 in particular provides specific guidance. For mixing fluids having
viscosities up to 1000 cP, impeller diameter is set at approximately 1/3 of vessel diameter. As fluid viscosity increases to
10,000 cP, impeller diameter should be increased to approximately 1/2 of vessel diameter. Except for close proximity agitators,
agitator diameter should not exceed 0.7 times vessel diameter for any viscosity. Except for very small impellers, impeller
diameters are specified in the nearest whole inch or 25 mm increments.
Calculate Impeller Speed and Exact Diameter - For the set vessel geometry and approximate impeller diameter, impeller
speed is then calculated to satisfy the stated process requirements.
1. For process requirement stated as a tip speed, impeller speed is given by:
é tip speed ù
N = ê ú Eq. (4)
ë πD û

For tip speed in ft/min (m/s),

where: D = impeller diameter, ft (m)
N = impeller speed, rpm (rps)

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DESIGN PROCEDURE (Cont)

2. For a process requirement stated as a power per unit volume, impeller speed is given by:
1/ 3 1/ 3
é (P ) ( V / 1000 ) ù é (P )( V / 1000 ) ù
N = 1564 ê v ú N = 10 ê v ú Eq. (5)
ê Np ρ D 5 ú ê Np ρ D 5 ú
ë û ë û

where: Np = power number, dimensionless

Pv = power per unit volume, HP/kgal (kW/km3)
V = vessel volume, gallons (m3)
ρ = fluid or slurry density, lb/ft3 (kg/m3)
Obtaining values for the power number, Np, from Figure 9 or 10 requires a knowledge of the impeller Reynolds number, NRe,
which is given by:
N Re = 60 ρ N D 2 / µ N Re = ρ N D 2 / µ Eq. (6)

where: µ = fluid or slurry viscosity, lb/ft hr (kg/ms)

Since N must be known to calculate the Reynolds number, an iterative calculation using Eqs. 5 and 6 may be required.
However, in the turbulent regime, Np is constant and independent of NRe. For non-standard geometries and for gas sparging,
the power number must be additionally modified as given in Figures 11, 12, 13, and 14.
3. For a process requirement stated as an impeller pumping capacity or discharge flow, impeller speed is given by:
é Q ù
N = ê ú Eq. (7)
êNq D 3 ú
ë û

where: Nq = impeller pumping number, dimensionless

Q = pumping capacity or discharge flow, ft3/min (m3/s)
The impeller discharge coefficient, Nq, for pitched blade turbines on the basis of total flow is given in Figure 8 as a function of
impeller Reynolds number. Reynolds number is calculated by Eq. (6) and in other than the turbulent region may require an
iterative calculation as discussed above. For “square pitch" propellers operating in the turbulent region, a value of 0.5 can be
used for Nq. This value is based on direct discharge flow. Additional flow will be entrained as discussed in Section XIII-B,
MISCIBLE FLUIDS.
The above calculations for impeller speed, N, usually will result in a speed other than one of the standard gear driver output
speeds which are listed in Table 2. The standard speed nearest the calculated speed should normally be selected. However,
since these speeds are spaced at approximate 20% intervals, this may result in a significant deviation from meeting the design
process requirement. To correct for this, the selected standard impeller speed should be entered in Eqs. 8, 9, and 10 to
recalculate the value for impeller diameter D (which can be more finely adjusted in value than N).
Thus,
Tip Speed Requirement
é tip speed ù
D = ê ú Eq. (8)
ë πN û

Power/Unit Volume Requirement

1/ 5 1/ 5
é (P )( v / 1000 ) ù é (P ) ( v / 1000 ) ù
D = 82.5 ê v ú D = 4ê v ú Eq. (9)
ê Np ρ N3 ú ê Np ρ N3 ú
ë û ë û

Pumping Capacity Requirement

1/ 3
é Q ù
D = ê ú Eq. (10)
êë N q N úû

The recalculated D is then normally rounded to the nearest whole inch or 0.1 m.

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DESIGN PROCEDURE (Cont)

Calculate Driver Power - For the selected vessel geometry and an impeller type and calculated impeller speed and diameter,
power dissipation to the fluid can be estimated as:

[
P = 2.62 x 10 −10 N p ρ N 3 D 5 ] P = N p ρ N 3 D 5 / 1000 Eq. (11)

where: P = power dissipation, HP (kW)

The power number, Np, for the specific mixing situation should be calculated as indicated in the Agitator Power Dissipation and
Discharge Flow discussion under the BASIC DESIGN CONSIDERATIONS. In the case of vessels which have multiple
functions or whose contents have varying properties, the maximum expected value of Np should be used. To allow for seal and
gear reducer losses and correlation and physical property uncertainties, the calculated power dissipation is multiplied by 1.25 to
obtain the driver power. For specification, the resulting power estimate is rounded up to the next larger standard electric motor
size as listed in Table 3.
Prepare Specification - Specification of an agitated tank can be approached from an equipment specification or from a duty
specification viewpoint. The approach in this DESIGN PROCEDURE forms the basis of an equipment specification. This
equipment specification typically includes vessel dimensions; nozzle or sparger description and locations; impeller type, size,
rotational speed or range of speeds, and position in vessel; baffle configuration; shaft and bearing description; driver power
rating and service factor; and materials of construction. With axial flow impellers the direction of fluid flow must be indicated.
Additionally with pitched blade turbines, blade width must be identified as being the actual width or as the projected width
(height) parallel to the axis of rotation of the turbine.
The duty specification approach can be followed to make use of the expertise and standard equipment sizes of mixing
equipment vendors. The duty specification typically includes the vessel size; quantities or flow rates of components to be
mixed; physical properties of the components (density, viscosity, surface or interfacial tension, particle size); operating
temperature and pressure; and a description of the desired mixing result. Some desired mixing results are listed in
BACKGROUND. Description of the desired result includes such considerations as blend time, uniformity of dispersion or
suspension, “vigor" of agitation, and experience criteria with regard to mixer type, speeds, or power consumption per unit
volume. On the basis of this duty specification, the equipment vendors would propose equipment specifications. Such
specifications can be compared or rated by using the information in DESIGN PROCEDURE.
For quick estimating purposes, Table 4 can be used for mixer sizing on the basis of a very general description of the type of
mixing needed. However, for actual design, the considerations and procedures which are covered in Sections XIII-A through
XIII-E for the various mixing situations should be followed.

IN-LINE MOTIONLESS AND TANK JET MIXERS

The Design Procedure for tank jet mixers is contained in Section XIII-B on Miscible Fluids and that for in-line motionless
mixers is contained in Section XIII-D on Immiscible Liquid - Liquid mixing.

SAMPLE PROBLEMS
Problem 1 - Calculation of Mechanical Agitation Design
(The quantities in metric system are not exact but rounded up)
Given: A mixer is desired for a 500 gal (2 m3) blending tank containing fluids having a density of 60 lb/ft3 (1000
kg/m3) and a viscosity of 10 centipoises (0.01 Pa.s). The stated process requirement is that the mixers have
a circulation capacity of 3000 gpm (0.2 m3/s).
Find: Appropriate tank geometry, mixer type and size, and driver horsepower.
Solution: “Standard geometry" is appropriate for this application (see Figure 7).
Vessel volume V = 500 gal = 66.8 ft3 V = 2 m3
Vessel diameter.
1/ 3 1/ 3
éæ 4 ö ù éæ 4 ö ù
T = êç ÷ (66.8)ú = 4.4 ft T = êç ÷ (2)ú = 1.37 m
π
ëè ø û π
ëè ø û

Round up to T = 4.5 ft T = 1.37 m

Flat bottom tank will result in Z = 4.2 ft Z = 1.36 m
The vessel should have four full-length wall baffles having a width between T/12 and T/10.

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SAMPLE PROBLEMS (Cont)

Thus, B = 5 in. B = 0.13 m
A top entering pitched blade turbine having w/D = 1/8 is appropriate for this blending service.
Trial turbine diameter:
D = T/3 = 1.5 ft D = 0.46 m
Process requirement is stated as a pumping or circulation capacity of 3000 gpm or 401 ft3/min (0.2 m3/s). Thus trial turbine
speed from Eq. (7).
Q 401 0 .2
N = 3
= 3
= 158 rpm N = = 2.7 rps
Nq D (0.75 )(1.5) (0.75 ) (0.46) 3

The value of Nq = 0.75 is from Figure 8 for NRe > 104. The calculated speed of 158 rpm (2.7 rps) should be rounded to the
standard gear driver output speed of 155 rpm (2.58 rps) (Table 2).
To more closely satisfy the process requirement after shaft speed rounding, turbine diameter D can be recalculated from Eq.
(10).
1/ 3 1/ 3 1/ 3
é Q ù é 401 ù é 0 .2 ù
D = ê ú =ê ú = 1.51 ft D = ê ú = 0.47 m
ëê Nq N ûú ë ( 0 . 75 ) (155 ) û ë ( 0 . 75 ) ( 2 . 58 ) û

Which after rounding is 18 in. (unchanged).

Viscosity µ = 10 cP = 10 x 2.42 lb/ft hr = 24.2 lb/ft hr µ = 0.01 kg/ms
The Reynolds number must be calculated to check the validity of Nq from Figure 8. Thus, from Eq. (6)
éρ N D2 ù é (60 )(155 )(1.5) 2 ù
NRe = 60 ê ú = 60 ê ú = 5.2 x 10
4
êë µ úû êë 24.2 úû

ρ N D2 1000 (2.58 ) 0.47 2

NRe = = = 5.7 x 10 4
µ 0.01

which indicates operation is in the turbulent regime as assumed.

The power dissipation to the fluid is then calculated from Eq. (11) as

P = 2.62 x 10-10 Np ρ N3 D5 P = Np ρ N3 D5/1000

= (2.62 x 10-10) (1.3) (60) (155)3 (1.5)5 = (1.3) (1000) (2.58)3 (0.47)5/1000
= 0.58 HP = 0.51 kW

where the value of Np = 1.3 is from Figure 9 for a pitched blade turbine of w/D = 1/8. Driver power (which includes mechanical
losses) is estimated by multiplying this dissipation by 1.25 to obtain 0.72 HP (0.64 kW). This power is rounded up to a standard
electric motor rating of 3/4 HP (0.75 kW) (Table 3).
In summary the design would be:

T = 4.5 ft T = 1.37 m D = 1.5 ft = 18 in. D = 0.47 m

Z = 4.2 ft Z = 1.36 m w/D = 1/8
B = 5 in. B = 0.13 m N = 155 rpm N = 2.58 rps
C = 1.5 ft (Figure 7) C = 0.46 m P = 3/4 HP P = 0.75 kW

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SAMPLE PROBLEMS (Cont)

Problem 2 - Estimation of Power Consumption for Non-Standard Geometry
Given: An existing reactor is equipped with dual flat blade turbine agitators. After the reaction is finished, it is
desired to nitrogen strip the reactor contents. The reactor and turbine sizes and fluid properties and flow
rates are:
tank diameter, T = 12 ft T = 4m
diameter of each turbine, D = 4 ft D = 1.33 m
distance between turbines, S = 3 ft S = 1.0 m
turbine blade width, w = 8 in. w = 0.2 m
tank wall baffles, 3 of width, B = 10 in. B = 0.25 m
turbine rotational speed, N = 100 rpm N = 1.67 rps
liquid density, ρ = 60 lb/ft3 ρ = 1000 kg/m3
liquid viscosity, = m 10 cP µ = 0.01 Pa.s
N2 stripping rate, Qg = 400 actual ft3/min Qg = 0.2 m3/s
Find: The power dissipation by the agitators during the nitrogen stripping operation.
Solution: Power number for standard turbine and geometry
Viscosity µ = 10 cP = 24.2 lb/ft hr
Impeller Reynolds number, NRe, from Eq. (6) is
éρ N D2 ù (60 )(60)(100 )( 4) 2
NRe = 60 ê ú = = 2.38 x 10 5
êë µ úû 24.2

ρ N D2 (1.67 )(1.33 ) 2
NRe = = = 2.95 x 10 5
µ 0.01

From Figure 9, the power number, Np, for a single flat blade turbine having a w / D ratio of 1/5 is 4.0.
Correction factor from non-standard blade with
Np is proportional to blade width.
For existing turbine w / D = 8/(12)(4) = 0.167 w/D = 0.2/1.33 = 0.15
( w / D)existing 0.167 0.15
The correction factor = = 0.835 = = 0.75
( w / D)standard 0 .2 0 .2

Correction factor for multiple turbines

From Figure 11 for the existing impeller spacing ratio of S / D = 0.75, the power numbers correction factor,
Np2 / Np1, for dual flat blade turbines is 2.2.
Correction factor for non-standard baffle width
Baffle size ratio Nb B / T = (3)(10)/(12)(12) = 0.208 Nb B / T = (3)(0.25)/4 = 0.188
D / T = 4 / 12 = 0.333 D / T =1.33 / 4 = 0.333

From Figure 13,

the correction factor is Np / Np(std) = 0.92. Np / Np(std) = 0.9
Correction factor for gas addition
Qg / N D3 = 400 /(100 )( 4)3 = 0.0625 Qg / N D3 = 0.2 /(1.67 )(1.33)3 = 0.0509

From Figure 14,

the correction factor Np (gas) / Np (no gas) = 0.51 Np (gas) / Np (no gas) = 0.55

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SAMPLE PROBLEMS (Cont)

Final corrected power number
The overall correction is the product of the various correction factors.
Thus, the final corrected power number
éblade ù émultiple ù ébaffle ù égas ù
ê úê úê úê ú
Np = (Np )standard ê width ú êturbine ú êwidth ú êadditionú
êëcorrect.úû êëcorrect. úû êëcorrect.úû êëcorrect. úû

is:
= (4.0)(0.835)(2.2)(0.92)(0.51) = 3.45 = (4.0)(0.75)(2.2)(0.9)(0.55) = 3.27
Agitator power dissipation
From Eq. (1)
P = 2.62 x 10 −10 (N p ρ N 3 D 5 ) P = N p ρ N 3 D 5 / 1000

= (2.62 x 10-10)(3.45)(60)(100)3(4)5 = 55.5 HP = (3.27)(1000)(1.67)3(1.33)5/1000 = 63.4 kW

NOMENCLATURE
B = Baffle width (radially), ft (m)
Bc = Baffle clearance to vessel wall, ft (m)
C = Impeller clearance above bottom of vessel, ft (m)
D = Impeller diameter, ft (m)
lbm ft
gc = Newton's law conversion factor, 32.2 . kg m / Ns 2 )
(10
lb f s 2
N = Impeller rotational speed, rpm (rps)
Nb = Number of baffles
ft lb f
P = Power, HP (1 HP = 33,000 )(kW )
min
Q = Impeller discharge rate or circulation, ft3/min (m3/s)
Qg = Gas sparging rate, ft3/min (m3/s)
S = Impeller spacing, ft (m)
T = Tank or vessel diameter, ft (m)
V = Vessel volume, ft3 (m3)
w = Blade width of impeller in direction parallel to axis of rotation, ft (m)
Z = Fluid depth in vessel, ft (m)
θ = Jet nozzle discharge angle above horizontal, degrees
µ = Fluid viscosity, lb/ft hr (kg/m s)
ρ = Fluid density, lbm/ft3 (kg/m3)

Dimensionless Numbers
P gc
Np = Power number,
ρ N3 D5
Q
Nq = Impeller pumping number,
N D3

ρ N D2
NRe = Impeller Reynolds number,
µ

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TABLE 1
SELECTION GUIDE FOR MIXING EQUIPMENT

RECOMMENDED RECOMMENDED EFFECT OF

MEASURE OF
NATURE OF IMPELLER FOR EQUIPMENT OTHER EXCESSIVE IMPORTANCE OF
SYSTEM EFFECTIVE
OPERATION AGITATED THAN AGITATED AGITATION ON FLOW AND SHEAR
AGITATION
VESSEL* VESSEL PROCESS
Pump-through shell- Rate None, except All process results
Heating and-tube exchanger backmixing is enhanced by high
increased flow; shear has
Reflux condenser for Rate Heat removal essentially no effect
cooling decreases;
Cooling
Miscible P, PBT, backmixing
Liquids Hydrofoils increases
Pipe, tee, in-line Rate; absence None, except
Chemical Reaction mixer, airlift, pump- of undesirable backmixing
around loop, jet side products increases
Uniformity; rapid
Blending
tank turnover
Dissolving Jets, colloid mill,
Melting homogenizer Rate — —
Leaching
Bottom motion; Friable particles Basically enhanced
off-bottom are broken by high flow; shear
Solids Suspension suspension; may break friable
Solid P, PBT, FBT, uniform particles; for
Liquid Hydrofoils suspension slurrying, shear is
Rate; crystal Crystals are necessary to break
size and broken and more agglomerates; high
Crystallization shear not desirable
uniformity of nuclei may form
size if following
operation is filtration
Agglomerate Friable particles
Slurrying breakup; particle are broken
wetting
Inline mixer for Uniform Difficult-to-break Balance of flow to
continuous suspension; emulsions are shear; shear
Liquid Dispersion operations ease of breaking formed, and necessary to give
dispersion backmixing drop breakup and
increases flow necessary to
Liquid PBT, FBT, some Rate; efficiency; move material
Liquid Extraction Hydrofoils ease of breaking through impeller
dispersion
Colloid mill, Rate; particle Too-small particles
homogenizer, high size and
Emulsification
shear impellers uniformity of
size
Inline mixer for Efficient vapor- Difficult-to-break Balance of flow to
Gas Dispersion
continuous operation, liquid contacting foams are formed; shear
Gas bubble column and back-mixing
Liquid DFBT, CD6 Rate; efficiency
ease of foam increases
Absorption
separation

*P = Propeller; PBT = Pitched blade turbine; FBT = Flat blade turbine; DFBT = Disk Flat Blade Turbine, CD6 = Chemineer CD6 impeller
Note: Propellers are generally suitable only up to fluid viscosities of 3 Pa.s (3000 cp), turbines and anchors are suitable up to 50 Pa.s (50,000
cp), helical ribbons are appropriate for higher viscosities.

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TABLE 2
AGMA GEAR DRIVE STANDARD OUTPUT SPEEDS

RPM RPS RPM RPS RPM RPS

1.0 0.017 11.0 0.183 125 2.08
1.2 0.02 13.5 0.225 155 2.58
1.5 0.025 16.5 0.275 190 3.17
1.8 0.03 20 0.333 230 3.83
2.2 0.037 25 0.417 280 4.67
2.7 0.045 30 0.5 350 5.83
3.3 0.055 37 0.617 420 7.0
4.0 0.067 45 0.75 520 8.67
5.0 0.083 56 0.933 640 10.67
6.0 0.1 68 1.13 780 13.0
7.5 0.125 84 1.4 950 15.8
9.0 0.15 100 1.67 1170 19.5
1430 23.8

Note:
This table specifically applies to gear speed reducers corresponding to American-Gear Manufacturer Association
standards and operated by 60 hertz electric motors. Sometimes other speeds are available due to individual vendor
practice or to the employment of 50 hertz electric power.

TABLE 3
STANDARD POWER RATINGS OF INDUCTION MOTORS IN HP
(Power Ratings in kW Can be Obtained by Multiplying HP by 0.746)

1/4 20 250
1/3 25 300
½ 30 350
¾ 40 400
1 50 450
1-1/2 60 500
2 75 600
3 100 700
5 125 800
7-1/2 150 900
10 200 1000
15

Note:
For information on higher horsepower electric motors and on motor efficiencies and power factors, see Table 1 of
Design Practices Section XI (Compressors), Section XIII-L (Electric Motors).

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TABLE 4
QUICK GUIDE FOR SIZE ESTIMATION OF PITCHED BLADE TURBINE

VESSEL MIXER SPEED AND DRIVE POWER FOR INDICATED AGITATION INTENSITY
DIAMETER
IMPELLER MILD MODERATE HIGH
AND VOLUME
DIAMETER 0.5 HP/1000 gal 3 HP/1000 gal 10 HP/1000 gal
LIQUID
TO FLUID TO FLUID TO FLUID
HEIGHT
Speed Power Speed Power Speed Power
(ft) (gal) (ft)
(rpm) (HP) (rpm) (HP) (rpm) (HP)
3 160 1 155 1/8 280 3/4 420 2
4 375 1.33 125 1/4 230 1.5 350 5
5 735 1.77 100 1/2 190 5 280 10
6 1270 2 100 1 190 7-1/2 280 20
8 3010 2.6 84 2 155 15 230 40
10 5870 3.38 68 5 125 25 190 100
12 10,150 4.2 56 7.5 100 40 155 150
15 19,800 4.8 56 15 100 75 155 250
20 47,000 6.6 45 30 84 200 125 700

VESSEL MIXER SPEED AND DRIVE POWER FOR INDICATED AGITATION INTENSITY
DIAMETER
IMPELLER
AND VOLUME MILD MODERATE HIGH
DIAMETER
LIQUID 0.1 kW/m3 0.6 kW/m3 2.0 kW/m3
HEIGHT
Speed Power Speed Power Speed Power
(m) (m3) (m)
(rps) (kW) (rps) (kW) (rps) (kW)
0.9 0.6 0.3 2.58 0.09 4.67 0.6 7.0 1.5
1.2 1.4 0.4 2.08 0.19 3.83 1.1 5.83 3.7
1.5 2.8 0.5 1.67 0.37 3.17 3.7 4.67 7.5
1.8 4.8 0.6 1.67 0.75 3.17 5.6 4.67 15
2.4 11.4 0.8 1.4 1.5 2.58 11.2 3.83 29.8
3.0 22.2 1.0 1.13 3.7 2.08 18.7 3.17 75
3.6 38.4 1.2 0.93 5.6 1.67 29.8 2.58 112
4.5 75 1.5 0.93 11.2 1.67 56 2.58 187
6.0 178 2.0 0.75 22.4 1.4 149 2.08 522
Notes: Table is based on 45 pitched blade turbine (PBT) of w / D=0.125 operating in water in a straight sided tank of standard
geometry (Figure 7). Horsepower consumption of other turbines at same rpm would be proportional to their power
number, Np, with respect to that of the PBT value of 1.3. The table is intended for quick estimation purposes only and
is not recommended for actual design use.
Mild Agitation Intensity - for establishing fluid motion and mild blending.
Moderate Agitation Intensity - for blending, off-bottom solids suspension, and moderate liquid/liquid and gas/liquid
dispersion.
High Agitation Intensity - for mass transfer limited reactions, uniform solids suspension, and high dispersion in
liquid/liquid and gas/liquid systems.

TABLE 5
Np AND Nq VALUES AT HIGH NRe FOR SOME HYDROFOIL IMPELLERS
IMPELLER Np Nq
Lightnin A310 0.3 0.56
Lightnin A315 0.75 0.73
Chemineer HE3 0.25 0.47 - 0.5
Ekato Interprop 0.45

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FIGURE 1
STANDARD TANK GEOMETRY AND NOMENCLATURE

BC

W
S
Z

D
C

T T Flat or Ellipical Bottom

for "Standard" Geometry: Z = T, D = ,C = ,
3 3

T T T
B= to , BC = ,
12 10 72

D D
W= to
8 5 DP13Af01

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FIGURE 2
COMMON IMPELLER TYPES

A. Axial

Marine Propeller Pitched Blade Pfaudler

Turbine (PBT) Retreat Curve

Ekato Mig Ekato Intermig

B. Radial

Rushton Turbine Blackswept Turbine Chemineer CD6

C. Hydrofoil

Lightnin A310 Chemineer HE - 3 EMI Rotofoil

Lightnin A315 Prochem Maxflo Ekato Interprop

D. Close - Clearance

DP13Af02

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FIGURE 3A
AXIAL FLOW PATTERN IN BAFFLED TANK WITH A PITCHED BLADE TURBINE

Baffles

Top View

Side View

DP13Af3a

FIGURE 3B
RADIAL FLOW PATTERN IN BAFFLED TANK WITH A FLAT BLADE TURBINE

Baffles

Top View

Side View

DP13Af3b

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FIGURE 4
VENDOR PROPRIETARY STATIC MIXERS

KENICS

TORAY HI-MIXER SULZER SMX LIGHTNIN

KOMAX ETOFLO ROSS LLPD

DP13Af04

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FIGURE 5
JET NOZZLE FOR TANK MIXING

Length to suit
15° angle Y
Min
15°
A
B

Detail at "A"

DP13Af05

FIGURE 6
LIQUID JET EDUCTOR

Motive Discharge
Fluid

Suction DP13Af06

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FIGURE 7
FLOW PATTERNS IN UNBAFFLED TANK WITH A SIDE ENTERING PROPELLER

Side View

Top View

Mixer
Clockwise
Rotation
Angle
between
7° and 12°

PROPER PROPELLER POSITION

DP13Af07

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FIGURE 8
PUMPING NUMBER FOR 45° PITCHED BLADE TURBINE VS. IMPELLER REYNOLDS NUMBER

1.0
0.25
0.9
0.3
Pumping Numbers, N Q = Q/ ND 3

0.8

0.4
0.7

D/T = 0.5
0.6

Ratio of Impeller Diameter to Tank Diameter

0.5

0.4

0.3
102 2 4 6 8 103 2 4 6 8 104 2 4 6 8 105 2 4 6 8 106

ρ N D2
Impeller Reynolds Number, N Re = µ DP13Af08

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FIGURE 9
CORRELATIONS FOR MIXING POWER NUMBER VS. REYNOLDS NUMBER

500

Curve 1 Curve 2 Curve 3 Curve 4 Curve 5 Curve 6

100

50
Np = P gc / ρ N3 D5

W/D = 1/5 W/D = 1/5 W/D = 1/8 W/D = 1/8 W/D = 1/8 W/D = 1/8

10

5 1
Curve 7 2
Glassed Steel 3
3-Blade Retreat 4 5
5

6
1

7
0.5
1 10 102 103 104 105

NRe = ρ N D2/µ DP13Af09

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GENERAL CONCEPTS AND EQUIPMENT SIZES
December, 2001 DESIGN PRACTICES

FIGURE 10
POWER NUMBER CORRELATIONS FOR PROPELLERS
100

Propeller
Curve Pitch

10.0
1 1.0
2 1.4
ρ N3 D5
P gc

3 1.8
Np =

1.0
3

2
1

0.1
1 10 102 103 104 105

ρ N D2
NRe =
µ DP13Af10

FIGURE 11
EFFECT OF DUAL IMPELLER SPACING ON POWER NUMBER

2.5

FBT
2.0
Two Impellers to One Impeller

PBT
Power Number Ratio of

1.5

1.0

0.5

0
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Impeller Spacing Ratio - Si / D DP13Af11

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XIII-A 27 of 29
GENERAL CONCEPTS AND EQUIPMENT SIZES
DESIGN PRACTICES December, 2001

FIGURE 12
DUAL PROPELLER POWER EFFECT

2.0
Ratio of Power Number of

Propeller Power Number

Dual Propeller to Single

1.5
Np2 / Np1,

1.0
0.4 0.5 0.6 0.7 0.8 1.0 1.5 2.0 2.5 3.0 3.5 4.0 5.0

S/D, Propeller Spacing to Propeller Diameter Ratio DP13Af12

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XIII-A 28 of 29
GENERAL CONCEPTS AND EQUIPMENT SIZES
December, 2001 DESIGN PRACTICES

FIGURE 13
EFFECT OF BAFFLING AND D/T ON POWER NUMBER
1.2

1.1 D/T
0.5

1.0
Np / Np (Standard Configuration)

0.4
0.9

0.32
D/T
0.8 0.25
0.25
0.32
0.7
B = Baffle Width
D = Impeller Diameter
0.4 Nb = Number of Baffles
0.6 T = Tank Diameter

0.5

0.5 4 Baffles
T/12 T/10

0.4
0 0.2 0.4 0.6 0.8 1.0
Baffle Size Ratio, Nb B / T DP13A13

FIGURE 14
EFFECT OF GAS ADDITION ON POWER
1.0

0.8
Power Number with No Gas Flow
Power Number with Gas Flow

Qg = Volumetric Gas Flow

N = Impeller Speed
D = Impeller Diameter
0.6

0.4

0.2

0
0 2 4 6 8 10 12 14
Qg
x 100 DP13Af14
N D3

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GENERAL CONCEPTS AND EQUIPMENT SIZES
DESIGN PRACTICES December, 2001

FIGURE 15
SCALE-UP BY POWER PER UNIT VOLUME

P / V = Constant V y

Constant Blend Time y = 2/3

Vortex y = 1/6
Dispersion
P/V

y = 0
Solids
y = – 1/12

y = – 1/3
Flow Velocity

Log - Log Plot

DP13Af15

MIXING SCALE-UP CRITERION RECOMMENDED VALUE OF “y”

Same blend time 0.67
Same relative vortexing 0.17
Same dispersion drop size 0
Same quality of solids suspension – 0.08
Same flow velocities – 0.33

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