mixing funda

PRINCIPLES OF FLUID MIXING 12764 Greenly Street Phone: 616/399-5600 Holland, MI 49424 Fax: 616/399·3084

TABLE OF CONTENTS

Types of Mixers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1

Mixer Terminology 2

DIT and ZIT 3

Axial Flow and Radial Flow 4

Flow and Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5

Power and Reynolds Numbers 6

Turbine Design Effects 7

Horsepower (Work, Power, Shaft) 8

Torq ue 9

Pumping Capacity . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. 10

Shaft Terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11

Impeller Weight and Equivalent Weight '.' . . . . . . . . . . . . . . . . .. 12

Shaft Length and Critical Speed ~ . . . . .. 13

Nomenclature 14

© Copyright 1995 BRAWN MIXER, INC. 08/01/95 Page 8-i

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PRINCIPLES OF FLUID MIXING 12764 Greenly Street Phone: 616/399-5600 Holland, MI 49424 Fax: 616/399-3084

TYPES OF MIXERS

Many types of mixers are available. Some mixers are designed specifically for one special application, while others are more versatile with many options such as variable speed, changeable impellers and shafts and a wide range of motor horsepowers. This data sheet will clarify some of the designations commonly used when discussing mixers.

Aerator - A mixer or other device used to dissolve air into water, usually for biological waste treatment. It may operate at the surface by splashing, or submerged with a pipe, or with a sparge providing air to the impeller.

Air Mixer - A mixer with a motor that uses compressed air instead of electricity is sometimes called an air mixer or air-drive mixer, or pneumatic mixer.

Direct Drive - A direct drive has an output shaft which rotates at the same speed as the motor. Direct-drive mixers are relatively simple and offer a higher component of shear to the process.

Disperser - A special purpose high-shear mixer or just the blade or impeller. Typically, a ~Iighspeed device often with sharp edges (some look like circular saw blades with bent teeth) used to break up powders or particles to dissolve or suspend them.

Dry Well Mixer _ A vertically-mounted mixer which utilizes a gear drive that has an oil dam called a "dry well" around the output shaft. The oil dam extends above the oil level of gearbox so that oil cannot run out of the gearbox during operation.

Fixed Mount. A mixer with mounting base bolted to mounting beams, a tank flange, or an angle riser plate. This mixer is usually installed as an integral part of the system.

Flocculator - A relatively slow-RPM mixer, which is used to enhance the contact of particles in suspension to agglomerate them for easier settling or separation.

Gear Drive - A mixer with an output shaft that has a speed lower than the motor speed because of a gear reducer between the motor and output shaft. This mixer transmits higher torque and has higher pumping efficiency per horsepower.

Homogenizer - A very high speed mixer used to blend immiscible phases of a solution into a cream or emulsion. Portable Mixers - These mixers are relatively easily moved from tank to tank and mounted to tank walls with a C-clamp or adjustable plate mount.

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TYPES OF MIXERS Continued ...

Right-Angle Mixer - A mixer with the motor shaft input perpendicular to the gearbox output shaft. The motor suspends off the side of the gearbox, keeping the required headroom to a minimum.

Side-Entry Mixers - Mixers mounted on a flange through the side of a tank or chest.

Stainless Steel Mixers - A mixer whose drive components (motor, gearbox) are made from stainless steel. These are used in sanitary and washdown environments, as well as highly corrosive atmospheres.

Static Mixers - These are pipes with specially-designed baffles inside which blend fluids as they flow through. These mixers do not have any moving parts.

Top-Entry Mixers - Mixers mounted on the rim, on beams, or on a flange above the top of the tank.

© Copyrighl1995 BRAWN MIXER, INC. 08/01195 Page 8-1.2

PRINCIPLES OF FLUID MIXING Phone: 616/399-560012764 Greenly Street

Fax: 616/399-3084Holland, MI 49424

MIXER TERMINOLOGY

Axial Flow. Fluid flow directed aXially along the mixer shaft, from top to bottom (down-pumping) or from bottom to top (up-pumping) is called axial flow. [See Page 8-4.1]

Baffles. Structures attached to an inside tank straight side, either directly or on tabs to direct the fluid flow vertically in the tank, preventing swirl and vortexing. [See Page 8-3.1]

Bending Moment. The product of force times distance. Fluid forces are exerted on a mixer shaft at each impeller. The force (Ibs) times the distance from the impeller to the lowest shaft bearing (in) is the bending moment (in-Ib). For multiple impellers, the shaft bending moment is the sum of the individual bending moments. [See Page 8-8.1]

Case Size. Speed reducer size on gear-driven mixers. When torque design limits are reached, or when a larger diameter shaft is required to meet other design criteria, the next larger size gear box (case size) must be used. A given case size may accommodate many various horsepower and inpUt/output speed combinations, but carries the same torque and shaft size.

Coverage. The distance between the impeller and the liquid surface. Typica.1 optimum coverage is equal to twice the impeller diameter. Insufficient coverage may cause vortexing and/or air entrainment. [See Page 8-3.1]

Critical Speed. A rotational speed which is a multiple of a shaft natural frequency. Operating a shaft at critical speed may amplify vibrations leading to shaft failure.

O/T. The ratio of impeller diameter (0) to tank diameter (T). [See Page 8-3.1]

Equivalent Weight. A calculated value representing the combined impeller weight at the shaft end when several impellers are installed on a shaft. [See Page 8-12.1]

Entrainment. The result of the drawing force produced by a flowing fluid, which drags additional fluid (entrained flow) or air (air entrainment) along with the pumped fluid.

Flow. One of two components resulting from the action of a mixer impeller (see "Shear'). The bulk movement of the fluid. Primary impeller pumping rate in gallons per minute is often referred to as flow. [See Page 8-5.1] .

Fluid Forces. The forces exerted on a mixer shaft through the impeller as a result of the fluid motion in the tank. Fluid forces are calculated for each impeller and used to calculate the shaft bending moment. [See Page 8-11.1]

@ Copyright 1995 BRAWN MIXER, INC. 08/01/95 Page 8-2.1

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MIXER TERMINOLOGY Continued ...

Frame Size - Relating to the physical size of a motor. Frame size is dependent on motor HP. enclosure, speed, power supply voltage and phase. Example: Y2 HP, 1800 RPM, 230/460V has a NEMA 56 frame; 3 HP, 1800 RPM, 230/460V has a NEMA 182 frame.

Freeboard - The distance from the liquid surface to the top of a tank. This distance must be taken into account when sizing a mixer shaft to ensure adequate coverage. [See Page 8-3.1]

Free Flow I Plug Flow - The unobstructed flow of a fluid. Mixer characteristics, such as pumping capacity and power requirement, are based on the assumption that no obstructions or flow constrictions are present.

Off-Bottom - The distance from the impeller to the tank bottom. Typically, the off-bottom is between one to two times the impeller diameter. [See Page 8-3.1]

Power Number - A number characterizing the power requirement of a particular impeller geometry. Power number varies with Reynolds number, but may be treated as a constant if the Reynolds number is sufficiently high.

Radial Flow. Impellers that draw from above and below the impeller and discharge it toward the tank wall, perpendicularly from the mixer shaft, are radial flow impellers. This type of flow is called radial flow. [See Page 8-4.1]

Reynolds Number - A dimensionless number used to indicate the type of fluid motion being produced. The value of this number determines the value of the power number, which affects the HP draw. Reynolds numbers below 1,000 are considered laminar and above 2,500 are turbulent flow. [See Page 8-4.1]

Service Factor - Equipment having a service factor of 1.'0 for a given level of performance is designed to operate without excessive wear or failure over its lifetime at that performance level. For instance, a 1 HP motor rotating at 1725 RPM with a service factor of 1.0 will operate for many years under a 1 HP load. A gearbox designed to transmit 1 HP has a service factor of 1.0 when loaded to 1 HP. If, however, that same gear box is loaded to only Y2 HP, it now has a service factor of 2.0, indicating that it is capable of heavier duty than the current use and should have a longer service life.

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PRINCIPLES OF FLUID MIXING 12764 Gree nty Street Phone: 616/399-5600 Holland, MI 49424 Fax: 616/399-3084

MIXER TERMINOLOGY Continued ...

Shaft StreSS. The intensity of the straining force on a mixer shaft that tends to deform its shape or cause it to fracture. It is usually expressed in PSI. Shaft stress is calculated from the bending moment. Stress limits are known for various materials under static loads. For mixer shafts which are subjected to alternating stresses because of their rotation, a fatigue stress limit must be established which is much less than the static limit. Mixers should not be designed with a shaft stress higher than 15,000 PSI.

Shear. One of two components resulting from the action of a mixer impeller (see "Flow"). Different velocities existing simultaneously (velocity gradient = shear rate) which produce stresses on the fluid. Shear rate X Viscosity = shear stress in PSI. Shear stress is responsible for smallscale fluid intermixing.

Specific Gravity. The ratio of fluid density e.g. (Ib/gal) to the density of water (8.33 Ib/gal @ 25° C, 1 atm pressure) under the current conditions.

Tip Speed. The peripheral speed of a rotating impeller. Tip speed is something used to estimate the shear applied to a fluid. Tip Speed =RPM X D X n.

Velocity Head. For the mixer concepts presented in these data sheets, velocity head and shear have the same meaning. (See "Shear".)

© Copyright 1995 BRAWN MIXER. INC. 08/01/95 Page 8-2.3


OfT and ZfT TANK DESIGN CONSIDERATIONS

-Freob

.---

-~ Baffle-.

oJ I II L

~D~ '-

z

Off Sottom

oard

rage

-

Cove

Four (4) baffles, 90° apart, are typical. Baffle width is 1/12 the tank diameter; length is from the liquid level down to 6 inches off bottom.

DfT is the ratio of impeller diameter to tank diameter. For most mixing applications, it ranges from 0.20 to 0.60. A OfT that is too small may leave areas unmixed. A OfT too large may choke off the upflow between the impeller and the tank wall. Mixer sizing for general blending starts with a DfT of 0.25. The impeller diameter is then adjusted to fit the most economical drive selection. A smaller OfT may be offset by high flow created by turning at higher RPM.

ZIT is the ratio of liquid height to tank diameter. When this ratio exceeds 1.2, dual impellers should be used.

Off-bottom distance is normally 1 to 2 impeller diameters. Coverage is typically 2 to 4 impeller diameters.

@ Copyright 1995 BRAWN MIXER, INC. 08/01/95 Page 8-3.1

PRINCIPLES OF FLUID MIXING . 12764 Greenly Street Phone: 616/399·5600 Holland, MI 49424 Fax: 616/399-3084

AXIAL FLOW and RADIAL FLOW

AXIAL FLOW RADIAL FLOW

@ Copyright 1995 BRAWN MIXER, INC. 08/01/95 -4.1

PRINCIPLES OF FLUID MIXING 12764 Greenly Street Phone: 616/399·5600 Holland, MI 49424 Fax: 616/399-3084

FLOW and SHEAR

Impeller Type

Rake Helix Hydrofoil Propeller Axial-flow

TurbIne

Radial-flow Turbine

Bar Turbine Sawtooth Impeller &

stator

Homogenizer

FLOW Q

. SHEAR S···· .. ·.

. (Velocity Head) .

. . . . . . .

The energy which a mixer transmits to the fluid results in two effects - flow and shear (or velocity head) - by the following relationship:

p ex. Q x S x S.G. where: P = Power

Q = Flow S . = Shear (head)

S.G. = Specific Gravity

For a given power level, a mixer can be designed so that either the shear component or the flow component represents most of the power applied. In general, a mixer with a small diameter impeller, turning at a high speed, will result in the fluid seeing the applied power as mostly shear. This is represented by the bottom of the graph above. Conversely. a low-speed mixer with a larger diameter impeller will discharge a

higher volume of fluid, resulting in high flow. The required ratio of tAese components is determined by the application.

Homogenizers are relatively small-bladed, very high RPM mixers, which produce tremendous amounts of shear for tearing two phases into an emulsion. Flocculators, by way of contrast, are typically slow-moving, large diameters, which gently push liquid around a tank to build large particles from smaller ones with the aid of chemical addition. Shear in flocculation would have a negative effect.

The importance of understanding this principle lies mainly in recognizing that equal power does not mean equal mixing result. The process result is always a function of impeller type and speed.

Mixing : processes such as blending, dissolving and solids suspension are flow or pumping-controlled and make up most mixer applications. If shear is not an essential component in achieving your result, you should· lean toward lower speed, larger diameter impellers to get more flow per utility dollar.

The list of impellers at the left of our graph is just a sampling, but it illustrates that different impeller shapes produce different ratios of flow and shear.


PRINCIPLES OF FLUID MIXING Phone: 616/399-5600

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POWER and REYNOLDS NUMBERS

Power Number (Np) is a characteristic of each impeller shape. It is a number obtained empirically. Knowing the impeller speed and diameter, the fluid specific gravity, and measuring the shaft horsepower, we can use the following equation to calculate the impeller Power Number, Np.

Np = 1.53 X 1013 SHP N3 0 5 S.G.

SHP = Shaft horsepower (H P)

N = Speed (RPM)

0 = Impeller diameter (INCHES)

S.G. = Specific Gravity

This Power Number is constant for each impeller, as long as the Reynolds Number is sufficiently high. Power Number is a function of Reynolds Number.

Nre = 10.754 N 0 2 S.G. viscosity

visco = fluid viscosity (cP)

This mixing Reynolds Number is the indicator of the type of fluid motion your mixer will produce in the fluid you are mixing. If the Reynolds Number is above 2,500, you are generally operating in the region where the power number is constant (turbulent flow). If the Reynolds Number you calculate is less than 1,000 (laminar flow), then the Power Number is really higher than the constant assigned to the type of impeller you are using. Consequently, the shaft horsepower you calculate will be incorrect. In this case, you will need to obtain an Np vS. Nre curve from the impeller manufacturer or by experimentation. This curve shows how the Power Number for each impeller varies with changes in Reynolds Number.

The example below shows that, as Reynolds Number drops, we reach a point where the power number begins to increase sharply. This point depends on the impeller in use, but it is commonly between Nre 1000 and Nre 2500.

Np \_log L-.. _

log Nre

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POWER and REYNOLDS NUMBERS Continued ...

Notice that, for very high Reynolds Numbers, the Np curve is flat. This indicates that the Power Number is constant. Calculating horsepower with this constant Np can be accomplished using the equation as shown in the "HORSEPOWER (Work, Power, Shaft)" section.

For flow-controlled applications, which account for 90% of Brawn Mixer applications...

Process Result oc Work ~ Flow (K) ~ Torque ~ $

Page 8-6.2 ® Copyright 1995 BRAWN MIXER. INC. 08101/95


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TURBINE DESIGN EFFECTS Power No. (Np) vs. Reynolds No. (Nre)

100

A3S

AF,J

0.\ g

Nre

Np = 1.53 x 1013 SHP N3 0 5 S.G.

Nre = 10.754 N 0 2 S.G. viscosity

o

goo

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HORSEPOWER (Work, Power, Shaft)

When a mixer moves liquid, it does ''work''. The amount of work is a function of how much liquid is moved per unit time, what type of liquid is moved, and how far it is moved. It takes the same amount of work to move 1 gallon of liquid one foot, regardless of how long it takes - one year or one second. The difference is the rate at which the work is applied. This rate is what we call "power". It requires much more capability, or power, to move that liquid in 1 second.

The most common unit of power used when working with mixers is "horsepower" (HP) or KW.

KW= HP X 0.75

[Calculations in this section are shown in HPJ

The power available from a motor (motor HP) is a characteristic of the motor design, but just putting a 2 HP motor on a 1 HP mixer will not change results unless the mixer is modified to use that extra power. The power applied to a fluid by a mixer produces flow and shear (velocity head) in the liquid. Some of the power is lost as heat, due to motor and drive inefficiency.

Except for calculating the efficiency of the mixer, we are not interested in the power losses. Rather, we are interested in the power applied to our fluid. The power applied to the fluid, through the mixer shaft, is what we isolate for application purposes and tenn "shaft horsepower", or "brake horsepower".

Shaft horsepower is calculated by the following equation:

SHP = Np N3 0 5 S.G. 1.53x1013

Np = Power Number of impeller N = Impeller speed (RPM) 0 = Impeller diameter (IN)

S.G. = Specific Gravity 1.53 x 10'3 = Conversion factor

Knowing the impeller Power Number (which the manufacturer can supply), the speed, the diameter, and the specific gravity of the liquid, we can predict the shaft horsepower required. By knowing or assuming how much power is lost, and how much extra we want available as a safety factor, we know what size motor is required and how much power the mixer components will have to be designed to transmit safely without excessive wear or failure.

Dual Impellers - The power draw of two impellers may be less than twice the power required by one impeller, but it is customary to play it safe and assume that two impellers require two times the power of one impeller of the same size.

Power is also affected by such variables as off-bottom distance and fluid characteristics. Consult your mixer applications engineer if the mixer under study is for other than a waterlike application.



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TORQUE

Torque is the twisting or turning force acting to produce rotation on the mixer shaft. Gear-driven mixers generally produce the highest torque. The torque on a mixer shaft must be known for proper shaft design and gear box selection.

Torque = HP x 63025 RPM

In flow-controlled mixing systems, torque = mixer flow or velocity head, which is, in turn, equal to process result. Also, higher torque (not necessarily higher HP) =higher mixer cost. Mixer torque per unit volume is also an important scale-up criteria.

Torque ~ Flow (K) oc Process Result ~ $

Torque must also be calculated for proper rnixer support design.



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PUMPING CAPACITY

Pumping capacity is the ability of a mixer impeller, rotating at a given speed, to pump liquid. The flow produced directly by the impeller and through the impeller area is known as primary flow. The amount of that flow, usually stated in gallons per minute, is the primary pumping capacity. In addition to primary flow, liquid is drawn by and pushed by the primary flow to produce an "induced flow". The primary and induced flow together make up the total flow. Total flow is difficult to measure or calculate, but experiments have shown that total flow is typically several times higher than primary flow. This distinction is very important when comparing mixer performance and efficiency. Mixers should be compared using primary pumping capacity. Total flow may be estimated by the mixer manufacturer, but it is a less meaningful and less dependable number than primary flow.

For comparison and simplicity, pumping capacity calculations assume "free flow" or plug flow where the impeller is not too close to the tank bottom and flow is not hindered by other constrictions. Water is used as the standard liquid, with a specific gravity of 1.0 and a viscosity of 1.0 centipoise. The result is sometimes referred to as the water pumping rate or water pumping capacity, since pumping capacity for the actual conditions can also be calculated by adjusting the flow number for the fluid characteristics and tank geometry.

The following equation is used to calculate PRIMARY pumping capacity:

Q = Ng N 0 3

231

Q = Flow in gallons per minute (GPM) Nq = Flow number for impeller

N = Mixer speed (RPM) 0 = Impeller diameter (IN)

231 = Conversion factor

Nq, the flow number, is determined empirically for each impeller type. It is constant for the impeller under standard conditions (water, free flow). The impeller manufacturer should supply this number to you if you are calculating pumping capacity.

Dual Impellers - Depending on how the impellers are spaced, the fluid characteristics, tank geometry and other variables, two impellers will pump somewhat less than twice the amount one pumps. For standard conditions, with a gear-drive mixer and two impellers, spaced two diameters apart, the primary pumping capacity will be 1.7 times the value calculated for one impeller of equal diameter and speed. This factor is commonly used to estimate the primary pumping capacity of duals under a variety of conditions.

While this pumping capacity is a very useful concept for comparing mixers, caution must be exercised when using it as a sizing criteria, since the same liquid in one small area of the tank may be pumped over and over, while other areas do not get mixed. orr, off-bottom distance, number and location of impellers must also be correct.



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Bearing spacing, Sb

~ndi~ moment. M

Shaft length, L

SHAFT TERMINOLOGY

t t

FORCES AT WORK ON A MIXER SHAFT

""'- NOTE: The concern is for the stress on the shaft at the lower bearing.

Torque, T

~ Fw• Fp, and Ft act axially at center of Impeller shaft.

Turbine hydraulic force, Fh

Weight of Thrust Axial-flow shaft and due to turbine

impellers, Fw pressure, Fp thrust, Ft



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IMPELLER WEIGHT and EQUIVALENT WEIGHT FOR CRITICAL SPEED

Impeller weight can be obtained from the manufacturer or calculated, knowing the material density and the dimensions of all the impeller components, but this weight is only directly useful if there is only one impeller on the shaft, located at the very end of the shaft.

For shaft calculations, we are more often concerned with the effect of the impeller(s) on the end of the shaft than the effect of the impeller(s) as positioned along the shaft. The equivalent weight is the apparent weight of all the impellers on the end of the shaft.

If we have two or more impellers, the weight used to calculate critical speed is not the total of all impellers. This would only be correct if all the impellers were located at the shaft lower end. To accurately calculate critical speed, we need to determine the "equivalent weight" based on the weights of the various impellers and their position on the shaft.

Adjustable impellers should be safe at all operating positions. The simple way to be assured of this is to locate all the impellers at their lowest possible position, calculate the equivalent weight and critical speed under this worst-case scenario. If your result is below the maximum critical speed ratio, the impellers are safe at any position.

MOUNTING SURFACE

L2]3We = W1 + W2 [L1 !J

•i L2

We = Equivalent weight (LB) W" 2, 3 = Weights of impellers 1, 2, 3 (LB)

L" 2, 3 = Length (I N) L,

~-

W3

~

W2

I

WI

The equivalent weight calculated for two or more impellers can be directly input into the critical speed equation (see "SHAFT LENGTH and CRITICAL SPEED")



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SHAFT LENGTH and CRITICAL SPEED

NATURAL FREQUENCY & ROTATIONAL FREQUENCY DETERMINE CRITICAL SPEED

A rigid body, like a mixer shaft, vibrates when subjected to outside forces. Like a tuning fork, it has a predetermined vibrational frequency, which remains constant as long as the composition of the shaft and the shaft-impeller relationship is not altered. This vibrational frequency is called natural frequency. Unlike a tuning fork, however, a mixer shaft must also deal with the forces of rotation, either at a fixed speed, or through a range of variable speeds or rotational frequencies.

The rotational frequency is the number of turns, or revolutions, the shaft makes over a period of time: seconds, minutes, etc. If you could adjust the shaft speed so the rotational frequency exactly matched the natural frequency of the shaft, you would achieve critical speed, represented by Ncr in our equation. Critical speed is referred to in the singular, but, in reality, there are several critical speeds, which are multiples of the first critical speed.

CRITICAL SPEED CAN BE INJURIOUS TO YOUR SHAFT

These speeds are called "critical" because they are the speeds at which the two frequencies reinforce one another and have the potential to set up destructive vibrations or harmonics. This potential becomes more serious as the RPM's, shaft lengths, and impeller weights are increased. The relationship of shaft length to critical speed is given by the following equation. This equation calculates the first natural, or vibrational, frequency of the shaft.

Ncr =146.4

E

d = Shaft diameter (I N) I = Shaft length (I N)

a = Bearing spacing (IN) p = Density (LB/CU. IN)

We = Weight or equivalent of impeller(s) E = Modulus of elasticity

For steel and stainless steel, p =0.283; E = 30,000,000.

Some mixers which operate above critical speed are designed to pass through it with nothing more than a slight tremor on start-up or shut-down. Some smaller mixers can operate continuously at close to their critical speed without any problem. Generally speaking, however, with a stabilized impeller, it is good design practice to stay above or below the first critical speed by 20% or more. The ratio of operating speed to critical speed (NINer) is called the critical speed ratio. A critical speed ratio of 0.8 would indicate that the operating speed is 20% below the critical speed. A ratio of 1:2 indicates the operating speed is 20% above critical speed Both instances are acceptable running speed.



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NOMENCLATURE

The following terms are used in the sizing and selection of mixers, as well as the design and installation of these mixers.

A, a, SRSPC bearing space (inches) PC, Q pumping capacity (GPM)

d, SD shaft diameter (inches) Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. flow

D impeller diameter (inches) S . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. shear

E, MOD modulus of elasticity SD, d shaft diameter (inches)

FI FF fluid forces (LB) SHP shaft horsepower (HP)

HP . . . . . . . . . . . . . . . . . . . .. horsepower (H P) SPGR, Sp. Gr., S.G specific gravity

L, L, . . . . .. length, length of distance 1 (inches) SS shaft stress (PSI)

MS, Mb bending moment (IN-LB) T . . . . . . . . . . . . . . . . . . . . . . . . torque (I N-LS)

MHP motor horsepower (HP) T . . . . . . . . . . . , tank diameter

N speed (RPM) TS . . . . . . . . . . . . . . . . . .. tip speed (FTISEC)

Ncr, NCR critical speed (RPM) V . . . . . . . . . . . . . . . .. volume (liters) (gallons)

Np impeller power number VISC viscosity, (cP) (centipoise)

Nq . . . . . . . . . . . . . . . . .. impeller flow number W, W, weight, weight of impeller 1 (LS)

NRE, Nre . . . . . . . . . . . . . .. Reynolds Number We . . . . . . . . . . . . . . . .. equivalent weight (LB)

NUMI number of impellers on shaft Z . . . . . . . . . . . . . . . . . . .. liquid level (inches)

P power (HP) p, DENS density (LS/CU. IN.)


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