crane engineering principles of fluid mixing

7/28/2019 Crane Engineering Principles of Fluid Mixing

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PRINCIPLES OF FLUID MIXINGPhone: 616/399-5600

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TABLE OF CONTENTS

Types of Mixers 8.1

Mixer Terminology 8.3

D/T and Z/T 8.7

Axial Flow and Radial Flow 8.8

Flow and Shear 8.9

Horsepower (Work, Power, Shaft) 8.10

Reynolds Numbers 8.12

Pumping Capacity or Flow 8.14

Torque 8.15

Shaft Terminology 8.16

Critical Speed . 8.17

Impeller Effect on Critical Speed 8.18

Nomenclature 8.19

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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 andshafts, plus a wide range of motor horsepower. This data sheet will clarify some of the designationscommonly used when discussing mixers.

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

Air Mixer: A mixer with a motor which uses compressed air instead of electricity issometimes called an air mixer or air-drive mixer, or pneumatic mixer.

Bottom Entry: A mixer whose drive is mounted to the bottom head of a vessel. The mixer shaftenters through the tank bottom therefore must be equipped with some type ofshaft seal.

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 tothe process.

Disperser: A special purpose high-shear mixer or just the blade or impeller. Typically, ahigh-speed device often with sharp edges (some look like circular saw bladeswith bent teeth) used to break up powders or particles to dissolve or suspendthem. (See Rotor Stator definition also.)

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

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

Homogenizer: A very high-speed mixer used to blend immiscible phases of a solution into acream or emulsion.

Magnetic DriveMixer: One whose shaft and impeller is driven by a magnet. The internal mixer shaft is

driven by a magnetic field. The driven shaft does not penetrate the vesselaffording seal less mixing.

Portable Mixers: These mixers are relatively easily moved from tank to tank and mounted to tankwalls with a C-clamp or adjustable plate mount.

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TYPES OF MIXERS(continued)

Rotor Stator: A type of high shear mixer which utilizes a rotating head/impeller inside astationary shroud or cage.

Sanitary Mixers: A mixer whose drive components (motor, gearbox) are made from stainless steelor other approved materials. These are used in sanitary and washdownenvironments, as well as highly corrosive atmospheres.

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

very tall tanks to reduce capital cost.

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

Top-Entry Mixers: Mixers mounted on the rim, on beams, or on a flange entering from the top of thetank.

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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.

Baffles: Structures attached to an inside tank straight side, either directly or on tabs todirect the fluid flow vertically in the tank preventing swirl and vortexing.

Bending Moment: The product of force times distance. Fluid forces are exerted on a mixer shaft ateach impeller. The force (lbs) times the distance from the impeller to the lowestshaft bearing (in) is the bending moment (in lb). For multiple impellers, the shaftbending moment is the sum of the individual bending moments.

Bulk Fluid Velocity: The primary pumping rate of a mixer divided by the plan, cross sectional area ofthe mixed vessel. Example: Ft3/min Ft2 = Ft/min.

Case Size: Speed reducer size on gear-driven mixers. When torque design limits arereached, 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 mayaccommodate 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. Typical optimumcoverage is equal to twice the impeller diameter. Insufficient coverage may

cause vortexing and/or air entrainment.

Critical Speed: A rotational speed (rpm) of a mixer shaft which is operating at the shafts naturalvibration frequency (cycles/min). Operating a shaft at critical speed may amplifyvibrations leading to shaft failure by excessive deflection.

D/T: The ratio of impeller diameter (D) to tank diameter (T).

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

Equivalent Weight: A calculated value representing the combined impeller weight at the shaft endwhen several impellers are installed on a shaft.

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



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MIXER TERMINOLOGY

(continued)

Flow: One of two components resulting from the action of a mixer impeller (seeShear). The bulk movement of the fluid. Primary impeller pumping ratemeasured in gallons per minute is often referred to as flow.

Fluid Force: The forces exerted on a mixer shaft through the impeller as a result of the fluidmotion in the tank. Fluid forces are calculated for each impeller and used tocalculate the shaft bending moment.

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: HP, 1800

RPM, 230/460V has a NEMA 56 frame; 3 HP, 1800 RPM, 230/460V has a NEMA182 frame.

Freeboard: The distance from the liquid surface to the top of a tank. This distance must betaken into account when sizing a mixer shaft to ensure adequate coverage.

Free Flow/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 flowconstrictions are present.

HP (Horsepower): A unit for measuring the power of motors, equal to 746 Watts. In mixer

applications, horsepower may be expressed as shaft HP or motor HP.

Impeller: The device responsible for the actual mixing action in a process. The rotatingimpeller is responsible for flow and shear imparted to the fluid as it rotates.

MHP (Motor Horsepower): The actual shaft horsepower, divided by motor efficiency, determines therequired motor nameplate horsepower.

Np: Power number. A constant, unique to each type of mixing impeller, used tocalculate power draw. Power number varies with Reynolds number, but may betreated, as a constant if the Reynolds number is sufficiently high.

NQ: Flow number. A constant, derived empirically for each unique geometric shapeof mixing impeller, used to calculate flow or pumping rate.

Off Bottom: The distance from the impeller to the tank bottom. Typically, the off-bottom isbetween one to two times the impeller diameter.



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MIXER TERMINOLOGY

(continued)

Prandl Number: A dimensionless number used to estimate the boundary layer film co-efficient inheat transfer calculations. In fluids, Prandl Numbers cannot be estimatedaccurately and therefore must be derived experimentally.

Q: Flow or pumping rate, measured in gallons per minute, which is the actualdischarge rate of a specific size and type of mixing impeller.

Radial Flow: Impellers that draw from above and below the impeller and discharge it towardthe tank wall, perpendicularly from the mixer shaft, are radial flow impellers. Thistype of flow is called radial flow.

Reynolds Number: A dimensionless number used to indicate the type of fluid motion beingproduced. The value of this number determines the value of the power number,which affects the HP draw. Reynolds numbers below 1,000 are consideredlaminar; above 2,500 is turbulent flow.

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

Service Factor: Equipment having a service factor of 1.0 for a given level of performance isdesigned 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 aservice factor of 1.0 will operate for many years under a 1 HP load. A gearboxdesigned to transmit 1 HP has a service factor of 1.0 when loaded to 1 HP. If,however, that same gearbox is loaded to only HP, it now has a service factorof 2.0, indicating that it is capable of heavier duty than the current use and shouldhave a longer service life.

Shaft Stress: The intensity of the straining force on a mixer shaft that tends to deform its shapeor cause it to fracture. It is usually expressed in PSI. Shaft stress is calculatedfrom the bending moment. Stress limits are known for various materials understatic loads. For mixer shafts which are subjected to alternating stressesbecause of their rotation, a fatigue stress limit must be established which is muchless than the static limit. Mixers should not be designed with a shaft stresshigher than 15,000 PSI.

Shear: One of two components resulting from the action of a mixer impeller (seeFlow). Different velocities existing simultaneously (velocity gradient = shearrate) which produce stresses on the fluid. Shear rate X viscosity = shear stressin PSI. Shear stress is responsible for small scale fluid intermixing.



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MIXER TERMINOLOGY

(continued)

SHP(Shaft Horsepower): The actual power required to drive the mixer impeller in the specific process fluid

at the rotational speed supplied to the mixer shaft.

Specific Gravity: The ratio of fluid density E.G. (lb/gal) to the density of water (8.33 lb/gal @ 25C,1 atm pressure) under current conditions.

T: Tank diameter.

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

.

Torque: The twisting force that is created by a motor and/or gearbox to produce rotationof a mixer shaft.

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

Viscosity: Internal fluid friction. The property of a fluid that enables it to develop andmaintain an amount of shearing stress dependent upon the velocity of flow andthen to offer continued resistance to flow.

Z: The designation used to signify the liquid level or height in a tank.



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D/T and Z/TTANK DESIGN CONSIDERATIONS

Other than the mixer itself, the mixing tankdesign is the single most important factor insuccessful process result.

In order for a mixing impeller to perform optimally,correct location and liquid coverage is essential.

Incorrect position of mixing impeller may hampermixing performance and be detrimental to theperformance life of the mixer drive.

D/T is the ratio of impeller diameter to tankdiameter. For most mixing applications, it rangesfrom 0.20 to 0.60. A D/T that is too small mayleave areas unmixed. A D/T too large may chokeoff the upflow between the impeller and the tankwall. Mixer sizing for general blending starts with aD/T of 0.25. The impeller diameter is then adjustedto fit the most economical drive selection. A

smaller D/T may be offset by high flow created byturning at higher RPM.

Z/T is the ratio of liquid height to tank diameter.When this ratio exceeds 1.2, dual impellers shouldbe used.

Illustration No. 1 Off-bottom distance is normally 1 to 2 impellerdiameters. Coverage is typically 2 to 4 impellerdiameters.

Typical Baffle Arrangements

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

Three (3) baffles, 120 apart. Baffle width 1/12 the tank diameter;length is from the liquid level down to 6 inches off bottom.



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PRINCIPLES OF FLUID MIXING

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AXIAL FLOW and RADIAL FLOW

Illustration No. 2 Illustration No. 3

Mo ).App isreq

st open impeller mixing applications operate in the turbulent regime (meaning low viscositylications requiring high flow are generally best performed with axial flow impellers. If high shear

uired, radial flow impellers may be preferred.

Close clearance impellers including those which scrap the tank interior work best in laminarflow (high viscosity) conditions.



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PRINCIPLES OF FLUID MIXING

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FLOW and SHEAR

Constant Horsepower

n genera , a m xer w t a sma ameter mpe er,

Impeller Type turning at a high speed, will result in the fluid seeing

the applied power as mostly shear. This is

Rake/Picket Fence represented by the bottom of the impeller spectrum

Helix Flow Q above. Conversely, a low-speed mixer with a larger

Hydrofoil diameter impeller will discharge a higher volume of

Propeller fluid, resulting in high flow. The required ratio

Axial-Flow of these components is determined according

Turbine to the application requirement.

Homogenizers are relatively small-bladed, very high

Radial-Flow RPM mixers, which produce tremendous amounts

Turbine of shear for dispersing two phases into an emulsion.

Bar Turbine Flocculators, by way of contrast, are typically

Sawtooth slow moving, large diameters, which gently push

Impeller & liquid around a tank to build large particles from

Stator Shear S smaller ones with the aid of chemical addition.

Velocit Head) An impeller which produces high flow would have

Homogenizer little effect in a process requiring dispersion.

Illustration No. 4 (Impeller Spectrum): The list of Shear in flocculation would have a negative

impellers at the left of our impeller spectrum is a effect.

sampling which illustrates that different impeller shapes

produce different ratios of flow and shear. The importance of understanding this principle

lies mainly in recognizing that equal power does

not mean equal mixing result. The process result

The energy which a mixer transmits to the fluid is always a function of impeller type AND speed

results in two effects - flow and shear (or velocity and diameter.

head) - by the following relationship:

In Section 8.1 we will further discuss how it is

PocQ x S x S.G. feasible to change the effect of mixing performance

where: P = Power without changing impeller type while maintaining

Q = Flow a constant horse power.

S = Shear (head)

S.G. = Specific Gravity Mixing processes such as blending, dissolving and

solids suspension are 'flow or pumping-controlled'For a given power level, a mixture can be designed and make up most mixing applications. If high shear

so that either the shear component or the flow is not an essential component in achieving your

component represents most of the power applied. result, you should select a mixer with lower speed,

and larger diameter impellers. This will produce

more flow per utility dollar.



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PRINCIPLES OF FLUID MIXING3389 128

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HORSEPOWER

The power consumed by a rotating impeller in a process fluid is easily measured. The units wetypically express this power in is horsepower. It is common to relate mixer performance tohorsepower. However, there are problems associated with this tendency.

Horsepower can be calculated for most mixer (turbulent flow) applications as follows:

SHP = Np N3 D5 S.G.1.53 x 1013

NP = Power Number of impellerN = Impeller speed (RPM)D = Impeller diameter (IN)S.G. = Specific Gravity1.53 x 1013 = Conversion factor

As can be seen from this formula, changes in RPM or impeller diameter have a major impact onrequired horsepower to operate your mixer. When we examine this horsepower effect closely and tie ittogether with the formula for pumping capacity(see Pumping Capacity, page 8) we can derive thefollowing:

QHP = D4/3

K

QHP = Flow at constant HPD = Impeller Diameter (inches)K = A Constant

What this means is, if horsepower is constant and we increase impeller diameter, (RPMs must godown) and hence increase D/T, we receive a disproportional gain in flow.

The following table illustrates this:

2HP Mixers

Model RPM Max AF3 Diameter Q(gpm)

BD200 1725 7.24 1559BGM200 350 18.85 5582BGM200-233 233 24.05 77173BTO2-68 68 50.4 20,727



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HORSEPOWER (Continued)

Viscosity Effect: As described in section 8-12 on Reynolds Number, as viscosity increases, impellerpower number may begin to increase. This becomes important in the HP calculations because aspower number begins to go up so does the horsepower required to drive the mixer. Simply increasingthe input horsepower may be the answer, but one must bear in mind that this change reduces theservice factor of the mixer drive, hence a bigger mixer may be required.

Viscosity increase also effects the flow characteristics of fluid as compared to water. A correction factor

may be obtained from a qualified mixer application engineer. However, most viscons fluids should bechecked in the lab to obtain a predictable viscosity profile.

Multiple Impellers: More than one impeller may be required for some processes. This may be due totank geometry or fluid characteristics. Regardless of how many impellers are required or why, it isimportant to realize the multiple effect on horsepower required.



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REYNOLDS NUMBERS

Viscosity Effect on Mixing Performance

Reynolds Number is a dimensionless number that can be derived as follows:

Nre = 10.75 N D2S.G.Viscosity

visc. = fluid viscosity (cPs)

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

The Reynolds number is the indicator of the type of mixing fluid regime your mixer will operate in, in theprocess fluid. If the Reynolds Number is above 2,000, you are generally operating in the fluid regimewhere the power number is constant (turbulent flow). When the Reynolds Number you calculate is lessthan 1,000 (laminar flow), then the Power Number increases as the Reynolds Number decreases (seeIllustration No. 5). Consequently, the shaft horsepower you calculate must be based on the correctedpower number. In this case, you will need to obtain an Np (Power Number) vs Nrey (ReynoldsNumber) curve from the impeller manufacturer or by experimentation. The Illustration shows how thePower Number for each impeller varies with changes in Reynolds Number.

The Illustration below shows that, as Reynolds Number drops, we reach a point where the powernumber begins to increase sharply. This point depends on the type of impeller in use. ReynoldsNumbers or Nrey between 1000 and 2000 are generally considered in transition.

A1

A2

Illustration No 5



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POWER NUMBERS

Each impeller of constant geometric design demonstrates a uniform Power Number curve. By knowingthe impeller speed and diameter, the fluid specific gravity, and measuring the shaft horsepower, we cancalculate the impeller Power Number with the following formula:

Np = 1.53 x 1013SHPN3D5S.G.

SHP = Shaft horsepower (HP)

N = Speed (RPM)

D = Impeller diameter (INCHES)

S.G. = Specific Gravity

Impeller Power Numbers are generally derived in water-like fluids.

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

Many open impeller mixing applications are what we commonly refer to as flow controlled applications.This means that the process result is a direct result of the mixer pumping rate or flow. This concept canbe seen in Illustration 6 on page 8-15.



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PUMPING CAPACITY OR FLOW

Pumping capacity is the measure of fluid discharged by a rotating impeller. This flow produced directlyby the impeller and through the impeller area is known as primary flow. In addition to primary flow,liquid is drawn by and pushed by the primary flow to produce induced flow. The primary and inducedflow together make up the total flow. Total flow is difficult to calculate, but can be measured in thelaboratory. Total flow is typically several times higher than primary flow. This distinction is veryimportant when comparing mixer performance and efficiency. Mixers should be compared usingprimary pumping capacity. Total flow may be estimated by the mixer manufacturer, but should not beused for comparison purposes.

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

The following equation is used to calculate PRIMARY pumping capacity:

Q = Nq N D3231

Q = Flow in gallons per minute (GPM)Nq = Flow number for impellerN = Mixer speed (RPM)D = Impeller diameter (IN)231 - Conversion factor

Nq, the flow number, is determined empirically for each impeller type (geometry). It is constant for theimpeller under standard conditions (water, free flow). The impeller manufacturer can supply thisnumber 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, multiple impellers will pump somewhat more than one impeller at like speed andhorsepower.

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



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TORQUE

Torque is the twisting or turning force acting to produce rotation on the mixer shaft.

Torque = HP x 73025RPM

In flow-controlled mixing processes, torque = mixer flow X a constant, which is, in turn, equal to processresult. Also, higher torque (not necessarily higher HP) = higher mixer cost. Mixer torque per unitvolume may be an important scale-up criteria.

The torque required for any mixing process will effect the size and type of mixer drive and also have adirect impact on mixer shaft design.

Process Result Flow

Flow Torque (K)

Torque $ (Capital Cost)

Illustration No. 6: Flow Controlled Applications



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CRITICAL SPEED

Natural Frequency & Rotational Frequency

A rigid body, like a mixer shaft, vibrates when subjected to outside forces. Like a tuning fork, it has apredetermined vibrational frequency (harmonic), which remains constant as long as the composition ofthe shaft and the shaft-impeller relationship is not altered. This vibrational frequency is called naturalfrequency. Unlike a tuning fork however, a mixer shaft must also deal with the forces of rotation.

The rotational frequency is the number of turns or revolutions the shaft makes over a period of time -

seconds, minutes, etc. We typically measure rotational frequency in revolutions per minute (RPM). Ifyou could adjust the shaft speed so the rotational frequency exactly matched the natural frequency ofthe shaft, you would achieve critical speed, represented by Ncr in our equation (Illustration No. 9).Additional critical speeds actually occur at several multiples of the first critical speed.

Critical Speed Can Be Dangerous

These speeds (vibration and rational) are called critical because they are the speeds at which the twofrequencies reinforce one another. This condition has the potential to set up destructive force. Therelationship of shaft length and impeller weight to critical speed is given by the following equation. Thisequation calculates the first natural, or vibrational, frequency of the shaft.

d = Shaft diameter (IN)l = Shaft length (IN)a = Bearing spacing (IN) = Density (LB/CU. IN)We = Weight or equivalent of impeller(s)E = Modulus of elasticity

Illustration No. 7

Some mixers are designed to operate above first critical speed. When designed this way the shaftpasses through critical speed with nothing more than a slight tremor at start up or shutdown. Generallyspeaking, it is good design practice to stay below the first critical speed by 20% or more. The ratio ofoperating speed to critical speed (N/Ncr) is called the critical speed ratio. A critical speed ratio of 0.8would indicate that the operating speed is 20% below the critical speed. A ratio of 1:2 indicates theoperating speed is 20% above critical speed.



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IMPELLER EFFECT ON CRITICAL SPEED

Weight and Equivalent Weight

Impeller weight can be calculated, knowing the material density and the dimensions of all the impellercomponents, but this weight is only directly useful if there is only one impeller on a shaft, located at thevery end of a shaft.

For shaft design calculations, we are concerned with the effect of the weight or equivalent weight ofmultiple impellers on the end of the shaft. The equivalent weight is the apparent weight of all theimpellers and is calculated using the following formula.

We = Equivalent weight (LB)W1,2,3 = Weights of impellers 1, 2, 3 (LB)L1, 2, 3 = Length (IN)

Illustration No. 8

When impellers are made adjustable, they must be safe at all operating conditions. The simple way toassume all the impellers are 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, theimpellers are safe at any position.

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



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NOMENCLATURE

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

A, a, BRSPC 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)

F, FF fluid forces (LB) SHP shaft horsepower (HP)

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

L, L1 length, length of distance 1 (inches) SS shaft stress (PSI)

MB, Mb bending moment (IN-LB) T torque (IN-LB)

MHP motor horsepower (HP) T tank diameter

N speed (RPM) TS tip speed (FT/SEC)

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

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

Nq impeller flow number W, W1 weight, weight of impeller 1 (LB)

NRE, Nre Reynolds Number We equivalent weight (LB)

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

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


crane engineering principles of fluid mixing

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