Why Study Particle Science?

by Dr. Ralph D. Nelson, Jr., P.E. Managing Editor of ERPT - 1999 Aug 20

Some 75% of chemical manufacturing processes involve small solid particles (fine particles) at some point. Proper design and handling of these fine particles often makes the difference between success and failure. Careful attention to particle characteristics during the design and operation of a facility can significantly improve environmental performance and increase profitability by improving product yield and reducing waste.

In the early stages of product and process R&D, as the process is scaled up from from bench-top glassware to several-gallon, then hundred-gallon, and finally production scale, technologists should explicitly consider how the particulate material in the system will behave in the sequence of unit operations and in the equipment for processing, storage, and transport.

For each particulate material -- raw material, intermediate, final product, or co-product consider the following:

SAMPLING AND ANALYSIS: To characterize the particles, you need a good sampling protocol, sound analytical procedures, and photographs that allow you to monitor the particles continuously on-line (best case) or through grab samples taken while trying to resolve a problem.

SIZE DISTRIBUTION: The particle size distribution should be carefully-controlled and consistent from batch to batch, or over time (in continuous reactors). It should be optimized to give the least trouble during processing and the best product characteristics.

SHAPE, STATE OF AGGREGATION, AREA: The particle shape, state of aggregation, and surface area per gram should be characterized after each key processing stage. Understanding and controlling the conditions which produce the particles can help you to optimize them for their intended use.

FLOW, SEDIMENTATION, BED DENSITY: Flow characteristics (powder or slurry), sedimentation rates (in liquid or gas), and bed density (sifted, settled, or packed) significantly affect processing, so you should characterize them and understand how changes in these parameters will affect the process.

ATTRITION: Attrition resistance (resistance to breakage) should be known, well-controlled and optimum for the task. Keep in mind that particle breakdown during processing can destroy carefully developed characteristics.

STATE OF DISPERSION (IN LIQUIDS): Particles suspended in liquid may flocculate, agglomerate, float, fail to wet-in, foul the walls, or stabilize foam.

STATE OF DISPERSION (IN GASES): Particles suspended in gas may pick up a charge, explode, form agglomerates, or coat the walls.

SAFETY, HEALTH, AND ENVIRONMENT: It is prudent (and generally required) that you evaluate and minimize hazards related to       explosion or fire (of a dust cloud or fluidized bed or pneumatic conveying line or dust buildup on equipment or walls)

      inhalation or contact with dusts or mists from the process       discharge to the environment of dust particles or sprays

The study of particle technology has many interesting technical facets and many rewarding economic aspects. Failure to consider the particle science involved in a process can result in very expensive or unpleasant consequences.

CPE 124 Particle Technology - Study Notes

Dr. Jie Zhang

Chapter 1. Characterisation of solid particles

What is particle technology?

Techniques for processing and handling particulate solids. It plays a major role in the production of materials in industry.

Chapter 1. Characterisation of solid particles

Individual solid particles are characterised by their size, shape, and density.

1.1 Particle shape

The shape of an individual particle is expressed in terms of the sphericity s, which is independent of particle size. The sphericity of a particle is the ratio of the surface-volume ratio of a sphere with equal volume as the particle and the surface-volume ratio of the particle. For a spherical particle of diameter D p, s =1; for a non-spherical particle, the sphericity is defined as

Dp: equivalent diameter of particle

Sp: surface area of one particle

vp: volume of one particle

The equivalent diameter is sometimes defined as the diameter of a sphere of equal

volume. For fine particles, Dp is usually taken to be the nominal size based on screen analysis or microscopic analysis. The surface area is found from adsorption measurements or from the pressure drop in a bed of particles. For many crushed materials, s is between 0.6 and 0.8. For particles rounded by abrasion, s may be as high as 0.95.

1.2 Particle size

In general "diameter" may be specified for any equidimensional particles. Particles that are not equidimensional, i.e. that are longer in one direction than in others, are often characterised by the second longest major dimension. For needle like particles, Dp would refer to the thickness of the particle, not their length. Units used for particle size depend on the size of particles.

Coarse particles: inches or millimetres

Fine particles: screen size

Very fine particles: micrometers or nanometers

Ultra fine particles: surface area per unit mass, m2/g

1.3 Mixed particle sizes and size analysis

In a sample of uniform particles of diameter Dp, the total volume of the particles is m/ p, where m = mass of the sample, p = density. Since the volume of one particle is vp, the total number of particle in the sample is

The total surface area of the particles is

To apply the above two equations to mixtures of particles having various size and densities, the mixture is sorted into fractions, each of constant density and approximately constant size.

1.4 Specific surface of mixture

If the particle density p and spericity s are known, the surface area of particles in

each fraction can be calculated and added to give the specific surface, Aw.

where xi = mass fraction in a given increment, = average diameter, taken as arithmetic average of the smallest and largest particle diameters in increment.

1.5 Average particle size

(1). Volume-surface mean diameter, , defined by

If the number of particles in each fraction Ni is known, then

(2). Arithmetic mean diameter

NT = number of particles in the entire sample

(3). Mass mean diameter

(4). Volume mean diameter

1.6 Number of particles in mixture

The volume of any particle is proportional to its "diameter" cubed.

a = volume shape factor

Assuming that a is independent of size

1.7 Screen analysis

Standard screens are used to measure the size (and size distribution) of particles in the size range between about 3 and 0.0015in (76mm and 38 m).

Screen is identified by meshes per inch, e.g. 10mesh, Dp = 1/10 = 0.1in.

The area of the openings in any one screen in the series is exactly twice that of the openings in the next smaller screen. The ratio of the actual mesh dimension of any

screen to that of the next smaller screen is =1.41.

Analysis using standard screen: Screens are arranged serially in a stack, with the smallest mesh at the bottom and the largest at the top. Materials are loaded at top and then shacked for a period of time (e.g. 20 minutes).

14/20: through 14 mesh and on 20 mesh

Screen analysis gives: xi and .

CPE 124 Particle Technology - Study Notes

Dr. Jie Zhang

Chapter 2. Motion of Particles through Fluids

2.1 Motion of particles through fluids

2.1.1 Mechanics of particle motion

Three forces acting on a particle moving through a fluid:

1). The external force, gravitational or centrifugal;

2). The buoyant force, which acts parallel with the external force but in the opposite direction;

3). The drag force, which appears whenever there is relative motion between the particle and the fluid

Drag: the force in the direction of flow exerted by the fluid on the solid is called drag.

2.1.2 Equations for one-dimensional motion of particle through fluid

Consider a particle of mass m moving through a fluid under the action of an external force Fe. Let the velocity of the particle relative to the fluid be u, let the buoyant force on the particle be Fb and let the drag be FD, then

(1)

The external force can be expressed as a product of the mass and the acceleration ae of the particle from this force,

(2)

The buoyant force is, be Archimedes’ law, the product of the mass of the fluid displaced by the particle and the acceleration from the external force. The volume of the particle is m/ p, the mass of fluid displaced is (m/ p) , where is the density of the fluid. The buoyant force is then

Fb = m ae/ p (3)

The drag force is

FD = CDu2 Ap/2 (4)

where CD is the drag coefficient, Ap is the projected area of the particle in the plane perpendicular to the flow direction.

By substituting the forces into Eq(1), we have

(5)

Motion from gravitational force:

In this case, ae = g

(6)

Motion in a centrifugal field:

ae = r 2

(7)

In this equation, u is the velocity of the particle relative to the fluid and is directed outwardly along a radius.

2.2 Terminal velocity

In gravitational settling, g is constant. Also, the drag always increases with velocity. The acceleration decreases with time and approaches zero. The particle quickly reaches a constant velocity which is the maximum attainable under the circumstances. This maximum settling velocity is called terminal velocity.

(8)

(9)

In motion from a centrifugal force, the velocity depends on the radius and the acceleration is not constant if the particle is in motion with respect to the fluid. In many practical use of centrifugal force, du/dt is small. If du/dt is neglected, then

(10)

Motion of spherical particles:

If the particles are spheres of diameter Dp, then

m = Dp3

p/6

Ap = Dp2/4

Substitution of m and Ap into the equation for ut gives the equation for gravity settling of spheres:

(11)

2.3 Drag coefficient

Drag coefficient is a function of Reynolds number. The drag curve applies only under restricted conditions:

i). The particle must be a solid sphere;

ii). The particle must be far from other particles and the vessel wall so that the flow pattern around the particle is not distorted;

iii). It must be moving at its terminal velocity with respect to the fluid.

Particle Reynolds number:

(12)

u: velocity of approaching stream

Dp: diameter of the particle

: density of fluid

: viscosity of fluid

Stokes’ law applies for particle Reynolds number less than 1.0

CD = 24/NRe,p (13)

From Eq(4)

FD = 3 ut Dp (14)

From Eq(11)

ut = g Dp2( p - )/(18 ) (15)

At NRe,p =1, CD =26.5 instead of 24 from the above equation.

Centrifugal: r 2 g.

For 1000 < NRe,p <200,000, use Newton’s law

CD = 0.44 (16)

FD= 0.055 Dp2 ut

2 (17)

(18)

Newton’s law applies to fairly large particles falling in gases or low viscosity fluids.

Terminal velocity can be found by trial and error after guessing NRe,p to get an initial

estimate of CD.

2.4 Criterion for settling regime

To identify the range in which the motion of the particle lies, the velocity term is eliminated from the Reynolds number by substituting ut from Stokes’ law

(19)

If Stokes’ law is to apply, NRe,p <1.0. Let us introduce a convenient criterion K

(20)

Then NRe,p = K3/18. Setting NRe,p = 1 and solving for K gives K=2.6. If K is less than 2.6 then Stokes’ law applies.

Substitution for ut using Newton’s law

NRe,p = 1.75K1.5

Setting NRe,p = 1000 and solving for K gives K = 68.9. Setting NRe,p = 200,000 and solving for K gives K = 2,360.

Stokes’ law range: K < 2.6

Newton’s law range: 68.9 < K < 2,360

when K > 2,360 or 2.6 < K < 68.9, ut is found from using a value of CD found by trial from the curve.

2.5 Hindered settling

In hindered settling, the velocity gradients around each particle are affected by the presence of nearby particles. So the normal drag correlations do not apply. Also, the particles in settling displace liquid, which flows upward and make the particle velocity relative to the fluid greater than the absolute settling velocity. For uniform suspension, the settling velocity us can be estimated from the terminal velocity for an isolated particle using the empirical equation of Maude and Whitmore

us = ut( )n

Exponent n changes from about 4.6 in the Stokes’ law range to about 2.5 in the Newton’s law region. For very small particles, the calculated ratio us/ut is 0.62 for =0.9 and 0.095 for =0.6. With large particles, the corresponding ratios are us/ut = 0.77 and 0.28; the hindered settling effect is not as profound because the boundary layer thickness is a smaller fraction of the particle size.

If particles of a given size are falling through a suspension of much finer solids, the terminal velocity of the larger particles should be calculated using the density and viscosity of the fine suspension. The Maude-Whitmore equation may then be used to estimate the settling velocity with taken as the volume fraction of the fine suspension, not the total void fraction.

Suspensions of very fine sand in water is used in separating coal from heavy minerals and the density of the suspension is adjusted to a value slightly greater than that of coal to make the coal particles rise to the surface, while the mineral particles sink to the bottom.

CPE 124 Particle Technology - Study Notes

Dr. Jie Zhang

Chapter 3. Size Reduction

Four commonly used methods for size reduction: 1). Compression; 2). Impact; 3). Attrition; 4). Cutting.

3.1 Principle of size reduction

Criteria for size reduction

An ideal crusher would (1) have a large capacity; (2) require a small power input per unit of product; and (3) yield a product of the single size distribution desired.

Energy and power requirements in size reduction

The cost of power is a major expense in crushing and grinding, so the factors that

control this cost are important.

3.2 Crushing efficiency

3.2.1 Empirical relationships: Rittinger’s and Kick’s law

The work required in crushing is proportional to the new surface created. This is equivalent to the statement that the crushing efficiency is constant and, for a giving machine and material, is independent of the sizes of feed and product. If the sphericities a (before size reduction) and b (after size reduction) are equal and the machine efficiency is constant, the Rittinger’s law can be written as

where P is the power required, is the feed rate to crusher, is the average particle

diameter before crushing, is the average particle diameter after crushing, and Kr is Rittinger’s coefficient.

Kick’s law: the work required for crushing a given mass of material is constant for the same reduction ratio, that is the ratio of the initial particle size to the finial particle size

where Kk is Kick’s coefficient.

3.2.2 Bond crushing law and work index

The work required to form particles of size Dp from very large feed is proportional to the square root of the surface-to-volume ratio of the product, sp/vp. Since s = 6/Dp, it follows that

where Kb is a constant that depends on the type of machine and on the material being crushed.

The work index, wi, is defined as the gross energy required in KWH per ton of feed to reduce a very large feed to such a size that 80% of the product passes a 100 m screen.

If Dp is in millimetres, P in KW, and in tons per hour, then

If 80% of the feed passes a mesh size of Dpa millimetres and 80% of the product a mesh of Dpb millimetres, it follows that

Example: What is the power required to crush 100 ton/h of limestone if 80% of the feed pass a 2-in screen and 80% of the product a 1/8 in screen? The work index for limestone is 12.74.

Solution: =100 ton/h, wi =12.74, Dpa =2 25.4=50.8 mm, Dpb =25.4/8=3.175 mm

3.3 Size reduction equipment

Size reduction equipment is divided into crushers, grinders, ultrafine grinders, and cutting machines. Crusher do the heavy work of breaking large pieces of solid material into small lumps. A primary crusher operates on run-of -mine material accepting anything that comes from mine face and breaking it into 150 to 250 mm lumps. A secondary crusher reduces these lumps into particles perhaps 6mm in size. Grinders reduce crushed feed to powder. The product from an intermediate grinder might pass a 40-mesh screen; most of the product from a fine grinder would pass a 200-mesh screen with a 74 m opening. An ultrafine grinder accepts feed particles no larger than 6mm and the product size is typically 1 to 5 m. Cutters give particles of definite size and shape, 2 to 10mm in length.

The principal types of size-reduction machines are as follows:

A. Crushers (coarse and fine)

1. Jaw crushers2. Gyratory crushers3. Crushing rolls

B. Grinders (intermediate and fine)

1. Hammer mills; impactors2. Rolling-compression mills

3. Attrition mills4. Tumbling mills

C. Ultrafine grinders

1. Hammer mills with internal classification2. Fluid-energy mills3. Agitated mills

D. Cutting machines

1. Knife cutters; dicers; slitters

CPE 124 Particle Technology - Study Notes

Dr. Jie Zhang

Chapter 4. Mechanical Separations

Mechanical separations are performed based on the physical difference between particles such as size, shape, or density. Mechanical separations are applicable to heterogeneous mixtures, not to homogeneous solutions.

4.1 Screening

Screening is a method of separating particles according to size alone.

Undersize: fines, pass through the screen openings

Oversize: tails, do not pass

A single screen can make but a single separation into two fractions. These are called unsized fractions, because although either the upper or lower limit of the particle sizes they contain is known, the other limit is unknown. Material passed through a series of screens of different sizes is separated into sized fractions, i.e. fractions in which both the maximum and minimum particle sizes are known.

4.1.1 Screening equipment

Stationary screens and grizzlies; Gyrating screens; Vibrating screens; Centrifugal

sitter.

Cutting diameter Dpc: marks the point of separation, usually Dpc is chosen to be the mesh opening of the screen.

Actual screens do not give a perfect separation about the cutting diameter. The undersize can contain certain amount of material coarser than Dpc, and the oversize can contain certain amount of material that is smaller than Dpc.

4.1.2 Material balances over a screen

Let F, D, and B be the mass flow rates of feed, overflow, and underflow, respectively, and xF, xD, and xB be the mass fractions of material A in the streams. The mass fractions of material B in the feed, overflow, and underflow are 1- xF, 1- xD, and 1- xB.

F = D + B

FxF = DxD + BxB

Elimination of B from the above equations gives

Elimination of D gives

4.1.3 Screen effectiveness

A common measure of screen effectiveness is the ratio of oversize material A that is actually in the overflow to the amount of A entering with the feed. These quantities are DxD and FxF respectively. Thus

where EA is the screen effectiveness based on the oversize. Similarly, an effectiveness EB based on the undersize materials is given by

A combined overall effectiveness can be defined as the product of the two individual ratios.

Example: A quartz mixture is screened through a 10-mesh screen. The cumulative screen analysis of feed, overflow and underfolw are given in the table. Calculate the mass ratios of the overflow and underflow to feed and the overall effectiveness of the screen.

Mesh Dp (mm) Feed Overflow Underflow

4 4.699 0 0 0

6 3.327 0.025 0.071 0

8 2.362 0.15 0.43 0

10 1.651 0.47 0.85 0.195

14 1.168 0.73 0.97 0.58

20 0.833 0.885 0.99 0.83

28 0.589 0.94 1.0 0.91

35 0.417 0.96 0.94

65 0.208 0.98 0.975

Pan 1.0 1.0

Solution:

From the table, xF=0.47, xD=0.85, xB=0.195

4.1.4 Capacity and effectiveness of screens

The capacity of a screen is measured by the mass of material that can be fed per unit time to a unit area of the screen. Capacity and effectiveness are opposing factors. To obtain maximum effectiveness, the capacity must be small, and large capacity is obtainable only at the expense of a reduction in effectiveness.

4.2 Filtration

Filtration is the removal of solid particles from a fluid by passing the fluid through a filtering medium, or septum, on which the solids are deposited. The fluid may be liquid or gas, the valuable stream from the filter may be fluid, or the solid, or both. Sometimes it is neither, as when waste solid must be separated from waste liquid prior to disposal.

Filters are divided into three main groups: cake filters, clarifying filters, and crossflow filters. Cake filters separate relatively large amount of solids as a cake of crystals or sludge. Often they include provisions for washing the cake and for removing some of the liquid from the solids before discharge. At the start of filtration in a cake filter, some solid particles enter the pores of the medium and are immobilised, but soon others begin to collect on the septum surface. After this brief period the cake of solids does the filtration, not the septum; a visible cake of appreciable thickness builds up on the surface and must be periodically removed. Clarifying filters remove small amount of solids to produce a clean gas or a sparkling clear liquid such as beverage. The solid particles are trapped inside the filter medium or on its external surfaces. Clarifying filters differ from screens in that the pores of the filter medium are much larger in diameter than the particles to be removed. In a crossflow filter, the feed suspension flows under pressure at a fairly high velocity across the filter medium. A thin layer of solids may form on the surface of the medium, but the high liquid velocity keeps the layer from building up. The filter medium is a ceramic, metal, or polymer membrane with pores small enough to exclude most of suspended particles. Some of the liquid passes through the medium as clear filtrate, leaving a more concentrated suspension

behind.

4.3 The theory of filtration

In cake filters, the particles forming the cake are small and the flow through the bed is slow. Streamline conditions are invariably obtained. From Kozeny equation,

(1)

where u is the velocity of the filtrate, L is the cake thickness, S is the specific surface of the particles, is the porosity of cake, is the viscosity of the filtrate, and P is the applied pressure difference. The filtrate velocity can also be written as

(2)

where V is the volume of filtrate which has passed in time t and A is the total cross-sectional area of the filter cake.

For incompressible cakes can be taken as constant and the quantity 3/[5(1- )2S2] is then a property of the particles forming the cake and should be constant for a given material. Therefore

(3)

where

(4)

Eq(3) is the basic filtration equation and r is termed the specific resistance. It is seen to depend on and S. For incompressible cakes it is taken as constant, but it will depend on the rate of deposition, nature of particles, and on forces between the particles.

In Eq(3), the variables V and L are connected, and the relation between them can be obtained by making a material balance between the solids in the slurry and in the cake.

Mass in the filter cake is (1- )AL s, where s is the density of the solids.

Mass of liquid retained in the filter cake is AL , where is the density of the filtrate.

If J is the mass fractions of solids in the original suspension

(5)

That is

(6)

Therefore

(7)

and

(8)

If v is the volume of cake deposited by unit volume of filtrate then:

or (9)

and from Eq(8):

(10)

Substituting for L in Eq(3)

or

(11)

Eq(11) can be regarded as the basic relation between P, V, and t. Two important types of operation will be considered: 1). where the pressure difference is maintained constant and, 2). where the rate of filtration is maintained constant.

Constant pressure difference

Eq(11) can be re-written as

(12)

Integrating Eq(12) gives

or (13)

Thus for a constant pressure filtration, there is a linear relation between V2 and t. Filtration at constant pressure is more frequently adopted in practical conditions.

Constant rate filtration

constant (14)

Therefore

or (15)

In this case, P is directly proportional to V.

Flow of filtrate through the septum and cake combined

Suppose that the filter septum to be equivalent to a thickness Ls of cake, then if P is the pressure drop across the cake and septum combined Eq(3) can be written as:

(16)

i.e.

(17)

For constant rate filtration we have

(18)

For constant pressure filtration we have

(19)

4.4 Separations based on the motion of particles through fluids

Devices that separate particles of differing densities are known as sorting classifiers. They use one of the two principal separation methods: sink-and-float and differential settling.

4.4.1. Sink-and-float methods

A sink-and-float method uses a liquid sorting medium, the density of which is intermediate between that of the light material and that of the heavy material. Then the heavy particles settle through the medium, and the lighter ones float, and a separation is thus obtained. This method has the advantage that, in principle, the separation depends only on the difference in the densities of the two substances and is independent of the particle size. This method is also known as the heavy-fluid separation.

Heavy fluid processes are used to treat relatively coarse particles, usually greater than 10-mesh. A comment choice of medium is a pseudoliquid consisting of a suspension in water of fine particles

4.4.2. Differential settling methods

Differential settling methods utilise the difference in terminal velocities that exist

between substances of different density. The density of the medium is less than that of either substance.

Consider particles of two materials A and B settling through a medium of density . Let A be the heavier. If the smallest particle of A settles faster than the largest particle of B, then complete separation of A and B can be achieved.

For settling in the Stokes’ law region, the terminal velocity can be calculated as

For equal-settling particles, utA = utB, therefore

For settling in the Newton’s law range

If the ratio of diameters of the smallest particle of A and the largest particle of B is larger than the equal-settling ratio, then perfect separation of A and B can be achieved.

] Education in particle technology

Gyratory Screen

ELECTRO FLUX Gyratory screen motion is the most effective method for screening. It is reliable and economical continuous process equipment, which provide solution to variety of needs of screening, sifting, classification, grading oversize or undersize removal de-dusting, de-watering, de-lumping ,fiber recovery, filtration, pre-filtration, scalping etc., Vibro screen are driven by a special type of vertically mounted heavy duty Energy efficiency Motor eccentric at the upper & lower end of the shaft.

Move Close

 

 

MODEL NO. Screen DIA mmScreening Area

Sq.cmMotor Hp

EFI - 01 600 1884 0.5EFI - 02 900 2886 1.0EFI - 03 1200 3768 2.0

  1500 4710 2.0 / 2.5 

Rotation of Unbalanced top weight causes vibration in Horizontal plane whereas the rotation of lower weight causes tilt & vibrations in vertical plane. By changing their lead angle, various spiral screening patterns are obtained to suit different application.

Anti-Blinding Devices:Ball Tray Anti-Blinding Device: Ball tray utilizes the multi-plane inertial vibration of the screener and bouncing elastomeric balls to prevent screen blinding.

The device consists of two screens spaced sufficiently apart to allow captive elastomeric balls to bounce between the upper "operating" screen and the lower coarse-mesh "ball screen" for the purpose of dislodging near-size, dry materials lodged in the apertures of the upper screen.

Ring Tray Screen, Anti-Blinding Device Screen Rings are effective at preventing fibrous, stringy and sticky materials from blinding the screen.

Multi-plane inertial vibration of the screener causes plastic rings to move continuously across a perforated stainless steel plate, shearing fibers and scraping away gummy materials. Because they are hollow, the rings promote product flow over the entire screen surface, maximizing screening efficiency.

Advantages :   Low power consumption   Varied range of application   High processing rate per unit

area of screen   Accurate separation   Minimum screen building   Screening up to 200 mesh   Ball tray for anti blinding   Multi-deck arrangements upto

Seven decks.

Applications :   Food Industry   Chemical

industry  

Pharmaceuticals   Ceramics   Plastics   Abrasives

Factors Determine Screening Capacity : Material Size, Bulk density of the material Nature of material, Moisture contamination, flow in temperature, type of feeding, etc.,

TROMMEL

A trommel (from the German word for drum, "Trommel") is a screened cylinder used to separate materials by size - for example, separating the biodegradable fraction of mixed municipal waste or separating different sizes of crushed stone.

Portable trommels (also called portable trommel screens) are often used in the production of organic products from various types of waste.

For example, excavation contractors may screen their site debris into two fractions; a saleable topsoil for farms, nurseries and site-work, as well as cleaned rock for aggregates or landscaping work. This allows the contractor to resell their waste, instead of incurring the cost of sending it for disposal.

The same principle applies to the production of compost, sand/gravel, lumber mill by-products and municipal waste.

 

Crushers o C40 Compact Jaw Crusher o C50 Jaw Crusher o C44 Cone Crusher o I54 Impactor

Vibrating Screeners Trommel Screeners Stacking Conveyors Used Equipment

Crushers

C40 Compact Jaw Crusher

The McCloskey C40 is a full featured compact jaw crusher for mobile operators. Easy to move, economical to operate and easy to use, all while maintaining the production levels required to get the job done.

C50 Jaw Crusher

McCloskey International is now breaking new ground with the introduction of the C50 crusher. With class leading capacity, 50" wide jaw, and large stockpile heights as standard, the new C50 crusher continues to push the boundaries of industry performance.

C44 Cone Crusher

Following from the recent introduction of the C50 Jaw Crusher, McCloskey International are launching the C44 Cone Crusher to add to its new full range of portable crushing plants.

Crushers o C40 Compact Jaw Crusher o C50 Jaw Crusher

o C44 Cone Crusher o I54 Impactor

Vibrating Screeners Trommel Screeners Stacking Conveyors Used Equipment

Crushers

C40 Compact Jaw Crusher

The McCloskey C40 is a full featured compact jaw crusher for mobile operators. Easy to move, economical to operate and easy to use, all while maintaining the production levels required to get the job done.

C50 Jaw Crusher

McCloskey International is now breaking new ground with the introduction of the C50 crusher. With class leading capacity, 50" wide jaw, and large stockpile heights as standard, the new C50 crusher continues to push the boundaries of industry performance.

C44 Cone Crusher

Following from the recent introduction of the C50 Jaw Crusher, McCloskey International are launching the C44 Cone Crusher to add to its new full range of portable crushing plants.

I54 Impactor

The I-54 Impactor is equipped with a 47" (1200mm) x 53" (1350mm) impactor chamber, built to bring high quality and high production McCloskey crushers to impactor applications. Incorporating an independent pre-screen and a class leading feed opening size the McCloskey I-54 is designed to lead the way in mobile impact crushing.

Crushers o C40 Compact Jaw Crusher o C50 Jaw Crusher o C44 Cone Crusher o I54 Impactor

Vibrating Screeners Trommel Screeners Stacking Conveyors Used Equipment

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New Jaw Crusher

McCloskey International have a proven reputation for designing quality, class leading machinery. McCloskey International is now breaking new ground with the introduction of the C50 crusher.

The first of McCloskey's full line of crushers, the C50 Jaw Crusher is continuing McCloskey's focus on quality, durability, and productivity. With a CAT C9 engine, 50'' wide Telsmith Jaw (the widest Jaw in its class), and user friendly control panel with excellent machine diagnostics, the C50 places McCloskey's at the fore of portable crushing machinery.

With class leading material throughput and capacity, the largest stockpile height in its class, and an extended side conveyor as standard, the new C50 crusher continues to push the boundaries of industry performance.

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Power Plant: 350 HP (261 kw) Tier III CAT C9 Engine

Jaw: 50'' x 26'' (1270mm x 660mm)

Hopper:6.8m³ (8.9yd³) Level hopper capacity

10.2m³ (13.3yd³) Gross hopper capacity

Transport Height: 11' - 2'' (3.4m)

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Transport Width: 9' - 6'' (2.9m)

Weight: 48,000 kg (105,821 lb)

 

Features and Benefits

Feeder

Folding hardox hopper mounted over vibrating feeder with integral pre-screen. Feeder rate can be regulated manually or automatically by the load sensing jaw.

Crusher

True 50"x26" (1270mmx660mm) Telsmith jaw. Reversible hydrostatic drive. Reversible jaw plates. Fully hydraulic closed size setting adjust and relief.

Conveyor

Extended 42 " main conveyor as standard, giving large stockpile capacity. Conveyor lowers and raises hydraulically and is easily removable for maintenance.

Power unit

CAT C9 ACERT 350hp (261kW) engine with all round access for maintenance. Innovative hydraulic system provides significant improvments in fuel economy.

Colour Control Panel

User friendly waterproof and dustproof control panel. Allows monitoring of pressures, fluid levels, fuel consumption. Provides push button control of jaw, track and feeder functions.

Options

Roll in bogie

Hopper Extension

Overband Magnet

Crusher Deflector Plate

Water pump and dust suppression

The S80 is the entry point to the McCloskey S-Series 3 way split range. It combines a High Energy 4.5' x 10' screenbox with a 8 cubic yard in a compact, easily transportable package

The McCloskey S130 represents the most advanced 14'x5' portable vibratory screening plant in porduction today. Combining this class leading screening with the McCloskey High Energy Screen technology ensures that no other similar size screener can compare.

0

The highly advanced S190 is capable of screening a diverse range of material in the most difficult conditions. Designed to meet the demands of high throughput operations in quarrying, crusher circuits, sand & gravel, and coal screening.

The Tripledeck is a highly aggressive machine producing four grades of material in an extremely productive way. Combining its class leading screening area with the McCloskey High Energy Screen technology ensures that no other screening plant can compare

123 Sizer

The McCloskey 123 Sizer is ideal for quarry and mining applications where only very heavy duty equipment will meet your needs. With a high strength bolted construction screen box, and a high tensile steel punch plate, the 123 Sizer has the ability to handle the heaviest of materials

Mini Sizer

The McCloskey Mini Sizer is a unique and compact solution for high quality screening when on-site space and transport options are at a minimum. With a high processing capability the Mini Sizer is an efficient and cost effective screener

Kompaq

With a highly aggressive screenbox, unrivalled mobility, and the ability to handle a wide range of material, the McCloskey Kompaq is a truely unique and versatile flatdeck screener, designed to meet your needs.

407

The McCloskey 407 leads the way in innovation. The world's most efficient compact trommel best suits smaller, on-demand jobs with production between 20 and 50 yards per hour.

412

The McCloskey 412 Trommel has a greater screening area with a patented 180º degrees radial stacking conveyor and quick drum exchange system.Also available are the 412RT and TA models which offer track mobility or tandem sprung suspension and more horsepower.

512 A / R

The 512 screeners provide our customers with an extended fines conveyor on the 512A, or our patented radial conveyor on the 512R. The 512 trommels are best suited for mid-size operations requiring portability and proven screening performance.

512 RET / RT

The 512 RET was designed by the most experienced design engineers in the industry with a collective experience of over 60 years. The 512 RET is ideal for composting and waste management applications.

516

The 516 is machine for operators looking for a medium sized machine that offers impressive production, a high quality production, and excellent mobility.

616

The 616 Trommel screen combines high productivity with ease of transport for operators and contractors alike.

621 / 628

The 621 Trommel Screener is suited for large heavy duty applications where production rates can reach 200+ tph in topsoil and sticky material or 300tph in sand and gravel. The 628 offers all the features of a 621 Trommel along with a 7ft longer drum.

733

The 733 Trommel screen is a very tough and reliable machine, offering extensive screening surface area that provides high production, and impressive stockpiling abilities

Sieve analysisFrom Wikipedia, the free encyclopedia

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A sieve analysis (or gradation test) is a practice or procedure used (commonly used in civil engineering) to assess the particle size distribution (also called gradation) of a granular material.

The size distribution is often of critical importance to the way the material performs in use. A sieve analysis can be performed on any type of non-organic or organic granular materials including sands, crushed rock, clays, granite, feldspars, coal, soil, a wide range of manufactured powders, grain and seeds, down to a minimum size depending on the exact method. Being such a simple technique of particle sizing, it is probably the most common.[1]

Contents

[hide]

1 Procedure o 1.1 Preparation

2 Results 3 Methods

o 3.1 Throw-action sieving o 3.2 Horizontal sieving o 3.3 Tapping sieving o 3.4 Sonic sieving o 3.5 Wet sieving o 3.6 Air Jet Sieving

4 Types of gradation relatively to the aggregate nature 5 Limitations of sieve analysis 6 Properties 7 Engineering applications 8 Forecast

o 8.1 "Sieving" with Digital Image Processing

Procedure

Sieves used for gradation test.

A mechanical shaker used for sieve analysis.

A gradation test is performed on a sample of aggregate in a laboratory. A typical sieve analysis involves a nested column of sieves with wire mesh cloth (screen). See the separate Mesh (scale) page for details of sieve sizing.

A representative weighed sample is poured into the top sieve which has the largest screen openings. Each lower sieve in the column has smaller openings than the one above. At the base is a round pan, called the receiver.

The column is typically placed in a mechanical shaker. The total time od shakeing is 10 minutes. The shaker shakes the column, usually for some fixed amount of time. After the shaking is complete the material on each sieve is weighed. The weight of the sample of each sieve is then divided by the total weight to give a percentage retained on each sieve.

The size of the average particles on each sieve then being analysis to get the cut-point or specific size range captured on screen.

The results of this test are used to describe the properties of the aggregate and to see if it is appropriate for various civil engineering purposes such as selecting the appropriate aggregate for concrete mixes and asphalt mixes as well as sizing of water production well screens.

The results of this test are provided in graphical form to identify the type of gradation of the aggregate. The complete procedure for this test is outlined in the American Society for Testing and Materials (ASTM) C 136[2] and the American Association and State Highway and Transportation Officials (AASHTO) T 27[3]

A suitable sieve size for the aggregate should be selected and placed in order of decreasing size, from top to bottom, in a mechanical sieve shaker. A pan should be placed underneath the nest of sieves to collect the aggregate that passes through the smallest. The entire nest is then agitated, and the material whose diameter is smaller than the mesh opening pass through the sieves. After the aggregate reaches the pan, the amount of material retained in each sieve is then weighed.[4]

[edit] Preparation

In order to perform the test, a sample of the aggregate must be obtained from the source. To prepare the sample, the aggregate should be mixed thoroughly and be reduced to a suitable size for testing. The total weight of the sample is also required.[4]

[edit] Results

The results are presented in a graph of percent passing versus the sieve size. On the graph the sieve size scale is logarithmic. To find the percent of aggregate passing through each sieve, first find the percent retained in each sieve. To do so, the following equation is used,

%Retained = ×100%

where WSieve is the weight of aggregate in the sieve and WTotal is the total weight of the aggregate. The next step is to find the cumulative percent of aggregate retained in each sieve. To do so, add up the total amount of aggregate that is retained in each sieve and the amount in the previous sieves. The cumulative percent passing of the aggregate is found by subtracting the percent retained from 100%.

%Cumulative Passing = 100% - %Cumulative Retained.

The values are then plotted on a graph with cumulative percent passing on the y axis and logarithmic sieve size on the x axis.[4]

[edit] Methods

There are different methods for carrying out sieve analyses, depending on the material to be measured.

[edit] Throw-action sieving

Throw-Action Sieving

Here a throwing motion acts on the sample. The vertical throwing motion is overlaid with a slight circular motion which results in distribution of the sample amount over the whole sieving surface. The particles are accelerated in the vertical direction (are thrown upwards). In the air they carry out free rotations and interact with the openings in the mesh of the sieve when they fall back. If the particles are smaller than the openings, they pass through the sieve. If they are larger, they are thrown upwards again. The rotating motion while suspended increases the probability that the particles present a different orientation to the mesh when they fall back again, and thus might eventually pass through the mesh.

Modern sieve shakers work with an electro-magnetic drive which moves a spring-mass system and transfers the resulting oscillation to the sieve stack. Amplitude and sieving time are set digitally and are continuously observed by an integrated control-unit. Therefore sieving results are reproducible and precise (an important precondition for a significant analysis). Adjustment of parameters like amplitude and sieving time serves to optimize the sieving for different types of material. This method is the most common in the laboratory sector[citation needed].

[edit] Horizontal sieving

Horizontal Sieving

In a horizontal sieve shaker the sieve stack moves in horizontal circles in a plane. Horizontal sieve shakers are preferably used for needle-shaped, flat, long or fibrous samples, as their horizontal orientation means that only a few disoriented particles enter the mesh and the sieve is not blocked so quickly. The large sieving area enables the sieving of large amounts of sample, for example as encountered in the particle-size analysis of construction materials and aggregates.

[edit] Tapping sieving

Tapping Sieving

A horizontal circular motion overlies a vertical motion which is created by a tapping impulse. These motional processes are characteristic of hand sieving and produce a higher degree of sieving for denser particles (e.g. abrasives) than throw-action sieve shakers.

[edit] Sonic sieving

The particles are lifted and forcibly dropped in a column of oscillating air at a frequency of thousands of cycles per minute. Sonic sievers are able to handle much finer dry powders than woven mesh screens.

[edit] Wet sieving

Most sieve analyses are carried out dry. But there are some applications which can only be carried out by wet sieving. This is the case when the sample which has to be analysed is e.g. a suspension which must not be dried; or when the sample is a very fine powder which tends to agglomerate (mostly < 45 µm) – in a dry sieving process this tendency would lead to a clogging of the sieve meshes and this would make a further sieving process impossible. A wet sieving process is set up like a dry process: the sieve stack is clamped onto the sieve shaker and the sample is placed on the top sieve. Above the top sieve a water-spray nozzle is placed which supports the sieving process additionally to the sieving motion. The rinsing is carried out until the liquid which is discharged through the receiver is clear. Sample residues on the sieves have to be dried and weighed. When it comes to wet sieving it is very important not to change to sample in its volume (no swelling, dissolving or reaction with the liquid).

[edit] Air Jet Sieving

Air jet sieving machines are ideally suited for very fine powders which tend to agglomerate and cannot be separated by vibrational sieving. The reason for the effectiveness of this sieving method is based on two components: A rotating slotted nozzle inside the sieving chamber and a powerful industrial vacuum cleaner which is connected to the chamber. The vacuum cleaner generates a vacuum inside the sieving chamber and sucks in fresh air through the slotted nozzle. When passing the narrow slit of the nozzle the air stream is accelerated and blown against the sieve mesh, dispersing the particles. Above the mesh, the air jet is distributed over the complete sieve surface and is sucked in with low speed through the sieve mesh. Thus the finer particles are transported through the mesh openings into the vacuum cleaner.

Air jet sieving machine

[edit] Types of gradation relatively to the aggregate nature

Dense gradation

A dense gradation refers to a sample that is approximately of equal amounts of various sizes of aggregate. By having a dense gradation, most of the air voids between the material are filled with particles. A dense gradation will result in an even curve on the gradation graph.[5]

Narrow gradation

Also known as uniform gradation, a narrow gradation is a sample that has aggregate of approximately the same size. The curve on the gradation graph is very steep, and occupies a small range of the aggregate.[4]

Gap gradation

A gap gradation refers to a sample with very little aggregate in the medium size range. This results in only coarse and fine aggregate. The curve is horizontal in the medium size range on the gradation graph.[4]

Open gradation

An open gradation refers an aggregate sample with very little fine aggregate particles. This results in many air voids, because there are no fine particles to fill them. On the gradation graph, it appears as a curve that is horizontal in the small size range.[4]

Rich gradation

A rich gradation refers to a sample of aggregate with a high proportion of particles of small sizes.[5]

[edit] Limitations of sieve analysis

Sieve analysis has, in general, been used for decades to monitor material quality based on particle size. For coarse material, sizes that range down to #100 mesh (150μm), a sieve analysis and particle size distribution is accurate and consistent.

However, for material that is finer than 100 mesh, dry sieving can be significantly less accurate. This is because the mechanical energy required to make particles pass through an opening and the surface attraction effects between the particles themselves and between particles and the screen increase as the particle size decreases. Wet sieve analysis can be utilized where the material analyzed is not affected by the liquid - except to disperse it. Suspending the particles in a suitable liquid transports fine material through the sieve much more efficiently than shaking the dry material.

Sieve analysis assumes that all particle will be round (spherical) or nearly so and will pass through the square openings when the particle diameter is less than the size of the square opening in the screen. For elongated and flat particles a sieve analysis will not yield reliable mass-based results, as the particle size reported will assume that the particles are spherical, where in fact an elongated particle might pass through the screen end-on, but would be prevented from doing so if it presented itself side-on.

[edit] Properties

Gradation affects many properties of an aggregate. It affects bulk density, physical stability and permeability. With careful selection of the gradation, it is possible to achieve high bulk density, high physical stability, and low permeability. This is important because in pavement design, a workable, stable mix with resistance to water is important. With an open gradation, the bulk density is relatively low, due to the lack of fine particles, the physical stability is moderate, and

the permeability is quite high. With a rich gradation, the bulk density will also be low, the physical stability is low, and the permeability is also low. The gradation can be affected to achieve the desired properties for the particular engineering application.[5]

[edit] Engineering applications

Gradation is usually specified for each engineering application it is used for. For example, foundations might only call for coarse aggregates, and therefore an open gradation is needed. Gradation is a primary concern in pavement mix design. Concrete could call for both coarse and fine particles and a dense graded aggregate would be needed. Asphalt design also calls for a dense graded aggregate. Gradation also applies to subgrades in paving, which is the material that a road is paved on. Gradation, in this case, depends on the type of road (i.e. highway, rural, suburban) that is being paved.

[edit] Forecast

Within the last years[when?] some methods for particle size distribution measurement were developed which work by means of laser diffraction or digital image processing.

[edit] "Sieving" with Digital Image Processing

The scope of information conveyed by sieve analysis is relatively small. It does not allow for a clear statement concerning the exact size of a single particle → it is just classified within a size range which is determined by two sieve sizes ("a particle is < than sieve size x and > than sieve size y"). And there is no additional information concerning other relevant properties like opacity or shape available. Devices which work with digital image processing enable to recall even this information and a lot more (surface analysis, etc.). The results can be fitted to sieve analysis so that a comparison between measurement results obtained with different methods is possible. Digital image processing is being used to sieve materials in mining, agriculture, and forestry industries on a regular basis.

[edit] References

1. ̂ p231 in "Characterisation of bulk solids" by Donald Mcglinchey, CRC Press, 2005.2. ̂ ASTM International - Standards Worldwide. (2006). ASTM C136-06. http://www.astm.org/cgi-

bin/SoftCart.exe/DATABASE.CART/REDLINE_PAGES/C136.htm?E+mystore3. ̂ AASHTO The Voice of Transportation. T0 27. (2006).

http://bookstore.transportation.org/item_details.aspx?ID=6594. ^ a b c d e f Pavement Interactive. Gradation Test. (2007).

http://pavementinteractive.org/index.php?title=Gradation_Test5. ^ a b c M.S. Mamlouk and J.P. Zaniewski, Materials for Civil and Construction Engineers, Addison-

Wesley, Menlo Park CA, 1999

[edit] See also

Soil gradation Automated Sieving using Photoanalysis Optical Granulometry

[edit] External links

Equipment for tests- shakers The Basic Principles of Sieve Analysis Soil test Sieve Analysis Example for Digital Image Processing Automated Sieve Analysis Software and Systems

Sieving & Fractioning

The Basic Principles of Sieve AnalysisPDF-Download:

Choose... [pdf] English (386 KB) [pdf] German (351 KB)

Many natural and manufactured materials occur in a disperse form, which means that they consist of differently shaped and sized particles. The particle size distribution, i.e. the number of particles of different sizes, is responsible for important physical and chemical properties.

Such as:• mechanical bulk behavior• surface reaction• taste

• miscibility• filtration properties• conductivityThis list could be continued at great length. The examples clearly show how important it is to have a knowledge of the particle distribution, particularly within the context of quality assurance in the production of bulk goods. If the particle distribution changes during the manufacturing process then the quality of the finished product will also change. Only a continuous monitoring of the particle size distribution can guarantee a constant product quality.

A log-normal distribution of coal-fired Fly Ash.

Significance

The PSD of a material can be important in understanding its physical and chemical properties. It affects the strength and load-bearing properties of rocks and soils. It affects the reactivity of solids participating in chemical reactions, and needs to be tightly controlled in many industrial products such as the manufacture of printer toner and cosmetics.

[edit] Significance in the Collection of Particulate Matter

Particle size distribution can greatly affect the efficacy of any collection device.

Settling Chambers will normally only collect very large particles, those that can be separated using sieve trays.

Centrifugal Collectors will normally collect particles down to about 20 μm. Higher efficiency models can collect particles down to 10 μm.

Fabric Filters are one of the most efficient and cost effective types of dust collectors available and can achieve a collection efficiency of more than 99% for very fine particules.

Wet Scrubbers that use liquid are commonly known as wet scrubbers. In these systems, the scrubbing liquid (usually water) comes into contact with a gas stream containing dust particles. The greater the contact of the gas and liquid streams, the higher the dust removal efficiency.

Electrostatic Precipitators use electrostatic forces to separate dust particles from exhaust gases. They can be very efficient at the collection of very fine particles.

Nomenclature

ρp: Actual particle density Density (g/cm3)

ρg: Gas or sample matrix density Density (g/cm3)

r2: Least-squares coefficient of determination Coefficient of determination. The closer this value is to 1.0, the better the data fit to a straight-line.

λ: Gas mean free path Mean free path (cm)

D50: Mass-median-diameter (MMD). The log-normal distribution mass median diameter. The MMD is considered to be the average particle diameter by mass.

σg: Geometric standard deviation Geometric standard deviation. This value is determined mathematically by the equation:

σg = D84.13 / D50 = D50 / D15.87

The value of σg determines the slope of the least-squares regression curve.

α: Relative standard deviation or degree of polydispersity Polydispersity index. This value is also determined mathematically. For values less than 0.1, the particulate sample can be considered to be monodisperse.

α = σg / D50

R e(P) : Particle Reynold's Number Sediment transport#Particle Reynolds Number. In contrast to the large numerical values noted for flow Reynolds number, particle Reynolds number for fine particles in gaseous mediums is typically less than 0.1.

R ef : Flow Reynold's Number Reynolds number.

Kn: Particle Knudsen Number Knudsen numbe

Types

The way PSD is expressed is usually defined by the method by which it is determined. The most easily understood method of determination is sieve analysis, where powder is separated on sieves of different sizes. Thus, the PSD is defined in terms of discrete size ranges: e.g. "% of sample between 45 μm and 53 μm", when sieves of these sizes are used. The PSD is usually determined over a list of size ranges that covers nearly all the sizes present in the sample. Some methods of determination allow much narrower size ranges to be defined than can be obtained by use of sieves, and are applicable to particle sizes outside the range available in sieves. However, the idea of the notional "sieve", that "retains" particles above a certain size, and "passes" particles below that size, is universally used in presenting PSD data of all kinds.

The PSD may be expressed as a "range" analysis, in which the amount in each size range is listed in order. It may also be presented in "cumulative" form, in which the total of all sizes "retained" or "passed" by a single notional "sieve" is given for a range of sizes. Range analysis is suitable when a particular ideal mid-range particle size is being sought, while cumulative analysis is used where the amount of "under-size" or "over-size" must be controlled.

The way in which "size" is expressed is open to a wide range of interpretations. A simple treatment assumes the particles are spheres that will just pass through a square hole in a "sieve". In practice, particles are irregular - often extremely so, for example in the case of fibrous materials - and the way in which such particles are characterized during analysis is very dependent on the method of measurement used.

[edit] Sieve analysis

This continues to be used for many measurements because of its simplicity, cheapness, and ease of interpretation. Methods may be simple shaking of the sample in sieves until the amount retained becomes more or less constant. Alternatively, the sample may be washed through with a non-reacting liquid (usually water) or blown through with an air current.

Technique Advantages: This technique is well-adapted for bulk materials. A large amount of materials can be readily loaded into 8-inch-diameter (200 mm) sieve trays. Two common uses in the power industry are wet-sieving of milled limestone and dry-sieving of milled coal.

Technique Disadvantages: The most obvious disadvantage is that the smallest practical sieve size (400 Mesh[3]) is 37 µm, and many PSDs are concerned with much smaller sizes than this. A 37 μm sieve is exceedingly fragile, and it is very difficult to get material to pass through it. Another disadvantage is that the amount of energy used to sieve the sample is arbitrarily determined. Over-energetic sieving causes attrition of the particles and thus changes the PSD, while insufficient energy fails to break down loose agglomerates. Although manual sieving procedures can be ineffective, automated sieving technologies using image fragmentation analysis software are available. These technologies can sieve material by capturing and analyzing a photo of material.

[edit] Air elutriation analysis

An air elutriator is a simple device which can separate particles into two or more groups. Material may be separated by means of an elutriator, which consists of a vertical tube up which fluid is passed at a controlled velocity. When the particles are introduced, often through a side tube, the smaller particles are carried over in the fluid stream while the large particles settle against the upward current. If we start with low flow rates small less dense particle attain terminal velocites, and flow with the stream, the particle from the stream is collected in overflow and hence will be separated from the feed. Flow rates can be increased to separate higher size ranges. Further size fractions may be collected if the overflow from the first tube is passed vertically upwards through a second tube of greater cross-section, and any number of such tubes can be arranged in series.

Technique Advantages: A bulk sample is analyzed using centrifugal classification and the technique is non-descructive. Each cut-point can be recovered for future size-respective chemical analyses. This technique has been used for decades in the Air Pollution Control industry (data used for design of control devices). This technique determines particle size as a function of settling velocity in an air stream (as opposed to water, or some other liquid).

Technique Disadvantages: A bulk sample (about ten grams) must be obtained. It is a fairly time-consuming analytical technique. The actual test method [4] has been withdrawn by ASME due to obsolescence. Instrument calibration materials are therefore no longer available.

[edit] PhotoanalysisMain article: Optical granulometry

Materials can now be analysed through photoanalysis procedures. Unlike sieve analyses which can be time-consuming and inaccurate, taking a photo of a sample of the materials to be measured and using software to analyze the photo can result in rapid, accurate measurements. Another advantage is that the material can be analyzed without being handled. This is beneficial in the agricultural industry, as handling of food products can lead to contamination. Photoanalysis equipment and software is currently being used in mining, forestry and agricultural industries worldwide.

[edit] Optical counting methods

PSDs can be measured microscopically by sizing against a graticule and counting, but for a statistically valid analysis, millions of particles must be measured. This is impossibly arduous when done manually, but automated analysis of electron micrographs is now commercially available. Instruments such as the Retsch Camsizer can perform this analysis on the run using standard camera technology.

[edit] Electroresistance counting methods

An example of this is the Coulter counter, which measures the momentary changes in the conductivity of a liquid passing through an orifice that take place when individual non-

conducting particles pass through. The particle count is obtained by counting pulses, and the size is dependent on the size of each pulse.

Technique Advantages: Very small sample aliquots can be examined.

Technique Disadvantages: Sample must be dispersed in a liquid medium... some particles may (partially or fully) dissolve in the medium altering the size distribution. The results are only related to the projected cross-sectional area that a particle displaces as it passes through an orifice. This is a physical diameter, not really related to mathematical descriptions of particles (e.g. terminal settling velocity[5]).

[edit] Sedimentation techniques

These are based upon study of the terminal velocity acquired by particles suspended in a viscous liquid. Sedimentation time is longest for the finest particles, so this technique is useful for sizes below 10 μm, but sub-micrometer particles cannot be reliably measured due to the effects of Brownian motion. Typical apparatus diperses the sample in liquid, then measures the density of the column at timed intervals. Other techniques determine the optical density of successive layers using visible light or x-rays.

Technique Advantages: This technique determines particle size as a function of settling velocity.

Technique Disadvantages: Sample must be dispersed in a liquid medium... some particles may (partially or fully) dissolve in the medium altering the size distribution, requiring careful selection of the dispersion media. Density is highly dependent upon fluid temperature remaining constant. X-Rays will not count carbon (organic) particles. Many of these instruments can require a bulk sample (e.g. two to five grams).

[edit] Laser diffraction methods

These depend upon analysis of the "halo" of diffracted light produced when a laser beam passes through a dispersion of particles in air or in a liquid. The angle of diffraction increases as particle size decreases, so that this method is particularly good for measuring sizes between 0.1 and 3,000 μm. Advances in sophisticated data processing and automation have allowed this to become the dominant method used in industrial PSD determination. A particular advantage is that the technique can generate a continuous measurement for analyzing process streams.

[edit] Acoustic spectroscopy or ultrasound attenuation spectroscopy

Instead of light, this method employs ultrasound for collecting information on the particles that are dispersed in fluid. Dispersed particles absorb and scatter ultrasound similarly to light. This has been known since Lord Rayleigh developed the first theory of ultrasound scattering and published a book "The Theory of Sound" in 1878.[6] There have been hundreds of papers studying ultrasound propagation through fluid particulates in the 20th century.[7] It turns out that instead of measuring scattered energy versus angle, as with light, in the case of ultrasound, measuring the transmitted energy versus frequency is a better choice. The resulting ultrasound

attenuation frequency spectra are the raw data for calculating particle size distribution. It can be measured for any fluid system with no dilution or other sample preparation. This is a big advantage of this method. Calculation of particle size distribution is based on theoretical models that are well verified for up to 50% by volume of dispersed particles.

[edit] Air pollution emissions measurements

Cascade Impactors – Particulate matter is withdrawn isokinetically from a source and segregated by size in a cascade impactor at the sampling point exhaust conditions of temperature, pressure, etc. Cascade impactors use the principle of inertial separation to size segregate particle samples from a particle laden gas stream. The mass of each size fraction is determined gravimetrically. The California Air Resources Board Method 501[8] is currently the most widely accepted test method for particle size distribution emissions measurements

Size Reduction The reason that size reduction or comminution is usually carried out is to increase the surface area of the material. This will maximise the area of solid in contact with the liquid or gas phase around it which enhances reaction, dissolution, catalytic effect etc and is therefore desirable. It should be noted however that very small particles are more difficult to handle, more dangerous in terms of toxic effect and explosive hazard and have other problems such as increased resistance to flow through them.

There are four mechanisms by which size reduction may be achieved:

impact

particle concussion by a single rigid force

compression

particle disintegration by two rigid forces

shear

produced by a fluid or by particle-particle interaction

attrition

arising from particles scraping against one another or against a rigid surface

Size reduction obviously requires energy input but the energy is consumed in size reduction apparatus at a much higher rate than would be predicted from the new surface area created, by a factor of about 1000. This 'lost' energy is consumed in

1.

Deforming the particle to its elastic limit

2.

Compacting particles after fracture

3.

Overcoming friction between particles

4.

Elastically deforming milling surfaces

5.

Deformation of fractured particles

This energy is dissipated as heat. There are also significant mechanical losses in the milling machinery.

It is interesting that around 5% of the world's energy consumption goes to size reduction.

Whereas it is impossible to predict from any theory the energy consumed in size reduction there are a number of empirical rules which allow data from one process to be extrapolated to another. All are based on the premise that the energy dE required to effect a small change in size, dL for unit mass of solids is a simple power function of the size ie:

putting P=-2 ie relating the energy to the surface area gives:

where E is the energy required per unit mass of solid.

Writing C = KRfc where fc is the crushing strength of the material in N/m2 and KR is Rittinger's constant for the material gives Rittinger's Law (1867):

If P = -1 then

putting C =  KKfc gives:

which is Kick's Law; KK is Kick's constant. This implies that the energy required depends on the 'reduction ratio' L1/L2 so that the energy required to reduce from 50 to 25mm is the same as that required to go from 12mm to 6mm.

Note that KR and KK are not dimensionless.

Kick's law is more appropriate to coarse crushing, Rittinger's law to fine grinding.

Bond suggested an intermediate relationship with P = -3/2 which gives:

where q = L1/L2

Ei the work index is the amount of energy required to reduce unit mass of material from an

infinite size to a size L2 of 100 m (ie q = ) is defined by:

C = 5Ei

thus

In all these equations the particle sizes are defined as the size of square hole through which 80% of the material will pass.

Factors Influencing Choice of Size Reduction Equipment

1. Feed and Product Size

  Feed Size Product Size

Coarse Crushers 1500 - 40mm 50 - 5mm

Intermediate Crushers 50 - 5mm 5 - 0.1mm

Fine Crushers.grinders 5 - 2mm <0.1mm

Fine Milling <0.2mmdown to 0.01 m

2. Nature of Material

1. Hardness - very hard materials are better in low speed or low contact machines

2. Structure - fibrous materials need tearing or cutting action

3.

Moisture content - materials with 5 - 50% moisture do not flow easily and can be difficult to process

4. Friability

5. Stickiness - sticky materials need easily cleaned machines

6. Soapiness - if coefficient of friction is low crushing may be difficult

7. Explosives - need inert atmosphere

8. Hazardous to health - need good confinement

9. Closeness of distribution

Types of Size Reduction Equipment

Jaw Crusher - Based on human jaw, one fixed plate, one moving. As the material moves down the crushing action increases. Liable to choking. Feed opening may be up to 2.5m x 2.0m, processing up to 1200te/h. Product size is adjusted by adjusting the gap size. Gyratory Crusher - The crushing cone rotates slowly on its eccentric shaft. Size is controlled by raising and lowering the cone. Crushing Rolls - The design criterion is that material is pulled down by friction.

  Figure 1: Crushing Rolls

The maximum size of particle crushable is found by resolving the upward and downward forces on the particle. If R is the force acting at the point of contact of the roller and the particle then the upwards force is

and the downwards force is

so

ie

A typical value of the coefficient of friction would be so

so

For rolls with R=1m and which are touching the maximum feed size is 8.2cm which increases as the gap increases.

Roller mills can be used for very hard materials by using a relatively wide gap and crushing a bed of particles using high pressures of 50 - 500MPa.

Disintegrators - Two contra-rotating discs with pins which interlock, material travels from axis to circumference. These can be used for fibrous materials which cannot be

crushed. A degree of product size selectivity is introduced by sieves on the circumference. Hammer Mills - The material is broken between the hammer and the breaker plate. Again a sieve arrangement is used to allow product to leave but retain oversize. Ball, Tube and Rod Mills - Cylindrical vessels containing spherical grinding agents or rods. Ball mills have length around 1 to 1.5 times the diameter, tube mills have length 2 - 4 times the diameter. Rod mills use rods rather than balls, the rods being longer than the diameter of the mill. The rotational speed is selected so that the balls or rods tumble over one another. They are run at around 0.75 of critical speed.

Size reduction occurs from a mixture of impact and shear between the balls. These mills are often run wet to reduce any hazards from the fine products.

Finer product is produced by smaller balls, higher ball density or longer residence time (ie lower feed rate). Tube mills have a higher residence time and hence a finer product. Rod mills are useful for sticky materials which would glue balls together.

Raymond (Pendulum) Mill The grinding wheels are thrown outwards against the grinding surface. The feed is fed below the wheels and is thrown into the grinding annulus by the ploughs. Ground material is drawn out by the airstream, oversize falls back into the

ploughs. The product is usually in the 20 - 200 m range. Fluid Energy Mills Fluid energy mills use high velocity jets of air or (more rarely) superheated steam to induce collisions between particles and between particles and

surfaces. The high stresses produced allow milling to below 25 m.

The Pancake Jet Mill has air or steam entering through slots in the periphery of the grinding chamber. Feed is injected into the mill with a stream of the grinding medium. The ground material is transported out by the grinding fluid at the axis of the mill. there is a classifying effect due to the spiral motion of the fluid. Wear is severe in these mills because a high proportion of the attrition as achieved by impact with the wall of the mill.

The Fluidised Jet Mill has the grinding taking place in a fluidised bed in the base of the mill where opposed jets of air create very energetic turbulent motion. At the top an air classifier allows undersize to leave and retains oversize. Size control is achieved through adjustment of the classifier wheel speed and/or of the air flow. Increasing the speed of the classifier wheel or using a lower flow of air at the jets will decrease the size of the particles.

Because the particles do not impact on the walls there is effectively no wear on this type of mill. The classifier wheel is, however, subject to wear and will last only about 2 years

According to rittengers law,the energy required in crushing is proportional to the new surface created.i.e..,P/m=kk(1/db-1/da),where P/m is the amount of power required,db and da are the diameters id particles after and before crushing respectively.

Comminution is the process in which solid materials are reduced in size, encompassing crushing, grinding and other techniques.[1][2] It is an important operation in mineral processing, the ceramic industry, the electronics industry and other fields. Within industrial uses, the purpose of comminution is to reduce the size and to increase the surface area of solids. It is also used to free useful materials from matrix materials in which they are embedded, and to concentrate minerals

Comminution energy

The comminution of solid materials consumes energy, which is being used to break up the solid into smaller pieces. The comminution energy can be estimated by:

Rittinger's law , which assumes that the energy consumed is proportional to the newly generated surface area;

Kick's law , which related the energy to the sizes of the feed particles and the product particles;

Bond's law , which assumes that the total work useful in breakage is inversely proportional to the square root of the size of the product particles;

Holmes's law , which modifies Bond's law by substituting the square root with an exponent that depends on the material

Comminution

Comminution is particle size reduction of materials. Comminution may be carried out on either dry materials or slurries. Crushing and grinding are the two primary comminution processes. Crushing is normally carried out on "run-of-mine"[2] ore, while grinding (normally carried out after crushing) may be conducted on dry or slurried material

Sizing

Sizing is the general term for separation of particles according to their size.

The simplest sizing process is screening, or passing the particles to be sized through a screen or number of screens. Screening equipment can include grizzlies,[3] bar screens, and wire mesh screens. Screens can be static (typically the case for very coarse material), or they can incorporate mechanisms to shake or vibrate the screen.

Classification refers to sizing operations that exploit the differences in settling velocities exhibited by particles of different size. Classification equipment may include ore sorters, gas cyclones, hydrocyclones, rotating trommels, rake classifiers or fluidized classifiers. When the

feed material contains particles of different densities as well as particles of different size, a degree of concentration takes place during classification because settling velocities are also dependent on particle density.

An important factor in both comminution and sizing operations is the determination of the particle size distribution of the materials being processed, commonly referred to as particle size analysis. Many techniques for analyzing particle size are used, and the techniques include both off-line analyses which require that a sample of the material be taken for analysis and on-line techniques that allow for analysis of the material as it flows through the process.

Jaw Crusher.gif|thumb|right|Crushing, a form of comminution, one of the unit operations of mineral processing]]

In the field of [[extractive metallurgy]], '''mineral processing''', also known as '''mineral dressing''' or '''ore dressing''', is the process of separating commercially valuable [[mineral]]s from their [[ore]]s.

==History==

[[File:Geevor waterwheel stamps.jpg|thumb|right|A set of Cornish stamps]]

{{Expand section|date=August 2010}}

Before the advent of heavy machinery the raw ore was broken up using hammers wielded by hand, a process called "spalling". Before long, mechanical means were found to achieve this. For instance, [[stamp mill]]s were used in [[Samarkand]] as early as 973. They were also in use in medieval [[Persia]]. By the 11th century, stamp mills were in widespread use throughout the [[Islamic Golden Age|medieval Islamic world]], from [[Al-Andalus|Islamic Spain]] and North Africa in the west to [[Central Asia]] in the east.<ref>Adam Robert Lucas (2005), "Industrial Milling in the Ancient and Medieval Worlds: A Survey of the Evidence for an Industrial Revolution in Medieval Europe", ''Technology and Culture'' '''46''' (1): 1-30 [10-1 & 27]</ref> A later example was the [[Cornish stamps]], consisting of a series of iron hammers mounted in a vertical frame, raised by [[cam]]s on the shaft of a [[waterwheel]] and falling on to the ore under gravity.

The simplest method of separating ore from gangue consists of the picking out the individual crystals of each. This is a very tedious process, particularly when the individual particles are small. Another comparatively simple method relies on the various minerals having different

[[specific gravity|densities]], causing them to collect in different places: metallic minerals (being heavier) will drop out of suspension more quickly than lighter ones, which will be carried further by a stream of water. Various devices known as 'buddles' were used to take advantage of this property.{{when}} Later, more advanced machines were used such as the [[vanning|Frue vanner]], invented in 1874.

Other equipment used historically includes the hutch, a trough used with some ore-dressing machines and the keeve or kieve, a large tub used for differential settlement.

==Unit operations==

Mineral processing can involve four general types of unit operation: ''comminution'' – particle size reduction; ''sizing'' – separation of particle sizes by screening or classification; ''concentration'' by taking advantage of physical and surface chemical properties; and ''dewatering'' – solid/liquid separation.

===Comminution===

[[Comminution]] is particle size reduction of materials. Comminution may be carried out on either dry materials or slurries. [[Crusher|Crushing]] and [[Mill (grinding)|grinding]] are the two primary comminution processes. Crushing is normally carried out on "run-of-mine"<ref>Run-of-mine: The raw mined material as it is delivered prior to treatment of any sort. {{cite web

|url=http://www.maden.hacettepe.edu.tr/dmmrt/dmmrt1017.html

|title=Dictionary of Mining, Mineral, and Related Terms

|publisher=Hacettepe University - Department of Mining Engineering

|accessdate=2010-08-07}}</ref> ore, while grinding (normally carried out after crushing) may be conducted on dry or slurried material.

===Sizing===

Sizing is the general term for separation of particles according to their size.

The simplest sizing process is screening, or passing the particles to be sized through a screen or number of screens. Screening equipment can include grizzlies,<ref>Grizzly: a grid of iron bars that allows ore of the correct size to travel down the ore pass to the bottom of the mine, ready for hoisting to the surface. {{cite web

|url=http://www.geevor.com/index.php?object=255

|title=Geevor Tin Mine: Grizzly men

|publisher=Geevor Tin Mine Museum

|accessdate=2010-08-07}}</ref> bar screens, and wire mesh screens. Screens can be static (typically the case for very coarse material), or they can incorporate mechanisms to shake or vibrate the screen.

Classification refers to sizing operations that exploit the differences in settling velocities exhibited by particles of different size. Classification equipment may include [[ore sorting|ore sorters]], [[gas cyclone]]s, [[hydrocyclone]]s, rotating [[trommel]]s, rake classifiers or fluidized classifiers. When the feed material contains particles of different densities as well as particles of different size, a degree of concentration takes place during classification because settling velocities are also dependent on particle density.

An important factor in both comminution and sizing operations is the determination of the particle size distribution of the materials being processed, commonly referred to as [[particle size analysis]]. Many techniques for analyzing particle size are used, and the techniques include both off-line analyses which require that a sample of the material be taken for analysis and on-line techniques that allow for analysis of the material as it flows through the process.

===Concentration===

There are a number of ways to increase the concentration of the wanted minerals: in any particular case the method chosen will depend on the relative physical and surface chemical properties of the mineral and the [[gangue]].

====Gravity concentration====

Historically the earliest method used, particles can be classified based on their [[specific gravity]]. Gravity concentration processes include:

* Heavy media or dense media separation

* Shaking tables, such as the Wilfley table<ref>{{cite web

|url=http://www.coppercountryexplorer.com/2007/09/mill-machines-the-wilfley-table/

|title=Mill Machines: The Wilfley Table

|publisher=Copper Country Explorer

|accessdate=2010-08-07}}</ref>

* [[Spiral separator]]s

* Centrifugal bowl concentrators

* Jig concentrators are continuous processing gravity concentration devices using a pulsating fluidized bed.

* Multi gravity separators

[[File:FlotationFalconbridgeOnt.jpg|thumb|right|Froth flotation cells used to concentrate copper and nickel sulfide minerals, Falconbridge, Ontario.]]

====Froth flotation====

Separation by [[froth flotation]] relies on the differing surface potentials of the particles. Hydrophobic particles are recovered to the froth, whereas hydrophilic particles are discharged with the tailings stream. Some mineral particles are naturally hydrophobic, whereas others require specific reagent additions to change their surface potentials. [[Oxide]] ores, such as [[spodumene]] and [[tantalite]] can be treated using [[oxalic acid]] based collectors. [[Sulfide]] ores can be recovered using xanthate or [[Thiophosphate#Dithiophasphate|dithiophosphate]] type collectors.

====Electrostatic separation====

Non-conducting particles maintain an electrostatic charge induced electrically, and so remain pinned to a charged drum. Conducting particles do not maintain the electrostatic charge and so fall off the drum, thus minerals such as [[ilmenite]] and [[rutile]] can be separated.

====Magnetic separation====

Minerals such as [[magnetite]] and [[pyrrhotite]] are naturally [[magnetic]], and so can be separated from non-magnetic particles using strong magnets.

===Dewatering===

{{Expand section|date=August 2010}}

Since many size reduction and separation processes involve the use of water, solid-liquid separation processes are also a subject of mineral processing.

==Other processes==

Many [[physical plant|mechanical plants]] also incorporate [[Hydrometallurgy|hydrometallurgical]] or [[Pyrometallurgy|pyrometallurgical]] processes as part of an extractive metallurgical operation. [[Geometallurgy]] is a branch of [[extractive metallurgy]] that combines mineral processing with the geologic sciences.

A number of auxiliary [[materials handling]] operations are also considered a branch of mineral processing such as storage (as in bin design), conveying, sampling, weighing, slurry transport, and pneumatic transport.

Grinding laws

In spite of a great number of studies in the field of fracture schemes there is no formula known which connects the technical grinding work with grinding results. To calculate the needed grinding work against the grain size changing three half-empirical models are used:

KICK for d > 50 mm

BOND for 50 mm > d > 0.05 mm

RITTINGER for d < 0.05 mm

with W as grinding work in kJ/kg, c as grinding coefficient, dA as grain size of the source material and dE as grain size of the ground material.

A reliable value for the grain sizes dA and dE is d80. This value signifies that 80% (mass) of the solid matter has a smaller grain size. The BOND's grinding coefficient for different materials can be found in various literature. To calculate the KICK's and RITTINGER's coefficients following formulas can be used

with the limits of BOND's range: upper dBU = 50 mm and lower dBL = 0.05 mm.

[edit] Grinding degree

To evaluate the grinding results the grain size disposition of the source material (1) and of the ground material (2) is needed. Grinding degree is the ratio of the sizes from the grain disposition. There are several definitions for this characteristic value:

Grinding degree referring to grain size d80

Instead of the value of d80 also d50 or other grain diameter can be used.

Grinding degree referring to specific surface

The specific surface area referring to volume Sv and the specific surface area referring to mass Sm

can be found out through experiments.

Pretended grinding degree

The discharge die gap a of the grinding machine is used for the ground solid matter in this formula.

[edit] Grinding machines

In materials processing a grinder is a machine for producing fine particle size reduction through attrition and compressive forces at the grain size level. See also crusher for mechanisms producing larger particles. Since the grinding process needs generally a lot of energy, an original experimental way to measure the energy used locally during milling with different machines was proposed recently.[1]

Operation of a ball mill

[edit] Ball mill

A typical type of fine grinder is the ball mill. A slightly inclined or horizontal rotating cylinder is partially filled with balls, usually stone or metal, which grinds material to the necessary fineness by friction and impact with the tumbling balls. Ball mills are characterized by their smaller (comparatively) diameter and longer length. The feed is at one end of the cylinder and the discharge is at the other. Ball mills are commonly used in the manufacture of Portland cement. These industrial ball mills are mainly big machines. Small versions of ball mills can be found in laboratories where they are used for grinding sample material for quality assurance.

[edit] Rod mill

A rotating drum causes friction and attrition between steel rods and ore particles.[citation needed] But note that the term 'rod mill' is also used as a synonym for a slitting mill, which makes rods of iron or other metal.

[edit] SAG mill

Principle of SAG Mill operation

SAG is an acronym for Semi-Autogenous Grinding, and applies to mills that utilize steel balls in addition to large rocks for grinding. A Sag mill is generally used as a primary or first stage grinding solution. The SAG mills use a minimal ball charge of 6 to 15%. SAG mills can be as large as 42' in diameter, using as much as 28,000 kW in power.

A rotating drum throws large rocks and steel balls in a cataracting motion which causes impact breakage of larger rocks and compressive grinding of finer particles. Attrition in the charge causes grinding of finer particles. SAG mills are characterized by their large diameter and short length. The inside of the mill is lined with lifting plates to lift the material inside up and around the inside of the mill, where it then falls off the plates and falls back down. SAG mills are primarily used in the gold, copper and platinum industries with applications also in the lead, zinc, silver, alumina and nickel industries.

[edit] Autogenous mill

A rotating drum throws large rocks in a cataracting motion which causes impact breakage of larger rocks and compressive grinding of finer particles. It is similar in operation to a SAG mill as described above but does not use steel balls in the mill. Attrition in the charge causes grinding of finer particles. Also known as ROM or "Run Of Mine" grinding.

[edit] Pebble mill

A rotating drum causes friction and attrition between rock pebbles and ore particles. May be used where product contamination by iron from steel balls must be avoided.

[edit] High pressure grinding rolls

The ore is fed between two rollers which are pushed firmly together while their rotating motion pushes the ore through a small gap between them. Extreme pressure causes the rocks to fracture into finer particles and also causes microfracturing at the grain size level.

It consists of a pair of horizontal cylindrical rollers through which material is passed. The two rollers rotate in opposite directions, "nipping" and crushing material between them. A similar type of intermediate crusher is the edge runner, which consists of a circular pan with two or more heavy wheels known as mullers rotating within it; material to be crushed is shoved underneath the wheels using attached plow blades.

[edit] Buhrstone mill

Another type of fine grinder commonly used is the buhrstone mill, which is similar to old-fashioned flour mills.

[edit] Vertical shaft impactor mill (VSI mill)

Type of fine grinder which uses a free impact of rock or ore particles with a wear plate. High speed of the motion of particles is achieved with a rotating accelerator. This type of mill uses the same principle as VSI Crusher

[edit] Types of grinding mills

A ball mill, a type of grinder, is a cylindrical device used in grinding (or mixing) materials like ores, chemicals, ceramic raw materials and paints[1]. Ball mills rotate around a horizontal axis, partially filled with the material to be ground plus the grinding medium. Different materials are

used as media, including ceramic balls, flint pebbles and stainless steel balls. An internal cascading effect reduces the material to a fine powder. Industrial ball mills can operate continuously, fed at one end and discharged at the other end. Large to medium-sized ball mills are mechanically rotated on their axis, but small ones normally consist of a cylindrical capped container that sits on two drive shafts (pulleys and belts are used to transmit rotary motion). A rock tumbler functions on the same principle. Ball mills are also used in pyrotechnics and the manufacture of black powder, but cannot be used in the preparation of some pyrotechnic mixtures such as flash powder because of their sensitivity to impact. High-quality ball mills are potentially expensive and can grind mixture particles to as small as 5 nm, enormously increasing surface area and reaction rates. The grinding works on principle of critical speed. The critical speed can be understood as that speed after which the steel balls (which are responsible for the grinding of particles) start rotating along the direction of the cylindrical device; thus causing no further grinding.

Ball mills are used extensively in the Mechanical alloying process[2] in which they are not only used for grinding but for cold welding as well, with the purpose of producing alloys from powders. One of most commonly used mills is the SPEX Mill

HIGH ENERGY BALL MILL

Ball mill

A ball mill is a type of grinder used to grind materials into extremely fine powder for use in mineral dressing processes, paints, pyrotechnics, and ceramics.

Contents

[hide]

1 Description 2 Grinding media 3 Varieties 4 History 5 See also 6 References 7 External links

[edit] Description

Bench top ball mill

Laboratory scale SPEX ball mill

High-energy ball milling

A ball mill, a type of grinder, is a cylindrical device used in grinding (or mixing) materials like ores, chemicals, ceramic raw materials and paints[1]. Ball mills rotate around a horizontal axis, partially filled with the material to be ground plus the grinding medium. Different materials are used as media, including ceramic balls, flint pebbles and stainless steel balls. An internal cascading effect reduces the material to a fine powder. Industrial ball mills can operate continuously, fed at one end and discharged at the other end. Large to medium-sized ball mills are mechanically rotated on their axis, but small ones normally consist of a cylindrical capped container that sits on two drive shafts (pulleys and belts are used to transmit rotary motion). A rock tumbler functions on the same principle. Ball mills are also used in pyrotechnics and the manufacture of black powder, but cannot be used in the preparation of some pyrotechnic mixtures such as flash powder because of their sensitivity to impact. High-quality ball mills are potentially expensive and can grind mixture particles to as small as 5 nm, enormously increasing surface area and reaction rates. The grinding works on principle of critical speed. The critical speed can be understood as that speed after which the steel balls (which are responsible for the grinding of particles) start rotating along the direction of the cylindrical device; thus causing no further grinding.

Ball mills are used extensively in the Mechanical alloying process[2] in which they are not only used for grinding but for cold welding as well, with the purpose of producing alloys from powders. One of most commonly used mills is the SPEX Mill[3].

[edit] Grinding media

Lead antimony grinding media with aluminum powder.

A ball mill inside the Mayflower Mill near Silverton, Colorado.

There are many types of grinding media suitable for use in a ball mill, each material having its own specific properties and advantages. Key properties of grinding media are size, density, hardness, and composition.

Size: The smaller the media particles, the smaller the particle size of the final product. At the same time, the grinding media particles should be substantially larger than the largest pieces of material to be ground.

Density: The media should be denser than the material being ground. It becomes a problem if the grinding media floats on top of the material to be ground.

Hardness: The grinding media needs to be durable enough to grind the material, but where possible should not be so tough that it also wears down the tumbler at a fast pace.

Composition: Various grinding applications have special requirements. Some of these requirements are based on the fact that some of the grinding media will be in the finished product. Others are based in how the media will react with the material being ground.

o Where the color of the finished product is important, the color of the grinding media must be considered.

o Where low contamination is important, the grinding media may be selected for ease of separation from the finished product (ie: steel dust produced from stainless

steel media can be magnetically separated from non-ferrous products). An alternative to separation is to use media of the same material as the product being ground.

o Flammable products have a tendency to become explosive in powder form (see: dust explosion). Steel media may spark, becoming an ignition source for these products. Either wet-grinding, or non-sparking media such as ceramic must be selected.

o Some media, such as iron, may react with corrosive materials. For this reason, stainless steel, ceramic, and flint grinding media may each be used when corrosive substances are present during grinding.

High density alumina media (90–95% alumina) is widely used in the ceramic industry to grind clay bodies, frits, glazes and other ingredients. It is more expensive than silica / silex media but is more efficient

[edit] Varieties

Aside from common ball mills there is a second type of ball mill called Planetary Ball Mill. Planetary ball mills are smaller than common ball mills and mainly used in laboratories for grinding sample material down to very small sizes. A planetary ball mill consists of at least one grinding jar which is arranged eccentrically on a so-called sun wheel. The direction of movement of the sun wheel is opposite to that of the grinding jars (ratio: 1:-2 or 1:-1 or else). The grinding balls in the grinding jars are subjected to superimposed rotational movements, the so-called Coriolis forces. The difference in speeds between the balls and grinding jars produces an interaction between frictional and impact forces, which releases high dynamic energies. The interplay between these forces produces the high and very effective degree of size reduction of the planetary ball mil

A colloid mill is a machine that is used to reduce the particle size of a solid in suspension in a liquid, or to reduce the droplet size of a liquid suspended in another liquid. This is done by applying high levels of hydraulic shear to the process liquid. It is frequently used to increase the stability of suspensions and emulsions.

In fluid dynamics, the drag coefficient (commonly denoted as: or ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area.[1]

The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag: skin friction and form drag. The drag coefficient of a lifting airfoil or hydrofoil also includes the effects of lift-induced drag.[2][3] The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag.

Definition

The drag coefficient is defined as:

where:

is the drag force, which is by definition the force component in the direction of the flow velocity,[6]

is the mass density of the fluid,[7]

v is the speed of the object relative to the fluid, andis the reference area.

The reference area depends on what type of drag coefficient is being measured. For automobiles and many other objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the cross sectional area of the vehicle, depending on where the cross section is

taken. For example, for a sphere (note this is not the surface area = ).

For airfoils, the reference area is the planform area. Since this tends to be a rather large area compared to the projected frontal area, the resulting drag coefficients tend to be low: much lower than for a car with the same drag, frontal area and at the same speed.

Airships and some bodies of revolution use the volumetric drag coefficient, in which the reference area is the square of the cube root of the airship volume. Submerged streamlined bodies use the wetted surface area.

Two objects having the same reference area moving at the same speed through a fluid will experience a drag force proportional to their respective drag coefficients. Coefficients for unstreamlined objects can be 1 or more, for streamlined objects much less.

Background

Flow around a plate, showing stagnation.

Main article: Drag equation

The drag equation:

is essentially a statement that the drag force on any object is proportional to the density of the fluid and proportional to the square of the relative speed between the object and the fluid.

Cd is not a constant but varies as a function of speed, flow direction, object shape, object size, fluid density and fluid viscosity. Speed, kinematic viscosity and a characteristic length scale of the object are incorporated into a dimensionless quantity called the Reynolds number or is thus a function of In compressible flow, the speed of sound is relevant and is also a function of Mach number

For a certain body shape the drag coefficient only depends on the Reynolds number

Mach number and the direction of the flow. For low Mach number the drag coefficient is independent of Mach number. Also the variation with Reynolds number within a practical range of interest is usually small, while for cars at highway speed and aircraft at cruising speed the incoming flow direction is as well more-or-less the same. So the drag coefficient can often be treated as a constant.[8]

For a streamlined body to achieve a low drag coefficient the boundary layer around the body must remain attached to the surface of the body for as long as possible, causing the wake to be narrow. A high form drag results in a broad wake. The boundary layer will transition from laminar to turbulent providing the Reynolds number of the flow around the body is high enough. Larger velocities, larger objects, and lower viscosities contribute to larger Reynolds numbers.[9]

For other objects, such as small particles, one can no longer consider that the drag coefficient is constant, but certainly is a function of Reynolds number.[10][11][12] At a low Reynolds number, the flow around the object does not transition to turbulent but remains laminar, even up to the point at which it separates from the surface of the object. At very low Reynolds numbers,

without flow separation, the drag force is proportional to instead of for a sphere this is known as Stokes law. Reynolds number will be low for small objects, low velocities, and high viscosity fluids.[9]

A equal to 1 would be obtained in a case where all of the fluid approaching the object is brought to rest, building up stagnation pressure over the whole front surface. The top figure shows a flat plate with the fluid coming from the right and stopping at the plate. The graph to the left of it shows equal pressure across the surface. In a real flat plate the fluid must turn around the sides, and full stagnation pressure is found only at the center, dropping off toward the edges as in the lower figure and graph. Only considering the front size, the of a real flat plate would be less than 1; except that there will be suction on the back side: a negative pressure (relative to ambient). The overall of a real square flat plate perpendicular to the flow is often given as 1.17. Flow patterns and therefore for some shapes can change with the Reynolds number and the roughness of the surfaces.

[edit] Drag coefficient cd examples

[edit] General

In general, is not an absolute constant for a given body shape. It varies with the speed of airflow (or more generally with Reynolds number). A smooth sphere, for example, has a that varies from high values for laminar (slow) flow to 0.47 for turbulent (faster) flow.

Shapes

cd

Item

0.7 a typical bicycle plus cyclist[citation needed]

0.48 rough sphere (Re = )

0.1 smooth sphere ( )

0.001 laminar flat plate parallel to the flow ( )

0.005 turbulent flat plate parallel to the flow ( )

0.24 lowest of production cars (Mercedes-Benz E-Class Coupé)[13]

0.295 bullet (not ogive, at subsonic velocity)

1.0–1.3 man (upright position)

1.28 flat plate perpendicular to flow (3D)

1.0–1.1 skier

1.0–1.3 wires and cables

1.1-1.3 ski jumper[14]

1.3–1.5 Empire State Building

1.8–2.0 Eiffel Tower

1.98–2.05 flat plate perpendicular to flow (2D)

2.1 a smooth brick[citation needed]

In dimensional analysis, a dimensionless quantity is a quantity without a physical unit - thus a pure number. Such a number is typically defined as a product or ratio of quantities that might have units individually, but which cancel out when taken in combination.

Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and also in everyday life.

Contents

[hide]

1 Properties 2 Buckingham π theorem

o 2.1 Example 3 Standards efforts 4 Examples 5 List of dimensionless quantities 6 Dimensionless physical constants 7 See also 8 References 9 External links

[edit] Properties

A dimensionless quantity has no physical unit associated with it. However, it is sometimes helpful to use the same units in both the numerator and denominator, such as kg/kg, to show the quantity being measured (for example to distinguish a mass ratio from a volume ratio).

A dimensionless proportion has the same value regardless of the measurement units used to calculate it. It has the same value whether it was calculated using the SI system of units or the imperial system of units. This doesn't hold for all dimensionless quantities; it is guaranteed to hold only for proportions[dubious – discuss].

[edit] Buckingham π theorem

According to the Buckingham π theorem of dimensional analysis, the functional dependence between a certain number (e.g., n) of variables can be reduced by the number (e.g., k) of independent dimensions occurring in those variables to give a set of p = n − k independent, dimensionless quantities. For the purposes of the experimenter, different systems which share the same description by dimensionless quantity are equivalent.

[edit] Example

The power consumption of a stirrer with a particular geometry is a function of the density and the viscosity of the fluid to be stirred, the size of the stirrer given by its diameter, and the speed of the stirrer. Therefore, we have n = 5 variables representing our example.

Those n = 5 variables are built up from k = 3 dimensions which are:

Length: L (m) Time: T (s) Mass: M (kg).

According to the π-theorem, the n = 5 variables can be reduced by the k = 3 dimensions to form p = n − k = 5 − 3 = 2 independent dimensionless numbers which are in case of the stirrer

Reynolds number (This is a very important dimensionless number; it describes the fluid flow regime)

Power number (describes the stirrer and also involves the density of the fluid).

[edit] Standards efforts

The CIPM Consultative Committee for Units contemplated defining the unit of 1 as the 'uno', but the idea was dropped.[1][2][3][4]

[edit] Examples

Consider this example: Sarah says, "Out of every 10 apples I gather, 1 is rotten.". The rotten-to-gathered ratio is (1 apple) / (10 apples) = 0.1 = 10%, which is a dimensionless quantity. Another more typical example in physics and engineering is the measure of plane angles. Angles are typically measured as the ratio of the length of an arc lying on a circle (with its center being the vertex of the angle) swept out by the angle, compared to some other length. The ratio, length divided by length, is dimensionless. When using the unit radians, the length that is compared is the length of the radius of the circle. When using the unit degree, the length that is compared is 1/360 of the circumference of the circle.

In case of dimensionless quantities the unit is a quotient of like dimensioned quantities that can be reduced to a number (kg/kg = 1, μg/g = 10−6). Dimensionless quantities can also carry dimensionless units like % (= 0.01), ppt (= 10−3), ppm (= 10−6), ppb (= 10−9).

[edit] List of dimensionless quantities

There are infinitely many dimensionless quantities and they are often called numbers. Some of those that are used most often have been given names, as in the following list of examples (alphabetical order):

NameStandard Symbol

Definition Field of application

Abbe number V optics (dispersion in optical materials)

Activity coefficient γchemistry (Proportion of "active" molecules or atoms)

Albedo αclimatology, astronomy (reflectivity of surfaces or bodies)

Archimedes number Ar motion of fluids due to density differences

Arrhenius Number α Ratio of activation energy to thermal energy [5]

Atomic weight M chemistry

Bagnold number Ba flow of bulk solids such as grain and sand.[6]

Bejan number(thermodynamics)

Bethe ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction[7]

Bejan number(fluid mechanics)

Be dimensionless pressure drop along a channel[8]

Bingham Number Bm Ratio of yield stress to viscous stress[5]

Biot number Bi surface vs. volume conductivity of solids

Bodenstein number residence-time distribution

Bond number Bo capillary action driven by buoyancy [9]

Brinkman number Brheat transfer by conduction from the wall to a viscous fluid

Brownell Katz number

combination of capillary number and Bond number

Capillary number Ca fluid flow influenced by surface tension

Coefficient of static friction

μs friction of solid bodies at rest

Coefficient of kinetic friction

μk friction of solid bodies in translational motion

Colburn j factor dimensionless heat transfer coefficient

Courant-Friedrich-Levy number

ν numerical solutions of hyperbolic PDEs [10]

Damkohler number Da reaction time scales vs. transport phenomena

Damping ratio ζ the level of damping in a system

Darcy friction factor Cf or f fluid flow

Dean number D vortices in curved ducts

Deborah number De rheology of viscoelastic fluids

Decibel dB ratio of two intensities, usually sound

Drag coefficient Cd flow resistance

Dukhin number Duratio of electric surface conductivity to the electric bulk conductivity in heterogeneous systems

Euler's number e mathematics

Eckert number Ec convective heat transfer

Ekman number Ek geophysics (frictional (viscous) forces)

Elasticity (economics) Ewidely used to measure how demand or supply responds to price changes

Eötvös number Eo determination of bubble/drop shape

Ericksen number Er liquid crystal flow behavior

Euler number Eu hydrodynamics (pressure forces vs. inertia forces)

Fanning friction factor

f fluid flow in pipes [11]

Feigenbaum constants

α,δ chaos theory (period doubling) [12]

Fine structure constant

α quantum electrodynamics (QED)

f-number f optics, photography

Foppl–von Karman number

thin-shell buckling

Fourier number Fo heat transfer

Fresnel number F slit diffraction [13]

Froude number Fr wave and surface behaviour

Gain electronics (signal output to signal input)

Galilei number Ga gravity-driven viscous flow

Golden ratio mathematics and aesthetics

Graetz number Gz heat flow

Grashof number Gr free convection

Hatta number Haadsorption enhancement due to chemical reaction

Hagen number Hg forced convection

Hydraulic gradient i groundwater flow

Karlovitz number turbulent combustion turbulent combustion

Keulegan–Carpenter number

KCratio of drag force to inertia for a bluff object in oscillatory fluid flow

Knudsen number Knratio of the molecular mean free path length to a representative physical length scale

Kt/V medicine

Kutateladze number K counter-current two-phase flow

Laplace number La free convection within immiscible fluids

Lewis number Le ratio of mass diffusivity and thermal diffusivity

Lift coefficient CLlift available from an airfoil at a given angle of attack

Lockhart-Martinelli parameter

χ flow of wet gases [14]

Lundquist number Sratio of a resistive time to an Alfvén wave crossing time in a plasma

Mach number M gas dynamics

Magnetic Reynolds number

Rm magnetohydrodynamics

Manning roughness coefficient

n open channel flow (flow driven by gravity) [15]

Marangoni number MgMarangoni flow due to thermal surface tension deviations

Morton number Mo determination of bubble/drop shape

Nusselt number Nu heat transfer with forced convection

Ohnesorge number Oh atomization of liquids, Marangoni flow

Péclet number Pe advection–diffusion problems

Peel number adhesion of microstructures with substrate [16]

Pi πmathematics (ratio of a circle's circumference to its diameter)

Poisson's ratio νelasticity (load in transverse and longitudinal direction)

Porosity φ geology

Power factor electronics (real power to apparent power)

Power number Np power consumption by agitators

Prandtl number Prconvection heat transfer (thickness of thermal and momentum boundary layers)

Pressure coefficient CP pressure experienced at a point on an airfoil

Q factor Qdescribes how under-damped an oscillator or resonator is

Radian rad measurement of angles

Rayleigh number Ra buoyancy and viscous forces in free convection

Refractive index n electromagnetism, optics

Reynolds number Re Ratio of fluid inertial and viscous forces[5]

Relative density RD hydrometers, material comparisons

Richardson number Ri effect of buoyancy on flow stability [17]

Rockwell scale mechanical hardness

Rolling resistance coefficient

Crr Vehicle dynamics

Rossby number Ro inertial forces in geophysics

Rouse number Z or P Sediment transport

Schmidt number Sc fluid dynamics (mass transfer and diffusion) [18]

Shape factor Hratio of displacement thickness to momentum thickness in boundary layer flow

Sherwood number Sh mass transfer with forced convection

Sommerfeld number boundary lubrication [19]

Stanton number St heat transfer in forced convection

Stefan number Ste heat transfer during phase change

Stokes number Stk particle dynamics

Strain ε materials science, elasticity

Strouhal number St continuous and pulsating flow [20]

Taylor number Ta rotating fluid flows

Ursell number Unonlinearity of surface gravity waves on a shallow fluid layer

Vadasz number Vagoverns the effects of porosity φ, the Prandtl number and the Darcy number on flow in a porous medium

van 't Hoff factor i quantitative analysis (Kf and Kb)

Wallis parameter J*nondimensional superficial velocity in multiphase flows

Weaver flame speed number

laminar burning velocity relative to hydrogen gas [21]

Weber number We multiphase flow with strongly curved surfaces

Weissenberg number Wi viscoelastic flows [22]

Womersley number α continuous and pulsating flows [23]

[edit] Dimensionless physical constants

Certain fundamental physical constants, such as the speed of light in a vacuum, the universal gravitational constant, and the constants of Planck and Boltzmann, are normalized to 1 if the units for time, length, mass, charge, and temperature are chosen appropriately. The resulting system of units is known as natural or Planck units. However, a handful of dimensionless physical constants cannot be eliminated in any system of units; their values must be determined experimentally. The resulting constants include:

α, the fine structure constant, the coupling constant for the electromagnetic interaction;

μ or β, the proton-to-electron mass ratio, the rest mass of the proton divided by that of the electron. More generally, the rest masses of all elementary particles relative to that of the electron;

αs, the coupling constant for the strong force; αG, the gravitational coupling constant.

In fluid dynamics, the drag equation is a practical formula used to calculate the force of drag experienced by an object due to movement through a fully-enclosing fluid. The equation is attributed to Lord Rayleigh, who originally used L2 in place of A (with L being some linear dimension). The force on a moving object due to a fluid is:

where

FD is the force of drag, which is by definition the force component in the direction of the flow velocity,[1]

ρ is the mass density of the fluid, [2]

u is the velocity of the object relative to the fluid,A is the reference area, andCD is the drag coefficient — a dimensionless constant, e.g. 0.25 to 0.45 for a car.

The reference area A is typically defined as the area of the orthographic projection of the object on a plane perpendicular to the direction of motion. For non-hollow objects with simple shape, such as a sphere, this is exactly the same as a cross sectional area. For other objects (for instance, a rolling tube or the body of a cyclist), A may be significantly larger than the area of any cross section along any plane perpendicular to the direction of motion. Airfoils use the square of the chord length as the reference area; since airfoil chords are usually defined with a length of 1, the reference area is also 1. Aircraft use the wing area (or rotor-blade area) as the reference area, which makes for an easy comparison to lift. Airships and bodies of revolution use the volumetric coefficient of drag, in which the reference area is the square of the cube root of the airship's volume. Sometimes different reference areas are given for the same object in which case a drag coefficient corresponding to each of these different areas must be given.

For sharp-cornered bluff bodies, like square cylinders and plates held transverse to the flow direction, this equation is applicable with the drag coefficient as a constant value when the Reynolds number is greater than 1000.[3] For smooth bodies, like a circular cylinder, the drag coefficient may vary significantly until Reynolds numbers up to 107 (ten million).[4]

Contents

[hide]

1 Discussion 2 Derivation

3 See also 4 References 5 Notes

[edit] Discussion

The equation is based on an idealized situation where all of the fluid impinges on the reference area and comes to a complete stop, building up stagnation pressure over the whole area. No real object exactly corresponds to this behavior. CD is the ratio of drag for any real object to that of the ideal object. In practice a rough unstreamlined body (a bluff body) will have a CD around 1, more or less. Smoother objects can have much lower values of CD. The equation is precise — it simply provides the definition of CD (drag coefficient), which varies with the Reynolds number and is found by experiment.

Of particular importance is the u2 dependence on velocity, meaning that fluid drag increases with the square of velocity. When velocity is doubled, for example, not only does the fluid strike with twice the velocity, but twice the mass of fluid strikes per second. Therefore the change of momentum per second is multiplied by four. Force is equivalent to the change of momentum divided by time. This is in contrast with solid-on-solid friction, which generally has very little velocity dependence.

[edit] Derivation

The drag equation may be derived to within a multiplicative constant by the method of dimensional analysis. If a moving fluid meets an object, it exerts a force on the object, according to a complicated (and not completely understood) law. We might suppose that the variables involved under some conditions to be the:

speed u, fluid density ρ, viscosity ν of the fluid, size of the body, expressed in terms of its frontal area A, and drag force FD.

Using the algorithm of the Buckingham π theorem, one can reduce these five variables to two dimensionless parameters:

drag coefficient CD and Reynolds number Re.

Alternatively, one can derive the dimensionless parameters via direct manipulation of the underlying differential equations.

That this is so becomes obvious when the drag force FD is expressed as part of a function of the other variables in the problem:

This rather odd form of expression is used because it does not assume a one-to-one relationship. Here, fa is some (as-yet-unknown) function that takes five arguments. We note that the right-hand side is zero in any system of units; so it should be possible to express the relationship described by fa in terms of only dimensionless groups.

There are many ways of combining the five arguments of fa to form dimensionless groups, but the Buckingham π theorem states that there will be two such groups. The most appropriate are the Reynolds number, given by

and the drag coefficient, given by

Thus the function of five variables may be replaced by another function of only two variables:

where fb is some function of two arguments. The original law is then reduced to a law involving only these two numbers.

Because the only unknown in the above equation is the drag force FD, it is possible to express it as

or

    and with    

Thus the force is simply ½ ρ A u2 times some (as-yet-unknown) function fc of the Reynolds number Re — a considerably simpler system than the original five-argument function given above.

Dimensional analysis thus makes a very complex problem (trying to determine the behavior of a function of five variables) a much simpler one: the determination of the drag as a function of only one variable, the Reynolds number.

The analysis also gives other information for free, so to speak. We know that, other things being equal, the drag force will be proportional to the density of the fluid. This kind of information often proves to be extremely valuable, especially in the early stages of a research project.

To empirically determine the Reynolds number dependence, instead of experimenting on huge bodies with fast-flowing fluids (such as real-size airplanes in wind-tunnels), one may just as well experiment on small models with more viscous and higher velocity fluids, because these two systems are similar.

he Kozeny–Carman equation is a relation used in the field of fluid dynamics to calculate the pressure drop of a fluid flowing through a packed bed of solids. It is named after Josef Kozeny and Philip C. Carman. The equation is only valid for laminar flow.

The equation is given as[1][2]:

where Δp is the pressure drop, L is the total height of the bed, is the superficial or "empty-tower" velocity, μ is the viscosity of the fluid, ε is the porosity of the bed, Φs is the sphericity of the particles in the packed bed, and Dp is the diameter of the related spherical particle[3]. This equation holds for flow through packed beds with particle Reynolds numbers up to approximately 1.0, after which point frequent shifting of flow channels in the bed causes considerable kinetic energy losses.

This equation can be expressed as "flow is proportional to the pressure drop and inversely proportional to the fluid viscosity", which is known as Darcy's law

Pressure drop is a term used to describe the decrease in pressure from one point in a pipe or tube to another point downstream. "Pressure drop" is the result of frictional forces on the fluid as it flows through the tube. The frictional forces are caused by a resistance to flow. The main factors impacting resistance to fluid flow are fluid velocity through the pipe and fluid viscosity. Tube convergence, divergence, turns, surface roughness and other physical properties will affect the pressure drop. High flow velocities and / or high fluid viscosities result in a larger pressure drop across a section of pipe or a valve or elbow. Low velocity will result in lower or no pressure drop. [1]

Pressure Drop is calculated by performing a mechanical energy balance to the flow.

Ergun equationFrom Wikipedia, the free encyclopedia

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It has been suggested that this article or section be merged into Packed bed. (Discuss)

The Ergun equation, derived by the Turkish chemical engineer Sabri Ergun in 1952, expresses the friction factor in a packed column as a function of the Reynolds number:

where fp and Grp are defined as

and

where: Δp is the pressure drop across the bed,L is the length of the bed (not the column),Dp is the equivalent spherical diameter of the packing,ρ is the density of fluid,μ is the dynamic viscosity of the fluid,Vs is the superficial velocity (i.e. the velocity that the fluid would have through the empty tube at the same volumetric flow rate), andε is the void fraction of the bed(Bed porosity at any time).

Fluidization (or fluidisation) is a process similar to liquefaction whereby a granular material is converted from a static solid-like state to a dynamic fluid-like state. This process occurs when a fluid (liquid or gas) is passed up through the granular material.

When a gas flow is introduced through the bottom of a bed of solid particles, it will move upwards through the bed via the empty spaces between the particles. At low gas velocities, aerodynamic drag on each particle is also low, and thus the bed remains in a fixed state. Increasing the velocity, the aerodynamic drag forces will begin to counteract the gravitational forces, causing the bed to expand in volume as the particles move away from each other. Further increasing the velocity, it will reach a critical value at which the upward drag forces will exactly equal the downward gravitational forces, causing the particles to become suspended within the fluid. At this critical value, the bed is said to be fluidized and will exhibit fluidic behavior. By further increasing gas velocity, the bulk density of the bed will continue to decrease, and its fluidization becomes more violent, until the particles no longer form a bed and are “conveyed” upwards by the gas flow.

When fluidized, a bed of solid particles will behave as a fluid, like a liquid or gas. Like water in a bucket: the bed will conform to the volume of the chamber, its surface remaining perpendicular to gravity; objects with a lower density than the bed density will float on its surface, bobbing up and down if pushed downwards, while objects with a higher density sink to the bottom of the bed. The fluidic behavior allows the particles to be transported like a fluid, channeled through pipes, not requiring mechanical transport (e.g. conveyer belt).

A simplified every-day-life example of a gas-solid fluidized bed would be a hot-air popcorn popper. The popcorn kernels, all being fairly uniform in size and shape, are suspended in the hot-air rising from the bottom chamber. Because of the intense mixing of the particles, akin to that of a boiling liquid, this allows for a uniform temperature of the kernels throughout the chamber, minimizing the amount of burnt popcorn. After popping, the now larger popcorn particles encounter increased aerodynamic drag which pushes them out of the chamber and into a bowl.

The process is also key in the formation of a sand volcano and fluid escape structures in sediments and sedimentary rocks.

[edit] Applications

In 1920s, the Winkler process was developed to gasify coal in a fluidized bed, using oxygen. It was not commercially successful.

The first large scale commercial implementation, in the early 1940s, was the fluid catalytic cracking (FCC) process, which converted heavier petroleum cuts into gasoline. Carbon-rich "coke" deposits on the catalyst particles and deactivates the catalyst in less than 1 second. The fluidized catalyst particles are shuttled between the fluidized bed reactor and a fluidized bed burner where the coke deposits are burned off, generating heat for the endothermic cracking reaction.

By the 1950s fluidized bed technology was being applied to mineral and metallurgical processes such as drying, calcining, and sulfide roasting.

In the 1960s, several fluidized bed processes dramatically reduced the cost of some important monomers. Examples are the Sohio process for acrylonitrile and the oxychlorination process for vinyl chloride.

In the late 1970s, a fluidized bed process for the synthesis of polyethylene dramatically reduced the cost of this important polymer, making its use economical in many new applications. The polymerization reaction generates heat and the intense mixing associated with fluidization prevents hot spots where the polyethylene particles would melt. A similar process is used for the synthesis of polypropylene.

Currently, most of the processes that are being developed for the industrial production of carbon nanotubes use a fluidized bed [1].

A new potential application of fluidization technology is chemical looping combustion, which has not yet been commercialized. One solution to reducing the potential effect of carbon dioxide generated by fuel combustion (e.g. in power stations) on global warming is carbon dioxide sequestration. Regular combustion with air produces a gas that is mostly nitrogen (as it is air's main component at about 80% by volume), which prevents economical sequestration. Chemical looping uses a metal oxide as a solid oxygen carrier. These metal oxide particles replace air (specifically oxygen in the air) in a combustion reaction with a solid, liquid or gaseous fuel in a fluidized bed, producing solid metal particles from the reduction of the metal oxides and a mixture of carbon dioxide and water vapor, the major products of any combustion reaction. The water vapor is condensed, leaving pure carbon dioxide which can be sequestered. The solid metal particles are circulated to another fluidized bed where they react with air (and again, specifically oxygen in the air), producing heat and oxidizing the metal particles to metal oxide particles that are recirculated to the fluidized bed combustor.

This article needs attention from an expert on the subject. See the talk page for details. WikiProject Chemical and Bio Engineering may be able to help recruit an expert. (September 2008)

Oldest power station utilizing circular fluidized bed technology, in Lünen, Germany

A fluidized bed is formed when a quantity of a solid particulate substance (usually present in a holding vessel) is placed under appropriate conditions to cause the solid/fluid mixture to behave as a fluid. This is usually achieved by the introduction of pressurized fluid through the particulate medium. This results in the medium then having many properties and characteristics of normal fluids; such as the ability to free-flow under gravity, or to be pumped using fluid type technologies.

The resulting phenomenon is called fluidization. Fluidized beds are used for several purposes, such as fluidized bed reactors (types of chemical reactors), fluid catalytic cracking, fluidized bed combustion, heat or mass transfer or interface modification, such as applying a coating onto solid items.

Contents

[hide]

1 Properties of fluidized beds 2 Application 3 History 4 Fluidized bed types 5 Flow behavior 6 Bed design

o 6.1 Basic model o 6.2 Geldart Groupings o 6.3 Distributor

7 See also 8 References 9 External links

[edit] Properties of fluidized beds

A fluidized bed consists of fluid-solid mixture that exhibits fluid-like properties. As such, the upper surface of the bed is relatively horizontal, which is analogous to hydrostatic behavior. The bed can be considered to be an inhomogeneous mixture of fluid and solid that can be represented by a single bulk density.

Furthermore, an object with a higher density than the bed will sink, whereas an object with a lower density than the bed will float, thus the bed can be considered to exhibit the fluid behavior expected of Archimedes' principle. As the "density", (actually the solid volume fraction of the suspension), of the bed can be altered by changing the fluid fraction, objects with different densities comparative to the bed can, by altering either the fluid or solid fraction, be caused to sink or float.

In fluidized beds, the contact of the solid particles with the fluidization medium (a gas or a liquid) is greatly enhanced when compared to packed beds. This behavior in fluidized combustion beds enables good thermal transport inside the system and good heat transfer between the bed and its container. Similarly to the good heat transfer, which enables thermal uniformity analogous to that of a well mixed gas, the bed can have a significant heat-capacity whilst maintaining a homogeneous temperature field.

[edit] Application

Fluidized beds are used as a technical process which has the ability to promote high levels of contact between gases and solids. In a fluidized bed a characteristic set of basic properties can be utilised, indispensable to modern process and chemical engineering, these properties include:

Extremely high surface area contact between fluid and solid per unit bed volume High relative velocities between the fluid and the dispersed solid phase. High levels of intermixing of the particulate phase. Frequent particle-particle and particle-wall collisions.

Taking an example from the food processing industry: fluidized beds are used to accelerate freezing in some IQF tunnel freezers. IQF means Individually Quick Frozen, or freezing unpackaged separate pieces. These fluidized bed tunnels are typically used on small food products like peas, shrimp or sliced vegetables, and may use cryogenic or vapor-compression refrigeration.

[edit] History

In 1922 von Winkler designed a reactor that for the first time utilized a coal gasification process. Further application of the fluidized bed included the catalytic cracking of mineral oils in the 1940s. During this time theoretical and experimental research improved the design of the fluidized bed. In the 1960s VAW-Lippewerk in Lönen implemented the first industrial bed for the combustion of coal and later for the calcination of aluminium hydroxide.

[edit] Fluidized bed types

Bed types can be coarsely classified by their flow behavior, including:

Stationary or bubbling beds, where the fluidization of the solids is relatively stationary, with some fine particles being entrained.

Circulating beds, where the fluidization suspends the particle bed, due to a larger kinetic energy of the fluid. As such the surface of the bed is less smooth and larger particles can be entrained from the bed than for stationary beds. These particles can be classified by a cyclone separator and separated from or returned to the bed, based upon particle cut size.

Vibratory Fluidized beds are similar to stationary beds, but add a mechanical vibration to further excite the particles for increased entrainment.

[edit] Flow behavior

Several flow regimes are generally used to describe bed flow, these include:

slugging bed: A bed in which air bubbles occupy entire cross sections of the vessel and divide the bed into layers.

boiling bed: A fluid bed in which the air or gas bubbles are approximately the same size as the solid particles.

channeling bed: A bed in which the air (or gas) forms channels in the bed through which most of the air passes.

spouting bed: A fluid bed in which the air forms a single opening through which some particles flow and fall to the outside. At higher airflow rates, agitation becomes more violent and the movement of solids becomes more vigorous.

[edit] Bed design

A diagram of a fluidized bed

[edit] Basic model

When the packed bed has a fluid passed over it, the pressure drop of the fluid is approximately proportional to the fluid's superficial velocity. In order to transition from a packed bed to a fluidized condition, the gas velocity is continually raised. For a free-standing bed there will exist a point, known as the minimum or incipient fluidisation point, whereby the bed's mass is suspended directly by the flow of the fluid stream. The corresponding fluid velocity, known as the "minimum fluidization velocity", umf.

Beyond the minimum fluidization velocity ( ), the bed material will be suspended by the gas-stream and further increases in the velocity will have a reduced effect on the pressure, owing to sufficient percolation of the gas flow. Thus the pressure drop from for u > umf is relatively constant.

At the base of the vessel the apparent pressure drop multiplied by the cross-section area of the bed can be equated to the force of the weight of the solid particles (less the buoyancy of the solid in the fluid).

Δpw = Hw(1 − εw)(ρs − ρf)g

[edit] Geldart Groupings

In 1973, Professor D. Geldart proposed the grouping of powders in to four so-called "Geldart Groups"[1]. The groups are defined by their locations on a diagram of solid-fluid density difference and particle size. Design methods for fluidized beds can be tailored based upon the particle's Geldart grouping.

Group A For this group the particle size is between 20 and 100 um, and the particle density is typically 1400kg/m3. Prior to the initiation of a bubbling bed phase, beds from these particles

will expand by a factor of 2 to 3 at incipient fluidization, due to a decreased bulk density. Most powder-catalyzed beds utilize this group.

Group B The particle size lies between 40 and 500 um and the particle density between 1400 and 4500 kg/m3. Bubbling typically forms directly at incipient fluidization.

Group C This group contains extremely fine and subsequently the most cohesive particles. With a size of 20 to 30 um, these particles fluidize under very difficult to achieve conditions, and may require the application of an external force, such as mechanical agitation.

Group D The particles in this region are above 600 um and typically have high particle densities. Fluidization of this group requires very high fluid energies and is typically associated with high levels of abrasion. Drying grains and peas, roasting coffee beans, gasifying coals, and some roasting metal ores are such solids, and they are usually processed in shallow beds or in the spouting mode.

[edit] Distributor

Typically, pressurized gas or liquid enters the fluidized bed vessel through numerous holes via a plate known as a distributor plate, located at the bottom of the fluidized bed. The fluid flows upward through the bed, causing the solid particles to be suspended. If the inlet fluid is disabled the bed may settle or pack onto the plate

ggested that Cyclone dust collector be merged into this article or section. (Discuss)

A cyclone separator

Cyclonic separation is a method of removing particulates from an air, gas or water stream, without the use of filters, through vortex separation. Rotational effects and gravity are used to separate mixtures of solids and fluids.

A high speed rotating (air)flow is established within a cylindrical or conical container called a cyclone. Air flows in a spiral pattern, beginning at the top (wide end) of the cyclone and ending at the bottom (narrow) end before exiting the cyclone in a straight stream through the center of the cyclone and out the top. Larger (denser) particles in the rotating stream have too much inertia to follow the tight curve of the stream and strike the outside wall, falling then to the bottom of the cyclone where they can be removed. In a conical system, as the rotating flow moves towards the narrow end of the cyclone the rotational radius of the stream is reduced, separating smaller and smaller particles. The cyclone geometry, together with flow rate, defines the cut point of the cyclone. This is the size of particle that will be removed from the stream with a 50% efficiency. Particles larger than the cut point will be removed with a greater efficiency, and smaller particles with a lower efficiency.

Airflow diagram for Aerodyne cyclone in horizontal position, an alternate design to minimize abrasion within the device

Airflow diagram for Aerodyne cyclone in standard vertical position

An alternative cyclone design uses a secondary air flow within the cyclone to keep the collected particles from striking the walls to protect them from abrasion. The primary air containing the particulate enters from the bottom of the cyclone and is forced into spiral rotation by a stationary spinner. The secondary air flow enters from the top of the cyclone and moves downward toward the bottom, intercepting the particulate from the primary air. The secondary air flow also allows the collector to be mounted horizontally because it pushes the particulate toward the collection area.

Large scale cyclones are used in sawmills to remove sawdust from extracted air. Cyclones are also used in oil refineries to separate oils and gases, and in the cement industry as components of kiln preheaters. Cyclones are increasingly used in the household, as the core technology in

bagless vacuum cleaners. Smaller cyclones are used to separate airborne particles for analysis. Some are small enough to be worn clipped to clothing and are used to separate respirable particles for later analysis.

Analogous devices for separating particles or solids from liquids are called hydrocyclones or hydroclones. These may be used to separate solid waste from water in wastewater and sewage treatment.

Contents

[hide]

1 Cyclone theory o 1.1 Steady state

2 Alternative Steady State Analysis 3 Alternate models 4 See also 5 References

[edit] Cyclone theory

[edit] Steady state

As the cyclone is essentially a two phase particle-fluid system, fluid mechanics and particle transport equations can be used to describe the behaviour of a cyclone. The air in a cyclone is initially introduced tangentially into the cyclone with an inlet velocity Vin. Assuming that the particle is spherical, a simple analysis to calculate critical separation particle sizes can be established.

Given that the fluid velocity is moving in a spiral the gas velocity can be broken into two component velocities: a tangential component, Vt, and a radial velocity component Vr. Assuming Stokes' law, the drag force on any particle in this inlet stream is therefore given by the following equation:

Fd = 6πrpμVr.

If one considers an isolated particle circling in the upper cylindrical component of the cyclone at a rotational radius of r from the cyclone's central axis, the particle is therefore subjected to centrifugal, drag and buoyant forces. The centrifugal component is given by:

The buoyant force component is obtained by the difference between the particle and fluid densities, ρp and ρf respectively:

The force balance can be created by summing the forces together

This rate is controlled by the diameter of the particle's orbit around the central axis of the cyclone. A particle in the cyclonic flow will move towards either the wall of the cyclone, or the central axis of the cyclone until the drag, buoyant and centrifugal forces are balanced. Assuming that the system has reached steady state, the particles will assume a characteristic radius dependent upon the force balance. Heavier, denser particles will assume a solid flow at some larger radius than light particles. The steady state balance assumes that for all particles, the forces are equated, hence:

Fd + Fc + Fb = 0

Which expands to:

This can be expressed by rearranging the above in terms of the particle radius. The particle radius as a function of cyclonic radius, fluid density and fluid tangential and rotational velocities can then be found to be:

Experimentally it is found that the velocity component of rotational flow is proportional to r2[1], therefore:

This means that the established feed velocity controls the vortex rate inside the cyclone, and the velocity at an arbitrary radius is therefore:

Subsequently, given a value for Vt, possibly based upon the injection angle, and a cutoff radius, a characteristic particle filtering radius can be estimated, above which particles will be removed from the gas stream.

[edit] Alternative Steady State Analysis

Assume we have a particle of radius rp and density ρp moving with a parcel of fluid of viscosity μf and density ρf. The particle and the fluid are moving along a curved trajectory with tangential velocity Vt with a radius of curvature of rc.

If we view the particle in a frame of reference moving with the fluid, we can describe the behavior of the particle by invoking the imaginary, inertial centrifugal force acting as a form of gravity directed outward, away from the axis of rotation. The magnitude of the centrifugal force will be give by

.

where mp is the mass of the particle.

If we ignore the universal downward force of gravity and viscous drag between the particle and the fluid parallel to the velocity, there are two other forces acting on the particle - radial viscous drag and buoyancy.

The viscous drag (Fd ) between the particle and the fluid resulting from radial movement of the particle through the fluid is given by

Fd = − 6πrpμfVr

where Vr is the radial drift velocity of the particle through the fluid and the sign reflects the opposition of the force to the motion.

The buoyancy force (Fb) exerted on the particle by the fluid is given by

where vp is the volume of the particle

If we assign upward (toward the center of rotation) as the positive radial direction (+) in our frame of reference, then Fc will be pointed in the negative direction, Fb will be pointed in the positive direction and the direction of Fd will depend on the direction of vp.

If we assume the system has reached dynamic equilibrium then the sum of the forces is zero

Fb + Fd + Fc = 0.

After applying the appropriate signs and expanding mp and vp explicitly we have

Solving this equation for Vr we have

.

Notice that if the density of the fluid is greater than the density of the particle, the motion is (+), toward the center of rotation and if the particle is denser than the fluid, the motion is (-), away from the center.

Expressing the motion in terms of angular velocity ω we have

Substituting into the equation above yields

.

In this analysis, Vr is the drift velocity at which dynamic equilibrium is attained - the drag friction generated by the movement of the particle through the fluid balances the centrifugal force of the rotation and the particle has no radial acceleration, traveling at a constant velocity. In the extreme case where μf = 0 (a fluid with no viscosity) the equilibrium drift velocity is undefined – the particle can accelerate without ever reaching equilibrium. In the opposite extreme, μf = ∞, the equilibrium drift velocity is 0, there is no outward radial movement and the particle is frozen in the fluid

In non-equilibrium conditions, the general case equation F=ma must be solved

The presence of both ar and vr makes this a differential equation and complicates the solution. Note that if the densities of the particle and fluid are equal, the solution is ar = vr = 0 and cyclonic separation is not possible.

In a cyclone particle separator, the design objective is to control the system geometry and the operating parameters so that the drift velocity will move the particle out of the fluid before it exits. In most cases, the steady state solution is used as guidance in designing a separator, but the actual performance must be evaluated and modified empirically.

[edit] Alternate models

The above equations are relatively simple and provide a basic approximation to the behaviour of a cyclone separator. These equations are, however, limited in many regards. For example, the geometry of the separator is not considered, the particles are assumed to achieve a steady state and the effect of the vortex inversion at the base of the cyclone is also ignored, all behaviours which are unlikely to be achieved in a cyclone at real operating conditions.

More complex differential equation based models exist, as many authors have studied the behaviour of cyclone separators [2]. Numerical modelling using computational fluid dynamics has also been used extensively in the study of cyclonic behaviour.[3][4]

In fluid dynamics the flow velocity, or velocity field, of a fluid is a vector field which is used to mathematically describe the motion of a fluid. The length of the flow velocity vector is the flow speed.

Contents

[hide]

1 Definition 2 Uses

o 2.1 Steady flow o 2.2 Incompressible flow o 2.3 Irrotational flow o 2.4 Vorticity

3 The velocity potential 4 Notes and references

[edit] Definition

The flow velocity u of a fluid is a vector field

which gives the velocity of an element of fluid at a position and time .

The flow speed q is the length of the flow velocity vector[1]

and is a scalar field.

[edit] Uses

The flow velocity of a fluid effectively describes everything about the motion of a fluid. Many physical properties of a fluid can be expressed mathematically in terms of the flow velocity. Some common examples follow:

[edit] Steady flowMain article: Steady flow

The flow of a fluid is said to be steady if does not vary with time. That is if

[edit] Incompressible flowMain article: Incompressible flow

A fluid is incompressible if the divergence of is zero:

That is, if is a solenoidal vector field.

[edit] Irrotational flowMain article: Irrotational flow

A flow is irrotational if the curl of is zero:

That is, if is an irrotational vector field.

[edit] VorticityMain article: Vorticity

The vorticity, ω, of a flow can be defined in terms of its flow velocity by

Thus in irrotational flow the vorticity is zero.

[edit] The velocity potential

Main article: Potential flow

If an irrotational flow occupies a simply-connected fluid region then there exists a scalar field φ such that

The scalar field φ is called the velocity potential for the flow. (See Irrotational vector field.)

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Mechanics of planar particle motionFrom Wikipedia, the free encyclopedia

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Classical mechanics

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For general derivations and discussion of fictitious forces, see Fictitious force.

See also: Classical mechanics and Analytical mechanics

This article describes a particle in planar motion[1] when observed from non-inertial reference frames.[2] [3][4] The most famous examples of planar motion are related to the motion of two spheres that are gravitationally attracted to one another, and the generalization of this problem to planetary motion.[5] See centrifugal force, two-body problem, orbit and Kepler's laws of planetary motion. Those problems fall in the general field of analytical dynamics, the determination of orbits from given laws of force.[6] This article is focused more on the kinematical issues surrounding planar motion, that is, determination of the forces necessary to result in a certain trajectory given the particle trajectory. General results presented in fictitious forces here are applied to observations of a moving particle as seen from several specific non-inertial frames, for example, a local frame (one tied to the moving particle so it appears stationary), and a co-rotating frame (one with an arbitrarily located but fixed axis and a rate of rotation that makes the particle appear to have only radial motion and zero azimuthal motion). The Lagrangian approach to fictitious forces is introduced.

Unlike real forces such as electromagnetic forces, fictitious forces do not originate from physical interactions between objects.

Contents

[hide]

1 Analysis using fictitious forces 2 Moving objects and observational frames of reference

o 2.1 Frame of reference and coordinate system o 2.2 Time varying coordinate systems

3 Fictitious forces in a local coordinate system 4 Fictitious forces in polar coordinates

o 4.1 Two terminologies 4.1.1 Lagrangian approach

o 4.2 Polar coordinates in an inertial frame of reference 4.2.1 Change of origin

o 4.3 Co-rotating frame o 4.4 Polar coordinates in a rotating frame of reference

4.4.1 More on the co-rotating frame 5 Fictitious forces in curvilinear coordinates

o 5.1 "State-of-motion" versus "coordinate" fictitious forces 6 Notes and references 7 Further reading 8 External links 9 See also

[edit] Analysis using fictitious forces

The appearance of fictitious forces normally is associated with use of a non-inertial frame of reference, and their absence with use of an inertial frame of reference. The connection between inertial frames and fictitious forces (also called inertial forces or pseudo-forces), is expressed, for example, by Arnol'd:[7]

The equations of motion in an non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a system.

– V. I. Arnol'd: Mathematical Methods of Classical Mechanics Second Edition, p. 129

A slightly different tack on the subject is provided by Iro:[8]

An additional force due to nonuniform relative motion of two reference frames is called a pseudo-force.

– H Iro in A Modern Approach to Classical Mechanics p. 180

Fictitious forces do not appear in the equations of motion in an inertial frame of reference: in an inertial frame, the motion of an object is explained by the real impressed forces. In a non-inertial frame such as a rotating frame, however, Newton's first and second laws still can be used to make accurate physical predictions provided fictitious forces are included along with the real forces. For solving problems of mechanics in non-inertial reference frames, the advice given in textbooks is to treat the fictitious forces like real forces and to pretend you are in an inertial frame.[9] [10]

Treat the fictitious forces like real forces, and pretend you are in an inertial frame.

– Louis N. Hand, Janet D. Finch Analytical Mechanics, p. 267

It should be mentioned that "treating the fictitious forces like real forces" means, in particular, that fictitious forces as seen in a particular non-inertial frame transform as vectors under coordinate transformations made within that frame, that is, like real forces.

[edit] Moving objects and observational frames of reference

Next, it is observed that time varying coordinates are used in both inertial and non-inertial frames of reference, so the use of time varying coordinates should not be confounded with a change of observer, but is only a change of the observer's choice of description. Elaboration of this point and some citations on the subject follow.

[edit] Frame of reference and coordinate system

The term frame of reference is used often in a very broad sense, but for the present discussion its meaning is restricted to refer to an observer's state of motion, that is, to either an inertial frame of reference or a non-inertial frame of reference.

The term coordinate system is used to differentiate between different possible choices for a set of variables to describe motion, choices available to any observer, regardless of their state of motion. Examples are Cartesian coordinates, polar coordinates and (more generally) curvilinear coordinates.

Here are two quotes relating "state of motion" and "coordinate system":[11][12]

We first introduce the notion of reference frame, itself related to the idea of observer: the reference frame is, in some sense, the "Euclidean space carried by the observer". Let us give a more mathematical definition:… the reference frame is... the set of all points in the Euclidean space with the rigid body motion of the observer. The frame, denoted , is said to move with the observer.… The spatial positions of particles are labelled relative to a frame by establishing a coordinate system R with origin O. The corresponding set of axes, sharing the rigid body motion of the frame , can be considered to give a physical realization of . In a frame , coordinates are changed from R to R' by carrying out, at each instant of time, the same

coordinate transformation on the components of intrinsic objects (vectors and tensors) introduced to represent physical quantities in this frame.

– Jean Salençon, Stephen Lyle. (2001). Handbook of Continuum Mechanics: General Concepts, Thermoelasticity p. 9

In traditional developments of special and general relativity it has been customary not to distinguish between two quite distinct ideas. The first is the notion of a coordinate system, understood simply as the smooth, invertible assignment of four numbers to events in spacetime neighborhoods. The second, the frame of reference, refers to an idealized system used to assign such numbers … To avoid unnecessary restrictions, we can divorce this arrangement from metrical notions. … Of special importance for our purposes is that each frame of reference has a definite state of motion at each event of spacetime.…Within the context of special relativity and as long as we restrict ourselves to frames of reference in inertial motion, then little of importance depends on the difference between an inertial frame of reference and the inertial coordinate system it induces. This comfortable circumstance ceases immediately once we begin to consider frames of reference in nonuniform motion even within special relativity.…the notion of frame of reference has reappeared as a structure distinct from a coordinate system.

– John D. Norton: General Covariance and the Foundations of General Relativity: eight decades of dispute, Rep. Prog. Phys., 56, pp. 835-7.

[edit] Time varying coordinate systems

In a general coordinate system, the basis vectors for the coordinates may vary in time at fixed positions, or they may vary with position at fixed times, or both. It may be noted that coordinate systems attached to both inertial frames and non-inertial frames can have basis vectors that vary in time, space or both, for example the description of a trajectory in polar coordinates as seen from an inertial frame.[13] or as seen from a rotating frame.[14] A time-dependent description of observations does not change the frame of reference in which the observations are made and recorded.

[edit] Fictitious forces in a local coordinate system

Figure 1: Local coordinate system for planar motion on a curve. Two different positions are shown for distances s and s + ds along the curve. At each position s, unit vector un points along the outward normal to the curve and unit vector ut is tangential to the path. The radius of curvature of the path is ρ as found from the rate of rotation of the tangent to the curve with respect to arc length, and is the radius of the osculating circle at position s. The unit circle on the left shows the rotation of the unit vectors with s.

See also: Generalized forces, Generalized force, Curvilinear coordinates, Generalized coordinates, and Frenet-Serret formulas

In discussion of a particle moving in a circular orbit,[15] in an inertial frame of reference one can identify the centripetal and tangential forces. It then seems to be no problem to switch hats, change perspective, and talk about the fictitious forces commonly called the centrifugal and Euler force. But what underlies this switch in vocabulary is a change of observational frame of reference from the inertial frame where we started, where centripetal and tangential forces make sense, to a rotating frame of reference where the particle appears motionless and fictitious centrifugal and Euler forces have to be brought into play. That switch is unconscious, but real.

Suppose we sit on a particle in general planar motion (not just a circular orbit). What analysis underlies a switch of hats to introduce fictitious centrifugal and Euler forces?

To explore that question, begin in an inertial frame of reference. By using a coordinate system commonly used in planar motion, the so-called local coordinate system ,[16] as shown in Figure 1, it becomes easy to identify formulas for the centripetal inward force normal to the trajectory (in direction opposite to un in Figure 1), and the tangential force parallel to the trajectory (in direction ut), as shown next.

To introduce the unit vectors of the local coordinate system shown in Figure 1, one approach is to begin in Cartesian coordinates in an inertial framework and describe the local coordinates in terms of these Cartesian coordinates. In Figure 1, the arc length s is the distance the particle has traveled along its path in time t. The path r (t) with components x(t), y(t) in Cartesian coordinates is described using arc length s(t) as:[17]

The arc length s(t) measures distance along the skywriter's trail. Image from NASA ASRS

One way to look at the use of s is to think of the path of the particle as sitting in space, like the trail left by a skywriter, independent of time. Any position on this path is described by stating its distance s from some starting point on the path. Then an incremental displacement along the path ds is described by:

where primes are introduced to denote derivatives with respect to s. The magnitude of this displacement is ds, showing that:[18]

    (Eq. 1)

This displacement is necessarily tangent to the curve at s, showing that the unit vector tangent to the curve is:

while the outward unit vector normal to the curve is

Orthogonality can be verified by showing the vector dot product is zero. The unit magnitude of these vectors is a consequence of Eq. 1.

As an aside, notice that the use of unit vectors that are not aligned along the Cartesian xy-axes does not mean we are no longer in an inertial frame. All it means is that we are using unit vectors that vary with s to describe the path, but still observe the motion from the inertial frame.

Using the tangent vector, the angle of the tangent to the curve, say θ, is given by:

  and  

The radius of curvature is introduced completely formally (without need for geometric interpretation) as:

The derivative of θ can be found from that for sin θ:

Now:

  in which the denominator is unity according to Eq. 1. With this formula for the derivative of the sine, the radius of curvature becomes:

 where the equivalence of the forms stems from differentiation of Eq. 1:

Having set up the description of any position on the path in terms of its associated value for s, and having found the properties of the path in terms of this description, motion of the particle is introduced by stating the particle position at any time t as the corresponding value s (t).

Using the above results for the path properties in terms of s, the acceleration in the inertial reference frame as described in terms of the components normal and tangential to the path of the particle can be found in terms of the function s(t) and its various time derivatives (as before, primes indicate differentiation with respect to s):

  

as can be verified by taking the dot product with the unit vectors ut(s) and un(s). This result for acceleration is the same as that for circular motion based on the radius ρ. Using this coordinate system in the inertial frame, it is easy to identify the force normal to the trajectory as the centripetal force and that parallel to the trajectory as the tangential force.

Next, we change observational frames. Sitting on the particle, we adopt a non-inertial frame where the particle is at rest (zero velocity). This frame has a continuously changing origin, which at time t is the center of curvature (the center of the osculating circle in Figure 1) of the path at time t, and whose rate of rotation is the angular rate of motion of the particle about that origin at time t. This non-inertial frame also employs unit vectors normal to the trajectory and parallel to it.

The angular velocity of this frame is the angular velocity of the particle about the center of curvature at time t. The centripetal force of the inertial frame is interpreted in the non-inertial frame where the body is at rest as a force necessary to overcome the centrifugal force. Likewise, the force causing any acceleration of speed along the path seen in the inertial frame becomes the force necessary to overcome the Euler force in the non-inertial frame where the particle is at rest. There is zero Coriolis force in the frame, because the particle has zero velocity in this frame. For a pilot in an airplane, for example, these fictitious forces are a matter of direct experience.[19] However, these fictitious forces cannot be related to a simple observational frame of reference other than the particle itself, unless it is in a particularly simple path, like a circle.

That said, from a qualitative standpoint, the path of an airplane can be approximated by an arc of a circle for a limited time, and for the limited time a particular radius of curvature applies, the centrifugal and Euler forces can be analyzed on the basis of circular motion with that radius. See article discussing turning an airplane.

Next, reference frames rotating about a fixed axis are discussed in more detail.

[edit] Fictitious forces in polar coordinates

Main article: polar coordinates

Description of particle motion often is simpler in non-Cartesian coordinate systems, for example, polar coordinates. When equations of motion are expressed in terms of any curvilinear coordinate system, extra terms appear that represent how the basis vectors change as the coordinates change. These terms arise automatically on transformation to polar (or cylindrical) coordinates and are thus not fictitious forces, but rather are simply added terms in the acceleration in polar coordinates.[20]

[edit] Two terminologies

In a purely mathematical treatment, regardless of the frame that the coordinate system is associated with (inertial or non-inertial), extra terms appear in the acceleration of an observed particle when using curvilinear coordinates. For example, in polar coordinates the acceleration is given by (see below for details):

which contains not just double time derivatives of the coordinates but added terms. This example employs polar coordinates, but more generally the added terms depend upon which coordinate system is chosen (that is, polar, elliptic, or whatever). Sometimes these coordinate-system dependent terms also are referred to as "fictitious forces", introducing a second meaning for "fictitious forces", despite the fact that these terms do not have the vector transformation properties expected of forces. For example, see Shankar[21] and Hildebrand.[22] According to this terminology, fictitious forces are determined in part by the coordinate system itself, regardless of the frame it is attached to, that is, regardless of whether the coordinate system is attached to an inertial or a non-inertial frame of reference. In contrast, the fictitious forces defined in terms of the state of motion of the observer vanish in inertial frames of reference. To distinguish these two terminologies, the fictitious forces that vanish in an inertial frame of reference, the inertial forces of Newtonian mechanics, are called in this article the "state-of-motion" fictitious forces and those that originate in the interpretation of time derivatives in particular coordinate systems are called "coordinate" fictitious forces.[23]

Assuming it is clear that "state of motion" and "coordinate system" are different, it follows that the dependence of centrifugal force (as in this article) upon "state of motion" and its independence from "coordinate system", which contrasts with the "coordinate" version with exactly the opposite dependencies, indicates that two different ideas are referred to by the terminology "fictitious force". The present article emphasizes one of these two ideas ("state-of-motion"), although the other also is described.

Below, polar coordinates are introduced for use in (first) an inertial frame of reference and then (second) in a rotating frame of reference. The two different uses of the term "fictitious force" are pointed out. First, however, follows a brief digression to explain further how the "coordinate" terminology for fictitious force has arisen.

[edit] Lagrangian approachSee also: Lagrangian, Lagrangian mechanics, Generalized coordinates, and Euler-Lagrange equations

To motivate the introduction of "coordinate" inertial forces by more than a reference to "mathematical convenience", what follows is a digression to show these forces correspond to what are called by some authors "generalized" fictitious forces or "generalized inertia forces".[24]

[25][26][27] These forces are introduced via the Lagrangian mechanics approach to mechanics based upon describing a system by generalized coordinates usually denoted as {qk}. The only requirement on these coordinates is that they are necessary and sufficient to uniquely characterize the state of the system: they need not be (although they could be) the coordinates of the particles in the system. Instead, they could be the angles and extensions of links in a robot arm, for instance. If a mechanical system consists of N particles and there are m independent kinematical conditions imposed, it is possible to characterize the system uniquely by n = 3N - m independent generalized coordinates {qk}.[28]

In classical mechanics, the Lagrangian is defined as the kinetic energy, T, of the system minus its potential energy, U.[29] In symbols,

Under conditions that are given in Lagrangian mechanics, if the Lagrangian of a system is known, then the equations of motion of the system may be obtained by a direct substitution of the expression for the Lagrangian into the Euler–Lagrange equation, a particular family of partial differential equations.

Here are some definitions:[30]

Definition:

is the Lagrange function or Lagrangian, qi are the generalized coordinates, are generalized velocities,

are  generalized momenta,

are  generalized forces,

are  Lagrange's equations.

It is not the purpose here to outline how Lagrangian mechanics works. The interested reader can look at other articles explaining this approach. For the moment, the goal is simply to show that the Lagrangian approach can lead to "generalized fictitious forces" that do not vanish in inertial frames. What is pertinent here is that in the case of a single particle, the Lagrangian approach can be arranged to capture exactly the "coordinate" fictitious forces just introduced.

To proceed, consider a single particle, and introduce the generalized coordinates as {qk} = (r, θ). Then Hildebrand [22] shows in polar coordinates with the qk = (r, θ) the "generalized momenta" are:

leading, for example, to the generalized force:

with Qr the impressed radial force. The connection between "generalized forces" and Newtonian forces varies with the choice of coordinates. This Lagrangian formulation introduces exactly the "coordinate" form of fictitious forces mentioned above that allows "fictitious" (generalized)

forces in inertial frames, for example, the term Careful reading of Hildebrand shows he doesn't discuss the role of "inertial frames of reference", and in fact, says "[The] presence or absence [of inertia forces] depends, not upon the particular problem at hand but upon the coordinate system chosen." By coordinate system presumably is meant the choice of {qk}. Later he says "If accelerations associated with generalized coordinates are to be of prime interest (as is usually the case), the [nonaccelerational] terms may be conveniently transferred to the right … and considered as additional (generalized) inertia forces. Such inertia forces are often said to be of the Coriolis type."

In short, the emphasis of some authors upon coordinates and their derivatives and their introduction of (generalized) fictitious forces that do not vanish in inertial frames of reference is an outgrowth of the use of generalized coordinates in Lagrangian mechanics. For example, see McQuarrie[31] Hildebrand,[22] and von Schwerin.[32] Below is an example of this usage as employed in the design of robotic manipulators:[33][34][35]

In the above [Lagrange-Euler] equations, there are three types of terms. The first involves the

second derivative of the generalized co-ordinates. The second is quadratic in where the coefficients may depend on . These are further classified into two types. Terms involving a

product of the type are called centrifugal forces while those involving a product of the type

for i ≠ j are called Coriolis forces. The third type is functions of only and are called gravitational forces.

– Shuzhi S. Ge, Tong Heng Lee & Christopher John Harris: Adaptive Neural Network Control of Robotic Manipulators, pp. 47-48

For a robot manipulator, the equations may be written in a form using Christoffel symbols Γijk (discussed further below) as:[36][37]

where M is the "manipulator inertia matrix" and V is the potential energy due to gravity (for example), and Υi are the generalized forces on joint i. The terms involving Christoffel symbols therefore determine the "generalized centrifugal" and "generalized Coriolis" terms.

The introduction of generalized fictitious forces often is done without notification and without specifying the word "generalized". This sloppy use of terminology leads to endless confusion because these generalized fictitious forces, unlike the standard "state-of-motion" fictitious forces, do not vanish in inertial frames of reference.

[edit] Polar coordinates in an inertial frame of reference

Below, the acceleration of a particle is derived as seen in an inertial frame using polar coordinates. There are no "state-of-motion" fictitious forces in an inertial frame, by definition. Following that presentation, the contrasting terminology of "coordinate" fictitious forces is presented and critiqued on the basis of the non-vectorial transformation behavior of these "forces".

In an inertial frame, let be the position vector of a moving particle. Its Cartesian components (x, y) are:

with polar coordinates r and θ depending on time t.

Unit vectors are defined in the radially outward direction :

and in the direction at right angles to :

These unit vectors vary in direction with time:

and:

Using these derivatives, the first and second derivatives of position are:

where dot-overmarkings indicate time differentiation. With this form for the acceleration , in an inertial frame of reference Newton's second law expressed in polar coordinates is:

where F is the net real force on the particle. No fictitious forces appear because all fictitious forces are zero by definition in an inertial frame.

From a mathematical standpoint, however, it sometimes is handy to put only the second-order derivatives on the right side of this equation; that is we write the above equation by rearrangement of terms as:

where a "coordinate" version of the "acceleration" is introduced:

consisting of only second-order time derivatives of the coordinates r and θ. The terms moved to the force-side of the equation are now treated as extra "fictitious forces" and, confusingly, the resulting forces also are called the "centrifugal" and "Coriolis" force.

These newly defined "forces" are non-zero in an inertial frame, and so certainly are not the same as the previously identified fictitious forces that are zero in an inertial frame and non-zero only in a non-inertial frame.[38] In this article, these newly defined forces are called the "coordinate" centrifugal force and the "coordinate" Coriolis force to separate them from the "state-of-motion" forces.

Figure 2: Two coordinate systems differing by a displacement of origin. Radial motion with constant

velocity v in one frame is not radial in the other frame. Angular rate , but   [edit] Change of origin

Here is an illustration showing the so called "centrifugal term" does not transform as a true force, putting any reference to this term not just as a "term", but as a centrifugal force, in a

dubious light. Suppose in frame S a particle moves radially away from the origin at a constant velocity. See Figure 2. The force on the particle is zero by Newton's first law. Now we look at the same thing from frame S' , which is the same, but displaced in origin. In S' the particle still is in straight line motion at constant speed, so again the force is zero.

What if we use polar coordinates in the two frames? In frame S the radial motion is constant and there is no angular motion. Hence, the acceleration is:

and each term individually is zero because and . There is no force,

including no "force" in frame S. In frame S' , however, we have:

In this case the azimuthal term is zero, being the rate of change of angular momentum. To obtain zero acceleration in the radial direction, however, we require:

The right-hand side is non-zero, inasmuch as neither nor is zero. That is, we cannot obtain zero force (zero ) if we retain only as the acceleration; we need both terms.

Despite the above facts, suppose we adopt polar coordinates, and wish to say that is "centrifugal force", and reinterpret as "acceleration" (without dwelling upon any possible justification). How does this decision fare when we consider that a proper formulation of physics is geometry and coordinate-independent? See the article on general covariance.[39] To attempt to form a covariant expression, this so-called centrifugal "force" can be put into vector notation as:

with:

and a unit vector normal to the plane of motion. Unfortunately, although this expression

formally looks like a vector, when an observer changes origin the value of changes (see Figure 2), so observers in the same frame of reference standing on different street corners see different "forces" even though the actual events they witness are identical. How can a physical force (be it fictitious or real) be zero in one frame S, but non-zero in another frame S' identical, but a few

feet away? Even for exactly the same particle behavior the expression is different in every

frame of reference, even for very trivial distinctions between frames. In short, if we take as "centrifugal force", it does not have a universal significance: it is unphysical.

Beyond this problem, the real impressed net force is zero. (There is no real impressed force in

straight-line motion at constant speed). If we adopt polar coordinates, and wish to say that is "centrifugal force", and reinterpret as "acceleration", the oddity results in frame S' that straight-line motion at constant speed requires a net force in polar coordinates, but not in Cartesian coordinates. Moreover, this perplexity applies in frame S', but not in frame S.

The absurdity of the behavior of indicates that one must say that is not centrifugal force, but simply one of two terms in the acceleration. This view, that the acceleration is composed of two terms, is frame-independent: there is zero centrifugal force in any and every inertial frame. It also is coordinate-system independent: we can use Cartesian, polar, or any other curvilinear system: they all produce zero.

Apart from the above physical arguments, of course, the derivation above, based upon application of the mathematical rules of differentiation, shows the radial acceleration does indeed

consist of the two terms .

That said, the next subsection shows there is a connection between these centrifugal and Coriolis terms and the fictitious forces that pertain to a particular rotating frame of reference (as distinct from an inertial frame).

Figure 3: Inertial frame of reference S and instantaneous non-inertial co-rotating frame of reference S' . The co-rotating frame rotates at angular rate Ω equal to the rate of rotation of the particle about the origin of S' at the particular moment t. Particle is located at vector position r(t) and unit vectors are shown in the radial direction to the particle from the origin, and also in the direction of increasing angle θ normal to the radial direction. These unit vectors need not be related to the tangent and normal to the path. Also, the radial distance r need not be related to the radius of curvature of the path.

[edit] Co-rotating frame

In the case of planar motion of a particle, the "coordinate" centrifugal and Coriolis acceleration terms found above to be non-zero in an inertial frame can be shown to be the negatives of the "state-of-motion" centrifugal and Coriolis terms that appear in a very particular non-inertial co-rotating frame (see next subsection).[40] See Figure 3. To define a co-rotating frame, first an origin is selected from which the distance r(t) to the particle is defined. An axis of rotation is set up that is perpendicular to the plane of motion of the particle, and passing through this origin. Then, at the selected moment t, the rate of rotation of the co-rotating frame Ω is made to match the rate of rotation of the particle about this axis, dθ/dt. The co-rotating frame applies only for a moment, and must be continuously re-selected as the particle moves. For more detail, see Polar coordinates, centrifugal and Coriolis terms.

[edit] Polar coordinates in a rotating frame of reference

Next, the same approach is used to find the fictitious forces of a (non-inertial) rotating frame. For example, if a rotating polar coordinate system is adopted for use in a rotating frame of observation, both rotating at the same constant counterclockwise rate Ω, we find the equations of motion in this frame as follows: the radial coordinate in the rotating frame is taken as r, but the angle θ' in the rotating frame changes with time:

Consequently,

Plugging this result into the acceleration using the unit vectors of the previous section:

The leading two terms are the same form as those in the inertial frame, and they are the only terms if the frame is not rotating, that is, if Ω=0. However, in this rotating frame we have the extra terms:[41]

The radial term Ω2 r is the centrifugal force per unit mass due to the system's rotation at rate Ω

and the radial term is the radial component of the Coriolis force per unit mass, where is the tangential component of the particle velocity as seen in the rotating frame. The term

is the so-called azimuthal component of the Coriolis force per unit mass. In fact, these extra terms can be used to measure Ω and provide a test to see whether or not the frame is rotating, just as explained in the example of rotating identical spheres. If the particle's motion can be described by the observer using Newton's laws of motion without these Ω-dependent terms, the observer is in an inertial frame of reference where Ω=0.

These "extra terms" in the acceleration of the particle are the "state of motion" fictitious forces for this rotating frame, the forces introduced by rotation of the frame at angular rate Ω.[42]

In this rotating frame, what are the "coordinate" fictitious forces? As before, suppose we choose to put only the second-order time derivatives on the right side of Newton's law:

  If we choose for convenience to treat as some so-called "acceleration", then the terms

are added to the so-called "fictitious force", which are not "state-of-motion" fictitious forces, but are actually components of force that persist even when Ω=0, that is, they persist even in an inertial frame of reference. Because these extra terms are added, the "coordinate" fictitious force is not the same as the "state-of-motion" fictitious force. Because of these extra terms, the "coordinate" fictitious force is not zero even in an inertial frame of reference.

[edit] More on the co-rotating frame

Notice however, the case of a rotating frame that happens to have the same angular rate as the particle, so that Ω = dθ/dt at some particular moment (that is, the polar coordinates are set up in the instantaneous, non-inertial co-rotating frame of Figure 3). In this case, at this moment, dθ'/dt = 0. In this co-rotating non-inertial frame at this moment the "coordinate" fictitious forces are only those due to the motion of the frame, that is, they are the same as the "state-of-motion" fictitious forces, as discussed in the remarks about the co-rotating frame of Figure 3 in the previous section.

[edit] Fictitious forces in curvilinear coordinates

See also: Curvilinear coordinate system and Covariant derivative

Figure 4: Coordinate surfaces, coordinate lines, and coordinate axes of general curvilinear coordinates.

To quote Bullo and Lewis: "Only in exceptional circumstances can the configuration of Lagrangian system be described by a vector in a vector space. In the natural mathematical setting, the system's configuration space is described loosely as a curved space, or more accurately as a differentiable manifold."[43]

Instead of Cartesian coordinates, when equations of motion are expressed in a curvilinear coordinate system, Christoffel symbols appear in the acceleration of a particle expressed in this coordinate system, as described below in more detail. Consider description of a particle motion from the viewpoint of an inertial frame of reference in curvilinear coordinates. Suppose the position of a point P in Cartesian coordinates is (x, y, z) and in curvilinear coordinates is (q1, q2. q3). Then functions exist that relate these descriptions:

 and so forth. (The number of dimensions may be larger than three.) An important aspect of such coordinate systems is the element of arc length that allows distances to be determined. If the curvilinear coordinates form an orthogonal coordinate system, the element of arc length ds is expressed as:

where the quantities hk are called scale factors.[44] A change dqk in qk causes a displacement hk dqk

along the coordinate line for qk. At a point P, we place unit vectors ek each tangent to a coordinate line of a variable qk. Then any vector can be expressed in terms of these basis vectors, for example, from an inertial frame of reference, the position vector of a moving particle r located at time t at position P becomes:

where qk is the vector dot product of r and ek. The velocity v of a particle at P, can be expressed at P as:

where vk is the vector dot product of v and ek, and over dots indicate time differentiation. The time derivatives of the basis vectors can be expressed in terms of the scale factors introduced above. for example:

 or, in general,  

in which the coefficients of the unit vectors are the Christoffel symbols for the coordinate system. The general notation and formulas for the Christoffel symbols are:[45][46]

   

and the symbol is zero when all the indices are different. Despite appearances to the contrary, the Christoffel symbols do not form the components of a tensor. For example, they are zero in Cartesian coordinates, but not in polar coordinates.[47]

Using relations like this one,[48]

which allows all the time derivatives to be evaluated. For example, for the velocity:

with the Γ-notation for the Christoffel symbols replacing the curly bracket notation. Using the same approach, the acceleration is then

Looking at the relation for acceleration, the first summation contains the time derivatives of velocity, which would be associated with acceleration if these were Cartesian coordinates, and the second summation (the one with Christoffel symbols) contains terms related to the way the unit vectors change with time.[49]

[edit] "State-of-motion" versus "coordinate" fictitious forces

Earlier in this article a distinction was introduced between two terminologies, the fictitious forces that vanish in an inertial frame of reference are called in this article the "state-of-motion" fictitious forces and those that originate from differentiation in a particular coordinate system are called "coordinate" fictitious forces. Using the expression for the acceleration above, Newton's law of motion in the inertial frame of reference becomes:

where F is the net real force on the particle. No "state-of-motion" fictitious forces are present because the frame is inertial, and "state-of-motion" fictitious forces are zero in an inertial frame, by definition.

The "coordinate" approach to Newton's law above is to retain the second-order time derivatives of the coordinates {qk} as the only terms on the right side of this equation, motivated more by mathematical convenience than by physics. To that end, the force law can be rewritten, taking the second summation to the force-side of the equation as:

with the convention that the "acceleration" is now:

In the expression above, the summation added to the force-side of the equation now is treated as if added "forces" were present. These summation terms are customarily called fictitious forces within this "coordinate" approach, although in this inertial frame of reference all "state-of-motion" fictitious forces are identically zero. Moreover, these "forces" do not transform under coordinate transformations as vectors. Thus, the designation of the terms of the summation as "fictitious forces" uses this terminology for contributions that are completely different from any real force, and from the "state-of-motion" fictitious forces. What adds to this confusion is that these "coordinate" fictitious forces are divided into two groups and given the same names as the "state-of-motion" fictitious forces, that is, they are divided into "centrifugal" and "Coriolis" terms, despite their inclusion of terms that are not the "state-of-motion" centrifugal and Coriolis terms. For example, these "coordinate" centrifugal and Coriolis terms can be nonzero even in an inertial frame of reference where the "state-of-motion" centrifugal force (the subject of this article) and Coriolis force always are zero.[50]

If the frame is not inertial, for example, in a rotating frame of reference, the "state-of-motion" fictitious forces are included in the above "coordinate" fictitious force expression.[51] Also, if the "acceleration" expressed in terms of first-order time derivatives of the velocity happens to result in terms that are not simply second-order derivatives of the coordinates {qk} in time, then these terms that are not second-order also are brought to the force-side of the equation and included with the fictitious forces. From the standpoint of a Lagrangian formulation, they can be called generalized fictitious forces. See Hildebrand [22], for example.

Formulation of dynamics in terms of Christoffel symbols and the "coordinate" version of fictitious forces is used often in the design of robots in connection with a Lagrangian formulation of the equations of motion.

VelocityFrom Wikipedia, the free encyclopedia

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This article is about velocity in physics. For other uses, see Velocity (disambiguation).

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In physics, velocity is the rate of change of displacement (position). It is a vector physical quantity; both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is speed, a quantity that is measured in meters per second (m/s or ms−1) when using the SI (metric) system.

For example, "5 meters per second" is a scalar and not a vector, whereas "5 meters per second

east" is a vector. The average velocity v of an object moving through a displacement during a time interval (Δt) is described by the formula:

The rate of change of velocity is acceleration – how an object's speed or direction changes over time, and how it is changing at a particular point in time.

Contents

[hide]

1 Equation of motion 2 Relative velocity

o 2.1 Scalar velocities 3 Polar coordinates 4 See also 5 References 6 External links

[edit] Equation of motion

Main article: Equation of motion

The instantaneous velocity vector v of an object that has positions x(t) at time t and x(t + Δt) at time t + Δt, can be computed as the derivative of position:

Average velocity magnitude is always smaller than or equal to average speed of a given particle. Instantaneous velocity is always tangential to trajectory. Slope of tangent of position or displacement time graph is instantaneous velocity and its slope of chord is average velocity.

The equation for an object's velocity can be obtained mathematically by evaluating the integral of the equation for its acceleration beginning from some initial period time t0 to some point in time later tn.

The final velocity v of an object which starts with velocity u and then accelerates at constant acceleration a for a period of time Δt is:

The average velocity of an object undergoing constant acceleration is , where u is the initial velocity and v is the final velocity. To find the position, x, of such an accelerating object during a time interval, Δt, then:

When only the object's initial velocity is known, the expression,

can be used.

This can be expanded to give the position at any time t in the following way:

These basic equations for final velocity and position can be combined to form an equation that is independent of time, also known as Torricelli's equation:

The above equations are valid for both Newtonian mechanics and special relativity. Where Newtonian mechanics and special relativity differ is in how different observers would describe the same situation. In particular, in Newtonian mechanics, all observers agree on the value of t and the transformation rules for position create a situation in which all non-accelerating

observers would describe the acceleration of an object with the same values. Neither is true for special relativity. In other words only relative velocity can be calculated.

In Newtonian mechanics, the kinetic energy (energy of motion), EK, of a moving object is linear with both its mass and the square of its velocity:

The kinetic energy is a scalar quantity.

Escape velocity is the minimum velocity a body must have in order to escape from the gravitational field of the earth. To escape from the Earth's gravitational field an object must have greater kinetic energy than its gravitational potential energy. The value of the escape velocity from the Earth's surface is approximately 11100 m/s.

[edit] Relative velocity

Main article: Relative velocity

Relative velocity is a measurement of velocity between two objects as determined in a single coordinate system. Relative velocity is fundamental in both classical and modern physics, since many systems in physics deal with the relative motion of two or more particles. In Newtonian mechanics, the relative velocity is independent of the chosen inertial reference frame. This is not the case anymore with special relativity in which velocities depend on the choice of reference frame.

If an object A is moving with velocity vector v and an object B with velocity vector w, then the velocity of object A relative to object B is defined as the difference of the two velocity vectors:

Similarly the relative velocity of object B moving with velocity w, relative to object A moving with velocity v is:

Usually the inertial frame is chosen in which the latter of the two mentioned objects is in rest.

[edit] Scalar velocities

In the one dimensional case,[1] the velocities are scalars and the equation is either:

, if the two objects are moving in opposite directions, or:

, if the two objects are moving in the same direction.

[edit] Polar coordinates

In polar coordinates, a two-dimensional velocity is described by a radial velocity, defined as the component of velocity away from or toward the origin (also known as velocity made good), and an angular velocity, which is the rate of rotation about the origin (with positive quantities representing counter-clockwise rotation and negative quantities representing clockwise rotation, in a right-handed coordinate system).

The radial and angular velocities can be derived from the Cartesian velocity and displacement vectors by decomposing the velocity vector into radial and transverse components. The transverse velocity is the component of velocity along a circle centered at the origin.

where

is the transverse velocity

is the radial velocity.

The magnitude of the radial velocity is the dot product of the velocity vector and the unit vector in the direction of the displacement.

where

is displacement.

The magnitude of the transverse velocity is that of the cross product of the unit vector in the direction of the displacement and the velocity vector. It is also the product of the angular speed ω and the magnitude of the displacement.

such that

Angular momentum in scalar form is the mass times the distance to the origin times the transverse velocity, or equivalently, the mass times the distance squared times the angular speed. The sign convention for angular momentum is the same as that for angular velocity.

where

is mass

The expression mr2 is known as moment of inertia. If forces are in the radial direction only with an inverse square dependence, as in the case of a gravitational orbit, angular momentum is constant, and transverse speed is inversely proportional to the distance, angular speed is inversely proportional to the distance squared, and the rate at which area is swept out is constant. These relations are known as Kepler's laws of planetary motion.

[edit]

Equations of motion are equations that describe the behavior of a system (e.g., the motion of a particle under the influence of a force) as a function of time.[1] Sometimes the term refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.

Contents

[hide]

1 Equations of uniformly accelerated linear motion 2 Classic version

o 2.1 Examples o 2.2 Extension

3 Equations of circular motion 4 Derivation

o 4.1 Equation 2 o 4.2 Equation 3 o 4.3 Equation 4

5 See also 6 External links 7 References

[edit] Equations of uniformly accelerated linear motion

The equations that apply to bodies moving linearly (in one dimension) with constant acceleration are often referred to as "SUVAT" equations where the five variables are represented by those letters (s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time); the five letters may be shown in a different order.

The body is considered between two instants in time: one initial point and one current (or final) point. Problems in kinematics may deal with more than two instants, and several applications of the equations are then required. If a is constant, a differential, a dt, may be integrated over an interval from 0 to Δt (Δt = t − ti), to obtain a linear relationship for velocity. Integration of the velocity yields a quadratic relationship for position at the end of the interval.

where...

is the body's initial velocity

is the body's initial position

and its current state is described by:

, The velocity at the end of the interval

, the position at the end of the interval (displacement)

, the time interval between the initial and current states

, the constant acceleration, or in the case of bodies moving under the influence of gravity, g.

Note that each of the equations contains four of the five variables. Thus, in this situation it is sufficient to know three out of the five variables to calculate the remaining two.

[edit] Classic version

The equations below (often informally known as the "suvat"[2] equations) are often written in the following form:[3]

By substituting (1) into (2), we can get (3), (4) and (5). (6) can be constructed by rearranging (1).

where

s = the distance between initial and final positions (displacement) (sometimes denoted R or x)

u = the initial velocity (speed in a given direction)

v = the final velocity

a = the constant acceleration

t = the time taken to move from the initial state to the final state

[edit] Examples

Many examples in kinematics involve projectiles, for example a ball thrown upwards into the air.

Given initial speed u, one can calculate how high the ball will travel before it begins to fall.

The acceleration is local acceleration of gravity g. At this point one must remember that while these quantities appear to be scalars, the direction of displacement, speed and acceleration is important. They could in fact be considered as uni-directional vectors. Choosing s to measure up from the ground, the acceleration a must be in fact −g, since the force of gravity acts downwards and therefore also the acceleration on the ball due to it.

At the highest point, the ball will be at rest: therefore v = 0. Using the fifth equation, we have:

Substituting and cancelling minus signs gives:

[edit] Extension

More complex versions of these equations can include a quantity Δs for the variation on displacement (s − s0), s0 for the initial position of the body, and v0 for u for consistency.

[edit] Equations of circular motion

The analogues of the above equations can be written for rotation:

where:

α is the angular acceleration

ω is the angular velocity

φ is the angular displacement

ω0 is the initial angular velocity.

[edit] Derivation

These equations assume constant acceleration and non-relativistic velocities.

[edit] Equation 2

By definition:

Hence:

[edit] Equation 3

Using equation 2, substitute t with above:

[edit] Equation 4

Using equation 1 to substitute u in equation 2 gives:

In fluid dynamics an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the air, water or other fluid through which it is moving.

A free-falling object achieves its terminal velocity when the downward force of gravity (Fg) equals the upward force of drag (Fd). This causes the net force on the object to be zero, resulting in an acceleration of zero.[1]

As the object accelerates (usually downwards due to gravity), the drag force acting on the object increases, causing the acceleration to decrease. At a particular speed, the drag force produced will equal the object's weight (mg). At this point the object ceases to accelerate altogether and continues falling at a constant speed called terminal velocity (also called settling velocity). Terminal velocity varies directly with the ratio of weight to drag. More drag means a lower terminal velocity, while increased weight means a higher terminal velocity. An object moving downward with greater than terminal velocity (for example because it was affected by a downward force or it fell from a thinner part of the atmosphere or it changed shape) will slow until it reaches terminal velocity.

Contents

[hide]

1 Examples o 1.1 Derivation for terminal velocity

2 Terminal velocity in the presence of buoyancy force o 2.1 Terminal velocity in creeping flow o 2.2 Applications

3 See also 4 References 5 External links

[edit] Examples

Based on wind resistance, for example, the terminal velocity of a skydiver in a belly to earth free-fall position is about 195 km/h (122 mph or 55 m/s).[2] This velocity is the asymptotic limiting value of the acceleration process, because the effective forces on the body balance each other more and more closely as the terminal velocity is approached. In this example, a speed of 50% of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on. Higher speeds can be attained if the skydiver pulls in his or her limbs (see also freeflying). In this case, the terminal velocity increases to about 320 km/h (200 mph or 90 m/s),[2] which is also the terminal velocity of the peregrine falcon diving down on its prey.[3] And the same terminal velocity is reached for a typical .30-06 bullet travelling in the downward vertical direction — when it is returning to earth having been fired upwards, or perhaps just dropped from a tower — according to a 1920 U.S. Army Ordnance study.[4]

Competition speed skydivers fly in the head down position and reach even higher speeds. The current world record is 614 mph (988 km/h) by Joseph Kittinger, set at high altitude where the lesser density of the atmosphere decreased drag.[2]

An object falling toward the surface of the Earth will fall 9.81 meters (or 32.18 feet) per second faster every second (an acceleration of 9.81 m/s² or 32.18 ft/s²). The reason an object reaches a

terminal velocity is that the drag force resisting motion is approximately proportional to the square of its speed. At low speeds, the drag is much less than the gravitational force and so the object accelerates. As it accelerates, the drag increases, until it equals the weight. Drag also depends on the projected area. This is why things with a large projected area, such as parachutes, have a lower terminal velocity than small objects such as bullets.

Mathematically, terminal velocity — without considering the buoyancy effects — is given by

where

Vt = terminal velocity,

m = mass of the falling object,

g = acceleration due to gravity,

Cd = drag coefficient,

ρ = density of the fluid through which the object is falling, and

A = projected area of the object.

Mathematically, an object approaches its terminal velocity asymptotically.

Buoyancy effects, due to the upward force on the object by the surrounding fluid, can be taken into account using Archimedes' principle: the mass m has to be reduced by the displaced fluid

mass , with the volume of the object. So instead of m use the reduced mass

in this and subsequent formulas.

On Earth, the terminal velocity of an object changes due to the properties of the fluid, the mass of the object and its projected cross-sectional surface area.

Air density increases with decreasing altitude, ca. 1% per 80 metres (262 ft) (see barometric formula). For objects falling through the atmosphere, for every 160 metres (525 ft) of falling, the terminal velocity decreases 1%. After reaching the local terminal velocity, while continuing the fall, speed decreases to change with the local terminal velocity.

[edit] Derivation for terminal velocity

Mathematically, defining down to be positive, the net force acting on an object falling near the surface of Earth is (according to the drag equation):

At equilibrium, the net force is zero (F = 0);

Solving for v yields

[show]Derivation of the solution for the velocity v as a function of time t

[edit] Terminal velocity in the presence of buoyancy force

When the buoyancy effects are taken into account, an object falling through a fluid under its own weight can reach a terminal velocity (settling velocity) if the net force acting on the object becomes zero. When the terminal velocity is reached the weight of the object is exactly balanced by the upward buoyancy force and drag force. That is

where

W = weight of the object,

Fb = buoyancy force acting on the object, and

D = drag force acting on the object.

If the falling object is spherical in shape, the expression for the three forces are given below:

where

d = diameter of the spherical object

g = gravitational acceleration,

ρ = density of the fluid,

ρs = density of the object,

A = πd2 / 4 = projected area of the sphere,

Cd = drag coefficient, and

V = characteristic velocity (taken as terminal velocity, Vt).

Substitution of equations (2–4) in equation (1) and solving for terminal velocity, Vt to yield the following expression

.

[edit] Terminal velocity in creeping flow

Creeping flow past a sphere: streamlines, drag force Fd and force by gravity Fg.

For very slow motion of the fluid, the inertia forces of the fluid are negligible (assumption of massless fluid) in comparison to other forces. Such flows are called creeping flows and the condition to be satisfied for the flow to be creeping flows is the Reynolds number, . The equation of motion for creeping flow (simplified Navier-Stokes equation) is given by

where

= velocity vector field

p = pressure field

μ = fluid viscosity

The analytical solution for the creeping flow around a sphere was first given by Stokes in 1851. From Stokes' solution, the drag force acting on the sphere can be obtained as

where the Reynold's number, . The expression for the drag force given by equation (6) is called Stokes law.

When the value of Cd is substituted in the equation (5), we obtain the expression for terminal velocity of a spherical object moving under creeping flow conditions:

[edit] Applications

The creeping flow results can be applied in order to study the settling of sediment particles near the ocean bottom and the fall of moisture drops in the atmosphere. The principle is also applied in the falling sphere viscometer, an experimental device used to measure the viscosity of high viscous fluids

In 1851, George Gabriel Stokes derived an expression, now known as Stokes' law, for the frictional force — also called drag force — exerted on spherical objects with very small Reynolds numbers (e.g., very small particles) in a continuous viscous fluid. Stokes' law is derived by solving the Stokes flow limit for small Reynolds numbers of the generally unsolvable Navier–Stokes equations:[1]

where:

Fd is the frictional force acting on the interface between the fluid and the particle (in N), η is the fluid's viscosity (in [kg m-1 s-1]), R is the radius of the spherical object (in m), and V is the particle's velocity (in m/s).

If the particles are falling in the viscous fluid by their own weight due to gravity, then a terminal velocity, also known as the settling velocity, is reached when this frictional force combined with the buoyant force exactly balance the gravitational force. The resulting settling velocity (or terminal velocity) is given by:[2]

where:

Vs is the particles' settling velocity (m/s) (vertically downwards if ρp > ρf, upwards if ρp < ρf ),

g is the gravitational acceleration (m/s2), ρp is the mass density of the particles (kg/m3), and ρf is the mass density of the fluid (kg/m3).

Note that for molecules Stokes' law is used to define their Stokes radius.

The CGS unit of kinematic viscosity was named "stokes" after his work.

Contents

[hide]

1 Applications 2 Stokes flow around a sphere

o 2.1 Steady Stokes flow o 2.2 Flow around a sphere o 2.3 Terminal velocity

3 See also 4 Notes 5 References

[edit] Applications

Stokes's law is the basis of the falling-sphere viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of known size and density is allowed to descend through the liquid. If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube. Electronic sensing can be used for opaque fluids. Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes' law can be used to calculate the viscosity of the fluid. A series of steel ball bearings of different diameter is normally used in the classic experiment to improve the accuracy of the calculation. The school experiment uses glycerine or golden syrup as the fluid, and the technique is used industrially to check the viscosity of fluids used in processes. It includes many different oils, and polymer liquids such as solutions.

The importance of Stokes' law is illustrated by the fact that it played a critical role in the research leading to at least 3 Nobel Prizes.[3]

Stokes' law is important to understanding the swimming of microorganisms and sperm; also, the sedimentation, under the force of gravity, of small particles and organisms, in water.[4]

In air, the same theory can be used to explain why small water droplets (or ice crystals) can remain suspended in air (as clouds) until they grow to a critical size and start falling as rain (or snow and hail). Similar use of the equation can be made in the settlement of fine particles in water or other fluids.

[edit] Stokes flow around a sphere

[edit] Steady Stokes flow

In Stokes flow, at very low Reynolds number, the convective acceleration terms in the Navier–Stokes equations are neglected. Then the flow equations become, for an incompressible steady flow:[5]

where:

p is the fluid pressure (in Pa), u is the flow velocity (in m/s), and ω is the vorticity (in s-1), defined as

By using some vector calculus identities, these equations can be shown to result in Laplace's equations for the pressure and each of the components of the vorticity vector:[5]

and

Additional forces like those by gravity and buoyancy have not been taken into account, but can easily be added since the above equations are linear, so linear superposition of solutions and associated forces can be applied.

[edit] Flow around a sphere

For the case of a sphere in a uniform far field flow, it is advantageous to use a cylindrical coordinate system ( r , φ , z ). The z–axis is through the centre of the sphere and aligned with the mean flow direction, while r is the radius as measured perpendicular to the z–axis. The origin is at the sphere centre. Because the flow is axisymmetric around the z–axis, it is independent of the azimuth φ.

In this cylindrical coordinate system, the incompressible flow can be described with a Stokes stream function ψ, depending on r and z:[6][7]

with v and w the flow velocity components in the r and z direction, respectively. The azimuthal velocity component in the φ–direction is equal to zero, in this axisymmetric case. The volume flux, through a tube bounded by a surface of some constant value ψ, is equal to 2π ψ and is constant.[6]

For this case of an axisymmetric flow, the only non-zero of the vorticity vector ω is the azimuthal φ–component ωφ

[8][9]

The Laplace operator, applied to the vorticity ωφ, becomes in this cylindrical coordinate system with axisymmetry:[9]

From the previous two equations, and with the appropriate boundary conditions, for a far-field uniform-flow velocity V in the z–direction and a sphere of radius R, the solution is found to be[10]

The viscous force per unit area σ, exerted by the flow on the surface on the sphere, is in the z–direction everywhere. More strikingly, it has also the same value everywhere on the sphere:[1]

with ez the unit vector in the z–direction. For other shapes than spherical, σ is not constant along the body surface. Integration of the viscous force per unit area σ over the sphere surface gives the frictional force Fd according to Stokes' law.

[edit] Terminal velocity

At terminal velocity — or settling velocity — the frictional force Fd on the sphere is balanced by the excess force Fg due to the difference of the weight of the sphere and its buoyancy, both caused by gravity:[2]

with ρp and ρf the mass density of the sphere and the fluid, respectively, and g the gravitational acceleration. Demanding force balance: Fd = Fg and solving for the velocity V gives the terminal velocity Vs.

In fluid dynamics, the drag coefficient (commonly denoted as: or ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area.[1]

The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag: skin friction and form drag. The drag coefficient of a lifting airfoil or hydrofoil also includes the effects of lift-induced drag.[2][3] The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag.[4][5]

Contents

[hide]

1 Definition 2 Background 3 Drag coefficient c d examples

o 3.1 General o 3.2 Aircraft o 3.3 Automobile

4 See also 5 References 6 External links 7 Notes

[edit] Definition

The drag coefficient is defined as:

where:

is the drag force, which is by definition the force component in the direction of the flow velocity,[6]

is the mass density of the fluid,[7]

v is the speed of the object relative to the fluid, and

is the reference area.

The reference area depends on what type of drag coefficient is being measured. For automobiles and many other objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the cross sectional area of the vehicle, depending on where the cross section is

taken. For example, for a sphere (note this is not the surface area = ).

For airfoils, the reference area is the planform area. Since this tends to be a rather large area compared to the projected frontal area, the resulting drag coefficients tend to be low: much lower than for a car with the same drag, frontal area and at the same speed.

Airships and some bodies of revolution use the volumetric drag coefficient, in which the reference area is the square of the cube root of the airship volume. Submerged streamlined bodies use the wetted surface area.

Two objects having the same reference area moving at the same speed through a fluid will experience a drag force proportional to their respective drag coefficients. Coefficients for unstreamlined objects can be 1 or more, for streamlined objects much less.

[edit] Background

Flow around a plate, showing stagnation.

Main article: Drag equation

The drag equation:

is essentially a statement that the drag force on any object is proportional to the density of the fluid and proportional to the square of the relative speed between the object and the fluid.

Cd is not a constant but varies as a function of speed, flow direction, object shape, object size, fluid density and fluid viscosity. Speed, kinematic viscosity and a characteristic length scale of the object are incorporated into a dimensionless quantity called the Reynolds number or is thus a function of In compressible flow, the speed of sound is relevant and is also a function of Mach number

For a certain body shape the drag coefficient only depends on the Reynolds number

Mach number and the direction of the flow. For low Mach number the drag coefficient is independent of Mach number. Also the variation with Reynolds number within a practical range of interest is usually small, while for cars at highway speed and aircraft at cruising speed the incoming flow direction is as well more-or-less the same. So the drag coefficient can often be treated as a constant.[8]

For a streamlined body to achieve a low drag coefficient the boundary layer around the body must remain attached to the surface of the body for as long as possible, causing the wake to be narrow. A high form drag results in a broad wake. The boundary layer will transition from laminar to turbulent providing the Reynolds number of the flow around the body is high enough. Larger velocities, larger objects, and lower viscosities contribute to larger Reynolds numbers.[9]

For other objects, such as small particles, one can no longer consider that the drag coefficient is constant, but certainly is a function of Reynolds number.[10][11][12] At a low Reynolds number, the flow around the object does not transition to turbulent but remains laminar, even up to the point at which it separates from the surface of the object. At very low Reynolds numbers,

without flow separation, the drag force is proportional to instead of for a sphere this is known as Stokes law. Reynolds number will be low for small objects, low velocities, and high viscosity fluids.[9]

A equal to 1 would be obtained in a case where all of the fluid approaching the object is brought to rest, building up stagnation pressure over the whole front surface. The top figure shows a flat plate with the fluid coming from the right and stopping at the plate. The graph to the left of it shows equal pressure across the surface. In a real flat plate the fluid must turn around the sides, and full stagnation pressure is found only at the center, dropping off toward the edges as in the lower figure and graph. Only considering the front size, the of a real flat plate would be less than 1; except that there will be suction on the back side: a negative pressure (relative to ambient). The overall of a real square flat plate perpendicular to the flow is often given as 1.17. Flow patterns and therefore for some shapes can change with the Reynolds number and the roughness of the surfaces.

[edit] Drag coefficient cd examples

[edit] General

In general, is not an absolute constant for a given body shape. It varies with the speed of airflow (or more generally with Reynolds number). A smooth sphere, for example, has a that varies from high values for laminar (slow) flow to 0.47 for turbulent (faster) flow.

Shapes

cd Item

0.7 a typical bicycle plus cyclist[citation needed]

0.48 rough sphere (Re = )

0.1 smooth sphere ( )

0.001 laminar flat plate parallel to the flow ( )

0.005 turbulent flat plate parallel to the flow ( )

0.24 lowest of production cars (Mercedes-Benz E-Class Coupé)[13]

0.295 bullet (not ogive, at subsonic velocity)

1.0–1.3 man (upright position)

1.28 flat plate perpendicular to flow (3D)

1.0–1.1 skier

1.0–1.3 wires and cables

1.1-1.3 ski jumper[14]

1.3–1.5 Empire State Building

1.8–2.0 Eiffel Tower

1.98–2.05 flat plate perpendicular to flow (2D)

2.1 a smooth brick[citation needed]

[edit] Aircraft

As noted above, aircraft use wing area as the reference area when computing while automobiles (and many other objects) use frontal cross sectional area; thus, coefficients are not directly comparable between these classes of vehicles.

Aircraft[15]

cd Aircraft model

0.021 F-4 Phantom II (subsonic)

0.022 Learjet 24

0.024 Boeing 787 [16]

0.027 Cessna 172/182

0.027 Cessna 310

0.031 Boeing 747

0.044 F-4 Phantom II (supersonic)

0.048 F-104 Starfighter

0.095 X-15 (Not confirmed)

[edit] AutomobileMain article: Automobile drag coefficient

Centrifugal Oil Mist Control Systems Guide

Centrifugal Oil Mist Control Systems, remove mist and provide fluid metalworking recycling.  Commonly known as centrifugal separators, the apparatus consists of a spinning chamber or drum that flings heavy droplets of oil into an outer collection chamber, which in turn drains oil back to the machine via hoses.  Centrifugal mist eliminators are designed to filter oil, synthetic and water based metal working fluids.  The centrifugal process effectiveness is limited to fluids only.  Smoke and solid particulate contaminants will either pass through or impede the operation of the centrifugal mist eliminator. Read more

Product Pros Considerations Features Application MSRP

Aercology E-Type Mist Eliminator

• Small size.

• No need to clean disposable filter liners.

• Requires frequent maintenance to avoid downtime.

• Vibration from

• 100-900 CFM

• Centrifugal separator

• Optional HEPA

 • direct machine mount source capture w/ducting

Not Published

Read more about this oil mist

spinning drum may reduce machine tool precision.

• Requires periodic filter liner replacement and disposal.

• Coated perforated rotating drum

• Collection chamber

• Drain system

• smoke

• clean synthetic mist

• clean oil mist

• not for mist with heavy particulate

eliminator at Aercology's web site.

Royal FilterMist Mist Eliminator

• Very small - takes almost no space

• Fluid savings: drains coolant back into machine.

• Versatile mounting options.

• Requires electrician to install.

• Several parts require frequent maintenance.

• Requires periodic replacement of disposable drum pads.

• Motor starter not included.

• Vibration from spinning drum may reduce machine tool precision.

• 275-1200 CFM

• centrifugal separator

• Various pre & post filters

• Optional noise attenuator

• Various mounting options

• Optional maintenance kit

• direct mount to machine or ducted capture

• coolant mist

• dry smoke

$1,380-$3,240

Learn more on this mist eliminator at Royal's web site.

Royal Stainless Steel FilterMist Mist Eliminator

• Very small - takes almost no space.

• Fluid savings: drains coolant back into machine.

• Versatile mounting options.

• Stainless steel parts resist corrosion.

• Requires electrician to install.

• Several parts require frequent maintenance.

• Requires periodic replacement of disposable drum pads.

• Motor starter not included.

• Vibration from spinning drum may reduce machine tool precision.

• 275-1200 CFM

• centrifugal separator

• Various pre & post filters

• Optional noise attenuator

• Various mounting options

• Optional maintenance kit

• direct mount to machine or ducted capture

• coolant mist

• dry smoke

• aqueous parts washers with caustic soap

• food processing oil spray

$2,750-$3,850

Research more on this mist eliminator at Royal's web site.

Centrifugal Separator Mist Eliminators Product Reviewby Mark Schreiber

Centrifugal oil mist eliminators spin a drum at high speeds around 3400 RPMs in order to pull in contaminated air.  These large spinning parts cause noise and vibration.  To prevent vibration or shaking from affecting the quality of parts being machined, the centrifugal mist separator should be isolated from the machine via ducting.  Once oil mist and smoke is drawn inside its spinning drum, liquid droplets are thrown to the outer wall and collected in another chamber.  Fine mist and oil smoke passes through the unit.  A media type HEPA after filter is needed to collect smoke and fine mist.  There is also a disposable media filter inside the collection chamber.  Both media filters cost at least several hundred dollars and typically need to be replaced 2-3 times per year.

Unlike other machine mount technologies, centrifugal coolant mist eliminators require an electrician to hard wire power and controls. Other machine mount mist eliminators, like the MistBuster, use a standard electrical plug, that you simply plug into a standard outlet.  The centrifugal mist eliminators in the comparison chart above always require some sort of mounting hardware. On the other hand, the MistBuster, for example, has an inlet opening that is 16” x 9” which can be set over any hole in the top of the machine tool that is 6” in diameter.  Anyone with shop knowledge can cut a hole and bolt on a Mistbuster.

If you are planning to use a centrifugal mist eliminator, you will need to gear up for a rigorous maintenance schedule.  Internal contamination build up is a big problem for centrifugal oil mist separators.  They require periodic drum cleaning, annual or monthly inspections (depending on use) and usually a complete rebuild every 3 to 5 years, including over 30 wear items

The CINC Liquid-Liquid Centrifugal Separator utilizes the force generated by rotating an object about a central axis. By spinning two fluids of different densities within a rotating container or rotor the heavier fluid is forced to the wall at the inside of the rotor while the lighter fluid is forced toward the center of the rotor.

In the figure the mixed fluid is shown in green, the lighter phase fluid in yellow and the heavier phase fluid in blue. As can be seen the input fluids enter already mixed (separation process) or independently (extraction process) through one or both inlets. The fluids mix in the annulus between the rotor and the inside of the housing in the mixing zone. The fluids are then fed through an inlet or hole at the bottom of the rotor. A diverter plate or disk is used to direct the fluid to the inside of the rotor sleeve (shown in gray).

As additional fluid is introduced to the rotor the fluid within the rotor is forced upward to the rotor underflows and weirs. The light phase fluid having a lower density flows toward the center of the rotor (shown in yellow) where it exits the rotor over the lighter phase weir through the lighter phase outlets. The heavy phase fluid continues up the rotor (shown in blue) through the underflows, then exits over the heavy phase weir. Each fluid is collected in its own collector ring and then leaves the separator through the heavy and light phase outlets.

Theory of Separation

 The separation performance of the CINC separator is measured by the effluent quality of one or both of the output fluid phases.  There are several parameters that need to be considered in optimizing the performance of the CINC unit for a specific process.  These parameters include viscosity and density of the two liquid phases (at the process temperature), the input ratios, the total flow rate, and the rotor speed (RPM).   How efficiently two fluids will separate in a centrifuge is best described by Stokes Law:

 where:             Vc         =  the centrifugal settling velocity                        d          =  liquid droplet diameter                        rH         =  density of heavy phase

                        rL                   =  density of light phase                        r           =  radial distance of liquid from rotor axis                         w         =  angular velocity (RPM of rotor)                        havg            =  average viscosity of processed fluids The settling velocity, Vc , is an  important parameter in phase separation, as it is a measure of how rapidly two immiscible phases will separate.  From this equation, the parameters that will result in the most efficient phase separation (largest Vc) can be evaluated.  Parameters that would increase Vc include:  larger droplet size, increasing the density difference between two phases, high RPM, and low viscosity.  The converse is also true - less efficient phase separation is observed in systems with:  smaller droplet size, small density differences, low RPM, and viscous fluids.  One parameter that the operator can readily control when optimizing the CINC equipment is the RPM.  Another is fluid residence time while in the rotor, which is directly controlled by feed rate.  Lowering the feed rate can improve the quality of both separated phases by allowing more time to achieve efficient separation. Because the CINC separator was originally designed to operate as a contactor,  fluids are premixed in the annulus between the housing and the spinning rotor.  Although higher RPM�s (w) result in more g-forces inside the rotor, they also result in more mixing in the annulus, and therefore smaller droplet size (d).  As a result of this, an increase in RPM�s will sometimes result in no improvement to separation efficiency (Vc does not increase), as the increased angular momentum (w) is being offset by a decreasing droplet size (d).  Therefore, if better phase separation is needed, increasing the rotor speed will sometimes be of benefit (greater g-forces generated), but sometimes not (smaller droplet size).  This must be determined for each set of application conditions and the fluids processed.     To improve separation for shear sensitive fluids, or in applications where pre-mixing is of no benefit, CINC has developed a low-mixing option that minimizes mixing in the annulus.  This option, referred to as the low-mixing sleeve, allows operation at higher RPM�s with minimal increase in mixing. The low mixing sleeve is recommended for applications where separation is the most important (e.g. oil/water separation, phases already premixed, shear sensitive fluids).

Introduction

Description

Centrifuges accelerate liquid- liquid separations by enhancing the specific gravity difference between the two liquid concerned Two immiscible liquids with slight gravity differences can be separated rapidly and cleanly and on a continuous basis by a centrifuge. Liquid/ liquid dispersions that require hours to separate at 1”G” can be greatly enhanced both in speed and efficiency at 200 “G”.

There are 4 basic operational functions of the centrifuge. The set up differs slightly for each of the process’s which are;

1. Separations2. Extractions and water washes (Mixing and separation)3. Multi stage, gravity fed, continuous counter current Extractions4. Re-actions

In order to conduct a separation using equipment from CINC SOLUTIONS you should familiarise yourself with the function of the low mix sleeve and how the unit optimizes the separation at the top of the rotor on fixed light phase weir, before separating by the designated discharge outlets.

Mixed liquids of any ratio and with differing Specific Gravities are continually pumped (low pressure) or gravity fed into one of the inlets (1) provided on the housing (the spare (12) is blocked off). During separations, a sleeve (2) (low mix sleeve option) is installed to protect the liquids entering the housing from contacting the spinning rotor (3) (and therefore preventing further mixing before separating). The liquids, after entering the housing drop to the base plate of

the centrifuge, which has directional vanes (4) that direct the liquids to the entry point (5) at the base of the spinning rotor.Inside the rotor at the base of the vane package (6) a mild pumping action takes place to continually fill the rotor at the pre determined feed rate. As the liquids are entering the spinning rotor they contact with a deflector plate (7), which forces the mixed liquids to the outside of the rotor wall at the bottom of the rotor. At this point the mixed liquids are first subjected to the “G” force created by the spinning rotor. As the unit is continually fed the liquid gradually and continually moves up the inside of the rotor sleeve and is subjected to centrifugal force between 100 “G” to 600 “G” inside the separation zone (8). The internal height of the rotor is significant, as this, along with the liquid flow rate fed to the unit will determine the length of time (the retention time) the liquids are subjected to “G” force and are therefore en hanced to be an efficient separation. The slower the unit feeds, the longer the liquids remain in the rotor, the longer they are subjected to “G” force, the better the separation efficiency. This is significant if liquids have specific gravities that are close together or are emulsified and are subsequently difficult to separate.

Light & Heavy Phase DischargeDuring the period of retention the mixed phases inside the spinning rotor are subjected to the “ G “ forces and two distinct phases will appear inside the rotor. The heavy phase will move toward the rotor wall and the light phase will settle on top of the heavy phase. When the two, now separate phases reach the top of the rotor they optimize at the centre of the “Fixed” light phase weir (9). At this point the now separated phases are able to exit the top of the rotor for discharge. There are 4 heavy phase exit points at the top of the rotor (10) which allow the heavy phase liquid to enter the top heavy phase chamber (16) past the pre determined changeable heavy phase weir (11) and out through the heavy phase discharge outlet (12). The light phase will gradually separate from the heavy phase and sit “on top” as both liquids spin in the rotor. As both phases reach the fixed light phase weir (9) the optimum separation point, is its centre. This is the optimum separation point at which physical separation takes place sending the two separated phases into different discharge outlets in the housing.

Evidence of carryover exiting a phase discharge can be corrected by adjusting the motor RPM. Whilst it is recognised the optimum separation position is the centre of the fixed light phase weir allowing both phases to exit the required discharge there may be occasions when ratios of phases dictate slight adjustment of this position are required. Slight increase or decrease of the motor speed will increase or decrease the amount of “G” force inside the unit. This will effect the position of the optimum separate phase on the fixed light phase weir (9), moving this phase to or from its exit point by increasing or decreasing the motor speed and can be used to adjust the unit in order to prevent carryover.

As the rotor continues to fill from the bottom the light phase volume at the optimum point will exit from the light phase exit (13) into the light phase collector ring (14) and out via the light phase discharge outlet (15). The heavy Phase exits the rotor at point (10), up into the heavy phase chamber (16) out into the heavy phase collector ring (17) and discharged out of the heavy phase discharge outlet (12).

Introduction

Separations

Extractions & Water washes

Multi stage, gravity fed, continuous counter current Extractions

FABs

Tuesday 05 October 2010

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Centrifugal separators are typically used for separating solids of the order of a micron (0.2 to 10 µm) with very small differences in density (30 to 300 kg/m3) as well as liquid mixtures produced by washing or extraction processes with very small density differences (20 to 400 kg/m3).The acceptable concentration of solids for these types of centrifuges varies from 0.1 to 25 % vol/vol.

Liquid phases are separated continuously. Solids are ejected either continuously (nozzles), sequentially (self-cleaning) or collected in a receptacle provided for the purpose (solid wall bowl).

Depending on the application, Westfalia Separator centrifuges can be explosionproofed and made to run in an inert-gas atmosphere.

How a centrifugal separator works

1 Feed, product 8 Hydrostop® system

2 "Self-thinker" system 9 Discharge, solids

3 Double-walled hood 10 Hood flushing

4 Short-spindle drive 11 Hydrohermetic feed

5 Dampening 12 Hydrohermetic seal

6 Vibration monitoring 13 Discharge

7 Operating water feed    

 

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The basic types are as follows :

Nozzle separator.

Solid-wall disc-type bowl separator.

Self-cleaning separator.

The strong points of Westfalia Separator centrifugal

separators are :

All parts in contact with the product are made of stainless steel.

All Westfalia Separator separators have been developed to comply with the most stringent hygiene standards.

Belt drive.

Patent "Hydrostop" type self-cleaning system.

The machines can be fireproofed, leakproofed and made to run in an inert-gas atmosphere if required.

Centrifugal Separators from LAKOS Centrifugal Separators from LAKOS employ centrifugal action to remove troublesome solids from liquids which will:

Extend the effective life of process liquids.

Protect process equipment from abrasive wear and fouling.

Control or eliminate waste/solids.

Reduce downtime and maintenance.

Keep your fluids systems operating at optimum efficiency.

Centrifugal Separators Features and Benefits Include:

No moving parts to wear out. No screens, cartridges, cones or filter elements to clean or replace. No backwashing. No routine maintrnance or downtime requirements. No standby equipment needs. Low and steady pressure loss. Easily automated. Compact, space-saving profiles. Little or no liquid loss. Effective solids concentration for easy disposal/recovery.

Cyclones and Hydrocyclones

A cyclone is a commonly-used apparatus that makes use of gravity and centrifugal force to separate solid particles from a gas stream. A typical cyclone is a cylindrical vessel with a tangential inlet and top and bottom outlets. Cyclones are widely used in various industries because they are easy to build, inspect and maintain.

Hydrocyclones are similar devices to cyclones where the operating fluid is a liquid rather then a gas. Hydrocyclones operate under pressure. The feed, a mixture of possibly gases, liquids and solids enters the hydrocyclone tangentially through the inlet which forces the mixture to spin inside the cyclone. This spinning motion generates centrifugal forces which cause the gas to disengage quickly and exit through the vortex finder. The liquid passes down into the conical section where the reduction in diameter accelerates the fluid thus generating centrifugal forces strong enough to cause the solids to separate from the liquid. The solids are forced towards the

wall, because of density difference, and then travel down the length of the conical section of the hydrocyclone in a spiral pattern towards the solids outlet, termed the underflow. The gas and liquids migrate towards the center of the hydrocyclone where the flow reverses and moves upwards towards the over-flow, through the vortex finder. Separated solids fall down under gravity into the accumulator vessel situated beneath the hydrocyclone.

Because of the highly complex flows induced by the swirl, and the details of the cyclone geometry, even the fluid flow is difficult to simulate accurately. For this application, the Second Moment Closure turbulence models available in the ANSYS CFX software are very valuable for the correct prediction of the fluid flow. The behavior of the particulates can then be simulated using either the Eulerian multiphase model or the particle transport model.

ANSYS CFX simulation of a hydrocyclone.Picture courtesy of ESSS and Petrobras.

Sedimentation is the tendency for particles in suspension to settle out of the fluid in which they are entrained, and come to rest against a barrier. This is due to their motion through the fluid in response to the forces acting on them: these forces can be due to gravity, centrifugal acceleration or electromagnetism. In geology sedimentation is often used as the polar opposite of erosion, i.e., the terminal end of sediment transport. In that sense it includes the termination of transport by saltation or true bedload transport. Settling is the falling of suspended particles through the liquid, whereas sedimentation is the termination of the settling process.

Sedimentation may pertain to objects of various sizes, ranging from large rocks in flowing water to suspensions of dust and pollen particles to cellular suspensions to solutions of single molecules such as proteins and peptides. Even small molecules such as aspirin can be sedimented, although it can be difficult to apply a sufficiently strong force to produce significant sedimentation.

The term is typically used in geology, to describe the deposition of sediment which results in the formation of sedimentary rock, and in various chemical and environmental fields to describe the

motions of often-smaller particles and molecules. Process is also used in biotech industry to separate out cells from the culture media.

Contents

[hide]

1 Experiments 2 Geology 3 Chemistry 4 Biology 5 See also 6 Notes

[edit] Experiments

In a sedimentation experiment, the applied force accelerates the particles to a terminal velocity vterm at which the applied force is exactly canceled by an opposing drag force. For small enough particles (low Reynolds number), the drag force varies linearly with the terminal velocity, i.e., Fdrag = fvterm (Stokes flow) where f depends only on the properties of the particle and the surrounding fluid. Similarly, the applied force generally varies linearly with some coupling constant (denoted here as q) that depends only on the properties of the particle, Fapp = qEapp.

Hence, it is generally possible to define a sedimentation coefficient that depends only on the properties of the particle and the surrounding fluid. Thus, measuring s can reveal underlying properties of the particle.

In many cases, the motion of the particles is blocked by a hard boundary; the resulting accumulation of particles at the boundary is called a sediment. The concentration of particles at the boundary is opposed by the diffusion of the particles.

The sedimentation of particles under gravity is described by the Mason–Weaver equation, which has a simple exact solution. The sedimentation coefficient s in this case equals mb / f, where mb is the buoyant mass.

The sedimentation of particles under the centrifugal force is described by the Lamm equation, which likewise has an exact solution. The sedimentation coefficient s also equals mb / f, where mb

is the buoyant mass. However, the Lamm equation differs from the Mason–Weaver equation because the centrifugal force depends on radius from the origin of rotation, whereas gravity is presumed constant. The Lamm equation also has extra terms, since it pertains to sector-shaped cells, whereas the Mason–Weaver equation pertains to box-shaped cells (i.e., cells whose walls are aligned with the three Cartesian axes).

Particles with a charge or dipole moment can be sedimented by an electric field or electric field gradient, respectively. These processes are called electrophoresis and dielectrophoresis,

respectively. For electrophoresis, the sedimentation coefficient corresponds to the particle charge divided by its drag (the electrophoretic mobility). Similarly, for dielectrophoresis, the sedimentation coefficient equals the particle's electric dipole moment divided by its drag.

[edit] Geology

Siltation

In geology, sedimentation is the deposition of particles carried by a fluid flow. For suspended load, this can be expressed mathematically by the Exner equation, and results in the formation of depositional landforms and the rocks that constitute sedimentary record. An undesired increased transport and sedimentation of suspended material is called [[siltation, and it is a major source of pollution in waterways in some parts of the world.[1][2] Climate change also affect siltation rates.[3]

[edit] Chemistry

In chemistry, sedimentation has been used to measure the size of large molecules (macromolecule), where the force of gravity is augmented with centrifugal force in a centrifuge.

Home Lecture

Quiz Design Example

Settling Purpose of SettlingPrinciple of Settling Types of SettlingType I SettlingTypes of Settling TanksInlet and Outlet ArrangementWeir Overflow RatesSettling OperationsDesign Details

SettlingSolid liquid separation process in which a suspension is separated into two phases –

Clarified supernatant leaving the top of the sedimentation tank (overflow).

Concentrated sludge leaving the bottom of the sedimentation tank (underflow).

Purpose of Settling

To remove coarse dispersed phase. To remove coagulated and flocculated impurities. To remove precipitated impurities after chemical treatment. To settle the sludge (biomass) after activated sludge process

/ tricking filters.

Principle of Settling

Suspended solids present in water having specific gravity greater than that of water tend to settle down by gravity as soon as the turbulence is retarded by offering storage.

Basin in which the flow is retarded is called settling tank. Theoretical average time for which the water is detained in

the settling tank is called the detention period.

Types of Settling

Type I: Discrete particle settling - Particles settle individually without interaction with neighboring particles. Type II: Flocculent Particles – Flocculation causes the particles to increase in mass and settle at a faster rate.Type III: Hindered or Zone settling –The mass of particles tends to settle as a unit with individual particles remaining in fixed positions with respect to each other.Type IV: Compression – The concentration of particles is so

high that sedimentation can only occur through compaction of the structure.

Type I Settling

Size, shape and specific gravity of the particles do not change with time.

Settling velocity remains constant.

If a particle is suspended in water, it initially has two forces acting upon it:

(1) force of gravity: Fg=pgVp

(2) the buoyant force quantified by Archimedes as: Fb=gVp

If the density of the particle differs from that of the water, a net force is exerted and the particle is accelaratd in the direction of the force:

Fnet=(p-)gVp This net force becomes the driving force.Once the motion has been initiated, a third force is created due to viscous friction. This force, called the drag force, is quantified by:

Fd=CDApv2/2CD= drag coefficient.Ap = projected area of the particle.Because the drag force acts in the opposite direction to the driving force and increases as the square of the velocity, accelaration occurs at a decreasing rate until a steady velocity is reached at a point where the drag force equals the driving force:

(p-)gVp = CDApv2/2For spherical particles,

Vp=d3/6 and Ap=d2/4

Thus, v2= 4g( p- )d   3   CDExpressions for CD change with characteristics of different flow regimes. For laminar, transition, and turbulent flow, the values of CD

are:CD = 24  (laminar)          Re                                                   CD= 24 + 3      +0.34 (transition)       Re     Re

1/2

CD= 0.4  (turbulent)where Re is the Reynolds number:Re= vd

Reynolds number less than 1.0 indicate laminar flow, while values greater than 10 indicate turbulent flow. Intermediate values indicate transitional flow.

Stokes Flow

For laminar flow, terminal settling velocity equation becomes:           v= ( p- )gd 2

                   18which is known as the stokes equation.

Transition FlowNeed to solve non-linear equations:

v2=   4g( p- )d                 3   CDCD= 24 + 3      +0.34            Re     Re

1/2

Re= vd           

Calculate velocity using Stokes law or turbulent expression. Calculate and check Reynolds number. Calculate CD. Use general formula. Repeat from step 2 until convergence.

Types of Settling Tanks

Sedimentation  tanks  may  function  either  intermittently  or continuously.The intermittent tanks also called quiescent type tanks are those which store water for a certain period and keep it in complete rest. In a continuous flow type tank, the flow velocity is only reduced and the water is not brought to complete rest as is done in an intermittent type.

Settling basins may be either long rectangular or circular in plan. Long narrow rectangular tanks with horizontal flow are generally preferred to the circular tanks with radial or spiral flow.

Long Rectangular Settling Basin

Long rectangular basins are hydraulically more stable, and flow control for large volumes is easier with this configuration.

A typical long rectangular tank have length ranging from 2 to

4 times their width. The bottom is slightly sloped to facilitate sludge scraping. A slow moving mechanical sludge scraper continuously pulls the settled material into a sludge hopper from where it is pumped out periodically.

Inlet and Outlet Arrangement

Inlet devices: Inlets shall be designed to distribute the water equally and at uniform velocities. A baffle should be constructed across the basin close to the inlet and should project several feet below the water surface to dissipate inlet velocities and provide uniform flow;

Outlet Devices: Outlet weirs or submerged orifices shall be designed to maintain velocities suitable for settling in the basin and to minimize short-circuiting. Weirs shall be adjustable, and at least equivalent in length to the perimeter of the tank. However, peripheral weirs are not acceptable as

they tend to cause excessive short-circuiting.

Weir Overflow Rates

Large weir overflow rates result in excessive velocities at the outlet. These velocities extend backward into the settling zone, causing particles and flocs to be drawn into the outlet. Weir loadings are generally used upto 300 m3/d/m. It may be necessary to provide special inboard weir designs as shown to lower the weir overflow rates.

Inboard Weir Arrangement to Increase Weir Length

Circular Basins

Circular settling  basins have  the same functional zones as the long rectangular basin, but the flow regime is different. When the flow enters at the center and is baffled to flow radially towards the perimeter, the horizontal velocity of the water is continuously decreasing as the distance from the center increases. Thus, the particle path in a circular basin is a parabola as opposed to the straight line path in the long rectangular tank.

Sludge  removal mechanisms in  circular  tanks are  simpler and require less maintenance.

 

Settling Operations

Particles falling through the settling basin have two components of velocity:1) Vertical component: vt=( p- )gd 2                                                 18

2) Horizontal component: vh=Q/A

The path of the particle is given by the vector sum of horizontal velocity vh and vertical settling velocity vt.

Assume that a settling column is suspended in the flow of the settling zone and that the column travels with the flow across the settling zone. Consider the particle in the batch analysis for type-1 settling which was initially at the surface and settled through the depth of the column Z0, in the time t0. If t0 also corresponds to the time required for the column to be carried horizontally across the settling zone, then the particle will fall into the sludge zone and be removed from the suspension at the point at which the column reaches the end of the settling zone.All particles with vt>v0 will be removed from suspension at some point along the settling zone.

Now consider the particle with settling velocity < v0. If the initial depth of this particle was such that Zp/vt=t0, this particle will also be removed. Therefore, the removal of suspended particles passing through the settling zone will be in proportion to the ratio of the individual settling velocities to the settling velocity v0.The time t0 corresponds to the retention time in the settling zone. t= V = LZ0W             Q     Q

Also, t0= Z0               v0 Therefore,  Z0 = LZ0W and v0=   Q                   v0      Q                 LW                              or v0=   Q              AS

Thus, the depth of the basin is not a factor in determining the size particle that can be removed completely in the settling zone. The determining factor is the quantity Q/As, which has the units of velocity and is referred to as the overflow rate q0. This overflow rate is the design factor for settling basins and corresponds to the terminal setting velocity of the particle

that is 100% removed.

Design Details

1. Detention period: for plain sedimentation: 3 to 4 h, and for coagulated sedimentation: 2 to 2.5 h.

2. Velocity of flow: Not greater than 30 cm/min (horizontal flow).

Abstract

All classical models for thickening assume one-dimensional continuity. However, the free-settling domain in continuous thickeners is not one-dimensional. Therefore, a two-dimensional model is investigated. The two-dimensional model gives the same values for thickener area demands as the one-dimensional model, but the relationships between batch and steady-state thickening are not the same. Free-settling Kynch characteristics can arise in the continuous operation that do not arise in batch tests. Therefore, design procedures that rely on Kynch theory, such as that of Talmage and Fitch, are not completely valid.

A method is developed, based on extrapolating the Kynch or free-settling segment of a batch settling, curve, that yields an improved prediction for thickener area demand.

nature : the calculation of continuous concentrator area of the settlement equation. When there Suspensions interference settlement, the formation of a clear settlement interface. The interface velocity is a function of particle concentration. The continuous concentrator, from an unexpected row of dense plasma concentration levels of change. Therefore velocity layers is changing. 1916 Coe-Clevenger make such a concentrator for a settlement area (m2) of the formula : G for solid handling capacity (kg dry material / s); Gamma liquid density (kg/m3); Du for discharge Consistency Pulp dilution (kg liquid / kg dry material); D1 to feed dilution and Pai Pulp dilution Du between a critical dilution rate (kg liquid / kg dry material); v for the dilution D1 the interface velocity (m / s). Design and calculation must be done to the settlement experiment, measured D1 the interface velocity v values into the on-calculate the maximum value of the design. According Kynch theory can be converted to on-Talmage-Fitch equation

+

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Stormwater Design Example: Sand Filter

SANDFILTER DESIGN EXAMPLE

This example describes in detail the design of a sand filter to treat stormwater runoff from the Brown Civic Center (Figure 1). The filter must meet the following design criteria:

Provide Recharge Treat the Water Quality Volume

Site Specific Data:

Existing ground elevation at BMP location is 22.0 feet, mean sea level. Soil boring observations reveal that the seasonally high water table is at 13.0 feet. Adjacent creek invert is at 12.0'. Hydrology analyses results are in Table 1.

Step1. Compute Water Quality Volume:

WQv previously determined to be 6,752 cubic feet (Table 2).

Step 2. Determine available head (See Figure 2).

Low point at parking lot is 23.5'. Subtract 2' to pass Q10 discharge (21.5) and a half foot for channel to facility (21.0). Low point at stream invert is 12.0'. Set outfall underdrain pipe 2' above stream invert and add 0.5' to this value for drain (14.5). Add to this value 8" for the gravel blanket over the underdrains, and 18" for the sand bed (16.67). The total available head is 21.0 - 16.67 or 4.33 feet. Therefore, the allowable depth (2) (hf) = 4.33', and hf = 2.17'.

Step 3. Compute Recharge Volume:

This surface sand filter design will have an "open bottom" sedimentation basin to allow ground water recharge. The exact dimensions will be sized later, but the volume stored within the sediment chamber must at least be 1,688 cubic feet.

Step 4. Compute WQv peak discharge (qp):

Compute modified CN for 1" rainfall (Note: In this example the WQv corresponds to the runoff from a 1" storm.)

P = 1.0"

Q = 0.62"

CN = 1000/[10+5P+10Q-10(Q2+1.25*Q*P)½]

= 1000/[10+5*1.0+10*0.62-10(0.622+1.25*0.62*1.0)½]

= 95.6

Use CN = 96

For CN = 96 and the Tc = 0.16 hours, compute the qp for a 1" storm. With the CN = 96, a 1.0" storm will produce 0.62" of runoff. From TR-55, Chapter 4, Ia = 0.083, therefore I a/P = 0.083/1.0 = 0.083. From Exhibit 4 - II (page 4-6 of TR-55), q u = 900 csm/in, and therefore qp = (900 csm/in) (0.62") (3.0 ac/640ac/sq mi.) = 2.6 cfs.

The modified curve number approach adjusts for the fact that TR-55 typically underpredicts the runoff from small storm events. The curve number is calculated based on the runoff volume calculated in the "Sizing Options Design Example".

Step 5. Size flow diversion structure (see Figure 3):

Size a low flow orifice to pass 2.6 cfs with 1.5' of head using the Orifice equation.

Q = CA(2gh)1/2 ; 2.6 cfs = (0.6) (A) [(2) (32.2 ft/s2) (1.5')]1/2

A = 0.44 sq ft = d2/4: d = 0.75' or 8.0"; use 8 inches

Size the 10-year overflow as follows: the 10-year WSE is set at 21.0. Use a concrete weir to pass the ten-year flow (14.0 cfs) into a grassed overflow channel using the Weir equation. Assume 2' of head to pass this event.

Q = CLH3/2

* = 3.1 (L) (2')1.5

L = 1.6'; use L = 2'-0" which sets flow diversion chamber dimension.

Weir wall elev. = 19.0. Set low flow invert at 19.0 - [1.5' + (0.5*8"*1ft/12")] = 17.17.

 

Step 6. Size filtration bed chamber (see Figure 4):

From the City of Austin's 1988 Environmental Criteria Manual (Darcy's Law): +

Af = WQv (df) / [k (hf + df) (tf)]

where df = 18" (Depth of the filter)

k = 3.5 ft/day (Permeability of the sand)

hf = 2.17' (Average head above the filter)

tf = 40 hours (Drawdown time)

Af = (6,752 cubic feet) (1.5') / [3.5 (2.17' + 1.5') (40hr/24hr/day)]

Af = 473.1 sq ft; using a 2:1 ratio, say filter is 15.5' by 30.5' (= 473 sq ft)

Step 7. Size sedimentation chamber

From Design Criteria - Filters, (Camp-Hazen), for I < 75%: As = 0.066 (WQv)

As = 0.066 (6,752 cubic ft) or 445.6 sq ft

given a width of 15.5 feet, the length will be 445.6'/15.5' or 28.75 feet ( use 15.5'x28'-9")

Step 8. Compute Vmin

Vmin = ¾(WQv) or 0.75 (6,752 cubic feet) = 5,064 cubic feet

See Design Criteria - Filters. Typically, the volume within the practice can be less than the total water quality volume for filter designs.

Step 9. Compute volume within practice:

Volume within filter bed (Vf): Vf = Af (df) (n); n = 0.4 for sand (Porosity)

Vf = (473 sq ft) (1.5') (0.4) = 284 cubic feet

temporary storage above filter bed (Vf-temp): Vf-temp = 2hfAf

Vf-temp = 2 (2.17') (473 sq ft) = 2053 cubic feet

Compute remaining volume for sedimentation chamber (Vs):

Vs = Vmin - [ Vf + Vf-temp] or 5,064 - [284 + 2053] = 2,727 cubic feet

compute height in sedimentation chamber (hs): hs = Vs/As

(2,727 cubic ft)/(15.5' x 28.75') = 6.12' which is larger than the head available (4.33'); increase the size of the settling chamber, using 4.33' as the design height;

(2727 cubic ft)/4.33' = 630 sq ft; 630/15.5' yields a length of 40.6 feet (say 40')

new sedimentation chamber dimensions are 15.5' by 40'

check recharge requirements: with adequate preparation of the bottom of the settling chamber (rototill earth, place gravel, then surge stone), the bottom will infiltrate water into the substrate. Note that runoff will enter the groundwater directly without treatment. This stone will eventually clog without protection from settling solids so use a removable geotextile to facilitate maintenance. Note that Vs = 2,727 cubic feet which is greater than the recharge requirement of 1,688 cubic feet. Also note that there is 2.17' of freeboard between bottom of recharge filter and water table.

Often, a depth of at least 2' is required between the practice bottom and the water table. See Design Criteria - Filters

Step 10. Compute overflow weir sizes

From sediment chamber (size to pass 2/3 of WQv peak discharge)

0.67 (2.6 cfs) = 1.7 cfs

From filtration chamber (size to pass 1/3 of WQv peak discharge)

0.33 (2.6 cfs) = 0.9 cfs

See Figure 5 for Site Plan View.

Sand filters are used for water purification. There are three main types;

1. rapid (gravity) sand filters 2. upflow sand filters3. slow sand filters

All three methods are used extensively in the water industry throughout the world. The first two require the use of flocculant chemicals to work effectively whilst slow sand filters can produce very high quality water free from pathogens, taste and odour without the need for chemical aids.

Contents

[hide]

1 Sand bed filtration in context o 1.1 Particulate solids capture mechanisms o 1.2 Operating regimes

o 1.3 Rapid pressure sand bed filter design o 1.4 Operating parameters for rapid pressure sand bed filters o 1.5 Uses in water treatment

2 References 3 See also

[edit] Sand bed filtration in context

A sand bed filter is a kind of depth filter. Broadly, there are two types of filter for separating particulate solids from fluids:

Surface filters, where particulates are captured on a permeable surface Depth filters, where particulates are captured within a porous body of material.[1]

In addition, there are passive and active devices for causing solid-liquid separation such as settling tanks, hydrocyclones and centrifuges.[1]

There are several kinds of depth filter, some employing fibrous material and others employing granular materials. Sand bed filters are an example of a granular loose media depth filter. They are usually used to separate small amounts (<10 parts per million or <10 g per cubic metre) of fine solids (<100 micrometres) from aqueous solutions.[2]:302-303 In addition, they are usually used to purify the fluid rather than capture the solids as a valuable material. Therefore they find most of their uses in liquid effluent (wastewater) treatment.

[edit] Particulate solids capture mechanisms

Sand bed filters work by providing the particulate solids with many opportunities to be captured on the surface of a sand grain. As fluid flows through the porous sand along a tortuous route, the particulates come close to sand grains. They can be captured by one of several mechanisms:

Direct collision Van der Waals or London force attraction Surface charge attraction Diffusion.[1]

In addition, particulate solids can be prevented from being captured by surface charge repulsion if the surface charge of the sand is of the same sign (positive or negative) as that of the particulate solid. Furthermore, it is possible to dislodge captured particulates although they may be re-captured at a greater depth within the bed. Finally, a sand grain that is already contaminated with particulate solids may become more attractive or repel addition particulate solids. This can occur if by adhering to the sand grain the particulate loses surface charge and becomes attractive to additional particulates or the opposite and surface charge is retained repelling further particulates from the sand grain.

In some applications it is necessary to pre-treat the effluent flowing into a sand bed to ensure that the particulate solids can be captured. This can be achieved by one of several methods:

Adjusting the surface charge on the particles and the sand by changing the pH Coagulation – adding small, highly charged cations (aluminium 3+ or calcium 2+ are usually

used) Flocculation – adding small amounts of charge polymer chains which either form a bridge

between the particulate solids (making them bigger) or between the particulate solids and the sand.

[edit] Operating regimes

They can be operated either with upward flowing fluids or downward flowing fluids the latter being much more usual. For downward flowing devices the fluid can flow under pressure or by gravity alone. Pressure sand bed filters tend to be used in industrial applications and often referred to as rapid sand bed filters. Gravity fed units are used in water purification especially drinking water and these filters have found wide use in developing countries (slow sand filters).

Overall, there are several categories of sand bed filter:

1. rapid (gravity) sand filters2. rapid (pressure) sand bed filters3. upflow sand filters4. slow sand filters.

[edit] Rapid pressure sand bed filter design

Smaller sand grains provide more surface area and therefore a higher decontamination of the inlet water, but it also requires more pumping energy to drive the fluid through the bed. A compromise is that most rapid pressure sand bed filters use grains in the range 0.6 to 1.2 mm although for specialist applications other sizes may be specified. Larger feed particles (>100 micrometres) will tend to block the pores of the bed and turn it into a surface filter that blinds rapidly. Larger sand grains can be used to overcome this problem, but if significant amounts of large solids are in the feed they need to be removed upstream of the sand bed filter by a process such as settling.[2]:302-303

The depth of the sand bed is recommended to be around 0.6-1.8 m (2-6 ft) regardless of the application. This is linked to the maximum throughput discussed below.[2]:302-303

Guidance on the design of rapid sand bed filters suggests that they should be operated with a maximum flow rate of 9 m3/m2/hr (220 US gal/ft2/hr).[3] Using the required throughput and the maximum flowrate, the required area of the bed can be calculated.

The final key design point is to be sure that the fluid is properly distributed across the bed and that there are no preferred fluid paths where the sand may be washed away and the filter be compromised.

[edit] Operating parameters for rapid pressure sand bed filters

Rapid pressure sand bed filters are typically operated with a feed pressure of 2 to 5 bar(a) (28 to 70 psi(a)). The pressure drop across a clean sand bed is usually very low. It builds as particulate solids are captured on the bed. Particulate solids are not captured uniformly with depth, more are captured higher up with bed with the concentration gradient decaying exponentially.[2]:302-303

This filter type will capture particles down to very small sizes, and does not have a true cut off size below which particles will always pass. The shape of the filter particle size-efficiency curve is a U-shape with high rates of particle capture for the smallest and largest particles with a dip in between for mid-sized particles.[3]

The build-up of particulate solids causes an increase in the pressure lost across the bed for a given flow rate. For a gravity fed bed when the pressure available is constant, the flow rate will fall. When the pressure loss or flow is unacceptable the bed is back washed to remove the accumulated particles. For a pressurised rapid sand bed filter this occurs when the pressure drop is around 0.5 bar. The back wash fluid is pumped backwards through the bed until it is fluidised and has expanded by up to about 30% (the sand grains start to mix and as they rub together they drive off the particulate solids). The smaller particulate solids are washed away with the back wash fluid and captured usually in a settling tank. The fluid flow required to fluidise the bed is typically 3 to 10 m3/m2/hr but not run for long (a few minutes).[2]:224-235 Small amounts of sand can be lost in the back washing process and the bed may need to be topped up periodically.

[edit] Uses in water treatment

All three methods are used extensively in the water industry throughout the world. The first two and third in the list above require the use of flocculant chemicals to work effectively whilst slow sand filters can produce very high quality water free from pathogens, taste and odour without the need for chemical aids.

Passing flocculated water through a rapid gravity sand filter strains out the floc and the particles trapped within it reducing numbers of bacteria and removing most of the solids. The medium of the filter is sand of varying grades. Where taste and odour may be a problem (organoleptic impacts), the sand filter may include a layer of activated carbon to remove such taste and odour.

Sand filters become clogged with floc after a period in use and they are then backwashed or pressure washed to remove the floc. This backwash water is run into settling tanks so that the floc can settle out and it is then disposed of as waste material. The supernatant water is then run back into the treatment process or disposed off as a waste-water stream. In some countries the sludge may be used as a soil conditioner. Inadequate filter maintenance has been the cause of occasional drinking water contamination.

Sand filters are occasionally used in the treatment of sewage as a final polishing stage (see Sewage treatment). In these filters the sand traps residual suspended material and bacteria and provides a physical matrix for bacterial decomposition of nitrogenous material, including ammonia and nitrates, into nitrogen gas.

The rapid sand filter or rapid gravity filter is a type of filter used in water purification and is commonly used in municipal drinking water facilities as part of a multiple-stage treatment system.[1] Rapid sand filters were first used in the United States in 1896 and were widely used in large municipal water systems by the 1920s, because they require smaller land areas compared to slow sand filters.

Contents

[hide]

1 Filter description o 1.1 Design and operation o 1.2 Maintenance

2 Advantages and Disadvantages 3 References

[edit] Filter description

[edit] Design and operation

Rapid sand filters use relatively coarse sand and other granular media to remove particles and impurities that have been trapped in a floc through the use of flocculation chemicals--typically salts of aluminium or iron. Water and flocs flows through the filter medium under gravity or under pumped pressure and the flocculated material is trapped in the sand matrix.

Mixing, flocculation and sedimentation processes are typical treatment stages that precede filtration. Chemical additives, such as coagulants, are often used in conjunction with the filtration system.[1]:7-9

Types:Gravity type e.g, Paterson's filter and Pressure type e.g.Candy's filter.

A disinfection system (typically using chlorine or ozone) is commonly used following filtration.[1]:9-11 Rapid sand filtration has very little effect on taste and smell and dissolved impurities of drinking water, unless activated carbon is included in the filter medium.

[edit] Maintenance

Rapid sand filters must be cleaned frequently, often several times a day, by backwashing, which involves reversing the direction of the water and adding compressed air. During backwashing, the bed is fluidized and care must be taken not to wash away the media.

[edit] Advantages and Disadvantages

Rapid sand filters are typically designed as part of multi-stage treatment systems used by large municipalities. These systems are complex and expensive to operate and maintain, and therefore less suitable for small communities and developing nations.

Advantages

Much higher flow rate than a slow sand filter; about 150 to 200 million gallons of water per acre per day

Requires relatively small land area Less sensitive to changes in raw water quality, e.g. turbidity

Disadvantages

Requires greater maintenance than a slow sand filter. For this reason, it is not usually classed as an "appropriate technology," as the term is applied in less-developed countries.

Generally ineffective against taste and odour problems. Produces large volumes of sludge for disposal. Requires on-going investment in costly flocculation reagents.

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Vertical Leaf FilterAn innovative vertical pressure leaf filter has many advantages and reduces the operational costs heavily. Vertical leaf filter is an easy to operate apparatus that adds incredibly to the

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DescriptionThe Vertical pressure leaf filters are highly useful in filtration of slurry. Vertical pressure leaf filter is mounted on four legs, with the internal Leaves being mounted on manifolds. For opening and closing the vertical pressure leaf filter it is provided with eye bolts and devit and devit arm for the rotatable arrangement. There is no need to open the lid during the discharge of the cake, as the pneumatic vibrator system is provided on the top of leaf filters to dislodge the cake.

Product RangeAvailable in 5 sq. m to 70 sq. m.

Process RequirementsThe main purpose of this vertical leaf filter is to recover the filtrate and the filtered cake, with least manual inputs and minimum spillage. The target has always been to provide an automated system, in which the filtered cake is as dry as possible.

AdvantagesThere are many benefits of Vertical industrial filter and vertical leaf filter as it takes care of both increasing productivity and reducing costs. Some of its eminent advantages are: -» Increased daily production due to high rate of filtration.» A user friendly approach.» Drastically reduced recurring expenses due to no filter cloth requirement.» No spillage due to closed and compact operation.» Very economical operational costs.

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Filter press (sometimes called Plate-and-Frame Filter press) which describes the style of filters developed from the 1800s onwards. The majority of today's filters are more correctly called "chamber filter press", "Membrane filter press", or "Membrane Plate Filter". Many processes in the food, chemical or pharmaceutical industries make products from liquid-solid suspensions or slurries. These mixtures are a little like a runny mud or milk shake. The solids in them do not dissolve in the liquid, but are carried along in it. Filter presses separate the solids from the liquids so that the useful part can be processed, packaged or delivered to the next step.

Filter presses generally work in a "batch" manner. They are loaded with slurry before completing a filtering cycle and producing a batch of solid filtered material, called the filter "cake". The solid is removed, the press re-loaded with slurry and the filtering cycle repeated.

A filter press uses increased pressure to maximize the rate of filtration and produce a final filter cake with a low water content. This is more efficient than filtration using a funnel and paper, which utilizes the low pressure caused by the weight of liquid above the filter paper.

A filter press consists of a series of filter chambers containing square, rectangular or round filter plates supported in a frame. Once the filter chambers are loaded with slurry, the filter plates are forced together with hydraulic rams that generate pressures typically in the region of 100 pounds per square inch (70,000 kg per m2).

In addition to the filter plate filtration medium, the growing cake enhances removal of fine particles in the slurry. The solution coming through the filter press water bibs, called the filtrate, will be very pure.

The filtrate can be drained away for safe disposal, or it can be kept in a water tank for recycled use. At the end of filtration, the solid filter cake can be removed. The whole filtration process is often controlled by electronics to make it automatic or semi-automatic.

The belt filter (sometimes called a belt filter press) is an industrial machine, used for solid/liquid separation processes, particularly the dewatering of sludges in the chemical industry, mining and water treatment. The process of filtration is primarily obtained by passing a pair of filtering cloths and belts through a system of rollers.

Contents

[hide]

1 Operation 2 Improvements 3 References 4 Pictures 5 Further reading

[edit] Operation

The feed sludge to be dewatered is introduced from a hopper between two filter cloths (supported by perforated belts) which pass through a convoluted arrangement of rollers. As the belts are fed through the rollers, water is squeezed out of the sludge. When the belts pass through the final pair of rollers in the process, the filter cloths are separated and the filter cake is scraped off into a suitable container.[1] Belt filter is generally used in phosphatic fertiliser plant to separate the solid from slurry. It comprises washing to different zone to minimise the product losses. Belt filter are under vacuum system to minimise offgas and effluent during operations.

[edit] Improvements

The effectiveness of the operation can be increased by creating a pressure difference across the filter cloth. The filter cloth is directed though a zone where either pressure or vacuum pushes water from the filter cloths and ultimately to drain. [2]

The sludge can be combined with a filter aid or flocculant the help the filtration process and reduce blinding of the filter cloth. [1]

Filter cloths can be cleaned throughout the operation of the process by means of water sprays positioned on the return section of the belt. [3]

Belt Filter Press, How Does It Work?

Most Belt Filter Press operations can be divided into three general stages - initial de-watering, which makes the sludge pulp; pressing or medium pressure filtration, which conditions the sludge for high pressure filtration quality; and high pressure filtration, which raises the dry solids content in the sludge cake to the optimum.

The process begins as the sludge enters the press, where it is mixed with a chemical , either in the press, or in a conditioning tank prior to the press. From this flocculation or preparation zone the sludge enters the gravity drainage zone (#2 and #3 on below illustration), where a large rotating drum agitates the floc and drains approximately 70% of the free water. The resulting capture rate can be as high as 99%.

Pressure is first applied in a low pressure wedge zone (#4), which begins squeezing remaining water out of the sludge. Further de-watering occurs in the medium pressure zone (#5). where two large

Illustration Of A Working Belt Filter Press

perforated drums of decreasing size apply the pressure. Rollers perform the final de-watering in the high pressure zone (#6). The sludge cake (filtered solids) then exits the machine at (#7). (#8) indicates the locations of the belt cleaning spray stations. The belting on a belt filter press must be continuously washed with clear water to keep it from blinding, and this is accomplished by water spray bars placed above returning belt.

Belt Filter Presses are used in mining, mineral processing, municipal waste treatment, industrial and some chemical operations.

The photo at right shows a Roediger Belt Filter Press.

The illustration at left shows how a belt filter press operates, by illustrating the various stages of de-watering.

The Horizontal Belt Filter

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to maximize the image

Description

Horizontal Belt Filters are, in broad terms, the most commonly used vacuum filters in the industry due to their flexibility of operation, adaptation to corrosive slurries and suitability to handle large throughputs.

The development of the Horizontal Belt Filters for the chemical process industries was closely associated with the progress in rubber technology since they incorporate an endless and thick rubber belt of a complex design to support the cake retained by the filter cloth.

The first known filters were the Landskrona and Lurgi built in the 20's and the Giorgini which was a belt filter but with attached trays. The belts were very narrow and short, with a 30 cm wide by 4-5 meters length, and were primarily applied to the washing of phosphate rock. Later, being top feed filters that facilitated multi-washing stages, they were applied in phosphoric acid plants to replace the chains of 3 or 4 internal feed rubber covered Drum Filters used for gypsum washing. As the demand for area has gone up filters were manufactured with three and four 30 cm wide belts running in parallel since the rubber manufacturers were unable to catch-up with the growth of the chemical plants. For this reason the main rivals over the years to belt filters were the Tilting Pan and Table Filters so when rubber belts were the constraint to filtration area growth these filters were in demand and vice versa. Nowadays it is high time for belt filters since rubber technology has made a

big step forwards in the past 10 years. Belts 4 meter wide for 120 m2 filters weigh more than 10 ton and are manufactured in one piece from sophisticated rubber compounds. 

Belt speed is another parameter that sets forth a race among the designers of filters since for many applications a short cycle time is essential. The constraining factor on belt speed is purely mechanical and depends largely on the supporting method of the heavy belt with its cake on it. Belt filters are the fastest filters available today and the speed of modern filters can reach over 50 m/min and yield very short cycle times.

Typical flowschemes and their operating sequence is shown below:

 

 

 

Belt Filter without Washing

This shows a

basic flowsheet existing

in all applications that require straight

forwards dewateri

ng. In these

applications the

objective is to

produce a cake

with the lowest

moisture and there

is no importan

 

 

ce that remaining liquid in the cake

retains its original quality.

Belt Filter with Washing

This flowsheet

shows the

addition of a cake washing stage at some point

downstream cake formation. In this application water,

or any other wash

liquid, is used to displace

the mother liquid

whenever the

process requires a cake that is

free of substance

s that contamin

ate the discharged cake.

 

Belt Filter with Counter-Current Washing

This flowsheet shows a counter current wash system that better utilizes the wash water than a co-current system. In this arrangement solids move in the direction of belt travel and the wash

 

 

liquid in the opposite direction. For efficient washing and sharp separation between the wash filtrates the wash boxes are positioned close to the partitions that are inside the vacuum box. The wash efficiency is defined as a percent of remaining contaminants in the final cake to the contaminants prior to wash.

 

Belt Filter with Counter-Current Washing and Cloudy Recycle

When a slurry is applied onto the permeable filter cloth a small amount of solids passes through the pores and finds its way to the mother filtrate. This can be avoided by inserting a partition in the vacuum box just at the point where the slurry

feed meets the filter cloth. It requires incorporating a small vacuum receiver with a seal tank the removes this  fraction of "cloudy" filtrate that contains the solid particles. The top of this receiver has a valve set to low vacuum so that a thin heel of cake forms on the filter cloth that serves as a filter medium over the porous cloth and produces a solid free

mother filtrate.

This flowsheet is applied to the production of phosphoric acid and the cloudy filtrate is recycled to the upstream reactor or back onto the filter cake as shown in the diagram.

The following animation shows the operation of a belt filter and its components:

Main Belt

Filter Cloth

Feed Box

Wash Box

Vacuum Box

Cloth Wash Box

Discharge Roll

Aligning Roll

Move mouse pointer over the menu to view the components

 

 

Take-Up Roll

Cloth Form Roll

The filter consists of the following components and subassemblies:

The Drainage Belt

An endless rubber belt with traversing grooves drains the filtrate towards holes positioned along the belt. The sides of the belt have elastic rubber curbs that contain the incoming slurry and then the cake as it moves towards the discharge end. Synthetic heavy duty polyester plies are encapsulated in the rubber part below the grooves serve to withstand the longitudinal stresses to which the belt is subjected during its travel.

Drainage belts are available in 2, 3 and 4.2 meter widths and thicknesses of 28, 32 and 39 mm. The belts may be supplied in SBR or EPDM rubbers and both are elastomers characterized by a wide range of applications.

The weight of a 3 m wide belt is 125 Kg/m and this is the heaviest single component to be considered for the design of the hoisting facilities.

The Filter Cloth

The filter cloth retains the cake and moves together with the belt. Nowadays, with some exceptions, they are made from synthetic materials such as

polypropylene or polyester with monofilament or multifilament yarns and with sophisticated weaves and layers. The images on the right show an ultrasonically welded joint and a clipper joint of the cloth ends. With clipper joints, as may be seen on the right, it is necessary to thread multifilament strings across the entire cloth width to retain the fines from passing through to the filtrate.

The entire subject of filter cloth and its selection will be

discussed in a separate section that was not yet constructed.

The Vacuum Box and Wear Belts

A vacuum box below the belt that is mounted along the filter and collects the filtrate through a manifold to the receivers. The box at its topside has two lips covered with low friction synthetic strip liners that seal through intermediate wear belts between the bottom side of the belt and the surface of the strips. Since the belt is the most expensive part of the filter these endless narrow belts serve as a sacrificial component that takes the wear between the surfaces, protects the rubber belt and secures against vacuum leaks.

 

The Vacuum Box Lowering Mechanism

A special mechanism allows parallel lowering or swinging of the vacuum box for cleaning from fines that may have settled inside. The mechanism is designed to accurately seal between the underside of the main belt and the two narrow wear belts that move together along the slide strips attached to the top shoulders of the vacuum box.

 

 

 

The Feed, Wash Boxes and Spray Manifolds 

A feed box and one or more wash boxes are mounted over the filter and designed to distribute evenly the slurry and wash water across the belt.

Spray washing as shown in the clip is also used quite often.

 

 

 

The Cake Discharge End

To watch the discharging cake please play the clip below:

Once the belt reaches the end of the vacuum box the cake drying portion of the cycle terminates and the cloth leaves the rubber belt. The cloth continues moving, changes direction over the discharge roll and the cake drops through a chute for further handling.

 

 

The Belt Supporting Deck

A deck attached to the frame and mounted underneath the belt is designed to support the heavy rubber belt and the cake load. The friction between the surfaces is reduced by injecting water for lubrication and blowing air that floats the belt or by a moving floor constructed of narrow endless belts that move together with the main rubber belt.

Mother Filtrate

Wash Filtrate 1

Wash Filtrate 2

Filtrate Manifold

Filtrate Receiver

Filtrate Pump

Vacuum Pump

To view the components move mouse pointer over the menu

The Filtrate Manifold

A filtrate manifold collects the mother and wash liquids to one or more vacuum receivers. It should be kept in mind that a short path of filtrate between the vacuum box and the receivers reduces to a minimum the losses of vacuum for both the single phase flow of the mother filtrate and the two phase flow of air and wash filtrates.

In the picture all filtrate outlets are connected to a common manifold with a single receiver so both mother and wash filtrates are mixed. However, as may be seen in the flowscheme, mother and wash filtrates may be delivered separately.

The Cloth Tracking Mechanism

A pneumatic or electrical tracking mechanism controls the filter cloth from slipping sideways by guiding it to the left or to the right.

There are several types of mechanisms but the following are very common:

Two pairs of rolls that pinch the cloth alternatively and are positioned on both sides. A roll is that spans across the cloth, is hinged at one end and swings forwards or

backwards on the other end.

 

Selection Criteria

Horizontal Belt Filters are selected in the following cases:

For solids that are fast settling and cannot be kept as a homogenous slurry in bottom or side feed filters such as Drum or Disc Filters.

When long drying time is required to reach asymptotic moisture in the cake. On , for example, the ratio of dry to form cannot normally exceed 1.5 since it is determined by its geometry and the number of circumferential compartments.

When very short cycle times are required for fast dewatering cakes such as phosphate slurry.

If a clear filtrate is required right from the start it is good practice to form a thin heel that serves as filter medium over the exposed cloth. This is done by either a "cloudy port outlet" that is recirculated or, if solids are settling fast, by allocating the first 20-30 cm to act as a "sedimentation pool" prior to entering the vacuum zone.

When intensive cake washing is required since belt filters make it possible to apply counter-current washing. On Drum Filters, for example, the time available for washing is rather limited due to its geometry.

When cakes tend to crack under vacuum measures such as a flapper, compression blanket or pressure roll may assist in sealing the cracks thus avoiding loss of vacuum. When such measures are used it is necessary to make sure that the belt supporting system can take these extra vertical loads.

When scale formation due to flash evaporation is a problem or filtrate temperature must be maintained a vacuum box steam jacketing may be provided.

When the cake tends to clog the cloth its continuous removal after cake discharge enables dislodging of particles by thorough washing of the cloth on both sides with high impact nozzles.

Maintenance

Horizontal Belt Filters are designed nowadays to meet a wide range of process requirements many of which are subjecting its components to severe and demanding conditions. Modern filters run at high speeds, handle thick and heavy cakes, operate at high temperatures and often in an unfriendly environment hence, they are of a sturdy design and made from sophisticated materials of construction.

The main points to observe are:

Evidence of cracks in the rubber belt may cause separation of the plies which are encapsulated between the rubber layers. This weakens the belt and should be repaired on site without delay.

The shrouds on both sides of the belt are subjected to high tension while going over the head and tail pulleys. Their duty is to contain the incoming feed and if the edges tear slurry may pour all over so inspection and their repair is essential.

The vacuum box is hinged and swings to one side so as to enable the periodical cleaning of its internals from settled fines. The repositioning of the box is one of the main reasons for loss of vacuum and special care must be taken to seal the box's anti-friction liners against the sacrificial wear belts and the bottom side of the main belt.

The endless wear belts must be inspected to ensure that they are in good condition otherwise the main belt may be damaged. Likewise, the wear belts should be checked if they seal properly between the stationary vacuum box and the moving belt.

The life of the belt and the main drive depend largely on the water lubrication between the surfaces of the moving and stationary parts hence, the tubes leading to those parts must be kept clean.

It is recommended that the alignment of the filter is inspected from time to time. This applies mainly to large filters since misalignment due to differential settling of the building foundations during the first years after start-up or any other reason may cause the following:

o Along the filter, difficulties may arise in sealing the long and segmented vacuum box.

o Across the filter, the thickness of the cake may taper in one direction causing uneven cake washing. The alignment across the filter is particularly important for thin cakes since a 0.5% slope on a 2 meter wide belt and a 20 mm cake reduces cake thickness on one side from 20 to 10 mm

Horizontal Vacuum Belt Filter Filtres Philippe™

  Filtres Philippe introduced one of the earliest horizontal vacuum belt filters to the marketplace in 1948. Since that time, we've continued to innovate to offer our clients systems designed for longevity and reliability, while always keeping cost-effectiveness in mind.

With over 500 systems installed worldwide, we've supplied solutions for a wide range of processes and challenges.A Filtres Philippe belt filter is an integral part of the environment in which it operates. That's why we pay careful attention to the details - from our endless factory-vulcanised rubber belts, to our turnkey support.

1 54445

Designed for the separation of liquids and solids, while allowing for a continuous filtration process. Can be used for up to a very high concentration of solids, while also offering the ability of efficiently washing the filtrate cake if required. Unique innovative solutions allow an increase in washing efficiencies and filtration parameters. This coupled with a 98% operating factor provides optimum productivity and material recover rate.

The ultimate result is increased profits for you. Filter frame: bolted, not welded, which allows for quick change out of the drainage belt with minimal disassembly.

Oliver-type rotary vacuum-drum filter.

Rotary vacuum filter drum consists of a drum rotating in a tub of liquid to be filtered.

The technique is well suited to high solids liquids that would blind or block other forms of filter. The drum is pre-coated with a filter aid, typically of diatomaceous earth (DE) or Perlite. After pre-coat has been applied, the liquid to be filtered is sent to the tub below the drum. The drum rotates through the liquid and the vacuum sucks liquid and solids onto the drum pre-coat surface, the liquid portion is "sucked" by the vacuum through the filter media to the internal portion of the drum, and the filtrate pumped away. The solids adhere to the outside of the drum, which then passes a knife, cutting off the solids and a small portion of the filter media to reveal a fresh media surface that will enter the liquid as the drum rotates. The knife advances automatically as the surface is removed.

The Rotary Drum Filter

Click on the thumbnail

to maximize the image

Description

The Rotary Vacuum Drum Filter belongs to the bottom feed group and is one of the oldest filters applied to the chemical process industry.

The filter consists of the following subassemblies:

Drum

Valve

Piping

Drive

Scraper

Agitator

Tank

To view the components move mouse pointer over the menu

 

The Drum

The drum is supported by a large diameter trunion on the valve end and a bearing on the drive end. The drum  face is divided into circumferential sectors each forming a separate vacuum cell. The internal piping that is connected to each sector passes through the trunion and ends up with a wear plate having ports that correspond to the number of sectors.

1. The Valve

A valve with a bridge setting controls the sequence of the cycle so that each sector is subjected to vacuum, blow and a dead zone. When a sector enters submergence vacuum commences and continues through washing, if required, to a point that it is cut-off and blow takes place to assist

To view the components move mouse pointer over the menu

Cake Formation

Cake Washing and Drying

Cake Blow Discharge

 

in discharging the cake.

The valve has on certain filters adjustable blocks and on others a fixed bridge ring. Adjustable bridge blocks enable the optimization of form to dry ratio within the filtration cycle as well as the "effective submergence" of the drum when the slurry level in the tank is at the maximum.

The majority of drum filters have a valve with three bridge blocks and a single row pipe plate as shown below and on the right. The duty of the bridges is: (please also refer to Operational Sequence)

1. Vacuum and blow zones separating bridge. This bridge cuts off the vacuum so it is slightly wider than the internal pipe port.

2. Dead zone bridge. This bridge opens to vacuum once a compartment submerges.

3. Start-up assist bridge. At start-up the upper vacuum zone is open to atmosphere and a cake may be formed only when closing the valve that controls this zone. Once the cake starts to emerge from the tank the valve is gradually opened and fully opened when the entire drum face is wrapped with the cake. Since in continuous operation both lower and upper zones are under vacuum this bridge is slightly narrower than the internal pipe port so that the vacuum is continuous and the cake is held onto

the drum.

However, there are also more complex drum filters such as lube oil dewaxers. These filters have a sophisticated valve that allows very quick evacuation of residual wash liquid from the descending compartments by purging inert gas through the internal piping manifold prior to cake discharge. The images below show the two different valves with their single and double row pipe plates:

The exploded view below shows the assembly components of a typical "one row" set-up:

Pipe Plate

Wear Plate

Main Valve

Bridge Block

Cake Form Conn.

Cake Dry Conn.

To view the components move mouse pointer over the menu

The Internal Piping

The internal piping manifold and the various leads and trail options discussed above are shown here:

The clip below shows the internal drum piping of the "two row" manifold. The trail pipes shown in red are normally handling the mother filtrate on the ascending side of the drum up to the 12 o’clock position and then the lead pipes shown in blue handle the wash filtrate on

the descending side. The trail pipes are always connected to the outer row and have a bigger diameter than the lead pipes that are connected to the inner row. The reason for this arrangement is that the trail pipes handle more liquid than the lead pipes so require a bigger

cross section to avoid vacuum losses.

The animation on the left shows a partial section of the

cycle of a single compartment as it passes

from cake washing down to cake formation on the

descending side of the drum.

Note the point when the vacuum is cut-off and the

trailing pipe opens to purge. At this point the leading pipe

evacuates the filtrate that remains in the piping and

compartment prior to blowing off the dry cake.

 

The Drum Deck

The drum deck is divided into separately isolated compartments each subjected to vacuum or blow while the drum is in rotation. The timing of vacuum or blow depends on the bridge setting of the main valve. The compartments are divided with grooved division strips along the drum

face and around the circumference of the drum heads. These division strips are holding synthetic grids shown on the right that cover the entire drum and serve to support the filter cloth. The filter cloth itself is fastened to the drum face by inserting special caulking ropes into the grooves.

The Filter Cloth

The filter cloth retains the cake and is fastened to the drum face by inserting special caulking ropes into the grooved division strips. Nowadays, with some exceptions, they are made from synthetic materials such as polypropylene or polyester with monofilament or multifilament yarns and with sophisticated weaves and layers. The image on the right shows the method of joining the cloth ends with clippers and to retain the fines from passing through to the filtrate multifilament strings are threaded across the entire cloth width. Another option quite often used on belt discharge filters is to join the ends with a special sewing machine.

The entire subject of filter cloth and its selection will be discussed in a separate section that was not yet constructed.

The Cake Discharge Mechanism

Click on the thumbnails to maximize images

 

The cake discharge mechanism that can be either a scraper, belt, roll and in very rare cases a string discharge. Blow is applied only to filters with scraper and roll discharge

mechanisms but not to filters with a belt or string discharge.

The images on the left illustrate the various mechanisms. 

The selection of a suitable type of mechanism depends largely on the release characteristics of the cake from the filter media and will vary from process to process. Scraper discharge mechanisms will suit cakes that release readily and roller discharge mechanism are better for thixotropic cakes.

The Drum Speed Variation

The drum filter has a drive with a variable speed that rotates the drum at cycle times that normally range from 1 to 10 MPR.

The Agitator

An agitator keeps gently the slurry in suspension and reciprocates between the drum face and tank bottom at 16 or so CPM.

The clip below shows a typical agitator:

The Tank

The tank that houses the drum and agitator has baffled slurry feed connections, an adjustable overflow box to set a desired drum submergence and a drain connection. The tanks are normally

designed for an "apparent submergence" of 33-35% however on certain applications 50% and

more is possible. With these special designs the tank ends are higher in order to accommodate stuffing boxes on both the drive shaft and valve end trunnion.

The Cake Washing Manifold

On applications where cake washing is required, 2 or 3 manifolds with overlapping nozzles are mounted to a pair of splash guards bolted to the tank ends. The position of the manifolds and the quantity of wash liquid are adjustable depending on the wash characteristics of the cake.

Control Instrumentation

Optional controls may be used to automate settings such as drum speed, applied wash liquid and drum submergence for a desired cake thickness or throughput. The monitoring of drum submergence controls the slurry feed valves so an adjustable overflow weir is not necessary except for a fixed connection in case of emergency.

The flow scheme of a Rotary Drum Filter Station will generally look like this: 

 

Operational Sequence

The entire filtration cycle on a rotary drum filter must be completed within a geometry of 360 degrees. Let us follow the cycle sequence of a single sector assuming that the drum rotates in a clockwise direction while viewing the valve end:

Cake Formation Zone

Cake Predrying Zone

Cake Washing Zone

Cake Final Drying Zone

Cake Discharge Zone

    To view the zones move the    mouse pointer over

the menu

 

Cake Formation With the overflow weir set to a maximum the "apparent submergence" is normally 33-35% so the slurry levels between 0400 and 0800 hrs. Once a sector enters submergence vacuum is applied and a cake starts to form up to a point where the sector emerges from

the slurry. The portion of the cycle available for formation is the "effective submergence" and its duration depends on the number of sectors, the slurry level in the tank and the

bridge setting which controls the form to dry ratio.

Cake Washing and Drying After emerging from submergence the drying portion of the cycle commences and for non-wash applications continues to about 0130 hrs where the vacuum is cut-off. If cake washing is required the wash manifolds will be located from about 1030 to 1130 hrs and the remaining time to vacuum cut-off at 0130 is the portion allocated to final cake drying.

Cake Discharge After vacuum for the entire sector is cut-off air blow commences at about 0200 hrs in order to facilitate cake discharge. The blow, depending on the position of the tip of the

scraper blade, will cut-off at approximately 0300 hrs. Drum filters are normally operated with a low pressure blow but on certain applications a snap blow is applied and to avoid

the snapping out of the caulking bars or ropes wire winding of the cloth is recommended . Blow is used on scraper and roll discharge mechanisms but on belt discharge filters

vacuum cuts-off when the filter media leaves the drum.

Dead Zone Once the blow is cut-off the sector passes through a zone blocked with bridges so that no air is drawn through the exposed filter media which might cause the loss of vacuum on the entire drum surface.

 

Selection Criteria

In broad terms drum filters are suitable to the following process requirements:

Slurries with solids that do not tend to settle rapidly and will remain in a uniform suspension under gentle agitation.

Cakes when a single washing stage is sufficient to remove residual contaminants from the cake or yield maximum recovery of filtrate.

Cakes which do not require long drying times to reach asymptotic moisture values.

Filtrates that generally do not require a sharp separation between the mother and wash filtrates. Some complex valves, however, enable atmospheric purging of the sectors and internal piping to facilitate a sharp separation of filtrates.

Filtrates that are acceptable with a low quantity of fines that pass trough the filter cloth in the first few seconds of cake formation. Broadly, and depending on particle size and cloth permeability, the filtrate may contain 1000 to 5000 ppm insolubles.

For very corrosive applications plastic drum filters are available with up to 10-15 m2 filtration area.

 

Maintenance

The slow rotation of the drum and reciprocation of the agitator reduce maintenance requirements to a minimum but the following should be inspected periodically:

The strip liner of the trunnion bearing at the valve end will normally wear at the lower half. However, in cases when the slurry has a high specific gravity, the drum may become

buoyant causing a wear to the upper half. At this point it should be mentioned that one way to remove the lower half of the liner, when hoisting facilities are not available or

operational, is to float the drum by filling the tank with a sufficiently concentrated solution.

The stuffing boxes on high submergence filters should be inspected for leakage and, if necessary, the stud nuts should be tightened. It should be noted that excess tightening can

increase substantially the load on the drum drive so the use of a torque wrench is recommended.

The face of the wear plate should be checked periodically and remachined if necessary. A whistling noise during operation is an indication the wear plate is worn out or the valve

spring requires tensioning. The drum has a bailer tube that protrudes from the drive end shaft and must be kept open

at all times since its blockage may cause the collapse of the drum. The bailer tube is a tell-tale indication to the following:

o If a lighter flame is drawn through the bailer tube to the inside of the drum it indicates that a vacuum leak exists in the drum shell or the internal piping. It

should be noted that in certain instances there is a possibility that explosive gases build-up inside the drum and may pose a safety hazard. In such cases the use of

aerosol type smokes or a light tissue paper should be used instead of an open flame to identify a vacuum leak.

o If liquid leakage is observed from the bailer tube it indicates that a hole exists in the drum head causing penetration of slurry from the tank into the drum.

The on-line filter on the wash headers manifold should be checked periodically for pressure build-up due to progressive blockage. Likewise, the nozzles on the wash headers should be kept clean in order to ensure overlapping for full coverage of the washed cake.

 

Introduction Types of Products

Anaerobic Digester | Digester Mixer | Belt Filter Press | Rotary Vacuum Drum Filter | Gravity Thickener | Dissolved Air Flotation Thickener

Rotary Vacuum Drum Filter (RVDF) is one of the most prevalent practices in the industry to dewater all kinds of sludge at low capital cost. Even though these units consume higher power due to deployment of Vacuum Pump, these units are still preferred in given situations in view of their low cost maintenance. These units can be supplied in various sizes upto 1000 sq.ft. filtration area each unit. Depending upon the type of sludge, the dewatered solid discharge mechanism can be in different configurations e.g. Belt Discharge, Knife Discharge, String Discharge etc. These units can also be provided in carbon steel, rubber lined and stainless steel construction to meet specific application requirement. The RVDF is supplied complete with filtrate receiver, moisture trap and other accessories like Pumps, Vacuum Pumps, Blowers etc.

ULTRAFREE -0.5 Centrifugal Filter Device

For Concentration of Biological Samples

Lit No.: P35951

The Ultrafree-0.5 centrifugal filter device is a disposable, single-use filter device used to process aqueous biological solutions in the 0.05 to 0.5 milliliter (mL) range. It is used in any centrifuge that accommodates 2.2 mL centrifuge tubes. Ultrafree-0.5 devices are available with a range of high-flux Biomax® ultrafiltration (UF) membranes. Because of its innovative design and excellent membrane performance, the Ultrafree-0.5 device can concentrate most 0.5 mL solutions down to 20 microliters (ìL) in about 10 minutes, although some solutions maytake longer.

The device’s novel design and vertical membrane configuration, parallel to the direction of the centrifugal force, reduce concentration polarization. This allows for the highest possible flow rates, even in solutions with high levels of particles. Concentrated protein is retrieved by pipette from a concentrate “pocket” located below the membrane surface.

Introduction to Cake

Filtration Analyses, Experiments and Applications Chi Tien

Department of Biomedical and Chemical EngineeringSyracuse UniversityNew York, USA

AMSTERDAM• BOSTON• HEIDELBERG• LONDON• NEW YORK• OXFORD PARIS•SAN DIEGO •SAN FRANCISCO •SINGAPORE

•SYDNEY •TOKY

v To B.F. Ruth, H.P. Grace, F.M. Tiller, M. Shirato and All other earlier workers of Cake Filtration Studie

Preface The idea of writing this volume came to me almost two decades ago shortly after I became seriously involved with cake filtration studies. By all account, cake filtration is an important solid/fluid separation process and has been widely applied in the process, chemical and mineral industries. It was (still is) one of the topics discussed in almost all undergraduate, unit operations texts since the publication of the first edition ofPrinciples

of Chemical Engineeringin 1927. However, there are only a few books and monographs

devoted exclusively to the subject and most of them are aimed at applications. The purpose of the present book is to give an introductory and yet fairly comprehensive account of cake filtration as a physical process in a more fundamental way. Hopefully, it will provide people who contemplate to do research and development work in cake filtration with a source of information and get them quickly on track.

This book is divided into three parts. Part I deals with cake filtration analyses using different approaches including the conventional theory of cake filtration, analysis based on the solution of the volume-averaged continuity equations and treatment of cake filtra- tion as a diffusion problem. Dynamic simulation of cake filtration which examines both filtration performance and cake structure and its evolution is also included. Descrip- tions and discussions of cake filtration experiments, the procedures used and the various methods used for the determination of cake properties constitute Part II. In Part III, three fluid/particle separation processes which feature

cake formation and growth together with other phenomena are discussed.

As stated earlier, I have prepared this book for the purpose of initiating those who are interested in cake filtration research and development work including students who plan to do their theses in this area. In order to gain a wider audience, the background information necessary to comprehend the materials presented is kept to a minimum. The level is consistent with what is taught at an accredited B.Sc. degree program in chemical, civil and mechanical engineering. It should therefore be possible to adopt the book as a text or part of text for graduate courses dealing with separation or solid/fluid separation, even though, strictly speaking, it is not written as a text.

There is another reason for writing this book. During the past two decades, we have seen considerable discussions and debates about the future of chemical engineering as a profession and as a discipline. Numerous suggestions and plans on chemical engineering education and research have been advanced for the purpose of restoring the

profession to its past glory. Somewhat overlooked in these efforts is the fact that the viability of any profession as a field of study depends, to a large degree, upon its appeal to talented young people on account of the intellectual challenges and practical relevancy it poses. In this regard, while the topic of unit operations is recognized as a core subject of the chemical engineering discipline, a search of library and publication catalogues reveals that most of texts and monographs dealing with this topic, but not on an elementary

viii PREFACE

level, were published more than three or four decades ago, thus giving the impression and creating the perception that the discipline has reached its maturity a long time ago. It is therefore not surprising that as a subject of study, chemical engineering nowadays is not able to attract a sufficiently large number of talented students as it once did. It is hoped that writing a book such as this one may, in a very small measure, contribute to rectify the prevailing erroneous impression.

A major part of this book is based on the studies of fluid/particle separation I conducted during the past 20 years at Syracuse University and the National University of Singapore. I would like to acknowledge the significant roles played by my former students and colleagues in these studies: Professor R. Bai, Professor M.S. Chiu, Professor Y.-W. Jung, B.V. Ramarao, Dr K. Stamatakis, Professor R.B.H. Tan, Dr S.-K. Teoh, and Professor C.-H. Wang. I am particularly indebted to R. Bai for his tireless efforts in obtaining some of the numerical results of cake formation and growth included in this book. I should also add that the countless hours of stimulating discussions on cake filtration and related problems I had with B.V. Ramarao during the past decade were certainly one of the major rewards of writing this book.

Finally, I would like to thank my former and present publishing editors, Anouschka Zwart and Louise Morris of Elsevier, for their efforts and assistance which made prompt publication of this book possible, Kathy Datthyn-Madigan for her keyboard skill in typing and assembling the manuscript and last but not the least, my wife,

Julia, for all the help and support she has given me for the past four and a half decades.

Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . vii 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .1

1.1 Cake Filtration as a Separation Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Cake Filtration vs. Deep Bed Filtration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Cake Filtration vs. Cross-Flow Filtration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 FiltrationCycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 10

Part I Analyses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .11 2 The Conventional Theory of Cake Filtration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1 BasicEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Expressions of Cake Filtration Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Pressure, Compressive Stress, Solidosity Profiles, and

Other Expressions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.4 An Improved Procedure for Calculating Filtration Performance. . . . . . . . . . 27

2.5 Extensions of the Conventional Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.5.1 Centrifugation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.5.2 Expression of solid/liquid

mixtures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.5.3 Optimum operating pressure and the skin layer effect. . . . . . . . . . . . . 39

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 44 Appendix 2A.1 Locations of Air/Liquid, Liquid/Suspension, Suspension/Cake Interfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Appendix 2A.2 Pressure and Compressive Stress Profiles in Centrifugal Filtration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Appendix 2A.3 A Procedure for Predicting Centrifugal Filtration Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3 Analysis of Cake Filtration: Solutions of the Volume-Averaged Continuity Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.1 Formulation of the Governing Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.2 ClosingRelationships. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3 Comparisons with Previous Studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.4 Numerical Analysis of Cake Filtration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.5 Examples of Numerical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.6 SedimentationEffect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.7 Effect of Fine Particle Retention. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.8 BatchFiltration/Consolidation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 89

 

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Chemineer - Agitators

Chemineer - AgitatorsModel 20 HT/GT AgitatorsThe Model 20 HT/GT agitators feature a high-efficiency gearbox designed specifically for agitator service. Models are available in right angle and parallel shaft configurations to meet specific application requirements from critical chemical reactor systems to routine storage. These agitators feature a modular design package with a wide range of speeds for improved process control and greater application versatility. The Model 20 HT/GT agitators are designed to meet AGMA, OSHA, ANSI, IEC, DIN, EU and ATEX standards and requirements.More... Model 20 HT/GT Product Literature (PDF)

MR MixersChemineer’s MID RANGE Mixers combine quality, durability and economy to supply unbeatable value in mixing equipment for the chemical, water and general processing industries. The MR agitators are designed to be mounted vertically over open or closed top tanks. More...Product Literature (PDF)

- Highest efficient gearing available reduces energy costs- Reduces wear rate for 20+ year service life

Housing and Lubrication Features- Cast Gearbox- Dry Well Seal- Grease and Bath Lubrication- Standard R&O OilsBenefits- Modular designs between right angle (HT) and parallel shaft (GT) - Eliminates lubrication leaks which are common in commercial gearboxes with no dry well- Ensures vital lubrication to gears and bearings at all operating speeds, eliminating internal/external lubrication pumps- No Synthetic Lubrication is required saving installation and maintenance costs

Bearing Design Features- Tapered Roller Output Bearings, Grease Lubricated- Tapered Roller/Roller Bearings, Oil LubricatedBenefits- High capacity to handle shaft/impeller loads while providing long life- Oil lubrication provides cooler operation, longer life, and lower maintenance over grease or permanently lubricated bearings

Seal Features and Benefits Features- Drop collar shaft support during seal change- Swing out or spacer spool seal change designs- Variety of seal options from major mechanical seal vendors such as John Crane, Flowserve, Chesterton and AES- Much more...Benefits- Shaft drops easily by loosening coupling bolts, and engages by tightening the coupling bolts- Shaft only drops 1/2" eliminating steady bearing disengagement- No need to pull shaft up through gearbox or in-tank shaft supports- Much more...

Shaft Design Both process and mechanical considerations determine shaft design. Shafts are sized to resist torsional loads and bending moments induced by hydraulic forces acting on the impeller, as well as to avoid excessive vibration due to the coincidence of critical frequencies and operating speed.

Shafting is straightened to tight tolerances for long seal life and smooth operation – less than 0.003 inches total run out per foot of shaft length (0.25 mm per meter). Custom couplings, impellers, shafts and steady bearings are available upon request, including sanitary designs.

Types of Shafts Shafting is supplied in a single piece design or in rigidly coupled sections for easy installation. For large diameter shafts, pipe shafting is a viable option with couplings and impeller hubs welded to the shafting. A wide range of materials and coating options are available.

Couplings To facilitate assembly in the field, extension shafts are attached to the drive shaft with flanged rigid couplings, eliminating the need for shafts to be installed through the gearbox. Optional in-tank couplings can either be removable tapered bore or welded simplifying installation of long shafts.

Steady Bearings Steady bearings are available to help support extremely long shafts. Cup tripod, bracket and pad-type steady bearings are standard design options.

Extended Keyways Extended keyways for adjusting impeller location offer process and design flexibility.

Product Literature

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HT Turbine Agitators have earned a worldwide reputation for long life, flexibility and ruggedness. As a result, they are the preferred agitators of many industries for harsh, demanding environments where peak performance is integral.

HT Turbine Agitators are robust, simple and designed for ease of maintenance. The drive has a minimum of moving parts, while NC machining of the housing and the subassemblies ensures trouble-free interchangeability and precision parts mating.

Engineered for the ultimate in process compatibility, the HT Turbine Agitator is available in 13 standard drive sizes from 1 to 1,000 hp - even more for specialized applications. A wide selection of mounting methods, materials of construction, shaft seals, shafts, impellers and accessories can provide the best turbine agitator for virtually any process.

Drive Components

Right-Angle DesignThe right-angle drive of the HT agitator is readily adaptable to nearly any mounting configuration - flanged nozzle, independent beam support and top or bottom entering. The right-angle design also simplifies the mounting, alignment and service of standard foot-mounted motors.

Helical and Spiral Bevel GearingHelical gears are hardened, precision-hobbed, then shaved to exacting tolerances for proper contact and longer life. All HT gearing is inspected for compliance with AGMA Quality 10 standards.

Timken Tapered Roller BearingsFor superior handling of both radial and thrust loads Timken ® tapered roller bearings are used throughout the HT drive. Drive bearings can be service rated to over 100,000 hours L-10 life.

Internal ShaftsBoth short-span and low-speed shafts feature maximum rigidity and are precision-turned on NC lathes for dimensional consistency and straightness.

Positive LubricationHigh -speed bearings are continuously protected through splash-lubrication. A specialized drywell shaft seal prevents oil leakage. Easily accessible grease fittings lubricate low-speed shaft

bearings.

Robust HousingsDrive housings, support pedestals and mounting feet are fabricated from steel plate. Each component must then pass a quality inspection on a computerized precision coordinate measuring inspection machine. Each housing features lifting lugs and eyebolts for simplified, safe handling of the agitator during installation and removal. Catalyzed,

polyurethane exterior finishes protect against corrosion in both indoor and outdoor operating environments.

 

Chemineer HTM Agitators

The Chemineeer HTM is an optional gearbox for high torque applications and is manufactured specifically for agitator service. The HTM agitator drive is available in both right angle and parallel shaft configurations and offers many of the same benefits as the HT drive.

Motors & Flexible Couplings

Foot-Mounted MotorsChemineer engineers have supplied nearly every imaginable power source for HT Turbine Agitators, including steam turbines, fluid drives, internal combustion engines and others. However, the most common drive option is the standard, industrial foot-mounted motor. Easy to mount, align and service, these standard motors are NEMA Class B in design, with a 1.0 service factor, and are available from 1 to 350 hp. Speeds are 1800, 1200 and 900 rpm. Motor enclosures are either TEFC or explosion-proof. For severe chemical service, motors with Class F insulation and a 1.15 service factor can be specified.

OptionsVariable frequency, electronic controls are available for applications requiring responsive speed changes. Tachometers, signal interfaces and transformers are available. Variable-speed belt drives offer process flexibility with three-to-one speed range.

Flexible CouplingsHT agitators up to 50 hp are shipped standard with flexible couplings for improved shock and vibration absorption. Other coupling configurations include gear couplings, flexible element, disc-type and fluid couplings.

Oversized ShaftingAll Chemineer shafting is sized and tested to resist torsional loads and bending moments resulting from hydraulic forces acting on the impeller during mixing. Chemineer will work with you to determine optimum sizing for your application.

HT agitator shafts are available in diameters of 1-1/2 to 10 inches and afford maximum resistance to shock loads. All shafts are straightened to 0.003 inches of total runout per foot of shaft length to minimize vibration and maximize seal life. Our experience with special applications enables you to specify practically any machinable alloy or protective coating suited to your process.

TypesShafts are available in single piece or rigidly coupled designs. Pipe shafting, ideal for large diameter shafts, feature couplings and impellers welded to the shafting.

OptionsExtended keyways for adjusting impeller position offer flexibility in case your processes change. A variety of surface finishes provide protection in harsh service environments.

CouplingsEasier extension-shaft-to-drive-shaft field assembly is achieved with flanged rigid couplings with removable coupling halves or welded coupling halves. Optional in-tank couplings simplify installation of long shafts.

Steady BearingsSupport of extremely long shafts requires the use of steady bearings. All Chemineer steady bearings have a replaceable wear sleeve that can be fabricated from a variety of materials. Both bracket- and tripod-mount designs are available.

Product Literature

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We have proven that it is possible to develop an economical mixer that provides quality workmanship, design excellence, performance and reliability of high performance at an economical cost. The Chemineer QED Plus Mixer combines Quality, Economy and Durability for unbeatable mixing value. QED Plus Mixers are well-suited for agitator service in chemical processing, petrochemical, pharmaceutical and general industrial applications.

Application Versatility

Engineered for versatility, the QED Plus Mixer is compatible with 140 and 180 TC frame motors, three impeller types and three sealing options. Its compact right-angle drive is compatible with various mounting arrangements. For open tank applications, the QED Plus Mixer is equipped with removable, steel plate mounting feet for easy attachment to a steel beam or any other support structure. The QED Plus Mixer mounts easily to closed tanks with an integral pedestal/stuffing box/mounting flange that is ANSI or DIN compatible. It fits either a 150 lb. ANSI 6" connection or a 150 mm 16 bar ISO connection.

Heavy-Duty Shafts

All Chemineer shafts are straight to less than 0.003 inches total runout per foot of shaft length, resulting in longer seal life and quiet operation. Machined from carbon steel or 316 stainless steel, tapered shafts are included as standard on all QED Plus Mixers. Chemineer tapered shafts are manufactured to resist torsional loads and bending moments caused by hydraulic forces imparted upon the impeller. All QED Plus Mixers also have a shaft sleeve that facilitates easy removal of the gear drive from the impeller shaft.

Motors

QED Plus Mixers rely on NEMA or IEC C-face motors for reliable performance. Protected by a cast iron housing, rugged worm-drive and helical gearing and high-speed internal bearings ensure a smooth, efficient transfer of power from motor to shaft. Easy to install, operate and service, the 1750 rpm motor bolts directly to the drive mechanism reducing the risk of possible misalignment due to fluctuating temperatures, vibrations or deflection of the mounting pedestal. QED Plus motors have a service factor of 1.5 and come in sizes of 1 to 5 horsepower. Depending on gear ratios the QED Plus is capable of producing shaft speeds of 44, 70, 88 or 117 rpm.

Couplings

All QED Plus Mixers are supplied with flexible motor-to-gear reducer couplings made of a durable elastomeric material. Flexible couplings reduce mechanical shock and vibration, while compensating for minor motor misalignments. Coupling guards are included for safety and are easily removed for routine maintenance and repair.

Product Literature

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Biotechnology/ Pharmaceutical Mixing and Heat Transfer Solutions

Chemineer's sanitary mixers offer a variety of design configurations, materials and options needed to meet critical sanitary mixing applications and ensure the highest level of sanitary mixing. Chemineer also offers a wide variety of precision-engineered, high-performance impeller options.

Chemineer Sanitary Mixers

With Chemineer sanitary mixers, cleanability counts as all mixing surfaces promote the free draining of liquids. Chemineer has combined their thorough understanding of fluid mixing dynamics with current ASME-BPE guidelines to build robust, high quality mixers. With mixing volumes from 10 - 40,000 liters and the ability to custom size mixers to suit your requirement, Chemineer has a mixing solution for all of your sanitary needs.

Greerco Sanitary Pipeline Mixers and Colloid Mills

Greerco sanitary pipeline mixers and colloid mills are expertly designed for precision high-efficiency and cost-effective performance. The unique axial-in, axial-out flow

configuration of the pipeline mixers provides intense hydraulic and shear forces. The colloid mill is a high-speed, high-shear mixer capable of batch or in-line processing. It offers a number of sealing and mounting options to meet the needs of any pharmaceutical, biotechnology, cosmetic or food processing application. Both products come standard with 316 SS wetted parts and sanitary ferrule connections.

  

Kenics Static Mixers & Heat Exchangers

Kenics static mixers provide the highest level of purity and have a self-cleaning element design. The process fluid is completely mixed, eliminating gradients in temperature, velocity, or concentration. Kenics static mixers are available with 316 LSS construction, sanitary ferrule connections, and 3A certified design/construction.

Kenics heat exchangers offer maximum heat transfer for highly viscous, difficult-to-process materials while allowing uniform heat history, eliminating thermal degradation and reducing fouling. These sanitary heat exchangers are completely customized to fit your needs and are built in accordance with TEMA and ASME codes of construction.

Product Literature

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HS Side-Entering Agitators offer the same ruggedness, dependability and simplicity of design found in our other high-quality turbine agitators and mixers. At the heart of the HS Agitator is a right-angle drive exclusively engineered for side-entering agitator service.

Chemineer ® HS Side-Entering Turbine Agitators work efficiently when a tank is too large for convenient installation of a top-entering agitator, or where headroom is severely limited. Supporting a top-entering agitator on a large tank is often far more expensive than the installation of a side-entering agitator. Long shafts on extremely tall tanks can be eliminated for cost savings and design simplicity. For large tank installations, several smaller side-entering agitators may be more efficient and economical than a single, larger unit.

The HS Agitator is available in four standard sizes from 1 to 75 hp. Special designs, up to 250 hp, are available. The wide range of power selections and seal options, combined with two standard output speeds and accurately sized impellers, means that there is an HS agitator available for nearly every standard application. Consider HS Side-Entering Agitators for process applications involving continuous blending, heat transfer, mass transfer or solids suspension.

Drive Elements

Right-Angle Design The right-angle gear design of the HS Agitator reduces overhung load and minimizes nozzle reinforcement requirements. A structural steel support leg is standard on HS Agitators with optional adjustable tie-rods available.

Spiral Bevel Gearing HS drives utilize hardened spiral bevel gearing sized to provide heavy-duty performance and strength. All gears are load-rated per AGMA standards and inspected to AGMA Quality 10 levels.

High-Capacity Tapered Roller Bearings Rated at a minimum of 30,000 -hour L10 bearing life, the Timken ® high-capacity, tapered roller bearings throughout the HS drive provide long service life and exceptional wear resistance.

Positive Lubrication All gears and bearings in the HS drive are splash-lubricated by an exclusive system developed by Chemineer. Double lip seals on the drive shaft prevents oil loss or the infiltration of contaminants.

Extra Capacity Reducer Shaft Due to a large cross-section, the low-speed shaft inside the drive minimizes gear misalignment and deflection. The extension shaft is also designed to minimize deflection for superior seal life. Shafts are stocked in carbon steel as well as types 304 and 316 stainless steel. Machinable alloys are also available to address an even wider array of applications.

Motor Types and Mounting For installation flexibility and easy mounting, the HS Agitator is compatible with standard foot-mounted electric motors ranging from 1 to 75 hp. Vertical adjusting screws permit precise alignment of the motor even when the agitator is mounted on the tank. Readily available, standard couplings reduce costs and replacement difficulties.

Rugged Steel Construction Drive housings, support pedestals and mounting feet are fabricated from steel plate using high-tech NC machining equipment. Each component must then pass a quality inspection on a computerized precision coordinate measuring inspection machine. Each housing features lifting lugs and eyebolts for simplified, safe handling of the agitator during installation and removal.

Catalyzed, polyurethane exterior finishes protect against corrosion in both indoor and outdoor operating environments.

Tank Shut-Off System A retracting mechanism and seal shut-off are standard on all HS Agitators. This permits the replacement of cartridge mechanical seals or the repacking of stuffing boxes without emptying the tank.

The mechanical seal shut-off is engaged when the easily accessible retraction bolt pulls the shaft shut-off collar back into the flange housing. The shut-off seal is provided by a fluoroelastomer O-ring. The shaft is then rotated to lock the extension shaft into the housing. This locking feature assures positive shut-off and shaft stability during a mechanical seal change.

The stuffing box shut-off is accomplished by simply tightening the retraction bolt which pulls the shut-off collar back and holds it securely. The seal is provided by a corrosion-resistant gasket sandwiched between the shut-off collar and the mounting flange.

Product Literature

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Custon Designed Process Plant | Mobile Process Plant | UN Certified Bulk Containers | Case Studies

Features and Benefits

Sealed system - no contamination or emission

Low shear process - no product degradation

Homogeneous suspension of heavy slurries Rapid recirculation

- central jet 7 ft/s (2 m/sec) No aeration Low energy consumption Hygienic construction Ease of cleaning Flexible batch sizes

Reliability, Performance & Value

The MR model is the latest addition to Chemineer’s line of high performance and reliable agitators. The MR agitator’s gearbox is a proprietary, parallel-shaft, helical gear design that features minimum 30,000 hour L10 bearing life and an oversized output shaft for optimal performance and extended service life. Shaft speed selections are available from 7 to 380 rpm without the use of auxiliary reducers or electronic drives. When the MR gearbox is expertly matched with a wide variety of Chemineer impellers and other system components, MR agitators are capable of economically meeting your blending, dispersion, and other mixing needs.

Gearbox Designed for Agitator Duty

Commercially available gearboxes for agitators in this size range normally have low-speed output shafts and bearing designs that are poorly suited to agitator duty. Commercial gearboxes typically use smaller diameter output shafts, resulting in the need to select larger and more expensive units to handle the torsional loads and bending moments produced by the hydraulic

loads on agitator systems. These smaller output shafts and less robust bearing designs of commercial gearboxes also contribute to higher gear deflections, excessive vibration, higher maintenance costs, and a reduced life of many critical agitator system components. The MR gearbox addresses these concerns by incorporating a larger output shaft straightened to exact tolerances and high capacity tapered roller bearings into its design. The rugged cast iron housing of the MR gearbox features a double lip seal to effectively contain the gearbox lubricant as well as a swing out seal change design that saves maintenance labor and reduces downtime. These design features reduce the overall initial cost of the gearbox and other agitation system components and reduce the maintenance costs of the agitator.

Versatile Modular Design

The modular design of MR agitators makes them well-suited for a variety of mixing applications. MR agitators are designed to meet AGMA, OSHA, ANSI, IEC, DIN, EU and ATEX standards and requirements. They may be supplied with integral gearmotors, standard NEMA and IEC motors or explosion-proof motors. A variety of stuffing boxes or mechanical seals and many Chemineer custom pedestals, couplings, impellers, shafts, and steady bearings can be incorporated into the MR design as well. This product can be mounted to support beams or similar structures for open tank operation or to pedestals, plates or flanges for closed tank operation. The MR agitator and all of its system components are included in the Chemineer Expert Design System (CEDS®), the industry leading agitator design and analysis software program. CEDS® helps insure that MR components are selected and configured for optimal system performance and value.

Global Availability

To support the global manufacturing footprint of our customers, MR agitators are available in all major global markets with the same Chemineer assurance of reliability, performance and value. MR agitator gearboxes, mountings and system components are also interchangeable with the Chemineer Model 20 HT and GT agitators enabling customers to readily adapt or upgrade their agitator drives and system components to changes in application requirements or operating environments.

With all of its versatility, MR agitators can become your global process system standard helping drive efficiencies in procurement and reduce maintenance costs and replacement part investment.

Impeller Technology

Chemineer’s impeller process technology is effectively applied across your spectrum of applications ensuring successful, repeatable results from lab scale to full scale operations. Chemineer’s 50+ years of mixing expertise includes low shear liquid-liquid/solids blending, gas dispersion, high shear blending and viscous mixing. Whether it is R&D or production phase, Chemineer has the experience, products and services to solve your mixing challenges. An

impeller brochure, B710, is available with additional information.

Product Literature

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Supplier of Fluid Mixing Equipment | Chemineer GT Agitators

Chemineer GT Turbine Agitators

Premium Performance The line of Chemineer GT Turbine Agitators provides enhanced cost-efficiency and performance embodied in an advanced parallel shaft design.

The GT is available with either NEMA or IEC C-flange motors from 1 - 30 HP and shaft speeds of 11 - 155 rpm. The motor is shipped to your facility and can be attached to the integral motor coupling during the installation process. Lifting lugs cast directly into the housing make for safe, easy handling of the entire unit. Thanks to a low profile design and compact internal components, the GT features a small mounting footprint making it ideal for applications where clearances may be tight.

Unlike the competition that uses flimsy plastic and fiberglass components, the Chemineer GT Turbine Agitator features a housing completely manufactured from cast iron. Couple that with an abrasion-resistant, catalyzed polyurethane finish and you have a turbine agitator well-suited for use in both indoor and outdoor operating environments.

Key Features of the GT Turbine Agitator

Wide variety of seal types Small footprint Standard lubricants Double and triple reduction gear drive designs Completely cast iron housing Broad application versatility Worldwide compatibility

Simply Accessible For replacement of the mechanical seal, simply rotate the gearbox 90 degrees around the pivot pin. The top of the seal pedestal opens for a clear, line-of-site view and ample room for easy removal of the coupling half and seal cartridge.

Power + Efficiency Chemineer GT agitators feature a highly efficient drive specifically engineered for turbine agitator service. When compared to competitive designs, the GT agitator's double reduction configuration allows for a wider variety of speeds at low overall operating costs. The GT also easily accommodates a triple reduction drive for size 3 and 4 gearboxes.

Geared for Life Case-carburized, precision-ground, helical gear sets are manufactured to AGMA Quality 10 standards for long service and proper contact. The GT agitator's helical gearing provides minimal wear for optimum mechanical energy transmission resulting in more power for your mixing needs. CNC machining ensures exact, repeatable fits and finishes for improved parts

interchangeability and gear alignment.

The GT agitator's tapered roller bearings feature an L10 bearing life of 50,000 hours for long life and trouble-free operation. Its main support bearing is mounted in the rigid support base of the gearbox for reliable performance in severe bending applications. The competition's mixer, however, uses a drywell-mounted output bearing which has a tendency to crack thus limiting its application to less stressful service.

Standard Lubricants for a Lifetime of Smooth Operation The GT agitator drive utilizes typical gear oil lubricants as opposed to competitive, single reduction units which require expensive synthetic lubricants due to extreme pressure loads at the high speed pinion. The standard drywell, low speed shaft seal prevents lubricant leakage, eliminating the risk of process fluid contamination. Additionally, positive gear and bearing lubrication is provided even under variable speed applications and reverse rotation.

Oversized Shafting All Chemineer shafting is sized and tested to resist torsional loads and bending moments resulting from hydraulic forces acting on the impeller during mixing. Chemineer will work with you to determine optimum

sizing for your application.

GT shafts are available in diameters of 1-1/2 to 3-1/2 inches and afford maximum resistance to shock loads. All shafts are straightened to 0.003 inches of total runout per foot of shaft length to minimize vibration and maximize seal life. A variety of materials of construction ensure process compatibility. Options include the following: 316 SS, carbon steel, high alloys, C276 - high nickel alloy, chrome and mollybium cobalt.

Product Literature

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Chemineer’s unique new range of industrial agitators are designed for use with plastic transportable (IBC) containers. We supply a range of models suitable for a variety of applications including - blending light viscous liquid as well as re-suspension of settled solids and dissolution of powders.

Applications

Chemical Industries Dye stuffs & Pigments Slurries Paint & Varnish Food & Beverage Water treatment chemicals and flocculants Cosmetics Industry

 

Container

Designed for use on 1000 / 800 litre IBC containers with 150mm screw caps by Schutz, Sotralentz and Van Leer, suitable for most container types.

 

Technical Specification

Mixer Support

Lightweight stainless steel bridge which mounts directly onto the IBC frame and is secured in place with quick action toggle clamps.

Lifting Options

As standard the mixer is supplied with an eye bolt for lifting the mixer using a hoist, bolt on modules are also available for lifting the mixer using a fork lift truck.

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Motors

Electric Air

400 Volts 3ph 50Hz protection IP55, fited with Start / Stop push buttons and overload relays.

Connection to the unit is with a 4 pin, 16 amp

Are fitted with a flow control valve and muffler.

plug / socket, a 10 metre steel wire armoured flex extension cable is available as an optional extra.

A safety interlock is integrated into the mixer support bridge and wired to the motor control.

 

 

Gear Drives

Factory filled with a synthetic food quality lubricant and sealed for life.

 

Shaft and Impellers Folding Impeller

The mixer shaft and impellers are manufactured in 316 stainless steel. High speed mixers are fitted with single or dual fixed impellers and low speed mixers with E-400 Folding Impellers.

 

 

Models

HBC - high speed direct drive LBC - low speed gear drive Motors 0.37 - 1.5 kw electric or air Special designs are also available for introducing powders or liquids into the IBC

 

 

Mixer Sizing and Selection

The following tables provide a general selection guide. Our application engineers will be pleased to advise on mixers / agitators suitable for your specific application.

Mild to Medium Agitation - 100 Litre IBC

Viscosity Cp Mixer Model Drive Type

1.0100

 

HBC-37 Direct

3505001000

 

HBC-37 Gear

25005000

 

LBC-75 Gear

15000 LBC-150 Gear

Vigorous Agitation - 1000 Litre IBC

Viscosity Cp Mixer Model Drive Type

1.0100250

 

HBC-37 Gear

5001000

 

LBC-75 Gear

25005000

LBC-150 Gear

 

Enquiries / Ordering

Please mention container type and size: volume and mixing duty together with viscosity and SG when requesting a quotation or placing an order to enable our application engineers to confirm or propose a suitable IBC mixer selection

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Impellers

Impellers

If there were only one mixing job to do, only one impeller would be required. However, there is a very wide range of problems in agitation, and the best impeller for one application may not be the best impeller for another. The descriptions and discussions below are intended as a guide for impeller selection. Relative impeller sizes are compared to the P4 at equal horsepower and equal speed. For a more thorough application evaluation, contact your nearest Chemineer sales office .

SC-3 Impeller

Size relative to P-4              1.2

Favorable Applications:

The Chemineer® SC-3 Impeller features an advanced design engineered for deep tanks. It produces flow characteristics of much larger impellers, without the added weight, or the resulting loss in pumping efficiency. The highly efficient SC-3 Impeller's reduced weight allows for the use of longer shaft extensions for deeper tanks, and resolves associated critical speed limitations. The use of an SC-3 impeller can produce an overall agitator cost savings as much as 33%.

HE-3 Impeller

Size relative to P-4              1.3

Favorable Applications:

An extremely efficient turbulent flow impeller for blending, heat transfer and solids suspension.

Most effective for Reynolds numbers over 50. Developed to minimize the creation of trailing vortices and incorporating the otherwise wasted energy into macro-flow.

P-4 or Pitched Blade Impeller

Size relative to P-4              1.0

Favorable Applications:

A reasonably cost effective impeller in both turbulent and laminar flow. Good impeller for applications where the viscosity changes over a wide range causing the flow regime to vary between turbulent and laminar flow. A reasonably cost effective impeller for solids suspension.

S-4 or Straight Blade Impeller

Size relative to P-4              0.84

Favorable Applications:

A cost effective impeller for operation very near the floor of a tank for agitating the heel in solids suspension applications. Also an effective impeller in laminar flow applications, especially when impeller Reynolds numbers drop below 50.

BT-6 Impeller

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capacities in excess of 10,000 W/litre. For processes with very high heat loads, there are better solutions than batch reactors.

Fast temperature control response and uniform jacket heating and cooling is particularly important for crystallization processes or operations where the product or process is very temperature sensitive. There are several types of batch reactor cooling jackets:

[edit] Single external jacket

Batch reactor with single external cooling jacket

The single jacket design consists of an outer jacket which surrounds the vessel. Heat transfer fluid flows around the jacket and is injected at high velocity via nozzles. The temperature in the jacket is regulated to control heating or cooling.

The single jacket is probably the oldest design of external cooling jacket. Despite being a tried and tested solution, it has some limitations. On large vessels, it can take many minutes to adjust the temperature of the fluid in the cooling jacket. This results in sluggish temperature control. The distribution of heat transfer fluid is also far from ideal and the heating or cooling tends to vary between the side walls and bottom dish. Another issue to consider is the inlet temperature of the heat transfer fluid which can oscillate (in response to the temperature control valve) over a wide temperature range to cause hot or cold spots at the jacket inlet points.

[edit] Half coil jacket

Batch reactor with half coil jacket

The half coil jacket is made by welding a half pipe around the outside of the vessel to create a semi circular flow channel. The heat transfer fluid passes through the channel in a plug flow fashion. A large reactor may use several coils to deliver the heat transfer fluid. Like the single jacket, the temperature in the jacket is regulated to control heating or cooling.

The plug flow characteristics of a half coil jacket permits faster displacement of the heat transfer fluid in the jacket (typically less than 60 seconds). This is desirable for good temperature control. It also provides good distribution of heat transfer fluid which avoids the problems of non uniform heating or cooling between the side walls and bottom dish. Like the single jacket design however the inlet heat transfer fluid is also vulnerable to large oscillations (in response to the temperature control valve) in temperature.

[edit] Constant flux cooling jacket

Batch reactor with constant flux (Coflux) jacket

The constant flux cooling jacket is a relatively recent development. It is not a single jacket but has a series of 20 or more small jacket elements. The temperature control valve operates by opening and closing these channels as required. By varying the heat transfer area in this way, the process temperature can be regulated without altering the jacket temperature.

The constant flux jacket has very fast temperature control response (typically less than 5 seconds) due to the short length of the flow channels and high velocity of the heat transfer fluid. Like the half coil jacket the heating/cooling flux is uniform. Because the jacket operates at substantially constant temperature however the inlet temperature oscillations seen in other jackets are absent. An unusual feature of this type jacket is that process heat can be measured very sensitively. This allows the user to monitor the rate of reaction for detecting end points, controlling addition rates, controlling crystallization etc.

Alfa Laval Toftejorg dynamic tank cleaning machines

Alfa Laval Toftejorg dynamic tank cleaning machines are known for cleaning faster and deeper than static spray balls. Designed for the needs of the food, dairy, brewery, personal care and biopharm industries, the latest tank cleaning machine is even authorized to carry the 3-A symbol. Did you know that a dynamic tank cleaning machine can cut energy consumption by half, and water and chemical usage by as much as 90%?

 

  Toftejorg rotary spray head This dynamic spray head is suitable for applications where the products are relatively easy to clean. It offers a combination of physical impact and cascading flow of cleaning fluid that covers all internal surfaces.

 

  Toftejorg rotary jet head   The high-impact jet stream from a rotary jet head is widely used in tough and difficult to clean applications. With its pre-programmed cleaning pattern, designed for each application, this dynamic device ensures a reliable result even under challenging conditions.

Wind turbine designs are utilized to create wind turbines that exploit wind energy.[1] A wind turbine installation consists of the necessary systems needed to capture the wind's energy, point the turbine into the wind, convert mechanical rotation into electrical power, and other systems to start, stop, and control the turbine.

This article covers the design of horizontal axis wind turbines (HAWT) since the majority of commercial turbines use this design. Contrary to popular belief, considerable attention should be

given to the structural and foundation design of HAWTs. This is mainly due to the disproportionate amount that is spent on the foundations as a percentage of the total project cost.

Contents

[hide]

1 Design specification o 1.1 Low temperature

2 Aerodynamics 3 Power control

o 3.1 Stall o 3.2 Pitch control

4 Other controls o 4.1 Yawing o 4.2 Electrical braking o 4.3 Mechanical braking

5 Turbine size 6 Generator 7 Blades

o 7.1 Blade design o 7.2 Blade count o 7.3 Blade materials

8 Tower o 8.1 Tower height

9 Foundations 10 See also 11 References 12 External links

[edit] Design specification

The design specification for a wind-turbine will contain a power curve and guaranteed availability. With the data from the wind resource assessment it is possible to calculate commercial viability.[1] The typical operating temperature range is -20 to 40 °C (-4 to 104 °F). In areas with extreme climate (like Inner Mongolia or Rajasthan) specific cold and hot weather versions are required.

[edit] Low temperature

Utility-scale wind turbine generators have minimum temperature operating limits which apply in areas that experience temperatures below –20 °C. Wind turbines must be protected from ice accumulation, which can make anemometer readings inaccurate and which can cause high structure loads and damage. Some turbine manufacturers offer low-temperature packages at a

few percent extra cost, which include internal heaters, different lubricants, and different alloys for structural elements. If the low-temperature interval is combined with a low-wind condition, the wind turbine will require an external supply of power, equivalent to a few percent of its rated power, for internal heating. For example, the St. Leon, Manitoba project has a total rating of 99 MW and is estimated to need up to 3 MW (around 3% of capacity) of station service power a few days a year for temperatures down to –30 °C. This factor affects the economics of wind turbine operation in cold climates.

[edit] Aerodynamics

Main article: Wind turbine aerodynamics

The aerodynamics of a horizontal-axis wind turbine are not straightforward. The air flow at the blades is not the same as the airflow far away from the turbine. The very nature of the way in which energy is extracted from the air also causes air to be deflected by the turbine. In addition the aerodynamics of a wind turbine at the rotor surface exhibit phenomena that are rarely seen in other aerodynamic fields.

In 1919 the physicist Albert Betz showed that for a hypothetical ideal wind-energy extraction machine, the fundamental laws of conservation of mass and energy allowed no more than 16/27 (59.3%) of the kinetic energy of the wind to be captured. This Betz' law limit can be approached by modern turbine designs which may reach 70 to 80% of this theoretical limit.

[edit] Power control

A wind turbine is designed to produce a maximum of power at wide spectrum of wind speeds. The wind turbines have three modes of operation:

Below rated wind speed operation Around rated wind speed operation Above rated wind speed operation

If the rated wind speed is exceeded the power has to be limited. There are various ways to achieve this.

[edit] Stall

Plastic vortex generator stripes used to control stall characteristics of the blade - in this example protecting the blade from rapid fluctuations in wind speed.

Closeup look at the vortex generators (VGs) - the larger ones are closest to the root of the blade where the boundary layer is thicker(i.e., closest to the hub)

Stalling works by increasing the angle at which the relative wind strikes the blades (angle of attack), and it reduces the induced drag (drag associated with lift). Stalling is simple because it can be made to happen passively (it increases automatically when the winds speed up), but it increases the cross-section of the blade face-on to the wind, and thus the ordinary drag. A fully stalled turbine blade, when stopped, has the flat side of the blade facing directly into the wind.

A fixed-speed HAWT inherently increases its angle of attack at higher wind speed as the blades speed up. A natural strategy, then, is to allow the blade to stall when the wind speed increases. This technique was successfully used on many early HAWTs. However, on some of these blade sets, it was observed that the degree of blade pitch tended to increase audible noise levels.

Vortex generators may be used to control the lift characteristics of the blade. The VGs are placed on the airfoil to enhance the lift if they are placed on the lower (flatter) surface or limit the maximum lift if placed on the upper (higher camber) surface.[2]

[edit] Pitch control

Furling works by decreasing the angle of attack, which reduces the induced drag from the lift of the rotor, as well as the cross-section. One major problem in designing wind turbines is getting the blades to stall or furl quickly enough should a gust of wind cause sudden acceleration. A fully furled turbine blade, when stopped, has the edge of the blade facing into the wind.

Standard modern turbines all pitch the blades in high winds. Since pitching requires acting against the torque on the blade, it requires some form of pitch angle control. Many turbines use hydraulic systems. These systems are usually spring loaded, so that if hydraulic power fails, the blades automatically furl. Other turbines use an electric servomotor for every rotor blade. They have a small battery-reserve in case of an electric-grid breakdown. Small wind turbines (under

50 kW) with variable-pitching generally use systems operated by centrifugal force, either by flyweights or geometric design, and employ no electric or hydraulic controls.

[edit] Other controls

[edit] Yawing

Modern large wind turbines are typically actively controlled to face the wind direction measured by a wind vane situated on the back of the nacelle. By minimizing the yaw angle (the misalignment between wind and turbine pointing direction), the power output is maximized and non-symmetrical loads minimized. However, since the wind direction varies quickly the turbine will not strictly follow the direction and will have a small yaw angle on average. The power output losses can simply be approximated to fall with cos3(yaw angle).

[edit] Electrical braking

Dynamic braking resistor for wind turbine.

Braking of a small wind turbine can also be done by dumping energy from the generator into a resistor bank, converting the kinetic energy of the turbine rotation into heat. This method is useful if the kinetic load on the generator is suddenly reduced or is too small to keep the turbine speed within its allowed limit.

Cyclically braking causes the blades to slow down, which increases the stalling effect, reducing the efficiency of the blades. This way, the turbine's rotation can be kept at a safe speed in faster winds while maintaining (nominal) power output. This method is usually not applied on large grid-connected wind turbines.

[edit] Mechanical braking

A mechanical drum brake or disk brake is used to hold the turbine at rest for maintenance. Such brakes are usually applied only after blade furling and electromagnetic braking have reduced the turbine speed, as the mechanical brakes would wear quickly if used to stop the turbine from full speed. There can also be a stick brake.

[edit] Turbine size

A person standing beside medium size modern turbine blades.

For a given survivable wind speed, the mass of a turbine is approximately proportional to the cube of its blade-length. Wind power intercepted by the turbine is proportional to the square of its blade-length. The maximum blade-length of a turbine is limited by both the strength and stiffness of its material.

Labor and maintenance costs increase only gradually with increasing turbine size, so to minimize costs, wind farm turbines are basically limited by the strength of materials, and siting requirements.

Typical modern wind turbines have diameters of 40 to 90 metres (130 to 300 ft) and are rated between 500 kW and 2 MW. As of 2010 the most powerful turbine is rated at 7 MW.

[edit] Generator

10 Israeli wind turbines in the Golan Heights 600 kW each

For large, commercial size horizontal-axis wind turbines, the generator is mounted in a nacelle at the top of a tower, behind the hub of the turbine rotor. Typically wind turbines generate electricity through asynchronous machines that are directly connected with the electricity grid. Usually the rotational speed of the wind turbine is slower than the equivalent rotation speed of the electrical network - typical rotation speeds for a wind generators are 5-20 rpm while a directly connected machine will have an electrical speed between 750-3600 rpm. Therefore, a gearbox is inserted between the rotor hub and the generator. This also reduces the generator cost and weight.

Commercial size generators have a rotor carrying a field winding so that a rotating magnetic field is produced inside a set of windings called the stator. While the rotating field winding consumes a fraction of a percent of the generator output, adjustment of the field current allows good control over the generator output voltage. Enercon has produced gearless wind turbines with permanent magnet generators for many years, and Siemens produces a gearless "inverted generator" 3MW model[3][4] while developing a 6MW model.[5] This gives better reliability and performance than gear based systems.[citation needed] Gearless turbines

Parts of DIY Wind turbine

Older style wind generators rotate at a constant speed, to match power line frequency, which allowed the use of less costly induction generators. Newer wind turbines often turn at whatever speed generates electricity most efficiently. This can be solved using multiple technologies such as doubly fed induction generators or full-effect converters where the variable frequency current produced is converted to DC and then back to AC, matching the line frequency and voltage. Although such alternatives require costly equipment and cause power loss, the turbine can capture a significantly larger fraction of the wind energy. In some cases, especially when

turbines are sited offshore, the DC energy will be transmitted from the turbine to a central (onshore) inverter for connection to the grid.

[edit] Blades

[edit] Blade design

Blades can be made from simple objects as barrels

The ratio between the speed of the wind and the speed of the blade tips is called tip speed ratio. High efficiency 3-blade-turbines have tip speed/wind speed ratios of 6 to 7.

Modern wind turbines are designed to spin at varying speeds (a consequence of their generator design, see above). Use of aluminum and composite materials in their blades has contributed to low rotational inertia, which means that newer wind turbines can accelerate quickly if the winds pick up, keeping the tip speed ratio more nearly constant. Operating closer to their optimal tip speed ratio during energetic gusts of wind allows wind turbines to improve energy capture from sudden gusts that are typical in urban settings.

In contrast, older style wind turbines were designed with heavier steel blades, which have higher inertia, and rotated at speeds governed by the AC frequency of the power lines. The high inertia buffered the changes in rotation speed and thus made power output more stable.

The speed and torque at which a wind turbine rotates must be controlled for several reasons:

To optimize the aerodynamic efficiency of the rotor in light winds. To keep the generator within its speed and torque limits. To keep the rotor and hub within their centripetal force limits. The centripetal force from the

spinning rotors increases as the square of the rotation speed, which makes this structure sensitive to overspeed.

To keep the rotor and tower within their strength limits. Because the power of the wind increases as the cube of the wind speed, turbines have to be built to survive much higher wind loads (such as gusts of wind) than those from which they can practically generate power. Since

the blades generate more downwind force (and thus put far greater stress on the tower) when they are producing torque, most wind turbines have ways of reducing torque in high winds.

To enable maintenance; because it is dangerous to have people working on a wind turbine while it is active, it is sometimes necessary to bring a turbine to a full stop.

To reduce noise; As a rule of thumb, the noise from a wind turbine increases with the fifth power of the relative wind speed (as seen from the moving tip of the blades). In noise-sensitive environments, the tip speed can be limited to approximately 60 m/s (200 ft/s).

[edit] Blade count

The NASA Mod-0 research wind turbine at Glenn Research Center's Plum Brook station in Ohio tested a one-bladed rotor configuration

The determination of the number of blades involves design considerations of aerodynamic efficiency, component costs, system reliability, and aesthetics. Noise emissions are affected by the location of the blades upwind or downwind of the tower and the speed of the rotor. Given that the noise emissions from the blades' trailing edges and tips vary by the 5th power of blade speed, a small increase in tip speed can make a large difference.

Wind turbines developed over the last 50 years have almost universally used either two or three blades. Aerodynamic efficiency increases with number of blades but with diminishing return. Increasing the number of blades from one to two yields a six percent increase in aerodynamic efficiency, whereas increasing the blade count from two to three yields only an additional three percent in efficiency. Further increasing the blade count yields minimal improvements in aerodynamic efficiency and sacrifices too much in blade stiffness as the blades become thinner.

Component costs that are affected by blade count are primarily for materials and manufacturing of the turbine rotor and drive train. Generally, the fewer the number of blades, the lower the material and manufacturing costs will be. In addition, the fewer the number of blades, the higher the rotational speed can be. This is because blade stiffness requirements to avoid interference

with the tower limit how thin the blades can be manufactured, but only for upwind machines; deflection of blades in a downwind machine results in increased tower clearance. Fewer blades with higher rotational speeds reduce peak torques in the drive train, resulting in lower gearbox and generator costs.

The 98 meter diameter, two-bladed NASA/DOE Mod-5B wind turbine was the largest operating wind turbine in the world in the early 1990s

System reliability is affected by blade count primarily through the dynamic loading of the rotor into the drive train and tower systems. While aligning the wind turbine to changes in wind direction (yawing), each blade experiences a cyclic load at its root end depending on blade position. This is true of one, two, three blades or more. However, these cyclic loads when combined together at the drive train shaft are symmetrically balanced for three blades, yielding smoother operation during turbine yaw. Turbines with one or two blades can use a pivoting teetered hub to also nearly eliminate the cyclic loads into the drive shaft and system during yawing.

Finally, aesthetics can be considered a factor in that some people find that the three-bladed rotor is more pleasing to look at than a one- or two-bladed rotor.

[edit] Blade materials

New generation wind turbine designs are pushing power generation from the single megawatt range to upwards of 10 megawatts. The common trend of these larger capacity designs are larger and larger wind turbine blades. Covering a larger area effectively increases the tip-speed ratio of a turbine at a given wind speed, thus increasing the energy extraction capability of a turbine system.[6]

Current production wind turbine blades are manufactured as large as 100 meters in diameter with prototypes in the range of 110 to 120 meters. In 2001, an estimated 50 million kilograms of fiberglass laminate were used in wind turbine blades.[7] New materials and manufacturing

methods provide the opportunity to improve wind turbine efficiency by allowing for larger, stronger blades.

One of the most important goals when designing larger blade systems is to keep blade weight under control. Since blade mass scales as the cube of the turbine radius, loading due to gravity becomes a constraining design factor for systems with larger blades.[8]

Current manufacturing methods for blades in the 40 to 50 meter range involve various proven fiberglass composite fabrication techniques. Manufactures such as Nordex and GE Wind use an infusion process for blade manufacture. Other manufacturers use variations on this technique, some including carbon and wood with fiberglass in an epoxy matrix. Options also include prepreg fiberglass and vacuum-assisted resin transfer molding. Essentially each of these options are variations on the same theme: a glass-fiber reinforced polymer composite constructed through various means with differing complexity. Perhaps the largest issue with more simplistic, open-mold, wet systems are the emissions associated with the volatile organics released into the atmosphere. Preimpregnated materials and resin infusion techniques avoid the release of volatiles by containing all reaction gases. However, these contained processes have their own challenges, namely the production of thick laminates necessary for structural components becomes more difficult. As the preform resin permeability dictates the maximum laminate thickness, bleeding is required to eliminate voids and insure proper resin distribution.[7] A unique solution to resin distribution is the use of a partially preimpregnated fiberglass. During evacuation, the dry fabric provides a path for airflow and, once heat and pressure are applied, resin may flow into the dry region resulting in a thoroughly impregnated laminate structure.[7]

Epoxy-based composites are of greatest interest to wind turbine manufacturers because they deliver a key combination of environmental, production, and cost advantages over other resin systems. Epoxies also improve wind turbine blade composite manufacture by allowing for shorter cure cycles, increased durability, and improved surface finish. Prepreg operations further improve cost-effective operations by reducing processing cycles, and therefore manufacturing time, over wet lay-up systems. As turbine blades are approaching 60 meters and greater, infusion techniques are becoming more prevalent as the traditional resin transfer moulding injection time is too long as compared to the resin set-up time, thus limiting laminate thickness. Injection forces resin through a thicker ply stack, thus depositing the resin where in the laminate structure before gelatin occurs. Specialized epoxy resins have been developed to customize lifetimes and viscosity to tune resin performance in injection applications.[9]

Carbon fiber-reinforced load-bearing spars have recently been identified as a cost-effective means for reducing weight and increasing stiffness. The use of carbon fibers in 60 meter turbine blades is estimated to result in a 38% reduction in total blade mass and a 14% decrease in cost as compared to a 100% fiberglass design. The use of carbon fibers has the added benefit of reducing the thickness of fiberglass laminate sections, further addressing the problems associated with resin wetting of thick lay-up sections. Wind turbine applications of carbon fiber may also benefit from the general trend of increasing use and decreasing cost of carbon fiber materials.[7]

Smaller blades can be made from light metals such as aluminum. Wood and canvas sails were originally used on early windmills due to their low price, availability, and ease of manufacture.

These materials, however, require frequent maintenance during their lifetime. Also, wood and canvas have a relatively high drag (low aerodynamic efficiency) as compared to the force they capture. For these reasons they have been mostly replaced by solid airfoils.

[edit] Tower

Typically, 2 types of towers exist: floating towers and land-based towers.

[edit] Tower height

Wind velocities increase at higher altitudes due to surface aerodynamic drag (by land or water surfaces) and the viscosity of the air. The variation in velocity with altitude, called wind shear, is most dramatic near the surface.

Wind turbines generating electricity at the San Gorgonio Pass Wind Farm.

Typically, in daytime the variation follows the wind profile power law, which predicts that wind speed rises proportionally to the seventh root of altitude. Doubling the altitude of a turbine, then, increases the expected wind speeds by 10% and the expected power by 34%. To avoid buckling, doubling the tower height generally requires doubling the diameter of the tower as well, increasing the amount of material by a factor of at least four.

At night time, or when the atmosphere becomes stable, wind speed close to the ground usually subsides whereas at turbine hub altitude it does not decrease that much or may even increase. As a result the wind speed is higher and a turbine will produce more power than expected from the 1/7th power law: doubling the altitude may increase wind speed by 20% to 60%. A stable atmosphere is caused by radiative cooling of the surface and is common in a temperate climate: it usually occurs when there is a (partly) clear sky at night. When the (high altitude) wind is strong (a 10-meter (33 ft) wind speed higher than approximately 6 to 7 m/s (20–23 ft/s)) the stable atmosphere is disrupted because of friction turbulence and the atmosphere will turn neutral. A daytime atmosphere is either neutral (no net radiation; usually with strong winds and/or heavy clouding) or unstable (rising air because of ground heating — by the sun). Here again the 1/7th power law applies or is at least a good approximation of the wind profile. Indiana had been rated as having a wind capacity of 30,000 MW, but by raising the expected turbine height from 50 m

to 70 m, the wind capacity estimate was raised to 40,000 MW, and could be double that at 100 m.[10]

For HAWTs, tower heights approximately two to three times the blade length have been found to balance material costs of the tower against better utilisation of the more expensive active components.

[edit] Foundations

Wind turbines, by their nature, are very tall slender structures[11], this can cause a number of issues when the structural design of the foundations are considered.

The foundations for a conventional engineering structure are designed mainly to transfer the vertical load (dead weight) to the ground, this generally allows for a comparatively unsophisticated arrangement to be used. However in the case of wind turbines, due to the high wind and environmental loads experienced there is a significant horizontal load that needs to be accounted for.

This loading regime causes large moment loads to be applied to the foundations of a wind turbine. As a result, considerable attention needs to be given when designing the footings to ensure that the turbines are sufficiently restrained to operate efficiently[12]. In the current Det Norske Veritas (DNV) guidelines for the design of wind turbines the angular deflection of the foundations are limited to 0.5°.[13]

DIFFERENT TYPES OF MIXERS

In industrial process engineering, mixing is a unit operation that involves manipulating a heterogeneous physical system, with the intent to make it more homogeneous. Familiar examples include pumping of the water in a swimming pool to homogenize the water temperature, and the stirring of pancake batter to eliminate lumps.

Contents

[hide]

1 Solids mixing 2 Mixing mechanisms 3 Mixing Calculations 4 Laboratory mixing 5 Industrial mixing 6 See also

[edit] Solids mixing

Blending powders is one of the oldest unit-operations in the solids handling industries. For many decades powder blending has been used just to homogenise bulk materials. Many different machines have been designed in order to be able to handle materials with various bulk solids properties. On the basis of the practical experience gained with these different machines, engineering knowledge has been developed to construct reliable equipment and to predict scale-up and mixing behaviour. Nowadays the same mixing technologies are used for many more applications: to improve product quality, to coat particles, to fuse materials, to wet, to dispers in liquid, to agglomerate, to alter functional material properties, etc. This wide range of applications of mixing equipment requires a high level of knowledge, long time experience and extended test facilities in order to come to the optimal selection of equipment and processes.

[edit] Mixing mechanisms

In powder mixing two different dimensions in the mixing process can be determined: convective mixing and intensive mixing. In the case of convective mixing material in the mixer is transported from one location to another. This type of mixing process will lead to a less ordered state inside the mixer, the components which have to be mixed will be distributed over the other components. With progressing time the mixture will become more and more randomly ordered. After a certain mixing time the ultimate random state is reached. Usually this type of mixing is applied for free-flowing and coarse materials. Possible threat during macro mixing is the de-mixing of the components, since differences in size, shape or density of the different particles can lead to segregation. In the convective mixing range, Hosokawa has several processes available from silo mixers to horizontal mixers and conical mixers. The most well-known type is the Vrieco-Nauta® mixer, due to it’s ability to mix materials without segregation.

When materials are cohesive, which is the case with e.g. fine particles and also with wet material, convective mixing is no longer sufficient to obtain a randomly ordered mixture. The relative strong inter-particle forces will form lumps, which are not broken up by the mild transportation forces in the convective mixer. In order to decrease the lump size additional forces are necessary; i.e. more energy intensive mixing is required. These additional forces can either be impact forces or shear forces.

[edit] Mixing Calculations

The level of mixing is determined by the pumping effect or dynamic response that the mixer imparts into the fluid. When a mixing impeller rotates in the fluid, it generates a combination of flow and shear. The impeller generated flow can be calculated by using the following equation:

Flow = (Flow_Number * RPM * Impeller_Diameter^3) / 231

Output is in Gallons / Minute

Flow numbers for impellers have been published by the North American Mixing Forum, Post Mixing, and Fusion Fluid Equipment.

An online mixing calculator is available http://www.fusionfluid.com/html/Knowledge-MixingCalculator.html

[edit] Laboratory mixing

A magnetic stirrer

At a laboratory scale, mixing is achieved by magnetic stirrers or by simple hand-shaking.

[edit] Industrial mixing

Schematics of an agitated vessel

At an industrial scale, efficient mixing can be difficult to achieve. A great deal of engineering effort goes into designing and improving mixing processes. Mixing at industrial scale is done in batches (dynamic mixing) or with help of static mixers.

Typical example of a mixing process in the industry is concrete mixing, where cement, sand, small stones or gravel and water are commingled to a homogeneous self-hardening mass, used in the construction industry. Another classical mixing process is mulling foundry molding sand, where sand, bentonite clay, fine coal dust and water are mixed to a plastic, moldable and reusable mass, applied for molding and pouring molten metal to obtain sand castings that are metallic parts for automobile, machine building, construction or other industries.

The opposite of mixing is segregation. A classical example of segregation is the brazil nut effect.

[edit] See also

Wikimedia Commons has media related to: Mixing

Industrial mixer High Shear mixer Planetary mixer

Green sand Gravel Molding sand Concrete Cement Foundry Casting Foundry sand testing DISAMATIC Impeller

Industrial Mixers and Blenders are used to mix or blend a wide range of materials used in different industries including the food, chemical, pharmaceutical, plastic and mineral industries. They are mainly used to mix different materials using different types of blades to make a good quality homogeneous mixture. Included are dry blending devices, paste mixing designs for high viscosity products and high shear models for emulsification, particle size reduction and homogenization.

Industrial mixers range from laboratory to production line scale, including Ribbon Blender, V Blender, Cone Screw Blender, Screw blender, Double Cone Blender, Double Planetary High Viscosity Mixer, Counter-rotating, Double & Triple Shaft, Vacuum Mixer, Planetary Disperser, High Shear Rotor Stator and Dispersion Mixers, Paddle, Jet Mixer and Mobile Mixers. The Banbury mixer is effective at mixing or kneading viscous materials.

They can operate at different temperatures and pressures for mixing different solutions and can also have internal or external heating systems added to them. Options also exist where spray nozzles, CIP, PLC and pneumatic or electric systems can be used. Systems can come equipped with hydraulic or electronic soft start mechanisms so that they start and stop smoothly.

Basic Nomenclature

For liquid mixing, the nomenclature is rather standardized:

Impeller Diameter, "D" is measured for industrial mixers as the maximum diameter swept around the axis of rotation.

Rotational Speed, "N" is usually measured in revolutions per minute(RPM) or revolutions per second(RPS). This variable refers to the rotational speed of the impeller as this number can differ along several points of the drive train.

Tank Diameter, "T" The inside diameter of a cylindrical vessel. Most mixing vessels receiving industrial mixers will be cylindrical.

Power, "P" Is the energy input into a system usually by an electric motor or a pneumatic motor

Impeller Pumping Capacity, "Q" The resulting fluid motion from impeller rotation.

[edit] Mixing Calculations

The level of mixing is determined by the pumping effect or dynamic response that the mixer imparts into the fluid. When a mixing impeller rotates in the fluid, it generates a combination of flow and shear. The impeller generated flow can be calculated by using the following equation:

Flow (GPM) = (Flow_Number * RPM * Impeller_Diameter^3) / 231

To calculate power draw, use the following equation:

Power (HP) = (Power_Number * RPM^3 * Impeller_Diameter^5 * Fluid_Specific_Gravity) / (1.525 * 10^13)

Flow Numbers and Power Numbers for impellers have been published by the North American Mixing Forum, Post Mixing, and Fusion Fluid Equipment. An online mixing calculator is available http://www.fusionfluid.com/html/Knowledge-MixingCalculator.html

A planetary mixer is a device used to mix products including adhesives, pharmaceuticals, foods, chemicals, electronics, plastics and pigments.

This mixer is ideal for mixing and kneading viscous pastes (up to 6 million centipoise) under atmospheric or vacuum conditions. Capacities range from 1/2-pint through 750 gallons. Many

options including jacketing for heating or cooling, vacuum or pressure, vari speed drives, etc. are available.

The blades each rotate on their own axes, and at the same time on a common axis, thereby providng complete mixing in a very short timeframe.

A static mixer is a device for mixing two fluid materials. Most commonly, the fluids are liquid; however, static mixers are used to mix gas streams, disperse gas into liquid or disperse immiscible liquids. The device consists of mixer elements contained in a cylindrical (tube) or squared housing. These can vary from 6 mm to 6 meters diameter. Static mixer elements consist of a series of baffles that are made from metal or a variety of plastics. Similarly, the mixer housing can be made from metal or plastic. Typical materials of construction for the static mixer components included stainless steel, polypropylene, Teflon, Kynar and polyacetal.

The overall system design incorporates a method for delivering two streams of liquids into the static mixer. As the streams move through the mixer, the non-moving elements continuously blend the materials. Complete mixing is dependent on many variables including the fluid properties, tube inner diameter, the number of elements, and their design.

Principles of Operation

Depiction of how Flow Division and Radial Mixing occur in a static mixer

A static mixer is a series of fixed, typically helical, elements enclosed within a tubular housing. The fixed geometric design of the unit can simultaneously produce patterns of flow division and radial mixing.

Flow Division in a static mixer is a function of the number of elements in the mixer

Flow Division: In laminar flow, a processed material divides at the leading edge of each element of the mixer and follows the channels created by the element shape. At each succeeding element, the two channels are further divided, resulting in an exponential increase in stratification. The number of striations produced is 2n where 'n' is the number of elements in the mixer.

Radial Mixing: In either turbulent or laminar flow, rotational circulation of a processed material around its own hydraulic center in each channel of the mixer causes radial mixing of the material. Processed material is intermixed to reduce or eliminate radial gradients in temperature, velocity and material compositi

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Gravel is rock that is of a specific particle size range. Specifically, it is any loose rock that is larger than 2 mm (0.079 in) in its smallest dimension (about 1/12 of an inch) and no more than 64 mm (2.5 in). The next smaller size class in geology is sand, which is >0.0625 to 2 mm (0.0025 to 0.0787 in) in size. The next larger size is cobble, which is >64 to 256 mm (2.5 to 10.1 in). Gravel can be sub-categorized into granule (>2 to 4 mm/0.079 to 0.16 in) and pebble (>4 to 64 mm/0.16 to 2.5 in). One cubic yard of gravel typically weighs about 3000 pounds (or a cubic meter is about 1,800 kilograms).

Gravel is an important commercial product, with a number of applications. Many roadways are surfaced with gravel, especially in rural areas where there is little traffic. Globally, far more roads are surfaced with gravel than with concrete or tarmac; Russia alone has over 400,000 km (250,000 mi) of gravel-surfaced roads. Both sand and small gravel are also important for the manufacture of concrete.

Contents

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MULLER MIXERS

Method of sampling solid materials and sampling system to execute the method

United States Patent 5056962

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A method and the related system for sampling solid materials. Materials as continuously manufactured from a compression molding machine are sampled at fixed intervals and the materials thus sampled are fed into a transport pipe so as to be transferred by being accompanied by a transport plug into an inspecting station at low speed from its stand-by position in the pipe when a gas control means is set in a feed mode. After transferring sampled materials the transport plug left at its terminal position in the transport pipe is automatically returned to the stand-by position through the transport pipe when the gas control means is set in a suction mode. By executing the above steps repeatedly, sampled materials are successively transferred into the inspecting station by being accompanied by the transport plug under unmanned operation.

Apparatus for conveying material

United States Patent 4941777

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Rambus: 1990 - 2010Video: A Company of Inventors Award-winning technologywww.rambus.com

Apparatus for conveying material between two terminals using a reversible blower system that conveys a carrier member through a tube by suction from one terminal to an intermediate location and by pneumatic pressure from the intermediate location to the other terminal, and vice versa. The carrier member is gradually retarded and stopped at each terminal by a yieldable plate inclined into the path of the carrier member with a yieldable latching element urging the plate inwardly and also serving to latch the carrier member in its ultimate terminal position. The tube has separately manipulatable, open-ended, end portions in which the carrier member is retained for manipulation into position for receiving or discharging its contents. Covers on the carrier member are automatically removed and replaced at each terminal by radially movable latching elements on the cover that are manipulated by an axially movable central unlatching element. The carrier member has annular projections for sealing engagement of the tube. Each projection has an outwardly facing groove in which a compressible sealing strip is retained with a foamed elastomeric base strip behind the sealing strip to deflect the sealing strip outwardly into sealing disposition

KBr PRESS MODEL MP-15

The press is capable of producing pressure upto 15 tons. It is compact in construction & occupies very little bench space. Acrylic screens are provided for the safety of the operator. The base plate has a provision for bench mounting. A pressure gauge for indication of pressure release valve is provided. A telescopic handle is used for extra leverage.

KBr Press Model MP-15,fixing bolts for table mounting. Rubber antislide sheet, Oil Bottles-2 Nos., Safety sheets-2 Nos.

There are 3 methods by which a solid material is brought to the form acceptable to the instrument

KBr PRESS (AUTOMATIC) MODEL AP-15

This is electrically operated version of the manual press. The pumping is done by gearmotor drive. Simply press a button & it will start building pressure & will stop autom-atically at set pressure by means of a pressure switch.

KBr Press Model AP-15,Oil Bottles-2 Nos., Safety Sheets-2 Nos., Allen Key for pressure Adjustment.

Evacuated 13 mm KBr die, including two optically polished pellets & extractor ring for sample disc removal.

Most commonly used die is of 13 mm pellet size. It should have highly polished surfaces & should withstand atleast 10 tons pressure. Dies for other pellet sizes are available for specific applications

Dry Box

The dry box is specifically designed for the storage of accessories & windows which are affected by moisture. Transparent lid gives a clear view of the contents.

Usable Volume: 450 X 250 X 150 mm.Temperature   : 10° to 15° C above ambient,Power         : 230 V, 50 Hz, 100 W

Vibration Mill suitable for mixing of sample & KBr, using S S Ball. The mixing & blending of KBr with sample can be easily done using the Vibration Mill. The sample is contained in stainless Steel capsule and reduced to fine mixture of sample and KBr by the pulverising action of grinding balls. It is fitted with a 30 min adjustable timer for Auto Stop.

Dimensions : 215 mm x 285 mm x 180mmPower : 230 v 50 HzTimer : Digital upto 30 minutes adjustable in steps of minute.

Request Quote

This vibration mill is particularly suitable for DST user where in the sample quantity is too small and sample homogeneity therefore is very crucial.  For this application KBr is taken in good quantity ( say 1 gm) and sample also proportionally on the higher side ( say 10 to 20 mg) .  This mixture when used in the Vibration mill gets homogeneously mixed.  A small portion of this is taken for analysis with DST

Storage of Powders and Bulk Solids in Silos

Dietmar Schulze

Problems with the storage of bulk solids in bins and silos can be avoided if they are designed with respect to the flow properties of the bulk solid which has to be stored. The following essay considers the basic rules for the design of silos.

1 Stresses in silos

Figure 1 shows silos and the pressures and stresses, respectively, acting in the silos. While the pressure (for fluids we will use the word „pressure") would increase linearly downwards if the silo would have been filled with a fluid (a), the course of the vertical stress (for bulk solids we will use the word „stress") in a silo filled with a bulk solid is rather different (b,c): In the latter case in the vertical (cylindrical) section of the silo the vertical stress increases in a degressive way. If the height to diameter ratio of the silo is sufficiently large (usually: > 3), a constant vertical stress is attained. This means that the vertical stress will not increase further even if the

filling height is much larger. The reason for this course are the shear stresses acting between the bulk solid and the silo walls even if the bulk solid is at rest. Due to the shear stresses, the silo walls carry a part of the weight of the bulk solid. A method for the calculation of the stress course in the vertical section was derived by Janssen already in 1895 [1]. This method is the basis for most present standards for the calculation of the load on silo walls for structural silo design [2-4].

Figure 1: a. pressure in a silo filled with a fluid (imaginary); b. vertical stress after filling the silo with a bulk solid; c. vertical stress after the discharge of some bulk solid

The stresses acting in a hopper are different from those in the vertical section. Just after filling an empty silo, the so called filling stress state (also: active stress state, figure 1b) prevails, where the vertical stress in the hopper decreases less in the upper part of the hopper and then more near the imaginary hopper apex. As soon as some bulk solid is discharged for the first time after filling, the stresses in the hopper change and the so-called emptying stress state (also : passive stress state) prevails, figure 1c. When flowing downwards in the hopper, the bulk solid is compressed in the horizontal direction so that the walls of the hopper carry a larger part of the weight of the bulk solid and, hence, the vertical stress in the lower part of the hopper is clearly smaller than after filling. In the emptying stress state the vertical stresses in the lower part of the hopper are nearly proportional to the distance to the imaginary hopper tip or, in other words, the stresses are proportional to the local hopper diameter. This linear course of stress is called the radial stress field [7]. In principle, in the vertical section of the silo the stresses remain unchanged at discharge.

2 Flow Profiles: Mass Flow and Funnel Flow

Two different modes of flow can be observed if a bulk solid is discharged from a silo: mass flow and funnel flow (figure 2a). In case of mass flow, the whole contents of the silo are in motion at discharge. Mass flow is only possible, if the hopper walls are sufficiently steep and/or smooth, and the bulk solid is discharged across the whole outlet opening. If a hopper wall is too flat or too rough, funnel flow will appear. In case of funnel flow (figure 2b), only that bulk solid is in motion first, which is placed in the area more or less above the outlet. The bulk solid adjacent to the hopper walls remains at rest and is called „dead" or „stagnant" zone. This bulk solid can be discharged only when the silo is emptied completely. The dead zones can reach the surface of the bulk solid filling so that funnel flow becomes obviously when observing the surface. It is possible as well that the dead zones are located only in the lower part of the silo so that funnel flow cannot be recognised by observing the surface of the silo filling.

Figure 2a: Mass flow

Figure 2b: Funnel flow

3 Flow Problems

Typical problems which occur at the storage of bulk solids are:

o Arching: If a stable arch is formed above the outlet so that the flow of the bulk solid is stopped, then this situation is called arching (figure 3a). In case of fine grained, cohesive bulk solid, the reason of arching is the strength (unconfined yield strength) of the bulk solid which is caused by the adhesion forces acting between the particles. In case of coarse grained bulk solid, arching is caused by blocking of single particles. Arching can be prevented by sufficiently large outlets.

Figure 3a: Arching

o Ratholing occurs in case of funnel flow if only the bulk solid above the outlet is flowing out, and the remaining bulk solid - the dead zones - keeps on its place and forms the rathole. The reason for this is the strength (unconfined yield strength) of the bulk solid. If the bulk solid consolidates increasingly with increasing period of storage at rest, the risk of ratholing increases. If a funnel flow silo is not emptied completely in sufficiently small regular time intervals, the period of storage at rest can become very large thus causing a strong time consolidation.

Figure 3b: Ratholing

o Irregular flow occurs if arches and ratholes are formed and collapse alternately. Thereby fine grained bulk solids can become fluidized when falling downwards to the outlet opening, so that they flow out of the silo like a fluid. This behaviour is called flooding. Flooding can cause a lot of dust, a continuous discharge becomes impossible.

o Wide residence time distribution: If dead zones are formed (funnel flow), the bulk solid in this zones is discharged only at the complete emptying of the silo, whereas bulk solid, which is filled in later, but located closer to the axis of the silo, is discharged earlier. Because of that, a wide distribution of residence time appears which is disadvantageous in some cases (e.g. in case of storage of food or other products changing their properties with time).

o Segregation: If a heap is formed on the bulk solids' surface at filling of the silo, segregation is possible according to particle size or particle density (figure 3c). In case of centric filling as shown in figure 3c, the larger particles accumulate close to the silo walls, while the smaller particles collect in the centre. In case of funnel flow, the finer particles, which are placed close to the centre, are discharged first while the coarser particles are discharged at the end. If such a silo is used, for example, as a buffer for a packing machine, this behaviour will yield to different particle size distributions in each packing. In case of a mass flow, the bulk solid will segregate at filling in the same manner, but it will become "remixed" when flowing downwards in the hopper. Therewith, at mass flow the segregation effect described above is reduced significantly. (A short movie showing segregation due to particle size you will find here).

Figure 3c: Segregation

In a funnel flow silo, all problems mentioned above can occur generally, while in case of mass flow only arching has to be considered: segregation, ratholing, irregular flow and flooding of the bulk solid do not appear in a well designed mass flow silo. The residence time distribution of a mass flow silo is narrow, because it acts as a „first in - first out" system (see figure 2a).

Two steps are necessary for the design of mass flow silos: The calculation of the required hopper slope which ensures mass flow, and the determination of the minimum outlet size to prevent arching.

4 Silo design

The flow behaviour of a bulk solid is defined by several well-defined parameters [2,5-8,21]. In general, these are the bulk density b, the effective angle of internal friction e (a measure for the internal friction of the bulk solid at stationary flow), the unconfined yield strength c, and the wall friction angle x. For mass flow design, the wall friction angle x is the most important parameter, whereby the unconfined yield strength c is the most important parameter regarding arching. The wall friction angle x is defined as the friction angle between the surface of the silo wall and the corresponding bulk solid. The unconfined yield strength c is the compressive strength of a bulk solid. It has to be taken into account that all these parameters are dependent on the stress level, represented by the consolidation stress 1 [2,5-8,21].

The parameters mentioned are measured in dependency on the consolidation stress with shear testers [2,5-8,21], e.g. with the Jenike shear tester or a ring shear tester. The hopper slope required for mass flow and the minimum outlet size to prevent arching can be calculated with the measured values using Jenikes' theory [7]. This method showed its validity in many cases in more than 35 years.

The borders between funnel and mass flow, which result from the calculations of Jenike [7], are shown in figure 4a for the wedge shaped hopper and in figure 4b for the conical hopper. In the diagrams the wall friction angle x is drawn over the hopper slope angle measured against the vertical. The effective angle of internal friction e, which is a measure of the internal friction of the bulk solid, is the parameter of the mass flow/funnel flow borderlines. The borderlines separate all pairs of values leading to mass flow from those leading to funnel flow.

Figure 4a: Design diagram for mass flow (wedge-shaped hopper)

Figure 4b: Design diagram for mass flow (conical hopper)

Conditions which lie within the borderline yield mass flow whereas funnel flow is present in case of conditions outside of the borderline. If the wall friction angle x and the effective angle of

internal friction e are known (measured with a shear tester, e.g. with the ring shear tester), the maximum slope angle of the hopper wall against the vertical which ensures mass flow can be determined with this diagram. The courses of the borderlines indicate, that the larger the wall friction angle x is, the steeper (smaller ) the hopper has to be for mass flow. The wedge shaped hopper allows a somewhat (often 8° to 10°) larger slope angle against the vertical with the same material properties. That means that the walls of a wedge shaped mass flow hopper can be flatter than the walls of a conical mass flow hopper [7,12].

When bulk solid is discharged from a mass flow silo, the radial stress field prevails in the hopper as already described in section 1 (see figure 1c). In the hopper (at least beneath a sufficiently large distance from the vertical section) the major principal stress 1 is proportional to the local hopper diameter (figure 5). It decreases to zero towards the imaginary hopper apex. The stress 1 acts as a consolidation stress thus determining the properties of the bulk solid, e.g. the bulk density b and the unconfined yield strength c. The unconfined yield strength c of a bulk solid can be measured for each major principal stress (consolidation stress) 1 (see [21]). The function c =f(1) (figure 6) is called the flow function. Usually, the unconfined yield strength increases with the consolidation stress. If the flow function has been measured, the unconfined yield strength c can be drawn in figure 5 at each position of the hopper.

Figure 5: Stress conditions in the hopper (emptying)

1' is the bearing stress acting where an imaginary stable arch of bulk solid is carried by the hopper walls. 1' is proportional to the local hopper diameter such as 1. An arch can only be stable in that are of the hopper where the unconfined yield strength c is larger than the bearing stress 1' . This is the case beneath the point of intersection of the c curve with the 1' curve. Above that intersection the unconfined yield strength is smaller than the bearing stress of the arch. In this case, the unconfined yield strength is not large enough to support an arch, i.e. an

arch would not be stable at this position. The point of intersection indicates the lowest possible position in the hopper (height h*, figure 5) for an outlet opening large enough to avoid arching. The diameter of this minimum outlet opening is called dcrit. If a smaller outlet opening would be chosen, h* indicates up to where flow promoting devices have to be installed beginning at the outlet.

Figure 6: Flow function and time flow function

Some bulk solids tend to consolidate increasingly with the period of storage at rest (time consolidation [8,21]). It can be found a time flow function ct = f(1) (figure 6) for each storage time analogously to the flow function. If the time flow function would be drawn in figure 5 then this would yield to a point of intersection of the 1'-curve and the ct-curve, which would be above the already determined point of intersection of the 1c- and 1'-curves. This means that larger outlets are required to prevent arching with increasing storage time at rest.

For practical silo design, equations or diagrams derived by Jenike [7] are used to determine the stresses 1 and 1' in dependence on the flow properties measured (e, x, b) and the silo geometry (). With this means the minimum outlet sizes of conical as well as wedge-shaped hoppers can be calculated. Furthermore, the minimum outlet sizes for avoidung ratholing at funnel flow can be determined [7].

5 Choice of the hopper geometry

Figure 7 [7,9,12] shows some opportunities to design mass flow silos. The calculations of Jenike (see design diagrams, figure 4) refer to conical hoppers (a) and wedge shaped hoppers (b). In case of these basic hopper forms, the maximum slope angles of the walls to achieve mass flow (ax in case of a conical, eb in case of a wedge-shaped hopper) and the outlet dimensions (d, b) to prevent arching can be determined. In case of the wedge shaped hopper it is assumed, that the

influence of the vertical end walls can be neglected if the length of the outlet L is at least three times the width b.

Figure 7: Hopper forms [9]

The variants c and d are advantageous as well to ensure mass flow if the maximum slope angles as indicated in the figure are not exceeded. The pyramidal hopper geometry (e) is disadvantageous because the bulk solid has to flow from the top in the edges of the hopper and in the edges to the outlet. Thus, the bulk solid has to overcome wall friction at two sides what supports the formation of dead zones. If mass flow has to be achieved with such a hopper geometry, the edges have to be rounded on the inside, and the maximum slope angle against the vertical of the edges must not exceed ax. Because the walls of a pyramidal hopper are always steeper than the adjacent edges, a pyramidal mass flow hopper is steeper than a conical hopper for a specific bulk solid. Variant f is just a transition from a cylindrical section to a square outlet. In this case, the slope of the hopper walls against the vertical must not exceed ax at any position.

In order to achieve mass flow, variants e and f must have the steepest walls. The conical hopper (a) can be designed more shallow, and the largest slope angles measured against the vertical can be achieved with geometry b,c or d (wedge-shaped hoppers).

In some industries non-symmetrical silos are preferred (e.g. pyramidal hoppers with differently sloped walls). From the view of mass flow design, there is no reason to build such silos. If mass flow has to be achieved, symmetrical hoppers usually require the lowest height for the transition from the silo cross-section to the outlet cross-section to achieve mass flow [10].

6 Application of the results on the design of silos

In section 4 the silo design procedure due to the theory of Jenike [7] was described in a shortened way. Further details and information can be given besides the determination of the hopper slope for mass flow and the size of the outlet to prevent arching. Some examples are listed shortly in the following (further examples of silo design: [17,18,22,23]):

o Details about hopper slope and size of outlet for different hopper forms (see figure 7) and wall materials. Because of that, a comparison of manufacturing costs of different hopper forms and hopper materials is possible [18,19]. It can be find out, for example, whether lining of the hopper walls (e.g. with cold rolled stainless steel sheets) is useful regarding the costs.

o If the mass flow design yields an extremely steep mass flow hopper, or if in the case of a retrofit of an existing silo mass flow should be achieved without modifying the (too shallow) hopper walls, specially suited installations can be dimensioned on the basis of the measured flow properties and Jenikes' theory [15,16].

o In case of varying material properties (e.g. moisture [10,20]), it is possible to find out with shear tests which conditions would yield the worst flow properties. If the silo is designed for these conditions, proper operation is ensured in any case.

o In case of bulk solids which tend to time consolidation, it can be stated quantitatively which size of outlet is necessary to avoid arching in dependence on the storage time at rest. A mass flow silo provides the opportunity to keep the bulk solid in motion by regular discharge (and recirculation, if possible) of a small amount of bulk solid. In this way, the time consolidation and, hence, the size of the outlet [18] can be limited.

o With flow property tests (shear tests), the influence of additives (e.g. flow agents) can be determined in order to find the optimal mixture [13,18].

o In case of the storage of bulk solids sensitive to attrition or stresses as present in a silo, the limit stress can be examined above which that danger exists [22,23]. Because of those results, the silo can be designed in that manner that no stresses will occur which would have a negative influence on the quality of the product.

o To avoid vibrations emerging during discharge of a bulk solid, specially-suited installations can be designed (e.g. discharge tubes) [14,18].

o In general, shear tests are also applied for quality control and flowability tests [13].

Belt Conveyor Systems

The Benefits of Belt Conveyors:

The smooth, continuous surface of a conveyor belt is ideal for many product handling applications. Some of the benefits of belt conveyors include:

Small or delicate part handling Accumulation Inclining and elevating with high friction or cleated belts Clean room environments Small parts transfer Back lighted inspection Quiet operation

Belt Conveyors: The Dorner Advantage

Largest Selection of Belted Conveyors

Dorner offers the largest selection of belted conveyors in the industry with over 30 pre-engineered models for every application that are built to the customer’s specifications. This ensures each customers finds the perfect configuration for their product.

Cleated Belt Conveyor Systems

About Cleated Belt Conveyors:

Cleated conveyors are commonly used to control product on a horizontal or inclined conveyor. The key attributes for cleated conveyors are the accuracy of the cleat spacing and durability of the cleat in the application. Dorner uses proprietary in-house processes to attach cleats to the

belting material. The customer is ensured accurate spacing and durability of the cleat to belt interface.

Cleated Belt Conveyors: The Dorner Advantage

Engineered Process

Dorner has engineered a unique process that uses high frequency to welds the cleats onto the belt to guarantee the quality of the bond. Controlling the quality prevents cleat breakage and tear off for the customer, resulting in a stronger, longer lasting cleated belt.

Largest Selection of Cleated Belt Conveyor Offerings

Dorner offers the largest selection of cleats for cleated belt systems, including different heights and cleat angles. Also available are unique sidewall belts that, when combined with cleats, form a product pocket on the belt that prevents product spillage. This endures more consistent and efficient movement for the product.

Harry Harlick was an institution in the conveyor industry, and an inspiration in the founding of FloStor. Harry prepared the following information as a training manual for engineers at Conveyors & Casters (Hamerslag Equipment), which closed in 1985.

Significant advances have been achieved in conveyor technology since this manual first appeared, though many of the basics remain constant. This paper is provided as an introduction to the scope of factors considered by the FloStor professional sales engineers in specifying conveyors.

BASIC INTRODUCTION TO CONVEYORS

by Harry Harlick (1905-1987)

INDEX

ForwardSection One: Gravity ConveyorsSection Two: Powered Belt ConveyorsSection Three: Live Roller ConveyorsSection Four: Chain ConveyorsSection Five: SupportsSection Six: CouplingsSection Seven: AccessoriesSection Eight: Useful FormulasSection Nine: Essential Information RequiredSection Ten: A Brief History of Conveyor

FORWARD

The package conveyor business has been in existence for almost one hundred years.Material handling engineering, in an over-simplified, basically, consists of determining "how a product should be moved from one place to another, within the shortest allowable period of time, for the least cost and with the least amount of manual effort".We hope that this publication will help to guide you to the best possible solution to the many material handling problems, which you may encounter.It is extremely difficult to put in to writing the many years of problem solving experienced by "old-timers" in this industry, no two solutions are identical. This publication will merely give you an idea of the uses of the many different types of conveyors available, and, it will be up to you to sift through to determine the best conveyor for your particular application.

SECTION ONE

GRAVITY

APPLICATIONProbably no other type of conveyor is applied to so many gravity materials handling uses as roller and wheel conveyor, handling various packaged materials efficiently for distances as short as 2 ft. or as long as 100 ft. or more. Any item from light bulbs to bagged cement to heavy castings can be moved on gravity.

Most items are best handled on roller conveyor, however, wheel conveyor may be substituted where a portable type gravity conveyor is required, where light weight containers (38 lbs. per ft. in steel, 18 lbs. per ft. in aluminum) are to be handled and where semi-rigid filled multi-wall paper bags or bales are to be handled. In general, roller conveyor should not be used for conveying burlap bags of coffee beans, paper or cotton bags of rice, cotton bags of flour or freshly filled paper bags of cement because the type of material mentioned has a tendency to

drape over rollers.

Conveyors, when properly applied, confine the flow of materials thus conserving valuable production and storage space. Frequently, as in storage racks and production assembly lines, roller or wheel conveyor are used for storage providing accessibility and easy movement for processing or production. Breakage or damage is generally minimized when the products are supported and restricted during the travel on conveyor.

Supports should have some height adjustment and should be selected for convenient height for personnel.

CONVEYOR SELECTIONSkatewheel conveyor, as a rule, is generally used for handling smooth bottom, wood, fiber or plastic containers. Semi-rigid smooth bottom bags or bales may also be conveyed on some wheel conveyor. If there is any doubt, the product and container should be tested on an appropriate wheel conveyor. Such testing can help determine the suitable grade.

Skatewheel conveyor is not recommended for handling cans with chimes, open bottom crates, cleated containers or damp, soft, soggy cartons. It is further not recommended for conveying flexible filled bags or articles too small to span at least three rows of wheels. Extremely heavy or soft-bottomed cartons may fold around wheels and are therefore also not recommended for use on wheel conveyor.

From the Hytrol Catalog, you will note that skatewheel conveyor is available in varied widths and varied wheels per foot patterns. The selection of wheel conveyor is based upon the rigidity, size and weight of package to be conveyed. The denser the wheel pattern, the greater the range of cartons that can be handled on such wheel conveyor.

Roller conveyor are also used for handling smooth bottom, wood, fiber or plastic containers, crates (without wire binding), drums and cans with chimes, kegs and long narrow packaged materials.

Gravity conveyors are used as a level push line or down grade by utilizing the natural force of gravity. The use of gravity to convey the selected class of packages to move by their own weight, on a bed of rollers or wheels, is, perhaps, the most widely used means for conveying in industry. The weights to be conveyed may vary from a few ounces to several tons. For example, in department stores, conveyors are used for handling light weight boxes of hosiery and the same conveyors handle heavier boxes of dishes and appliances. The selection of rollers is tailored to fit the application.

Roller conveyor is not recommended for conveying soft bottom cartons or bags which will flex and fold or wrap around the upper carrying portion of the roller and thus deter the free motion of such containers.

The degree of decline required will vary depending on whether the bearings are dry or grease

packed, on the ambient temperature (if outdoors) and, in some areas, on humidity. The degree of decline also depends on the specific application. The first package will start rotation of the rollers. The second package if it followed shortly, would benefit from this rotation and would travel a bit faster than the first package and the third package even faster. In the course of the day's production, trains of packages could be traveling very fast on a degree of decline originally defined to start package movement from rest. Retarding devices to help control this situation are available.

A few elementary rules in the selection of roller conveyor are offered as follows:(1.) Packages to be handled should, in general, have smooth firm bottom riding surface.(2.) For normal conveying, at least three (3) rollers should be under the package being conveyed at all times.(3.) To select the proper roller, divide the weight of the package by the number of rollers supporting the package. The load capacity charts in the Hytrol General Catalog will help in your selection.

Other important areas to be considered are the actual items to be conveyed as well as their size. While the load capacity chart indicates that 50 lb. empty oil drums could be conveyed on 1.9" Dia. x 16 Ga. rollers, we would recommend the use of 2" Dia. x 12 Ga. rollers because of the greater wall thickness in handling a steel drum.

The tolerances of the various components, which make up a roller conveyor, may be such as to not present a perfect conveying surface. Uniformly loaded packages, with some flexibility, will distribute the weight approximately to each roller supporting the package, whereas rigid packages may impose their entire load on a reduced number of rollers. Wood or steel pallets may actually be supported by only 50 per cent of the rollers under them. Select from the Hytrol General Catalog a roller to suit the required load capacity, taking into consideration the type of product being handled, so that in the event the load is actually supported by one-half of the rollers under the product. The rollers selected will actually support this type of load. When roller lengths exceed the catalog lengths, the axle deflection may be the limiting factor in place of ball bearing capacity. Package roller conveyors are not normally considered to be precision equipment, and past experience indicates that the tops of all of the rollers in the conveyor may not be at exactly the same height. Where an excessive impact might occur in the loading area of a conveyor, it is advisable to consider providing twice the number of rollers normally required for conveying the package in this loading area only.

Nominal roller length is determined by the maximum width of the commodity to be conveyed. Ordinarily, rollers would be two to three inches longer than the widest package within the standards listed in the Hytrol General Catalog. It is, however, permissible, in certain package handling situations, for the package to extend beyond the ends of the rollers if the rollers are mounted in a high position in the side frames and provided the bottom of the package does not flex and make contact with the side frames.

GradesWhile it is difficult to recommend specific grades for various materials to be conveyed on wheel

or roller conveyer, we offer the following suggested grades based upon average conditions. The actual grade for a specific requirement should be determined by test. Grades required for roller conveyer may vary because light cartons with soft bottoms may require more grade than heavy packages with hard bottoms.Grades on curves are based upon the length of the outside rail and grades on straight roller curves should be increased 25 to 50 percent than charted in fig. 7.

The average roller conveyor line handling 40 to 45 lb. packages and equipment with ball bearing rollers requires a pitch of about ½" per lineal foot of travel, and for wheel conveyor the pitch is about 3/8" per lineal foot of travel. The pitch will increase or decrease according to the riding surface and the weight of the commodity to be conveyed. Also, the use of sleeve (sanitary) type bearings will affect the conveyor pitch.

CURVESRoller and wheel conveyor curves are made to match the straight conveyor. The radii of any curve are dependent upon the length and width of the package to be conveyed. The length and width of the package also determines the width (between rails) of the curve and generally, the width of the curve determines the width of the adjacent connecting straight conveyor. If a package is exceptionally long, as for florescent light tubes or cut flowers, the adjacent straight conveyor might normally be excessively wide for such a package, which condition, of course creates a costly conveyor. The imbalance of this type of situation can be corrected by using a narrower width curve and offset guard rails thus permitting the package to overhang the rollers on the curve but still keep the adjacent straight conveyor to a satisfactory width and help keep the price of the required conveyor within competitive limitations.

Wheel curves, because of the multiple rows of individual ball bearing wheels, perform an excellent job of conveying rectangular packages, as the individual wheels apply the necessary differential action to keep the package centered as it traverses the curve. Hytrol wheel curves are available in standard overall widths to join to adjacent straight sections, with 45° and 90° of curvature as standard.

Hytrol also has available tapered steel rollers, which also apply the necessary differential action to keep the package centered as it travels through the curve.

Straight roller curves are generally more satisfactory for handling cylindrical packages rather than rectangular packages because of the lack of the differential action required on this type of roller conveyer. Since a package has a longer distance to travel adjacent to the outer rail, the package in this type of curve has a tendency to slip to the outer frame.

Double roller (curves with a center frame midway between the two outer frames which splits the roller length) will convey a square or rectangular package better than the single straight roller curve because of the differential action of the two separate lanes of rollers.

For best results, gravity curves should have a straight gravity roller conveyor section at the infeed and the discharge ends of the curve of minimum length equal to approximately 2/3 of the

length of the package.

Gravity curves are not recommended for accumulation of square or rectangular packages. The line pressure will prevent the packages from maneuvering the gravity curves and generally will force the package against the outer guard thus blocking the free flow of further packages.

SPURSGravity roller or wheel conveyor spurs are used for merging and diverging of packages onto or off of a main line transportation conveyor. The standard angles are 30°, 45° and 90°. The 45° diverging unit is not normally recommended for automatic diverging of packages but should be manually attended. Turning wheels should be used as shown in the Hytrol General Catalog where spurs are used in the converging application.

"Y" AND SPUR CURVE SWITCHESThese switches utilizing skate wheels provide a simple method of diverting or converging products from one line to another as described in the Hytrol General Catalog.

GATE SECTIONSThese are hinged sections used as gates and are available for vertical movement of the section to provide access for personnel, lift trucks or other equipment. They are available with or without springs. The springs provide some assistance in lifting the heavier gate sections. Horizontal gate sections with a pivot pin on one end and caster supports on the opposite end are also available.

ROLLER CONSTRUCTIONThin wall rollers are perfectly satisfactory for most package handling, but should not be used for handling extremely heavy packages with steel strapping or filled steel drums regardless of the indicated roller capacity. Thin wall rollers may be easily bent, dented or cut, thus impairing their usefulness. The heavier rollers such as 2 ½" Dia. x 11 Ga., 2 9/16" Dia. x 7 Ga., and 3 ½" Dia. x 9 Ga. are much better suited for this latter application.

AXLESSpring-Loaded axle construction is a Hytrol standard for:1 3/8" Dia. x 18 Ga. Rollers using ¼" Dia. Galv. steel axles 1.9" Dia. x 16 Ga. Rollers using 7/16" Hex. steel axles 2" Dia. x 12 Ga. Rollers using 7/16" Hex. steel axles 2 ½" Dia. x 11 Ga. Rollers using 11/16" Hex. steel axles 2 9/16" Dia. x 7 Ga. Rollers using 11/16" Hex. steel axles.The spring-loaded construction which requires no hog rings or cotter pins permits the customer to easily remove and relocate or replace rollers.

COUPLINGSOther than wheel conveyor and 1 3/8" Dia. roller conveyor, which have bar and hook type couplings, all other frames have butt couplings for bolting sections together.

SUPPORTSHytrol stationary supports are available in light, medium and heavy duty styles. Consult the Hytrol General Catalog for further information.

Poly-tier supports for support of multi-level conveyor lines are also described in the Hytrol General Catalog.Ceiling hangers are 5/8" Dia. painted steel rods with threaded ends.Tripod stands are useful in setting up temporary conveyor lines, using skatewheel and/or 1 3/8" Dia. x 18 Ga. roller conveyor.For other types of supports, consult the Hytrol General Catalog.

GUARD RAILSMost overhead conveyor are usually required to be provided with guardrails both sides. Curves as an option, may also be provided with guards at the outside rail. Consult the Hytrol General Catalog for various types.

FRAMESSome frames are of steel galvanized, heat-treated aluminum, and powdercoat painted steel. Hytrol green is our standard color.

REPLACEMENT ROLLERSYou will at times, receive request to quote on replacement rollers even for frames, which may have been furnished by other than Hytrol. It is extremely important that exact information be furnished. DO NOT GUESS.1. Obtain roller diameter and gauge.2. Check axle size; i.e. ¼" Dia., 7/16" Hex, 11/16" Hex. etc. on 1 3/8" Dia. x 18 Ga. rollers, Hytrol furnishes ¼" Dia. Galv. steel spring loaded axles. Other conveyor suppliers may use 5/16" hex axles.3. Check to see if bearings are dry, grease packed or re-greasable.4. Measure the exact distance between existing frames.5. Measure the frame thickness, i.e. 12 Ga., 10 Ga., 3/16", ¼" etc.6. Some customers re-use their existing axles. Determine if axles should be furnished. If the customer uses rollers with spring-loaded axles, it is best that we furnish these complete.

QUESTIONS:If you have questions, the answers to which are not to be found in Hytrol Catalogs, do not hesitate to call your master Hytrol Distributor. He will obtain the information for you. Do not place collect calls to your master distributor.

SUGGESTED GRADES FOR ROLLER CONVEYER

COMMODITY LOAD WEIGHTGRADE:INCHES PER FT

GRADE:IN PERCENT

Fiber Cartons 5 to 10 lbs. 13/16" 6-1/2 to 7

Fiber Cartons 10 to 20 lbs. 3/4" 5-1/2 to 6

Special conditions, such as high or low temperature conditions, and dirty or wet conditions should be brought to the attention of your Master Hytrol Distributor prior to quoting. Relatively heavy packages should not be transferred onto the middle of a belt conveyor say one 20 feet or longer in length. Continual transfer of the relatively heavy packages would have a tendency to push the belt to the one side of the conveyor, and if these packages were to enter the belt conveyor as a continuous flow, then could push the belt over to the extent that the edge of the belt could possibly be damaged at the drive or tail ends. The best type of transfer described above would be with the use of 1ive roller conveyors. However, if for some reason, the use of live roller conveyors is not practical, then we should consider the use of the three-pulley device normally furnished with the integral powered feeder, at each side of the junction of the push-on or push-off location. This provides a tight belt in the strategic location. A thin strip of wood, plastic, or steel, along the one edge of the belt opposite the push-on or push-off would also be helpful in retaining the belt in the proper tracking position. The solutions suggested herein are not to be construed as approval to accomplish a specific described action, these are merely recommendations for alleviating a non-recommended condition.

A single direction non-reversing belt conveyor of reasonable length, may use a standard end drive with the 4" dia. drive pulley. A reversing belt conveyor should use a center drive, generally, with a larger than 4" dia. drive pulley, particularly with longer conveyor lengths or heavy loads on the belt. See the Hytrol General Catalog.

Horizontal belt conveyors usually consist of the following listed components:1. An end or center drive which would include a gear motor and a take-up.2. Either one or two end pulleys, depending upon the type of drive used, or a power take-off device.3. Bed sections, either slider or roller bed.4. A suitable length of flexible belt.5. Return idlers on approximately 10'-0" centers to support the return strand of belt.6. Floor or hanger supports on approximately 10'-0" centers.7. Electrical controls and field wiring (optional).

Incline and decline conveyors: Consists of the same components listed above except this unit would include a single or double noseover, possible a feeder section, one of the two types offered, and a "rough" surface belt on the incline (decline) instead of friction surface belt.

Brake and Meter BeltsThe Brake belt is used as a stop at the end of an accumulation (Live Roller) conveyor and the Meter belt is used as the speed up belt to obtain case separation. The Meter belt would normally have the drive and the Brake belt would be slave driven from the Meter belt through a power take-off similar to that used at the chain-feeder section of an inclined belt conveyor. Meter belts normally run 1 1/2 to 2 times faster than the Brake belt. Both Meter and Brake belts are normally provided with a "rough" top type belting, such as "Hilltopper". As a rule of thumb, the total length of the combination of Brake and Meter belts should be about 1/7 the total length of accumulation conveyor with the Brake and Meter belts. The length of the Meter belt, based upon the belt width would be the same as a powered feeder section. As an example: If the total length

of accumulation conveyor with Brake and Meter belts were 84 feet, then the total length of the combination Brake and Meter belts would be 12 feet; then, subtracting the length of the Meter belt would give us the length of the Brake belt portion.

Metal "Piano Hinge" conveyor: This is a hinged steel belt, ideal for carrying hot and oily parts from punch presses, forging machines, etc. This type of conveyor may be level, horizontal or inclined "S" shaped as required. The design and dimensional information is described in the Hytrol General Catalog.

Wire mesh belt conveyor: This type of belt conveyor, because of the open mesh, permitting the free flow of air, is excellent for conveying hot or cold materials too hot or too cold to handle on standard duck or PVC belts. The wire mesh belt can travel on rollers or longitudinal runners covered with a dense plastic material. The pulleys are generally cast with multiple teeth to grip the mesh of the belt. Under some circumstances, the pulleys can be standard rubber or neoprene lagged to grip the underside of the wire mesh belt. Since it carries no load, the return strand can also be supported by return idlers or by longitudinal runners.

Portable conveyors: The Hytrol General Catalog lists a large number of portable belt conveyors. A portable conveyor is one, which can be rolled from one position to another on caster wheels. In addition, Hytrol offers a large variety of skatewheel conveyors or 1 3/8" diameter roller conveyors with tripod stands and portable castered supports. The catalog also lists various extendible portable gravity conveyors, the descriptions of which are well covered in the Hytrol General Catalog.

Caution areas for belt conveyors: A reversible belt conveyor has been and will, no doubt, continue to be an item with which the operating results will be in doubt until the conveyor is installed and tested under no load and load conditions. Theoretically, a belt conveyor will not operate reversibly unless all revolving surfaces in contact with the belt are square with the frame or unless the belt tracking devices are properly adjusted. Conveyors & Casters employs capable Millwrights who have had extensive experience in installing and testing the reversible belt conveyors.

When a reversible belt starts to give belt-tracking trouble, even after it has worked for a number of years, random adjustments should not be made. It could easily get out of hand if someone who does not know the proper procedure tries to correct the trouble by making various adjustments. If, after operating satisfactorily for a number of years, it must be assumed that something must have happened to cause the belt to run off to one side.Before trying to make any adjustments the following points should be checked:1. If a new belt has been installed, has the belt been cut perfectly square or has it been cut on a cambor?2. Has the conveyor frame itself been pushed out of line by lift trucks or other devices?3. Have adjustments been made on the return idlers or the end pulleys by mechanics inexperienced in solving such problems?4. Have the bolts which hold the flange bearings pulley shafts become loose and shifted from their original positions?

5. Have any of the roller conveyor bearings or flange bearings become so worn as to effect their original square alignment?6. Have any of the return idler supporting clips or mountings become loose so as to affect the alignment of the belt?It is quite possible, if all of the above items are carefully checked and any corrections properly made that the belt will then track in its original squared up position in both directions. The belt tracking conditions should be approached by correcting those things which may have gone wrong due to the age of the conveyor components thus returning it as near as possible to its original condition.

The practice used in tracking a one-direction belt cannot be applied to a reversible belt conveyor. All moving parts in contact with the belt must be squared up with one another and all with the frame for the single direction only. Do not class a reversible belt conveyor in the same category as a single or one direction belt conveyor so far as installation time is concerned. The reversible belt conveyor does take considerably longer because of all the variable conditions herein described to install properly.

Belting: Belting manufacturers have come a long way in the manufacture of excellent quality belting. For example, most belting for level conveyors furnished by Hytrol will probably be PVC (poly vinyl chloride) machine woven nearly impervious to most liquids and ambient temperatures. The "Hilltopper" belt has a rough surface bonded to the PVC base. Other belts, some impervious to food oils and some approved by USDA (US Department of Agriculture) for food handling are also available. Check with the Hytrol Master Distributor for belt recommendations for specific special applications.

Motors: Hytrol Conveyor Company manufacturers their own gear reducers for most conveyor applications. The integral width gear reducer for "V" built variable speed drives and the "C" face reducer to receive any "C" face electric motor. Motors are available in open drip proof and totally enclosed, either single or 3 phase. In the Western States, we mostly use totally enclosed motors. Hytrol reducers are available in commercially standard speed ratios of 10 to 1, 20 to 1, etc. Hytrol Conveyor Company can provide variable speed motor drives at additional charge. They have one which is.2.7 to 1 ratio and another, which is 6 to 1 ratio. As an example, this means that the 2.7 to 1 ratio can have, lets say, a low speed range down to 10 F.P.M. and can be adjusted up to a maximum of 27 F.P.M. On the 6 to 1 ratio we can have, the low speed at 10 F.P.M. and the maximum speed at 60 F.P.M. We can adjust the low speed instead of using 10 F.P.M. to say 15 F.P.M. with the high-speed range greater than that stated above, within the speed capacity of the rollers, if the conveyor is a roller bed.

Electrical Controls:Many Hytrol portable conveyors are normally furnished with single phase motors and with reversing drum switch all for 115 volts. This reversing drum switch has no overload protection. When 3 Phase motors are used, then the push-button controls operating on.115 Volt single phase which in turn actuates a 3 phase magnetic starter which does have overload protection in the form of heater coils. If the motor, for any reason, is overloaded and starts to heat up in excess of its rated capacity, the heater coil automatically will be destroyed, which, in turn, interrupts the

electrical current to the motor. The motor stops undamaged and the condition which caused the heater coil to be destroyed, can be corrected, a new coil replaced in the starter and the system started up once again. It is extremely important that the proper coil size be used. Other than portable conveyors, Hytrol does not normally furnish electrical controls unless specifically requested to do so, at additional charge. Limit switches, photo cells and other controls can also be furnished at additional charge.Conveyors & Casters is proud to report they have "in house" capabilities to prepare sophisticated electrical wiring schematic drawings, at additional charge and can arrange with qualified local electrical contractors in order to provide a turn-key installation.

SECTION THREE

LIVE ROLLER CONVEYORS FOR UNIT HANDLING ONLY

Types of Live Roller Conveyor:

A. V-Belt DrivenB. Flat Belt DrivenC. Zero-PressureD. Single strand roller chain drivenE. Roller to roller chain driveF. Roller Slat Conveyor

ApplicationsLive roller conveyors, because of the relatively low coefficient of friction between the bed rollers and the items conveyed, are used in preference to belt conveyor where:1. Temporary utilization of the items being conveyed is a requirement.2. Items are stopped momentarily such as traffic control points.3. Items must be turned, say 90° on the conveyor.4. An air operated or manual stop is injected into the line so that the item may be inspected or some operation performed while the conveyor remains in motion.5. Side loading or unloading is required involving a sliding motion across the bed rollers.

Belt driven live roller using regular friction surface rubber filled belting is not recommended for use in high environmental temperature extremes. Rubber can become sticky and soft at temperatures exceeding 150°F, and this belting can stiffen considerably and crack in the minus zero range. PVC or cotton belting is a considerable improvement in the range described above. Check with your Master Hytrol Distributor for special cold room applications.

Keep in mind, that the belt travels in a direction opposite to the items being conveyed. This is unlike a belt conveyor where the items are being carried directly upon the belt, so they both go in the same direction.

V-Belt driven live roller conveyor is that type where a single strand of V-belt is under the roller bed, on one side of the rollers, adjacent to the side-frame and is powered in a direction opposite to that of the items being conveyed. We recommend this type of conveyor for light and medium duty loads. This type of conveyor is not recommended for use where moisture or oily conditions may exist. A very light contact with the underside of the bed rollers is all that is required to keep the items being conveyed in motion. This type of conveyor may also be reversible.

Belt driven tapered roller curves generally give good package conveying action. The tapered roller presents a true conveying surface on a curve giving the correct radial speed along the full length of each roller. The curve radius along with the taper on the roller which comes to a common focal point causes the package to leave the curve in much the same position in which it entered. For best results, there should be live rollers, a minimum of 2/3 of package length at the entry and at the discharge ends of the curve.

Two rail curves with straight rollers are not normally recommended for use as a live roller curve because both rows of rollers must be powered separately and with a different speed in order to obtain some semblance of differential action. Under some conditions, the center rail may be move off center, closer to the outer rail with the longer rollers powered.

Flat Belt driven live roller conveyor is that type where a flat width of belt is under the roller bed, generally in the center of the conveyor, but can be mounted off-of-center adjacent to the side frame if required. Because of the greater contact surface at the underside of the roller bed, this type of conveyor is recommended for handling medium to heavy duty loads, where moisture, hot, dirty or oily conditions do not exist. Again, the pressure rollers which snub the driving belt to the underside of the bed rollers are set to a minimum, just enough to convey the load, yet allow belt slip without undue wear or stress on the gear motor when the loads are momentarily blocked.

The above described conveyor design cannot be incorporated into a roller bed curve, and another type of live roller curve must be utilized where a curve is necessary.

Ripple Belt conveyor is one utilizing a belt, which varies in thickness at regular intervals along the full length of the belt. It is set so that the thicker portions of the belt make contact with the underside of the bed rollers. If the ripples are relatively far apart, only a few are in contact with the bed rollers. This makes for a fairly inexpensive live roller with reduced line pressure under blocked load conditions.

Controlled gravity live roller is similar, in construction, to flat belt or V-belt driven live roller conveyor, except that the conveyor is sloped at a grade just sufficient to allow the items to convey by gravity. On the flat belt conveyor the snubbing rollers are spaced further apart than the standard horizontal live roller. Since gravity is the driving force of the items being conveyed, the snubbing pressure is light enough to simply prevent the rollers from turning at excessive speeds particularly when trains of items coming one after another are being conveyed.

Hytrol Zero-Pressure Live Roller Conveyor is very completely described in the General Catalog

under the headings 190-ACO and 190-ACOC. This is a full length drive shaft arrangement, with each thread roller driven by a urethane o-ring from a 1.9" diameter longitudinal drive roller. The 190-ACOC curves, which are slave driven from the adjacent 190-ACO, is designed for applications that require accumulation of products without a build-up of line pressure. In addition, Hytrol has developed the model 190-ACA, a flat belt drive zero-pressure conveyor. In all zero-pressure live roller, the conveyor length is divided into zones, the length of each is greater than the maximum package length. Zero-pressure is achieved since the packages never touch one another.

Single strand chain driven live roller is a medium duty live roller conveyor, ideal for conveying hot or oily items, or items subject to wash down. In this type of live roller, "Type A" plate sprockets are welded to one end of each roller. Care must be taken that the dimension form the end of each roller is identical to keep the roller chain in a straight path. In this type of conveyor, the roller chain which powers each roller only makes contact with just one or tow teeth of the sprocket. The sprockets and the chain are completely enclosed by the chain guard which sometimes acts as a hold down for the upper strand of chain. Rack tooth sprockets must be used for this type of conveyor. If rollers used are a large diameter and would necessitate a greater roller spacing than desired, then idler (non-powered) rollers may be spaced between each driven roller.Because the chain guard on chain driven live roller conveyor forms a guardrail on the one side of the conveyor, items can only be transferred to and from the opposite side of the conveyor. Hytrol has developed a chain crossover, which simply crosses the chain over to the opposite side on a slave driven arrangement when items must be transferred to or from the driven side. Access is available from the one non-powered side only.

Single strand chain driven live roller curves can also be supplied using a side bow chain, especially designed to bend around a curve.

Roll to roll chain driven live roller is a heavy-duty live roller conveyor for use under the same conditions as for single strand live roller. In this instance, two type "A" sprockets are welded to one end of each roller. The roller chain then makes a complete loop around each pair of adjacent roller sprockets. With a greater number of sprocket teeth in contact with the roller chain, more power can be transmitted to and through each roller. Rack tooth sprockets must not be used on this type of conveyor.

Roll to roll chain driven live roller curves can also be supplied. A heavier duty roll to roll chain driven live roller conveyor utilizing two "B" type sprockets attached to the extended shaft on the outside of one side frame accomplishes the same as described above and permits the use of smaller drive sprockets, thus enabling us to keep the rollers to reasonable closer centers. This type of live roller can also allow access from either side of the conveyor provided the chain guard which covers the outboard row of sprockets does not project above the top of the conveyor side frame.

Roller slat conveyor utilizes extended pitch bushed roller chain with oversize rollers rolling in tracks adjacent to the outer rails. Using ball bearing rollers with the hexagon axles longer than

normal; these axle ends pass through the hexagon broached bushings of the chain and are generally cottered at both ends on the outside of the chain.

On a blocked load, the conveyor continues to run and the ball bearing rollers simply roll under the blocked load. The line pressure thus is kept to a reasonable low level.

This roller slat conveyor is an extremely heavy type of conveyor, and must be assembled at the job site as the assembled conveyor rollers in the chain are much too heavy to handle as an assembled unit. This is also a fairly expensive type of live roller and is used only under special conditions; such as heavy duty type for filled oil drums or perhaps for newspaper mail rooms where the blocked load of newspapers permit the roller slat to run under the newspapers without damage.

Except for Hytrol's Zero-Pressure 190-ACOC conveyor, under no circumstances should curves be used for accumulation of square or rectangular items. Cylindrical items only are permissible. The very nature of a square or rectangular conveyor would cause the corner of one container to dig into the corner of another.

Powered curves should not be warped because of the difficulty in providing power to the individual rollers of a warped curve.

SECTION FOUR

CHAIN CONVEYOR

There is a wide variety of chain conveyor classified into four separate types:

A. Sliding chain conveyors.B. Rolling chain conveyors.C. Pusher Bar chain conveyors.D. Vertical chain conveyors.

Sliding chain conveyor: This is the type of conveyor consisting generally of two parallel strands of chain. For light unit loads and for short distances, the chain can be a double pitch roller chain with the standard small rollers running in a track lined with high density low co efficient friction plastic material. For heavier loads, it is best to consider a heavy duty cast pintle chain which will also run in a channel track lined with a high density, low coefficient of friction plastic material of which there are many available today. The sliding chain conveyors carry the loads on the chains and the bottom of the chains are in low frictional contact with the track.

Rolling chain conveyors: This is the type of conveyor, which utilizes generally, two parallel strands of double pitch roller chains (sometimes three strands), with the rollers running on key stock material of width to fit between the side plates of the roller chain. Again, this design is used for fairly light loads and for short conveyors. For heavier loads, we can use the double pitch chain with oversize rollers where the rollers are greater in diameter than the width of the chain

side plates thus the rollers do project below the side plate of the chain. This rolling friction design utilizes a lower horsepower requirement and thus can be used for longer runs of chain driven conveyor. The loads are carried on attachments, which raise the load above the chain rollers.

A slat or apron conveyor using steel or wood slats or even a ball bearing conveyor rollers between the two parallel strands of roller chain actually fits the category description for roller slat conveyor previously described. In the use of steel or wood slats, heavy loads can be carried under such conditions where perhaps a PVC or a rubber belt could not possibly be utilized.

Also another type of sliding chain conveyor, which utilizes single strand of link chain riding in a plastic lined track in the center of the conveyor. Outboard of this center track on both sides to the outer frame rails are gravity rollers or wheels spaced on suitable centers compatible with the container being handled. The link chain, which is powered, projects slightly above the side rollers and is the driving force which carries the containers while the side rollers or wheels merely balance the load. Some advantages of this conveyor are:1. Excellent for wash down conditions.2. A single drive can be used to convey on the level, up an incline, down a decline, around a curve, etc.

Some disadvantages are that it can only be used satisfactorily for fairly light loads and inclines and declines cannot be too steep, probably not more than 15 degrees.

Pusher Bar Conveyors are similar in design to the horizontal slat conveyor in that we have two outboard strands of roller chain adjacent to the side frames. We can use an attachment on the chain to which we can fasten an angle, a flat bar or a round rod. This angle, flat bar or rod is the pusher bar. Under the chain track and between the side frames we have a slider bed. The units to be conveyed will slide on the slider bedplate and will be pushed by the pusher bars. The spacing of the pusher bars must be such as to permit the conveyed items to fit in between. Some advantages of this type of conveyor are:1. Can convey heavy items up much steeper inclines than conventional Hilltopper belt.2. Can handle wire bound crates or bales of hay.3. Can handle heavy burlap or cotton bags of flour, rice or green coffee items which might be difficult to incline or decline at angles in excess of 25 degrees on Hilltopper belt.

Some disadvantages are:1. The height of the pusher bars above the slider bed must be such that the containers will not fall forward or backward. This limits the variation of box sizes.2. The timing of containers is critical so two containers cannot try to get between the two pusher bars simultaneously.3. This type of conveyor can definitely not be used with sheet polyethylene bags, as the frictional heat generated would create holes in these bags.

Vertical chain conveyors can be designed for use to handle individual cartons as well as full pallet loads. The design can be similar to a dumb waiter style where the unit is a reciprocating

lift handling one unit at a time or can be a continuous lift with flights attached to side roller chains. Each flight can handle one unit, therefore the flight spacing vertically depends upon the maximum height of the unit being handled.

SECTION FIVE

SUPPORTS

Types of supports are listed as follows:

A. Tripod stands.B. Portable castered supports.C. Stationary floor supports.D. Polytier supports.E. Ceiling hangers.F. Under trussing.

Tripod Stands are used for temporary installations. It consists of a "T" shape upper top which fits under the cross brace of wheel conveyor or SSR/SAR roller conveyor. The bottom part of the "T" slips into a 3-legged tripod and is held in the height position by a friction grip.

Portable castered supports utilizes the "T" portion of the tripod stand which slips into a vertical pipe with a flat cross piece at the bottom to which are attached casters for portability.

Stationary/Floor supports consists of two pivot plates attached to the underside of the conveyor section, to which are attached formed steel channel legs. Adjustable feet are attached to the bottom of the legs. The feet are provided with holes for fastening the support to the floor. Stationary floor supports may also be fitted with castered supports.

Polytier supports are designed to provide sturdy supports for multi-level conveyor lines, utilizing formed steel channel uprights with 1 1/2 inch diameter pipe cross braces to which the conveyor lines are attached with "U" shaped brackets. Knee braces, which are angled between the upright leg and the underside of the conveyor frame, provide increased longitudinal rigidity.

Ceiling hangers consist of 5/8 inch diameter painted steel rods fastened to the 1 1/2 inch diameter cross pipe mounts on the underside of the bed sections and the upper portion is fastened either to ceiling beams or metal clips which in turn are fastened to ceiling beams.

SECTION 6

Couplings

Types of couplings are as follows:

A. Hook and rod normally used on conveyors at temporary installations. These are only provided on wheel or SSR/SAR roller conveyors. Hook and rod couplings can be used in fixed installations with stationary floor supports.B. Butt Couplings used in fixed installations and are attached to each corner of the bed section for bolting the sections together.

SECTION 7

Accessories

1. The traffic cop is a mechanical device with spring loaded arms and cams located at the junction of two powered conveyor lines and prevents the flow of carton traffic on one line from interfering with the flow on the adjacent line. In other words, it eliminates collision of cartons arriving at the junction simultaneously. If possible, the two conveyors should be of the live roller type.

2. Case stops of blade and roller type are available as hand operated and foot operated. The air cylinder operated type is available as the roller type only. The blades or rollers are located between the rollers on the live roller or gravity conveyors only. They cannot be used in the middle of a belt conveyor, for obvious reasons.

3. Turning wheels are used at the junction of a branch line to a main line to insure proper carton orientation and to prevent cartons from falling off the conveyor during the course of the transfer.

4. Angle end stop is mounted to the ends of the conveyor side frames to prevent the continued flow of cartons on the conveyor from falling off of the conveyor.

5. Guard rails are available in many shapes and sizes. Their purpose is to prevent cartons from falling off the conveyor and they must be used on all overhead conveyors.

6. Ball transfers consist of a large steel ball riding on a bed of smaller balls all contained within a steel stamping to hold and support the configuration together. We utilize a pattern arrangement of ball transfers on a steel bed in a conveyor line to permit cases to be manually positioned or rotated easily.

7. "Y" Switch of skatewheel design provides a simple method of converging or diverging cartons. Consult the Hytrol General Catalog for a description and photo.

8. Spur curve switch of skatewheel design also provides a simple method of converging or diverging cartons. Again consult the Hytrol General Catalog.

9. Carton push-offs come in various sizes and designs. All push-offs simply push a carton at right angles to the original direction of flow. The overhead push-off is a high speed air cylinder

actuated unit which can cycle up to 40 times per minute and can push carton with weights up to a maximum of 150 lbs. The medium duty horizontal push-off can push up to 300 lbs. and the heavy duty over 300 lbs. A horizontal push-off will cycle considerable less than the 40 cycles per minute available with the overhead unit.

10. Pop-up wheel diverter is specifically designed for use in the 190-ACC Accumulating conveyor. It provides for high speed automatic diverting of cartons onto a 30 degree spur. It consists of three rows of 2 1/2 inch diameter powered wheels, the mechanism of which is raised and lowered pneumatically. It can handle cartons of 150 lb. maximum weight up to 40 cycles per minute maximum. A description and photo is in you Hytrol General Catalog.

11. High speed diverter uses a powered diverting belt and can handle maximum weight cartons of 200 lbs. each. It is best used for rapid singulation and diverting. See the Hytrol General Catalog.

12. The powered turn-table is used when two parallel lines must be close together. The minimum turning radius is much less than our standard roller or even powered curves.

13. The manually operated turn-table simply consists of a given length of conveyor on a revolving mechanism, which allows the conveyor to be manually turned and positioned for "inline" flow of products. It is used where curves are unable to fit into the system. Pneumatic and motor indexing turntables are also available.

14. Plows can only be used to divert to a 30 degree spur from a main line. In addition to the manual1y positioned plow, Hytrol has the pneumatic positioned plow as well as the V-belt motorized and pneumatic positioned unit.

15. Manual Vertical Gates for gravity lines are available and the maximum length of gate is determined by the weight of the conveyor to be lifted. Gates are used to provide access through a conveyor line.

16. Spring Balanced Gate allows the use of heavier gates than with manual gates with the use of tension springs adjusted to provide a minimum weight lift.

17. Horizontal Swing Gates with castered supports can also be supplied. The conveyor in this instance may be powered as well as gravity.

18. Jump transfers are devices set between rollers of gravity or live roller conveyor to transfer the product at right angels from the conveyor. They perform the same function as the push-offs under more controlled circumstances. Hytrol has available the skatewheel transfer, the powered V-belt transfer and the powered chain transfer. In most instances, air bags are used to raise and lower the transfer.

SECTION 8

USEFUL FORMULAS

BELT CONVEYOR - HORSEPOWER CALCULATIONS

To determine the horsepower required for a belt conveyor, it is first necessary to determine the total belt pull. The belt pull, in turn, is based upon the live load plus the weight of all moving parts, multiplied by the coefficient of friction. The information required is listed as follows:1. Size and weight of each package.2. Belt speed.3. Number of bed rollers times the weight of each roller.4. Number of return idlers times the weight of each roller.5. Total weight of all of the belting.6. Total weight of all pulleys.7. On inclines (or declines), the additional belt pull is required for that portion of weight on the conveyor on the incline (or decline). This is equal to the weight of all packages on the incline (or decline) times the sine of the angle.

COEFFICIENT OF FRICTION

Type of Conveyor Friction Factor Multiplier

Roller Bed - Ball Brgs. 5% 0.05

Roller Bed - Wood Sleeve Brgs. 10% 0.1

Steel Slider Bed with Return Idlers 30% 0.35

Steel Slider Bed with Steel Return 35% 0.35

Belt Driven Live Roller 7.50% 0.075

A. Live Load

The live load is the actual load on the conveyor at a given time. First we multiply the weight of each package times the number of packages per minute; we divide this total by the belt speed in feet per minute. This gives us the live load per foot which when multiplied by the total length of conveyor results in the total live load.

B. Weight of Belt

This includes the actual weight of both the TDP and bottom runs, in other words, the belt on top

of the slider bed or carrying rollers and the return strand. See attached belt length formulas

WEIGHTS OF COMMONLY USED BELTS

Belt Description Weights per inch width x 12" long

3 Ply Solid Woven Cotton .040 lb.

Black PVC - 90 .040 lb.

Balck PVC - 120 .060 lb.

Black or White IWP-3 .047 lb.

Black Hilltopper .100 lb.

Brown - 3 Ply Neoprene - Ruff tip .120 lb.

 

How To Obtain Approximate Belt Lengths For Various ConveyorsNOTE: These formulas are for calculating horsepower only, not for determining replacement lengths of belts. *OAL = Overall Length

MODEL TYPE OF DRIVE FORMULA

TA4" or 8" Dia. End Drive4" or 8" Dia. Center Drive

2 x OAL + 1' - 0"2 x OAL + 3' - 6"

TR Same as for "TA"

TL8" End Drive, 4" or 6" Dia. Tail Pulleys8" Center Drive, 4" or 6" Dia. Tail Pulleys

2 x OAL + 1' - 0"2 x OAL + 3' - 6"

190 RB8" End Drive, 4" or 6" Dia. Tail Pulleys8" Center Drive, 4" or 6" Dia. Tail Pulleys

2 x OAL + 6"2 x OAL + 3' - 0"

25 RB12" or 16" End Drive12" or 16" Center Drive

2 x OAL + 3' - 0"2 x OAL + 6' - 0"

190 LR 8" Center Drive 2 x OAL + 3' - 6"

25 LR 12" or 16" Center Drive 2 x OAL + 6' - 0"

Notes:1. Add 2’ – 0” for double nose over on incline belts.2. Add 2’ – 6” for underside take-ups for all above, except 25 RB.3. Add 6’ – 6” for underside take-up for 25 RB.4. Add 2 x OAL + 6” for chain driven power feeders.5. Add 2 x OAL + 2’ – 6” for integral type power feeders.

 

C. Weight of Rollers: Include the total weight of all bed rollers and return idlers. When slider bed construction is use, include only the weight of the return idlers.

ROLLER WEIGHTS (IN POUNDS)

Roller Length 6" 12" 18" 24" 30" 36" 42" 48"

Roller Diameter

1 3/89 0.7 1.2 1.8 2.6 - - - -

1.9 x 16 Ga. 1 1.8 2.7 3.6 4.5 5.4 6.3 7.2

1.9 x 9 Ga. 2.1 3.8 5.4 7.1 8.8 10.5 12.1 13.8

2 1.6 2.8 4.3 5.7 7.2 8.6 10 11.5

2 1/8 2 3.2 4.9 6.5 8.1 9.7 11.3 12.9

2.5 2.4 4.1 6.1 8.2 10.2 12.2 14.3 16.3

2 5/8 3.5 5.9 8.8 11.8 14.7 17.6 20.6 23.5

 

D. Coefficient of Friction: Use the coefficient of friction which corresponds to one of the sketches pictured below. The percentages shown are for all types of belting on roller conveyor. Rubber covered belting is not normally recommended for slider bed construction, except for short lengths and light loads.

1. Roller bed with return idlers Coef. of frictiona. Ball bearings 5%b. Wood burning 10%

2. Roller bed with steel slider return Coef. of frictiona. Roller bed with slider return & F.S. x F.S. belt 30%b. With PVC belt 25%

3. Steel slider bed with return idlers Coef. of frictiona. With F.S. x F.S. belt 30%b. With PVC belt 25%

4. Steel slider bed with steel slider return Coef. of frictiona. With F.S. x F.S. belt 35%b. With PVC belt 30%

E. Weights of All Pulleys: Include total weight of all drive and idler pulleys, snub rollers, end and take-up pulleys.

PULLEY WEIGHTS (IN POUNDS)

Pulley Diameter 6" 12" 24" 30" 36" 42" 48"

4" 6 12 24 30 36 42 48

6" 9 16 33 42 50 58 67

8" 13 27 54 68 81 95 108

12" - - 108 135 162 189 216

 

F. Inclines or Declines: When all or any part of a conveyor is inclined or declined, an added belt pull is applied. This additional belt pull is obtained by multiplying the total live load on the inclined (or declined) portion by the sine of the angle.

SINE OF ANGLES

Angle Sine Angle Sine Angle Sine Angle Sine

2° 0.03 12° 0.21 22° 0.37 32° 0.53

4° 0.07 14° 0.24 24° 0.41 34° 0.56

6° 0.1 16° 0.28 26° 0.44 36° 0.59

8° 0.12 18° 0.31 28° 0.47 38° 0.62

 

Belt pull for inclined portion = Live Load on incline times sine of angle or incline.

G. Two and Three Pulley Device: Add 5% of the Live Load preceding the device.

H. Deflectors: To accurately determine the total belt pull, add 30% of the weight of the heaviest package being diverted. We normally do not recommend diverting from belt conveyors except for light weight packages.

Belt pull equals weight of heaviest package times coefficient of friction for specific belting being used. Use only a smooth top belting.

I. Mechanical Traffic Cop: Add 30% of the weight of the maximum number of packages which will be held back by the traffic cop arm. The maximum weight of the total number of packages should never exceed 250 lbs.

J. Formula:Horsepower = Effective belt pull x conveyor speed (feet per minute)33,000 x .85 x .951. One horsepower is defined as the power required to move 33,000 lbs. A distance of onefoot in one minute.2. .85 allows for 85% for worm gear efficiency. Hytrol gear boxes use worm gears.3. .95 allows for the roller chain drive efficiency.

Example (Level RB Belt Conveyor)1. Package weight = 45 lbs.2. No. of packages per minute = 203. Belt speed = 65 FPM4. Bed rollers = 12" CTRS. (Ball bearings)5. Return idlers = 10' - 0" CTRS.6. Belt width = 12" PVC 1207. Conveyor width = 15" BR8. Conveyor length = 100'= 0"9. Drive 8" pulley = Center drive and take-upLive load per foot = 45 x 20 = 14 lbs. Per foot65Live load = 100 ft. x 14 lbs. Per foot = 1400 lbs.Bed rollers = 100 x 1.5 lbs = 150 lbsReturn idlers = 10 x 1.5 lbs. = 15 lbs.Belting = 206 ft x .060 x 12 = 150 lbs.Center drive and end pulleys = 77 lbs.

TOTAL WEIGHT TO MOVE 1792 lbsCoef. of Friction 5% x .05EFFECTIVE BELT PULL 90 lbs.

HP = 90 lbs. X 65 FPM = .2033,000 x .85 x .95Summary: Use the minimum horsepower offered by Hytrol: 1/3 hp (1/3 more than required).

LIVE ROLLER - HORSEPOWER CALCULATIONSThe same method for belt conveyors can be used for belt driven live roller conveyors. If the live roller is to accumulate a blocked load, simply calculate as though it were a moving load then double the horsepower.Horsepower for single strand chain driven live roller as well as roller-to-roller chain driven live roller is calculated as follows:A. Determine the live load in the same manner as for belt conveyor.B. Add the weight of the rollers (See chart under belt conveyor).C. Add the weight of sprockets and roller chain.

Conveyor Type WEIGHT OF SPROCKETS

2 ½” Dia. #50 CH 2 ½” Dia. #60 CH 3 ½” Dia. #80 CH

Single strand .9#

Roller to roller 1.8# 3.0# 6.6#

WEIGHT OF CHAINS

Single strand 1.5#

Roller to roller 2.1# 3.0# 5.7#

 

D. Determine chain pull in the same manner as for belt pull under belt conveyor.

Chain Number

Allowable Chain Pull

Conveyor Speed F.P.M

to 65 65 to 80 80 to 100 100 to 150

RC 50 875# 800# 750# 650#

RC 60 1200# 1075# 1000# 850#

RC 80 2100# 1950# 1800# 1550#

 

SERVICE FACTORSOperation up to 24 hoursContinuous single strand: 1.0Roller to roller: 1.2Sudden stopping or reversing: 1.4Dirty conditions: 1.4

COEFFICIENT OF FRICTIONSingle strand 6%Roller to roller 5%

The formula to use is:HP = Effective chain pull x speed in FPM33,000 x .85 x .95Multiply the effective chain pull service factor to determine if it is higher or lower than the allowable chain pull.Horsepower calculations for chain conveyors are more complex in that shaft torque and bending moments farther the picture. Suggest checking with your Master Hytrol Distributor on applications which require chain conveyor.

Below is a formula for determining sprocket ratio, motor RPM, or belt speed:No. of teeth (motor spkt.) x Pulley Dia. (inches) x TT x Reducer shaft RPM = Belt speed (ft. per min)No. of teeth (pulley spkt.) 12Substitute known values and solve for unknown.EXAMPLE:Wanted number of teeth on motor sprocket:Known values:1. Drive pulley dia. = 8 inches.2. Reducer output shaft = 48 RPM3. Belt speed = 65 FPM4. Number of teeth (pulley sprocket) = 32Then: 65 x 32 x 12 = 21 teeth8 P x 48MORE MISCELLANEOUS USEFUL FORMULASRPM (pulley) = FPM (belt) x 12Pulley dia. (in inches) x PRPM (roller) = FPM belt x 12

Roller dia. (in inches) x PRPM (pulley) = Motor sprocket (no. of teeth)RPM (motor) Pulley sprocket (no. of teeth)FPM = RPM (motor) x no. teeth (motor spkt.) x pulley (or roller) dia. x PNo. of teeth (pulley sprocket x 12)HP = Torque (lb. -ft.) x RPM = Torque (lb - inch) x RPM2552 63,025Torque = Effective belt pull x ½ dia. of drive pulley.

SECTION NINE

ESSENTIAL INFORMATION REQUIRED FOR MOST PROBLEM SOLVING

1. Type of Products to be conveyed:

A. Carton (corrugated) (glued, stapled or taped bottom).B. Bag (multiwall paper, cotton or plastic).C. Bundle or bale (tight, steel or plastic bonds).D. Wood case (cleats on bottom).E. Plastic tray (smooth or grip bottom).

2. Size of Products:

Length: Max/MinWidth: Max/MinHeight: Max/MinWeight: Max/Min

3. How is product to be conveyed?

A. Lengthwise.B. Widthwise.

4. How will product be placed on conveyor?

A. Manually.B. Transferred from anther conveyor.

5. Method of Transport?

A. Gravity.B. Power.

C. Combination of gravity and power.

6. How many hours per day will conveyor be used?

A. 8 hours (one shift).B. 16 hours (two shifts).C. 24 hours (three shifts).

7. Available electrical current?

A. Volt Phase Hertz

8. Maximum (not average) production rate?

9. Will conveyors be floor supported or hang from overhead?

10. Will conveyors be subjected to unusual conditions?

A. Wash down.B. Extreme heat.C. Extreme cold.

11. Will the customer require engineering services?

SECTION 10

A BRIEF HISTORY OF THE CONVEYOR INDUSTRY

The conveyor industry actually started about 80 years ago [1900] in the Minneapolis-St. Paul area by a group of men unloading wood shingles from rail cars. The idea worked so well that part of the group decided to relocate to a steel tube mill location and selected Ellwood City Pennsylvania, the home of National Tube. This relocated group called itself Mathews Gravity Conveyer Company with Rufus P. Mathews as president.

The group that remained in the Minneapolis-St. Paul area also started a conveyor company named Standard Conveyor Company.

A Mr. Offutt was superintendent of National Tube in Ellwood City, Pennsylvania. At times, Mathews got into financial difficulty, and Mr. Offutt bailed them out and received stock in the company. He also secured employment for his son John in the Mathews engineering department. Also, Mr. Offutt's daughter was married to the Ellwood city bank president. Upon Mr. Offutt's death, John, his son, inherited all of the Mathews stock his father owned.

After Rufus P. Mathews, F.E. Moore became president. Then came Bill Dean, then Odd McLeary.

F.E. Moore set up Mailer-Searles in San Francisco as the west coast manufacturer of Mathews Conveyors and built a new plant in Port Hope, Ontario, Canada. Mailer-Searles sold the area west of the Mississippi River and maintained offices in Salt Lake City, Los Angeles, San Francisco, Portland Oregon, and Seattle.

Mathews Chief Engineer, Norton Meyer, and Chief Draftsman, John Offutt took Harry Harlick under their wings and taught him all about the application of conveyors to industry.In addition to Mathews, Mailer-Searles also acquired the Standard-Knapp line of packaging machines.

Bill Dean was jealous of Bill Jaenicke, president of Mailer-Searles because Jaenicke was offered the presidency of Mathews before Bill Dean, but, Jaenicke refused, saying he had been born and raised in San Francisco and did not care to relocate to Ellwood City.

Bill Dean decided to build a Mathews Plant in San Carlos and take the Mathews line back. He also appointed P.W. (Joie) Brown as President of Mathews-West Coast. The new plant had only 2 acres and quickly outgrew the San Carlos facility. They purchased 80 acres in Chico and built a new plant. P.W. Brown ultimately died of a heart attack and Bill Peppard was appointed Vice-President and General Manager.

When Mathews took the line from Mailer-Searles, Bill Jaenicke obtained the Alvey Conveyer line from Jack Alvey of St. Louis.

The Alvey Conveyor Company had started in the north barn of Anhuser-Busch in St. Louis, furnishing all the conveyor for the brewery. When Alvey solicited more work from other St. Louis breweries, he was politely told to move.

Alvey eventually passed away and Jack Alvey and Bob Mayer bought the company from his uncle's widow. Both Jack and Bob were standard Conveyor sales people in New York and specialized in brewery conveyors.

Meanwhile, Hartford-Empire, manufacturers of automatic blowmold glass making equipment bought Standard-Knapp. It was suggested that Mailer-Searles also sell to Hartford-Empire, later known as Emhart.

Bill Jaenicke later was told that Emhart was going to dissolve Mailer-Searles. Emhart formed a separate Standard-Knapp office in San Mateo and Harry Harlick was retained to finish up all outstanding Alvey business, after which he went to work for FMC corporation in Riverside, CA.

Now, Odd McLeary was President of Mathews and arranged a sale of Mathews to Rex-Chainbelt of Milwaukee Wisconsin. Rex also bought Nordberg a rock crushing equipment manufacturer and changed their name to Rexnord. The cost of Mathews to Rex was $9M with $25k per year retirement to Odd for a period of 5 years. Mathews had $9M in the bank, so the actual cost to Rex as zero.

FMC set aside $10M for the Riverside Division to get into the conveyor business. Since they were furnishing practically all conveyor to the citrus industry, they had a good start. The Riverside Division could purchase a conveyor company or start one from scratch. The Riverside Division also manufactured about 7 different product lines; the bulk feed trucks which deliver cattle and chicken feed, egg machines which automatically grade and package eggs for producers, along with juicers and other equipment for citrus growers.

Also FMC purchased some Palletizer patents from an inventor in Los Angeles. The rest of the patents were purchased by Lamson Corporation, of Syracuse, New York. This caused a legal battle between FMC and Lamson which nearly bankrupted Lamson. Both companies manufactured Palletizers.

FMC head office in San Jose discovered the Riverside Division was diverting conveyor funds to other product lines and fired all product managers and demoted the division manager Mr. Sid Boucher, the conveyor sales manager Don Derricott was allowed to retire.

About the time Tom Loberg (Hytrol) designed the bale conveyor, Bill Jaenicke also designed a variable speed bale conveyor to elevate bales of hay to truck beds. E.W. Buschman (Buschman) was a Rapistan salesman in Cincinnati when he decided to go into business for himself.

There was a wheel conveyor manufacturer in, I believe, Buffalo, New York, who hired local housewives to assemble wheel conveyors at hours they chose and paid minimum wages. Their profits were rock-bottom. Mathews also used women to assemble wheel conveyors. They did a very good job in Chico.

      ©2001 FloStor Engineering

Site Map  

Courtesy of RapistanConveyor systems have been a mainstay of material handling for over 100 years.  Overhead trolleys and belt conveyors were moving materials in manufacturing plants before the forklift was even invented.  New configurations and sophistication of controls have kept conveyor systems in the state-of-the-art category with other automated material handling systems.  The extensive range of applications for conveyers allows their use in small "mom and pop" type operations as well as in tier 1 manufacturing and distribution operations.  Conveyor is very cost effective and the ease of expandability and reconfiguration makes it ideal for growing operations.  A little imagination and a small investment can do wonders for reducing manual material handling through the use of conveyor systems.  Also see Hytrol's ABC Conveyor Book, an online guide to conveyor information and specs.

Courtesy of Hytrol Conveyor Company,

 

Gravity Skate Wheel Conveyor

Gravity flow skate wheel conveyor is a low cost option for conveying lightweight cartons, trays, or totes.  Used extensively in shipping/receiving and assembly areas, skate wheel conveyors reduce manual material handling of lightweight items over short distances.  I've used gravity skate wheel  conveyor in elaborate configurations as well as in small 1 or 2 section stand-alone units..

 

 

Courtesy of Hytrol Conveyor Company,

Gravity Roller Conveyor

Application for gravity roller conveyor is similar to that of gravity skate wheel. Its cost is a little higher and it is more effective where heavier items are being handled.

 

 

Courtesy of Hytrol Conveyor Company,

 

Automated Belt Conveyor

Automated belt conveyer has similar applications to gravity roller and skate wheel. Single units can be incorporated into gravity conveyor systems to create a simple low cost semi-automated system. 

 

Courtesy of Hytrol Conveyor Company,

 

Automated roller conveyor

The automated version of gravity roller conveyor, automated roller conveyor is used extensively in large conveyor systems.  A version of automated roller conveyor called Zero-Pressure Accumulating Conveyor is especially useful in avoiding the pressure buildup which normally occurs when product accumulates at a stationary operation.

 

Courtesy of Hytrol Conveyor Company,

 

Flexible Conveyor

Used extensively in shipping/receiving operations for package handling, flexible conveyor is usually anchored at one end to fixed gravity or automated conveyor allowing the other end to be expanded and flexed into trailers for loading and unloading.

 

  Unit Load Conveyor

Courtesy of Rapistan

 

Unit Load Conveyor is a heavy duty version of roller conveyor used for handling pallet loads or larger totes or trays.  Unit load conveyer can be gravity flow or automated and may be installed elevated or recessed into the floor..

 

Courtesy of Rapistan

 

High Volume Trailer Loading

This shows an application of conveyor in high volume trailer loading/unloading.  The section in the track in the floor automatically extends into the trailer during loading.

 

 

Courtesy of Rapistan

 

Sortation Systems

Sortation systems are the key to large elaborate conveyor systems.  The variety of sortation systems is extensive as are their applications.  Most frequently used in high volume case quantity and piece quantity picking, shipping, and parcel processing operations, there are also sortation systems for unit load system.

Several types of conveyor are available for many different applications. Below are some sample images and cutaways of the many different types of conveyor. If you have any questions about the best conveyor solution for your operation, please visit www.sjf.com contact one of our conveyor experts that can assist you in choosing the right kind of conveyor for your application.

Gravity Conveyors

Gravity Conveyors are non-powered, free flowing conveyors used in a push or level application to facilitate product movement. They can also be set up with declining stand heights to allow product to flow from a high to a lower elevation. Gravity conveyors are available in roller or skatewheel configuration. Both types can be used with a variety of powered conveyors to form a complete conveyor system.

Roller Conveyor

Gravity Roller Conveyors can be used when conveying flat, smooth bottomed surfaces like cartons, packages or pallets as well as most other items with an uneven bottom surface such as drums, cans, molds, etc.

While available in many custom lengths, gravity roller conveyor is typically sold in 10 foot sections while overall widths of 12, 18, 24, & 30 inches are considered industry standard. Several different roller sizes & types are also available.

Skatewheel Conveyor

While gravity is a good all-purpose gravity conveyor, skatewheel is best when conveying flat, smooth bottomed surfaces such as cartons, tote boxes, trays and plywood or masonite skids.

Gravity skatewheel conveyor is a lighter-weight and more economical alternative to gravity roller conveyor. Skatewheel conveyor is typically used in situations where its lighter weight makes it easily moved or reconfigured to make space for storage of larger products. It can be found everywhere from shipping areas to pick and pack stations. Both aluminum and steel frame models for lighter or heavier duty applications are typically available.

Power Conveyor

Many Different Power Conveyor types can be used in a conveyor system. Each has a different, but important function. Here are several of the more common varieties.

Accumulation Conveyor

Accumulation conveyor is typically used in conjunction with other conveyor types in a complete conveyor system. Accumulation conveyor consists of pop-up sensor rollers located in ‘zones’ which use a pressurized air system to hold your product in a queue until it receives a signal to release it to the next stage of operations. This can include moving products one at a time onto a weigh station, case sealer, sort system, palletizer, or any other work station.

There are several types of common accumulation conveyor, however two are more common than the others. Zero pressure accumulation conveyor will eliminate package collisions on the conveyor line by leaving gaps between each individual box, while minimum pressure accumulation conveyor will place the individual boxes next to each other with little back pressure.

Accumulation conveyor can be the most vital link in any large conveyor system. Without it, your sortation system, packaging machine, or other machines will quickly become overloaded and

will not function properly.

Belt Driven Live Roller Conveyor

Belt driven live roller conveyor consists of load rollers, a drive belt, return rollers and an external motor. The load rollers make up the surface on which product is transported. The rollers move using a belt that is located underneath the load rollers which provides friction directly on the rollers and creates forward movement. The return rollers are used to kep the belt in place under the conveyor as well as to maintain tension on the belt at all times.

Belt driven live roller conveyor can be used in accumulation, induction, and merge systems where product sizes and weights tend to vary. It provides limited capabilities for inclined movement or packages of differing shapes.

Belt Over Roller Conveyor (aka: Belt On Roller)

With belt over roller conveyor, the belt can be either sliderbed supported or supported by return rollers located underneath the load rollers. Belt on roller conveyor is a fairly common type of powered conveyor and is what many people think of when they envision powered conveyor. Belt on roller conveyor is very useful for transporting light and medium weight loads between locations.

In addition to being a good general purpose powered conveyor, belt over roller is also a desired

solution for inclines or declines. Powered belt over roller conveyor provides much control over the orientation and placement of loads, which can be good for bulky, irregularly shaped products. Because product orientation is easily controlled with belt over roller, it also makes a good conveyor to use in induction and sortation conveyor systems.

Lineshaft Conveyor

Lineshaft conveyors can be used used for both transporting and accumulating products. Lineshaft makes use of a drive shaft which runs the length of the underside of the conveyor, and drives the load rollers individually using belts. Since the rollers are individually powered, lineshaft conveyor can easily be used for accumulation operations where there is a minimum amount of backpressure on the product being transported.

The driveshaft is powered by a motor. Some configurations of lineshaft conveyor allow the conveyor to run both forwards or backwards depending on the situation desired. Because there are fewer moving parts, today’s lineshaft conveyor is typically quieter than traditional live roller conveyors. The belts also assist in reducing noise by holding the rollers firmly in place inside the frames which results in less rattling.

Chain Driven Conveyor

Chain driven live roller conveyor (sometimes referred to as pallet conveyor) is typically used to transport heavier loads at controlled speeds. Chains drive sprockets on the load rollers which in turn drives a chain and the sprocket on the next roller, etc. These systems transmit the same amount of power to each roller thus insuring a smooth, even ride.

Chain Driven conveyor offers several advantages that other types typically do not or cannot. For instance, because there is no belt(s) chain driven conveyor can transport both hot and cold loads that could damage other conveyor types. Chain driven conveyor can also resist contamination by grease and other particulate matter better than other conveyor types. Chain driven live roller conveyor is also better able to tolerate uneven pallet bottoms or drums.

Trash Conveyor

Trash conveyor and regular sliderbed conveyor are two very similar products with one important difference. Trash conveyor has guard rails attached to the sides of its frame to prevent materials from falling off the conveyor belt into the work area. Return rollers keep tension on the conveyor belt keeping it taut.

Trash conveyor is used mainly to transport empty boxes, paper trash and other light-weight refuse to a disposal area, compactor or incinerator while keeping it out of the way of production areas. It can help to create a better organized work area that will allow your employees to perform their work efficiently and without hinderance. Since trash conveyor utilizes a sliderbed design, there are few moving parts to create noise. The sliderbed design of trash conveyor also makes it great for transporting materials on inclines and declines.

Sliderbed Conveyor

Sliderbed conveyor and trash conveyor are very similar products, but regular sliderbed conveyor does not usually have guard rails. Many capacities of sliderbed are available, but lighter weights are more common. Sliderbed conveyor uses return rollers to run a conveyor belt along a smooth bed, thus allowing for the smooth transportation of many different load types.

Sliderbed can easily carry loose components and other materials that roller conveyors have a harder time transporting. Since sliderbed conveyor has few moving parts, it does not create much noise. The sliderbed conveyor design also makes it useful for transporting loads on inclines and declines. Typical sliderbed applications include inspection, transportation and assembly line operations.

Sortation Conveyor

Sortation systems complete with scanners, controls etc., often cost more than the average company can afford to spend - but you're in luck - my company, SJF believes that you don't need to invest a small fortune to incorporate one of these systems into your operation. SJF specializes in previously owned sortation systems that will do everything the new systems will do.  You'll have piece of mind knowing that we can provide everything from design, layout, programming and installation from one single source. We have successfully put several systems just like the ones below into operation for customers just like you. They are all currently sorting product at a fraction of the cost that a new system would have set them back. Take a look at the different types of sortation conveyor systems we can provide.

Cross Belt SortationAdvantages of cross-belt sorters include quietness, ability to have sort points close together, sorting to the right or left, and versatile layouts such as straight, “L” or oval paths with inclines and declines.

Tilt Tray SortationTrays, connected in a chain, tip to both sides, dumping into chutes or sides, Low noise levels and ability to sort small, flat or delicate items are advantages.

Tilt Slat SortationThe conveying surface is made up of slats that can be tilted to the right or left. Packages travel in close proximity and only the slats under them will be activated to tilt.

Pop-Up Belt/Chain SortationThese sort boxes or containers to either side of a main conveyor line. They work by pulling heavy packages onto angled spurs at high speeds. The belt or chain used is matched to the package being handled.

Sliding Shoe SortationOne of the fastest continuous sorters, a row of sliding shoes travels across the sorter path smoothly, easing containers onto takeaway spurs. Typically, this is used in conjunction with photo eyes that either puch the package onto an alternate lane or allow the package to continue down the main conveyor line to the correct lane.

Pusher/DiverterPusher diverters have spur or sort points located very close together and handle heavy products. P/Ds are slow to medium speed because the diverter mechanism must return across the belt before intercepting the next package.

Pop-Up Roller SortationThe pop-up roller is driven by its own motor at a higher speed than the main-line conveyor. In sorting, the roller grabs the leading edge of the container and leads it off onto a spur.

Swivel Wheel/Roller SortationThis diverter can work with belt or roller conveyors to drive packages off to the right or left using a roller that will swivel in place to either allow the package to pass or be diverted. Divert points can be as close as three-foot center. Main-line belt conveyors are typically less noisy than most roller types.

Magnetic separation is a process in which magnetically susceptible material is extracted from a mixture using a magnetic force. This separation technique can be useful in mining iron as it is attracted to a magnet.

In mines where wolframite was mixed with cassiterite, such as South Crofty and East Pool mine in Cornwall, magnetic separation was used to separate the ores. At these mines a device called a Wetherill's Magnetic Separator (invented by John Price Wetherill, 1844–1906)[1] was used. In this machine the raw ore, after calcination was fed onto a moving belt which passed underneath two pairs of electromagnets under which further belts ran at right angles to the feed belt. The first

pair of electromagnets was weakly magnetised and served to draw off any iron ore present. The second pair were strongly magnetised and attracted the wolframite, which is weakly magnetic. These machines were capable of treating 10 tons of ore a day.

magnetic separator - overbelt overband MAGNETIC SEPARATOR - PURPOSEMagnetic Separator Overbelt Overband delivers precise and efficient sorting of  ferrous metals from inert materials (glass, coal, plastic, paper, wood, garbage, fertilizers, etc.) and non-ferrous metals (aluminium, stainless steel, copper, brass). The Magnetic Separator Overbelt Overband is widely used by various waste recyclers for valuable material extraction and in such industries as plastics, glass, wood, paper, food, foundry, etc. to improve product purity and protect processing equipment from damage.  Due to our extensive experience we will determine with you an optimal solution to your specific need. We realize that we all win when we work together.

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HOW THE MAGNETIC SEPARATOR WORKSMagnetic Separator Overbelt Overband is placed crosswise or lengthwise above the conveyor tape at a fixed working distance. From flowing material iron objects are „captured“ by the magnetic power and with the overbelt magnets carried away. When the iron objects leave the area of the magnetic field they automatically drop into appropriate canals or containers.  Our engineering solutions offer you remarkable efficiency in iron extraction. This unprecedented level of sorting purity and efficiency is made possible thanks to high powerful, far-reaching magnetic fields and machines development for your specific needs.

 Cogelme produces different permanent Magnetic Separator and Electro Magnetic Separator types. The most suitable type to your situation depends on installation height, your material dimensions and the materials layer thickness.

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OVERBELT MAGNETIC SEPARATOR  MODELSMagnetic Separator with Permanent Magnets:

with Ferrite magnets - mod. SMF - are the most used for optimal extraction of middle size ferrous metals; with Neodymium magnets - mod. SMN - for optimal extraction of little ferrous metals parts: iron dusts,

little pieces of wired glass, iron powder and etc. An advantage of a permanent overbelt magnetic separator is free magnet maintenance and no need of electrical current for generation of the magnetic field.The magnetic separator suggestion for the best processing separation in your situation mainly depends from: kind of material, dimension of material and material thickness on the conveyor belt.

  The magnetic separator saves your costs, gives a high degree of operational security and ideally suites for application on mobile installations.Cogelme uses strong permanent magnets to generate their magnetic fields. The special engineering principles of a Cogelme permanent overbelt magnetic separator make it possible to adapt the magnetic field to the specific customers situations and precisely extract ferrous metals.

 

Overbelt Electro Magnetic Separator  mod. SEMFor perfect extraction of heavy ferrous metal pieces or ferrous metal extraction from high thickness materials (till 500/600 mm.).Our Electro Magnetic Separator demonstrates especially big magnetic power. Due to its high magnetic strength is extremely effective in big metal scraps extraction. These machines are built using 1st quality and stroger components that guarantee to all clients to work also in very difficult situations. Cogelme engineering achievements assure perfect sorting characteristics in different customers situations.

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CUSTOMER'S ADVANTAGES USING AMAGNETIC SEPARATOR COGELME

A big power on all the width of the separator created by extra long magnet body , that ensure an especially  good and clean iron ejection.

Special internal security system for keeping the magnets ensure safety for customers and machines. Machines are reliable and serves very long because of their resistant and strong structures, high quality

components. Also a possibility to change the shafts of the rolls extends the live of the machine and minimizes the costs. Clients find machines maintenance simple and quick, as big importance to this is paid engineering the

machines (for example it is possible to change the tape without disassembling the machine). Minimal running costs. Can be used independently or as part of a total system.

Very cost effective and high quality machines. We understand each customer’s unique needs and design a separator accordingly.

CUSTOMER'S RESULTSExtracted pure iron scrap, increased profitability and excellent integrated machine for a comfortable long-term use.

 

Magnetic separation<script src="http://adserver.adtechus.com/addyn/3.0/5308.1/1371312/0/170/ADTECH;target=_blank;grp=585;kvqsegs=D;kvtopicid=383742;kvchannel=SCIENCE;misc=1286789689879"></script>

Magnetic separation is based on the differing degrees of attraction exerted on various minerals by magnetic fields. Success requires that the feed particles fall within a special size spectrum (0.1 to 1 millimetre). With good results, strongly magnetic minerals such as magnetite, franklinite, and pyrrhotite can be removed from gangue minerals by low-intensity magnetic separators. High-intensity devices can separate oxide iron ores such as limonite and siderite as well as iron-bearing manganese, titanium, and tungsten ores and iron-bearing silicates.

Fundamentals of Centrifugal Separation Technology

Centrifugal force

Centrifugal separating technology utilizes fundamental physical laws and centrifugal force.

 

Centrifugal force is produced through rotation around an axis. The force generated through the rotation acts in an outward direction. Depending on the speed of the rotating body, it increases or drops on the circular path.  

 

Mechanical separation technology makes use of this property when light, heavy or substances of different density have to be separated from each other.

Centrifugal force

Centrifugal force

Centrifugal force 3

Centrifugal forces in a vessel

The centrifugal forces act on all particles. The particles with the specifically higher weight are spun outwards fastest and most effectively. They then deposit on the edge of the vessel.

 

Separation by means of centrifugal force is, however, faster when the vessel has an insert. Thanks to the insert, the specifically heavier particles deposit faster. The settling path is shortened by the insert. By this means, a higher throughput capacity is attained.

 

This means: larger volumes of liquid mixtures can be clarified or separated in the same period of time. The more inerts there are, the shorter the settling paths and the higher the throughput capacities.

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Electrostatic Separation

ELECTROSTATIC SEPARATION is defined as "the selective sorting of solid species by means of utilizing forces acting on charged or polarized bodies in an electric field. Separation is effected by adjusting the electric and coacting forces, such as gravity or centrifugal force, and the different trajectories at some predetermined time. Separations made in air are called Electrostatic Separation. Separations made using a corona discharge device, are called High Tension Separations. Separations made in liquids are termed separation by Dielectrophesis, and if motion is due to polarization

effects in nonuniform electric fields. Electrophoresis is when separations are made if motion is due to a free charge on the species in an electric field. There are no industrial applications of mineral concentrations by electrophoresis of dielectrophesis." 1

Electrostatic separation is important in the production of minerals, also in the reclamation of other valuable materials, as well as the cleaning of some food products. When every effort is being made by Process Engineers to make use of all concentrating equipment available for the recovery of critical minerals and reclaimed materials, the subject of applied

electrostatic separation is of interest. Refer to Fig.2, for a diagram of how standard electrostatic separators function.

Fig. 2, Typical Electrostatic Separator Diagram

A very simple demonstration of electrostatic separation can be made by taking a handful of salted peanuts, rubbing the skins off, then taking a comb, rubbing it on fur or the coat sleeve until a static charge has been collected on the comb, and passing it over the peanuts and skins. The skins are easily removed from the peanuts. Hulls may be removed from ground coffee in the same manner. Under the influence of an electrostatic charge there is a difference in the susceptibility and behavior of most materials, minerals, salts, and food products. This can be controlled to a great extent by potential, polarity, temperature, and conditioning of the surface of the particles. Oftentimes, by a combination of these factors, the desired separation is closely controlled.

References:1. J.E. Lawyer, Electrostatic and Magnetic Separation

2. H. Johnson, Applied Electrostatic Separation

To More on Electrostatic ProcessingReturn To Process Plant Menu

Separation by froth flotation relies on the differing surface potentials of the particles. Hydrophobic particles are recovered to the froth, whereas hydrophilic particles are discharged with the tailings stream. Some mineral particles are naturally hydrophobic, whereas others require specific reagent additions to change their surface potentials. Oxide ores, such as spodumene and tantalite can be treated using oxalic acid based collectors. Sulfide ores can be recovered using xanthate or dithiophosphate type collectors.

Chemicals of flotation

[edit] Collectors

Collectors either chemically bond (chemisorption) on a hydrophobic mineral surface, or adsorb onto the surface in the case of, for example, coal flotation through physisorption. Collectors increase the natural hydrophobicity of the surface, increasing the separability of the hydrophobic and hydrophilic particles.

Xanthates

Potassium Amyl Xanthate (PAX) Potassium Isobutyl Xanthate (PIBX) Potassium Ethyl Xanthate (KEX) Sodium Isobutyl Xanthate (SIBX) Sodium Isopropyl Xanthate (SIPX) Sodium Ethyl Xanthate (SEX)

Dithiophosphates

Thiocarbamates Xanthogen Formates Thionocarbamates Thiocarbanilide

[edit] Frothers

Pine oil Alcohols (MIBC) Polyglycols Polyoxyparafins | Cresylic Acid (Xylenol)

[edit] Modifiers

pH modifiers such as:

Lime CaO Soda ash Na2CO3

Caustic soda NaOH Acid H2SO4, HCl

Cationic modifiers:

Ba2+, Ca2+, Cu+, Pb2+, Zn2+, Ag+

Anionic modifiers:

SiO32-, PO4

3-, CN-, CO32-, S2-

Organic modifers:

Dextrin , starch, glue, CMC

Diagram of froth flotation cell. Numbered triangles show direction of stream flow. A mixture of ore and water called pulp [1] enters the cell from a conditioner, and flows to the bottom of the cell. Air [2] or nitrogen is passed down a vertical impeller where shearing forces break the air stream into small bubbles. The mineral concentrate froth is collected from the top of the cell [3], while the pulp [4] flows to another ce

Mechanics of flotation

The following steps are followed, following grinding to liberate the mineral particles:

1. Reagent conditioning to achieve hydrophobic surface charges on the desired particles2. Collection and upward transport by bubbles in an intimate contact with air or nitrogen3. Formation of a stable froth on the surface of the flotation cell4. Separation of the mineral laden froth from the bath (flotation cell)

Simple flotation circuit for mineral concentration. Numbered triangles show direction of stream flow, Various flotation reagents are added to a mixture of ore and water (called pulp) in a conditioning tank. The flow rate and tank size are designed to give the minerals enough time to be activated. The conditioner pulp [1] is fed to a bank of rougher cells which remove most of the desired minerals as a concentrate. The rougher pulp [2] passes to a bank of scavenger cells where additional reagents may be added. The scavenger cell froth [3] is usually returned to the rougher cells for additional treatment, but in some cases may be sent to special cleaner cells. The scavenger pulp is usually barren enough to be discarded as tails. More complex flotation circuits

have several sets of cleaner and re-cleaner cells, and intermediate re-grinding of pulp or concentrate.

Flotation equipment

Diagram of froth flotation cell. Numbered triangles show direction of stream flow. A mixture of ore and water called pulp [1] enters the cell from a conditioner, and flows to the bottom of the cell. Air [2] or nitrogen is passed down a vertical impeller where shearing forces break the air stream into small bubbles. The mineral concentrate froth is collected from the top of the cell [3], while the pulp [4] flows to another cell.

Flotation can be performed in rectangular or cylindrical mechanically agitated cells or tanks, flotation columns, Jameson cells or deinking flotation machines.

Mechanical cells use a large mixer and diffuser mechanism at the bottom of the mixing tank to introduce air and provide mixing action. Flotation columns use air spargers to introduce air at the bottom of a tall column while introducing slurry above. The countercurrent motion of the slurry flowing down and the air flowing up provides mixing action. Mechanical cells generally have a higher throughput rate, but produce material that is of lower quality, while flotation columns generally have a low throughput rate but produce higher quality material.

The Jameson cell uses neither impellers nor spargers, instead combining the slurry with air in a downcomer where high shear creates the turbulent conditions required for bubble particle contacting.

Science of flotation

To be effective on a given ore slurry, the surfactants are chosen based upon their selective wetting of the types of particles to be separated. A good surfactant candidate will completely wet one of the types of particles, while partially wetting the other type, which allows bubbles to attach to them and lift them into a froth. The wetting activity of a surfactant on a particle can be quantified by measuring the contact angles that the liquid/bubble interface makes with it. For complete wetting the contact angle is zero.

Another consideration, especially important for heavy particles, is to balance the weight of the particle with the surfactant adhesion and buoyant forces of the bubbles that would lift it.

For typical values of metal densities and surface tensions, if the bubbles are larger than the ore particles, and the particles are equal to or less than 1 mm radius, then particles will rise into the froth layer if:[5]

where is the radius of the particles, is the average surface tension between the three pairs of phases (particle, flotation solution, air), is the mass density of the particles, and is the acceleration of gravity (9.81 m/s2).

For particles larger than the bubbles, they too can rise into the froth, each buoyed by a swarm of bubbles, under similar conditions as those expressed in the inequality.

Principle of operation

Froth flotation commences by comminution (that is, crushing and grinding), which is used to increase the surface area of the ore for subsequent processing and break the rocks into the desired mineral and gangue in a process known as liberation, which then has to be separated from the desired mineral. The ore is ground into a fine powder and mixed with water to form a slurry. The desired mineral is rendered hydrophobic by the addition of a surfactant or collector chemical. The particular chemical depends on which mineral is being refined. As an example, pine oil is used to extract copper (see copper extraction). This slurry (more properly called the pulp) of hydrophobic mineral-bearing ore and hydrophilic gangue is then introduced to a water bath which is aerated, creating bubbles. The hydrophobic grains of mineral-bearing ore escape the water by attaching to the air bubbles, which rise to the surface, forming a foam or a scum (more properly called a froth). The froth is removed and the concentrated mineral is further refined.

Mining

Froth flotation to separate plastics, Argonne National Laboratory

Froth flotation cells to concentrate copper and nickel sulfide minerals, Falconbridge, Ontario.

Froth flotation is a process for separating minerals from gangue by taking advantage of differences in their hydrophobicity. Hydrophobicity differences between valuable minerals and waste gangue are increased through the use of surfactants and wetting agents. The selective separation of the minerals makes processing complex (that is, mixed) ores economically feasible. The flotation process is used for the separation of a large range of sulfides, carbonates and oxides prior to further refinement. Phosphates and coal are also processed upgraded by flotation technology.

[edit] Waste water treatment

The flotation process is also widely used in industrial waste water treatment plants, where it removes fats, oil, grease and suspended solids from waste water. These units are called Dissolved air flotation (DAF) units.[3] In particular, dissolved air flotation units are used in removing oil from the wastewater effluents of oil refineries, petrochemical and chemical plants, natural gas processing plants and similar industrial facilities.

Froth flotation is a process for selectively separating hydrophobic materials from hydrophilic. This is used in several processing industries. Historically this was first used in the mining industry.

Diagram of a cylindrical froth flotation cell with camera and light used in image analysis of the froth surface.

Flocculation is, in the field of chemistry, a process where colloids come out of suspension in the form of floc or flakes. The action differs from precipitation in that, prior to flocculation, colloids are merely suspended in a liquid and not actually dissolved in a solution. In the flocculated system there is no formation of a cake since all the flocs are in the suspension.

According to the IUPAC definition, flocculation is "a process of contact and adhesion whereby the particles of a dispersion form larger-size clusters." Flocculation is synonymous with agglomeration, aggregation, and coagulation / coalescence

Surface chemistry

In colloid chemistry, flocculation refers to the process by which fine particulates are caused to clump together into floc. The floc may then float to the top of the liquid, settle to the bottom of the liquid, or can be readily filtered from the liquid

Physical chemistry

For emulsions, flocculation describes clustering of individual dispersed droplets together, whereby the individual droplets do not lose their identity.[3] Flocculation is thus the initial step

leading to further aging of the emulsion (droplet coalescence and the ultimate separation of the phases).

Civil engineering/earth sciences

In civil engineering, and in the earth sciences, flocculation is a condition in which clays, polymers or other small charged particles become attached and form a fragile structure, a floc. In dispersed clay slurries, flocculation occurs after mechanical agitation ceases and the dispersed clay platelets spontaneously form flocs because of attractions between negative face charges and positive edge charges.

Biology

In biology, the process is used to refer to the asexual aggregation of microorganisms.

Flocculants

Particles finer than 0.1 µm (10-7m) in water remain continuously in motion due to electrostatic charge (often negative) which causes them to repel each other. Once their electrostatic charge is neutralized by the use of coagulant chemical, the finer particles start to collide and agglomerate (combine together) under the influence of Van der Waals's forces. These larger and heavier particles are called flocs.

Flocculants, or flocculating agents (also known as flocking agents), are chemicals that promote flocculation by causing colloids and other suspended particles in liquids to aggregate, forming a floc. Flocculants are used in water treatment processes to improve the sedimentation or filterability of small particles. For example, a flocculant may be used in swimming pool or drinking water filtration to aid removal of microscopic particles which would otherwise cause the water to be turbid (cloudy) and which would be difficult or impossible to remove by filtration alone.

Many flocculants are multivalent cations such as aluminium, iron, calcium or magnesium.[6] These positively charged molecules interact with negatively charged particles and molecules to reduce the barriers to aggregation. In addition, many of these chemicals, under appropriate pH and other conditions such as temperature and salinity, react with water to form insoluble hydroxides which, upon precipitating, link together to form long chains or meshes, physically trapping small particles into the larger floc.

Long-chain polymer flocculants, such as modified polyacrylamides, are manufactured and sold by the flocculant producing business. These can be supplied in dry or liquid form for use in the flocculation process. The most common liquid polyacrylamide is supplied as an emulsion with 10-40% actives and the rest is a carrier fluid, surfactants and latex. Emulsion polymers require activation to invert the emulsion and allow the electrolyte groups to be exposed.

The following chemicals are used as flocculants:[citation needed]

alum aluminium chlorohydrate aluminium sulfate calcium oxide calcium hydroxide iron(II) sulfate iron(III) chloride polyacrylamide polyDADMAC sodium aluminate sodium silicate

The following natural products are used as flocculants:[7]

Chitosan Isinglass Moringa oleifera seeds (Horseradish Tree) Gelatin Strychnos potatorum seeds (Nirmali nut tree) Guar gum Alginates (brown seaweed extracts)

Deflocculation

A deflocculant is a chemical that is added to prevent a colloid from coming out of suspension. (In this case deflocculation is a desired effect).

Deflocculation is also used to describe the undesired effect in an activated sludge basin if the sludge is subjected to high-speed mixing. Generally, deflocculation can be prevented or reduced by applying gentle mixing(e.g., by using submersible propeller mixers that utilize large/wide propeller blades and operate at low rotational speed).

Water treatment

Flocculation and sedimentation are widely employed in the purification of drinking water as well as sewage treatment, stormwater treatment and treatment of other industrial wastewater streams.

What is Flocculation?

Flocculation is the process whereby smaller particles (inorganic and organic), water-stable soil aggregates, or flocs aggregate to form larger particles (flocs) in a flowing medium. The formation of flocs is a complicated process that is driven by a combination of mechanisms, physical (e.g., turbulence), chemical (e.g., ionic concentration), and biological (bacterial populations and extracellular polymeric material).

The flocculation process is significant for sediment and contaminant transport, because it alters the hydrodynamic characteristics of suspended sediment: the effective particle sizes, shapes, porosity, density, water content, and compositional matrices of flocs differ significantly from those of the traditionally assumed primary particles. Flocculation also alters the chemical and biological behavior of sediment in terms of how it interacts with contaminants and the biological community and how it alters or degrades the contaminants or nutrients assimilated within or around the floc.

AquaKLEAR with Hydropath internationally patented technology creates a continuous flocculation effect by charging suspended particles, which encourages the creation of floc.  The floc is allows for these larger particles to be filtered more easily, and filter backwashing is accomplished in a significantly reduced amount of time.  The floc stays closer to the surface of the filter medium, instead of deeply imbedding within it, thus reducing the amount of time to conduct a backwash, and the frequency intervals are extended significantly.

Biomass Charcoal Briquetting

The agricultural residues are produced abundantly after harvest of each crop in our villages. Most of these residues are burnt in the open field. However using Biomass Charcoal Briquetting technologies, these residues, can be used for generating an alternative fuel which is cost effective and environmentally friendly. It can also add income to the family.

What is briquetting

Briquetting is the process of converting low bulk density biomass into high density and energy concentrated fuel briquettes

Methodology

There are two different methods of charcoal making.1. Direct method The direct method is to heat and form an incomplete combustion of the organic matter that results in the formation of charcoal.2. Indirect method In the indirect method an external heat source is used to "burn" organic matter kept in a closed but vented airless chamber. The indirect method results in production of high quality charcoal with less smoke and pollutants

MCRC’s method of charcoal briquetting

Requirements

1. Locally available biomass (eg casuarina leaf litter, sugarcane trash, rice husk, coir pith, groundnut shells, etc)2. Carbonizing chamber (furnace )3. Binder (starch or cassava flour)4. Mini Briquetting machine (10kg/hr)

Stepwise process of charcoal making

1.Collection of biomass

Collect the locally available biomass, sort them, chop the large-size raw materials into smaller pieces and dry at sunlight.

2. Carbonizationi. Designing the Furnace• Outer drum : A 200lits. metal oil drum with the top cut out and a 12" width x 10" height hole cut in the lower side• Two iron rids (8”) has to be fixed at the bottom of the metal drum running parallel from one side to the other side. This iron rods act as base to support the stainless steel inner drum.• Inner drum : A 100lits stainless steel drum with proper lids and six (3/8") holes at the bottom.• The inner drum is placed into the larger drum.

ii. Carbonizing the biomass• The biomass is tightly packed into the inner drum and fired for 45minutes to 1hr (Depending upon the biomass) using biomass.• After firing, the carbonized biomass in the inner drum has to collected and weighed. In this method 30 % of carbonized char can be obtained.

3. Preparation of binderThe binder material is used for strengthening the briquettes For every 100 kg of total weight of carbonized charcoal powder, prepare a binder mixture by adding 5 to 6 kg of starch or cassava flour to 60 - 100 litres of water (based on the weight of the raw materials)

4. MixingMix such that every particle of carbonised charcoal material is coated with binder. It will enhance charcoal adhesion and produce identical briquettes.

5. Briquetting. The charcoal mixture is made into briquettes either manually or using machines. Pour the mixture directly into the briquetting mould / machine to form uniform-sized briquettes.

6. Drying and PackagingCollect the briquettes in a tray, dry them under the sunlight, pack them in plastic bags and seal

General Characteristics of briquettesMoisture : 7.1%-7.8%Volatile Matter : 13.0%-13.5%Fixed Carbon : 81.0%-83.0%Ash : 3.7%-7.7%Sulfur : 0.0%Heating Value : 7,100-7,300 kcal/kgDensity : 970kg/m3

Advantages of the technology

1. Smokeless: The charcoal briquettes burn without any smoke during ignition and burning.2. Low Ash content: Minimum residual ash is formed (less than 5% of the original weight of the charcoal).3. Higher Fixed Carbon & calorific value: Normally the concentration of fixed carbon will be about 82%. The calorific value of charcoal briquettes is 7500 Kcal/KG.4. Odourless: The biomass charcoal briquette contains minimum evaporative substances, thus eliminating the possibility of odour. 5. Longer burning hours: Two times longer burning hours compared to hardwood charcoal.6. Sparkless: These charcoal briquettes will not produce sparks as compared to hardwood charcoal.7. Less crack & better strength: Less crack & better strength make the charcoal burn for a long time.

Optimization of the Pelletization Process in a Fluid-Bed Rotor Granulator Using Experimental DesignEvdokia S. Korakianiti,1  Dimitrios M. Rekkas,1  Paraskevas P. Dallas,1  and Nikolaos H. Choulis1 

1Division of Pharmaceutical Technology, School of Pharmacy, University of Athens, Panepistimiopolis, Zografou, Athens 157 71, Greece

Correspondence to:Dimitrios M. RekkasTel: (301) 727-4023Fax: (301) 727-4027Email: rekkas@pharm.uoa.gr

Submitted: July 28, 2000; Accepted: November 28, 2000; Published:

Keywords:  Pellets, Fluid-bed rotor granulator, Optimization, Factorial design

Abstract

This study examined the effect of rotor speed, amount of water sprayed, and atomizing air pressure on the geometric mean diameter and geometric standard deviation of pellets produced in a fluid-bed rotor granulator using a 23 factorial design and an optimization technique.

Pellets were prepared by wet granulation. Equal amounts of microcrystalline cellulose, α-lactose monohydrate, and distilled water were used as the granulation liquid. The size and the size distribution of the pellets were determined by sieve analysis.

The size of the pellets was found to be dependent on the amount of water added, while an increase in rotor speed decreased their size. Both factors were found to be statistically significant (P < .05). The effect of atomizing air pressure on pellet size was not statistically significant. None of the 3 factors significantly affected the geometric standard deviation of the pellets.

The rotor speed and the amount of water sprayed were further selected in order to construct a mathematical model that correlates these factors with the geometric mean diameter of the pellets. For this purpose, the optimization technique 32 was used. The derived equation described the relationship between the selected factors and the size of the pellets. As a result, the experimental design techniques applied were found to be suitable in optimizing the pelletization process carried out in a fluid-bed rotor granulator.

Introduction

Pellets as drug delivery systems offer not only technological advantages, such as better flow properties, less friable dosage form, narrow particle size distribution, ease of coating, and uniform packing, but also therapeutic advantages. Therapeutic advantages include less irritation of the gastrointestinal tract, a lowered risk of side effects associated with dose dumping, and a uniform distribution in the gastrointestinal tract resulting in a reduction of peak plasma fluctuations. The reduction of the variation in gastric emptying rates and the overall transit times is also a major advantage.1

Pellets can be produced in many different ways2; extrusion-spheronization, a 3-step process that has been studied extensively, is used most often. Alternative techniques for producing pellets are the single pot methods, where pellets are produced, dried, and coated in the same equipment. They are 1-step processes that take place in one machine, such as a high-sheer mixer or a rotary processor. Using one machine for the whole process ensure batch- to-batch reproducibility and reduction of production time and cost, and enables automation of the process.3

In this study, pellets were produced using a fluid-bed rotor granulator.4 The following techniques can be applied using this equipment: solution/suspension layering, spray congealing, spray drying of a solution or a suspension, and wet granulation, where the binder liquid is sprayed onto the powder mass so that the particles are granulated and spheronized at the same time. The wet granulation method was employed in this study.

Pelletization by means of wet granulation in a fluid-bed rotary processor is a multivariable process in which several factors affect the final characteristics of the pellets produced. Therefore, the application of experimental design techniques, such as factorial design and optimization, could be useful tools for the identification and correlation of significant factors that affect the process. They provide valid information while using only a limited number of structured experiments.

The objective of this study was to determine the effect of rotor speed, amount of water sprayed, and atomizing air pressure on the size (geometric mean diameter) and size distribution

(geometric standard deviation) of the pellets prepared by the above-mentioned wet granulation method, using a 23 factorial design and an optimization technique.

Materials and Methods

Materials

Avicel CL-611 was supplied by FMC Corporation, Princeton, NJ. Hydrocortisone acetate was purchased from Sigma Chemical Co., St. Louis, MI. Propylene glycol, methylparaben, propylparaben, cetyl alcohol, and glyceryl monostearate were all purchased from Spectrum Quality Products, New Brunswick, NJ. All solvents used in High Pressure Liquid Chromatography [HPLC] analysis were HPLC grade unless otherwise noted and were used as received. The commercial (oil/water) cream used in this study was Lanocort 10 containing 1% hydrocortisone acetate. Other ingredients in the formulation included aloe, ceteareth-20, cetearyl alcohol, cetyl alcohol, methylparaben, propylparaben, sorbitol, water, and zinc pyrithione.

Methods

Starting materials were a-lactose monohydrate (Pharmatose® 150 M, DMV, Veghel, The Netherlands, lot 23813) and microcrystalline cellulose (Avicel® PH 101, FMC, lot 6814C, Brussels, Belgium). All materials were of Ph. Eur. grade. Deionized water was used as the granulation liquid.

Preparation of pellets

The pellets were prepared in a fluid-bed rotor granulator (Glatt GPCG3, Glatt GmbH, Binzen, Germany) using the wet granulation technique. Equal amounts of microcrystalline cellulose and lactose were adequately mixed. One kg of the powder mixture was loaded into the product chamber of the machine. After a fluidization time of 3 minutes, a preweighed amount of water (Table 1) was sprayed through an atomizing nozzle (1.2 mm diameter) into the powder at a rate of 30 mL per minute with the aid of a peristaltic pump (Siemens, RexV/110, model 501R, Germany). The inlet air temperature was kept constant at 27 ± 1°C and the process airflow at 0.3-0.5 bar. Once all the water was sprayed, the pellets were dried for 15 minutes at 40°C.

Evaluation of pellets

The size of the pellets was determined by sieve analysis (Endecotts, Octagon Digital CE, London, UK). Based on these results, the geometric mean diameter on a weight basis (dg) and the geometric SD (σg) were computed using a log-probability plot. As dg was regarded the particle size equivalent to 50% of the probability scale, and as σg the quotient of the ratio 16% oversize/50% size.5

Experimental design and analysis

Factorial design6,7 is an experimental technique by which factors involved in a process can be identified and their relative importance assessed. It is thus a means of separating those factors that are important from those that are not and identifying the interactions, if any, between the factors chosen. Thus the construction of a factorial design involves the selection of parameters and the choice of responses.

A 23 factorial design was used to determine the effect of the rotor speed, the amount of water sprayed, and the atomizing air pressure on the geometric mean diameter and geometric SD of the pellets. The factors and the levels studied are shown in Table 1. The matrix of the factorial design is shown in Table 2.

*Factor A indicates rotor speed (rpm); Factor B, amount of water (mL); Factor C, atomizing air pressure (bar); -, low level; +, high level.

The different formulations consisted of all possible combinations of all factors at all levels and were conducted in a fully randomized order. The results for the geometric mean diameter and the geometric SD were evaluated by analysis of variance (ANOVA) using a commercial software package (Statgraphics Plus 4®, Manugistics, Inc, Rockville, MD).

Results

The results for the geometric mean diameter and the geometric SD of the pellets produced are listed in Table 2. Based on these data, the main effects of the factors under study and their interactions were calculated and statistically evaluated by ANOVA (Table 3).

*A indicates rotor speed (rpm); B, amount of water (mL); C, atomizing air pressure (bar).

**Statistically significant (P < .05)

Table 3 shows that an increase in the amount of water sprayed results in an increase in pellet diameter. The ANOVA results (Table 3) confirm that the effect is statistically significant (P < .05). As expected,8 the size of the pellets is highly dependent on the amount of water added. Many studies have shown the importance of the amount of the moistening liquid in controlling the size of the pellets produced.9-14 An increase in the amount of moistening liquid increases the wet surface available for agglomeration between the particles. According to Heng et al,10 the amount of moistening liquid should reach a minimum level so that pellets of a suitable size can be obtained. On the other hand, if too much moistening liquid is added, the pellets produced will show a skewed size distribution. Vertommen et al9 observed that wet massing of cohesive powders like microcrystalline cellulose, which consolidate during the process, is highly sensitive to the added amount of binding solution.

Table 3 also shows that pellet size is significantly affected (P < .05) by the speed of the rotor plate. Although this finding is in agreement with previous reports,8,15,16 not all the reports agree on whether the relationship between the 2 factors is proportional. More specifically, Hasznos et

al16 and Vertommen et al9 found that pellet size increased with an increase in spheronizer speed, while Helen et al15 reported the opposite. In the present study an increase in rotor speed was found to decrease the size of the pellets produced. Strong centrifugal forces may cause size reduction of the already formed pellets due to attrition or breakage. A possible explanation for the contradictory results regarding the effect of the rotor speed on pellet size could be that each study used a different method and/or equipment for the production of the pellets.

The effect of atomizing air pressure on pellet size was not statistically significant (P < .05), as seen in Table 3. In fluidized bed granulation, particle growth follows a nucleative process. Powder particles, when wetted, form nuclei that are held together by liquid bonds. The formation of these nuclei is influenced by the size of the droplets sprayed. Larger droplets form larger nuclei because they are able to bind more particles. The size of the droplets sprayed can be changed by varying the atomizing air pressure. According to Merkku and Yliruusi,12 an increase of the atomizing air pressure decreases the size of the droplets and consequently the size of the granules produced. However, these findings do not seem to apply in fluid bed pelletization. Wan et al17 investigated the effect of atomizing air pressure on spheroid size and found that the size of the droplets sprayed does not seem to have a significant effect on spheroid size. This could be because the centrifugal forces that act in a rotary processor are stronger than those in a fluid-bed granulator, and thus their effect on pellet size is predominant and masks the effect of the size of the droplet.

As shown in Table 3, all the interactions between the selected factors were found to be statistically significant (P < .05). This means, for example, that the magnitude of the effect of the rotor speed on geometric mean diameter of the pellets is strongly affected by the amount of water sprayed (AB interaction) or the atomizing air pressure (AC interaction). As can be seen in Figure 1, a change in rotor speed influences the mean geometric diameter of the pellets to a greater extent when the amount of water sprayed is set at high level compared with its effect at a low level.

The geometric SD was used to evaluate the size distribution of the pellets; the results are depicted in Table 3. It can be seen that an increase of the rotor speed results in pellets of a narrower size distribution, but this effect was not found to be statistically significant. Helen et al15 and Holm et al8 reported that an increase of the spheronization speed decreases the size distribution of the pellets. Table 3 also shows that when the amount of water sprayed is increased, the size distribution of the pellets is also increased, while an increase of the atomizing air pressure decreases the size distribution. Neither effect was found to be statistically significant (P < .05).

Because the geometric SD of the pellets was not statistically significantly affected by the selected factors, the study further focused only on pellet size. Therefore, the factors that were found to significantly affect pellet size (ie, the rotor speed and the amount of water sprayed) were further selected in order to construct a mathematical model that correlates these factors with the geometric mean diameter of the pellets. The optimization technique 32 was used for this purpose.6 The factors and their levels are shown in Table 4.

The atomizing pressure was kept constant at 3 bar. The results were further analyzed with multiple regression analysis using a commercially available package (Statgraphics Plus 2.11®, Manugistics, Inc). The polynomial equation obtained correlates the rotor speed (X1) and the amount of water (X2) with the geometric mean diameter (Y).

Y= 2.8375 + 0.0006 X12 - 0.0016 X22 - 4.5616 X1 +2.6347 X2 + 0.0027 X1 X2

R2 = 0.998, SE=22.681, P < .05

(1)

The surface plot for Equation 1 is shown in Figure 1. To assess the reliability of Equation 1, 2 additional experiments were conducted by varying the 2 independent variables (rotor speed, X1, and amount of water, X2) and estimating the dependent variable (geometric mean diameter, Y). The levels of the factors and the estimated and experimental values are shown in Table 5. It can be concluded that there is a good agreement between the estimated and the observed values.

Conclusion

Rotor speed and amount of water were found to significantly affect the geometric mean diameter of the pellets. Interactions between these factors were also found to be statistically significant. These findings suggest that those factors should be considered during pelletization, as far as their geometric mean diameter is concerned. However, the factors did not significantly affect the geometric SD of the pellets

Furthermore, the correlation of rotor speed, amount of water sprayed, and geometric mean diameter can be adequately described by Equation 1.

Finally, experimental design techniques such as factorial design and optimization proved to be useful for the identification and correlation of the significant factors that affect pellet size.

Acknowledgements

This work was supported by grant YPER97 from the Greek Secretariat of Research and Technology and has been presented at the 4th Arbeitsgemeinschaft fur Pharmazeutische Verfahrenstechnik e.V/Association de Pharmacie Galenique Industrielle (APV/APGI) World Meeting (Berlin, 2000).

Granulation is the act or process of forming or crystallizing into grains. [1] Granules typically have a size range between 0.2 to 4.0 mm depending on their subsequent use.

Synonym "Agglomeration": Agglomeration processes or in a more general term particle size enlargement technologies are great tools to modify product properties. Agglomeration of

powders is widely used to improve physical properties like: wettability, flowability, bulk density and product appearance.

Chemical industry

Granulation

In the chemical industry, granulation refers to the act or process in which large objects are cut or shredded and remelted into granules or pellets.

Why Granulation

Granulation is carried out for various reasons, one of those is to prevent the segregation of the constituents of powder mix. Segregation is due to differences in the size or density of the component of the mix. Normally, the smaller and/or denser particles tend to concentrate at the base of the container with the larger and/or less dense ones on the top. An ideal granulation will contain all the constituents of the mix in the correct proportion in each granule and segregation of granules will not occur.

Many powders, because of their small size, irregular shape or surface characteristics, are cohesive and do not flow well. Granules produced from such a cohesive system will be larger and more isodiametric, both factors contributing to improved flow properties.

Some powders are difficult to compact even if a readily compactable adhesive is included in the mix, but granules of the same powders are often more easily compacted. This is associated with the distribution of the adhesive within the granule and is a function of the method employed to produce the granule.

For example, if one were to make tablets from granulated sugar versus powdered sugar, powdered sugar would be difficult to compress into a tablet and granulated sugar would be easy to compress. Powdered sugar’s small particles have poor flow and compression characteristics. These small particles would have to be compressed very slowly for a long period of time to make a worthwhile tablet. Unless the powdered sugar is granulated, it could not efficiently be made into a tablet that has good tablet characteristics such as uniform content or consistent hardness.

Granulation techniques

In pharmaceutical industry, two types of granulation technologies are employed, namely, Wet Granulation and Dry Granulation.

[edit] Wet Granulation

Wet granulation, the process of adding a liquid solution to powders, is one of the most common ways to granulate. It involves the massing of a mix of dry primary powder particles using a granulating fluid. The fluid contains a solvent which must be volatile so that it can be removed by drying, and be non-toxic. Typical liquids include water, ethanol and isopropanol either alone or in combination. The liquid solution can be either aqueous based or solvent based. Aqueous solutions have the advantage of being safer to deal with than solvents.

Water mixed into the powders can form bonds between powder particles that are strong enough to lock them together. However, once the water dries, the powders may fall apart. Therefore, water may not be strong enough to create and hold a bond. In such instances, a liquid solution that includes a binder (pharmaceutical glue) is required. Povidone, which is a polyvinyl pyrrolidone (PVP), is one of the most commonly used pharmaceutical binders. PVP is dissolved in water or solvent and added to the process. When PVP and a solvent/water are mixed with powders, PVP forms a bond with the powders during the process, and the solvent/water evaporates (dries). Once the solvent/water has been dried and the powders have formed a more densely held mass, then the granulation is milled. This process results in the formation of granules.

The process can be very simple or very complex depending on the characteristics of the powders, the final objective of tablet making, and the equipment that is available. In the traditional wet granulation method the wet mass is forced trough a sieve to produce wet granules which is subsequently dried.

[edit] Dry Granulation

The dry granulation process is used to form granules without using a liquid solution because the product to be granulated may be sensitive to moisture and heat. Forming granules without moisture requires compacting and densifying the powders. In this process the primary powder particles are aggregated under high pressure.

Dry granulation can be conducted under two processes; either a large tablet (slug) is produced in a heavy duty tabletting press or the powder is squeezed between two rollers to produce a sheet of materials (roller compactor, commonly referred to as a chilsonator).

When a tablet press is used for dry granulation, the powders may not possess enough natural flow to feed the product uniformly into the die cavity, resulting in varying degrees of densification. The roller compactor uses an auger-feed system that will consistently deliver powder uniformly between two pressure rollers. The powders are compacted into a ribbon or small pellets between these rollers and milled through a low-shear mill. When the product is

compacted properly, then it can be passed through a mill and final blend before tablet compression.