The Bulk Density Measurement Engineering Essay

2.0 Introduction

This research presents a reappraisal of the literature associating to the flow belongings measurings, Jenike silo design method, cohesive arching and flow channel enlargement for majority atoms flow. The flow belongings measurings can be done utilizing simple examiners as described in subdivision 2.1 below, nevertheless these are non suited for design equipment, silos, hoppers etc. The shear examiners which will be discussed subsequently in subdivision 2.2 are required for silos and hoppers design. The flow maps will be considered and its utility to curving. Summaries of the consequences of different curving experiments and the attack angle measuring in base pipes will be discussed in subdivision 2.4.

2.1 Simple Testing

The followers are the normally used simple trials:

Angle of rest

Density measuring

Flow Funnels

Powder Rheometers

2.1.1 Angle of Repose

When majority atoms are dropped from a designated lift, they form a pile which is normally in the signifier of a incline. The angle between the incline of the pile and the horizontal surface is called the angle of rest. Bulk pulverization flow belongingss are determined by their angle of rest which is frequently used as a hint of a possible flow. This is normally determined by leting bulk pulverization to flux onto a level horizontal surface and so mensurating the angle of incline with regard to the horizontal surface ( Carr, 1965a ) . It was observed that during the experiment, that a larger angle of rest of a majority atom will ensue in a high flow and a smaller angle of rest will ensue in a low flow of the majority pulverization for illustration larger angles such as 50-60 indicates a trouble in flow while a smaller angle such 30-40 represents comparative easy flow of bulk pulverization ( Craik and Miller, 1958 ) . The add-on of wet content to bulk pulverization increases the angle of rest due to moisture being an of import factor impacting pulverization flow.

2.1.2 Bulk denseness measuring

The mass of majority atoms that occupies a unit volume of a container is normally called majority denseness. It is usually affected by the pulverization atom size, wet, chemical composing, managing and processing operation ( Johanson, 1971/1972 ) . When the atom sizes lessenings and the equilibrium relativity humidness additions, bulk pulverization lessenings in majority denseness ( Yan and Barbosa-Canovas, 1997 ) . Bulk denseness is usually used to find the squeezability of majority pulverization through the Hausner ratio which is the ratio between the tapped and loose bulk denseness as described below. The Hausner ratio is used to quantify the squeezability of majority pulverization. It is observed from old experiment that a larger squeezability will ensue in hard majority pulverization flow while a smaller squeezability which is as a consequence of increased atom size indicates an easy flow of majority solid ( Yan and Barbosa-Canovas, 1997 ) . The free flowing and non-free fluxing lodger line is about 20-21 % ( Carr, 1965b ) .

2.1.3 Tapped denseness

The tapped denseness testing is used in bulk pulverization flow to find the sum of colony in pass throughing bulk power to optimise battalion sizes for illustration rinsing pulverizations. Tapped denseness is gotten by raising a mensurating cylinder incorporating pulverization sample under the trial cylinder until it drops to a peculiar distance under its ain weight. The tapped denseness is determined by spliting the sample weight by the tapped volume. Bulk flow and squeezability can be measured utilizing the Hausner ratio and the Carr ratio. It is observed that in a free flowing majority pulverization, there is no demand for an inter-particle interaction and the tapped denseness will be nearing zero while for hard flow majority pulverization, the opposite is the instance. The Hausner ratio is closer to one indicates a better flow while a hausner ratio of 1.35 represent hapless flow ( Guo et al.,1985 ; Malave et Al, 1985 ) . The tapped denseness examiner which is shown in the figure 2.0 below differentiates between cohesive and free flowing stuffs. This is normally done through the computation of the Carr index and the Hausner ratio. The expression below are used for ciphering the Hausner ratio and the Carr index.

HR =

Carr = x 100 % ( Sjollema, 1963 )

Where = Tapped denseness

= poured denseness

Fig2.0 Tapped denseness examiner ( Dr. Rob berry, 2005 )

2.1.4 Other Simple Tester

The flodex shown in figure 2.1 below is normally used for look intoing whether the stuffs are free fluxing or non. The trial is usually done by make fulling the cup with hole with majority atoms and detecting if it discharges. There are a figure of different bases with different diameter holes. The pulverization rheometer in figure 2.2 below is used to mensurate flow energy of majority atoms.

Fig 2.1 Flodex ( Flow funnel ) ( Dr. Rob berry, 2005 )

Fig 2.2 Powder Rheometers ( Dr. Rob berry, 2005 )

2.1.5 Decision

The different qualitative measuring enumerated above may be utile if the experiment retroflex the procedure of involvement. The angle of rest is used to cognize the volume of reserves of different majority pulverizations. The flow funnel is used when the ceramic pulverization or metal pulverization flow freely into a dice in the fabrication of sinter constituents. The simple testing is non the best method of mensurating bulk pulverization flow due to its inaccuracy in its measuring. Shear examiner are now frequently used for the measuring of pulverizations because it gives a item analysis of the atoms used in the machine. The simple testing is still considered because it is inexpensive when compared to the shear examiner.

2.2 Shear Testing

The undermentioned pulverization flow belongingss can be measured by shear testing:

Flow map

Internal Clash

Wall clash

Bulk denseness

2.2.1 Flow map

The construct of the flow map is best illustrated by the ‘sand palace ‘ trial. In the first phase of the trial pulverization is consolidated in a cylindrical cell under a known emphasis i??1. In the 2nd phase the mold is removed to existent a compact of pulverization or ‘sand palace ‘ . An increasing emphasis is now applied to the top surface of the compact until failure occurs as shown in figure 2.3. The emphasis at failure is defined as the unconfined failure strength of the pulverization i??c. If the trial is repeated utilizing a larger value of consolidation emphasis i??1, so one would anticipate to obtain a larger value of unconfined failure strength at failure. The flow map represents a secret plan of the consolidation emphasis i??1 on the horizontal axis versus the unconfined failure strength i??c on the perpendicular axis as shown in figure 2.4. If the pulverization is free fluxing the strength is zero at all emphasiss so the flow map lies on the horizontal axis. As the pulverization additions strength and becomes cohesive the flow map moves up the graph.

Figure 2.3 Sand palace trials ( Dietmar Schulze, 1966 )

Figure 2.4 Flow map and lines of changeless flow ( Dietmar Schulze, 1966 )

The ratio which is the defined as the ratio of the consolidating emphasis to the unconfined failure strength in figure 2.4 above is used to qualify the flow of different majority atoms numerically runing from free fluxing to non fluxing. Flow map of majority atoms can be determine with a shear examiner that has both the consolidating emphasis and the unconfined output strength moving on the same way or about the same way. Both stress provinces are normally realised with the aid of a Jenike examiner which will be discussed subsequently on in the literature reappraisal. The flow map is normally based on the normal chief emphasiss of two Mohr circles which are the consolidation emphasis and the unconfined output strength. ( Dietmar Schulze, 1966 )

2.2.2 Internal Clash

The internal clash angle can be measured by taking a ratio of the force to the applied normal force required to do bulk atoms to travel or skid on each other. The angle obtained from internal clash is used to find stable inclines and hang up in bins ( Johanson, 1921/1972 ) . Internal clash angle are largely influenced by the atom surface clash, form, hardness, size, and size distribution of majority atoms. The information that are realised from internal clash can be used in ciphering sidelong force per unit areas on walls of storage bins and the design of gravitation flow bins and hopper ( Mohsenin, 1986 ; Rao, 1992 ) . The internal clash angles are normally measured through shear testing. ( Peleg and Mannheim, 1973 ; Teunou et al.. , 1999 ; Fitzpatrick et al. , 2004b )

2.2.3 Wall Clash

Wall clash is by and large defined as the frictional opposition to bulk flow that usually exist between atoms and palisade stuff ( Iqbal and Fitzpatrick, 2006 ) . It is usually applied in the design and operations of silos, hoppers and storage discharge chutes. The wall clash can be influenced by factors such as wall surface features, majority solid belongingss and managing status ( Prescott et al.. , 1999 ) . It besides some times can be affected by surface stuff, surface raggedness, surface wear and surface corrosion ( Bradley et al.. , 2000 ) .

2.2.4 Bulk Density

The majority denseness can be defined as the weight of the pulverizations divided by the volume occupied. It is a parametric quantity of the output point which represents the maximal shear emphasis a majority sample can back up under a certain normal emphasis. The majority denseness map is determined from a graph of the normal emphasis against the shear emphasis which generates Mohr circles when performed utilizing a shear examiner ( Peleg and Mannheim, 1973 ; Hollenbach et al. , 1983 ) .

2.3 Shear Examiner

The strength and flow belongingss of most bulk solids are normally measured with the assistance of a shear examiner ( Schwedes, 2002 ) . There are several types of examiner that are normally used for majority atoms strength and flow belongingss measuring:

Jenike shear cell

Walker annulate shear cell

Schulze ( pealing shear examiner ) annulate shear cell

Peschl rotational shear cell

Brookfield Powder flow examiner.

Shear examiner are classified into two groups which are:

Direct Shear examiner and

Indirect Shear examiner

Figure 2.5 below shows a elaborate categorization of the different sort of shear examiner used in pulverization flow. The indirect shear examiner has its chief stress way invariable and fixed during the trial while the direct examiner has its major chief emphasis rotates during the trial. ( J.Schwedes, 1983 ) . Shear examiner can be applied in both:

Dirt mechanics and

Powder engineering.

SHEAR TESTER

INDIRECT

Direct

TRIAXIAL

BIAXIAL

TRANSLATIONAAL

UNIAXIAL

ROTATIONALL

TRIAXIAL TESTER

BIAXIAL TESTER TESTER

CASAGRANDE TESTER

UNIAXIAL TESTER

TORSIONAL SHEAR TESTER

TRUE TRIAXIAL TESTER

TRUE BIAXAIL TESTER

HANG-UP INDICIZER

Ring SHEAR TESTER

JENIKE TESTER

MODIFIED TRIAXIAL TESTER

CAKING Examiner

Ring SHEAR TESTER ( 3 RINGS )

Simple SHEAR APPARATUS

a

DIRECTSHEAR CELL

Cell

MONOAXIAL TESTER

WALL FRICTION TESTER

LAMBDAMETER

Changeless VOLUME SHEAR TESTER

POWDER BED TESTER

WALL FRICTION TESTER

Fig 2.5 Shear examiners ( J.Schwedes, 1983 )

2.3.1 Jenike examiner

Jenike established the cardinal methods for finding the flow features of majority atoms through his shear cell which was later a standard method for analyzing the flow of solids in bins and silos. The shear cell is regarded as the chief portion of the Jenike examiner. It consists of a base, ring and a palpebra as shown in figure 2.6. The pealing usually rest on top of the base. The ring is normally filled with majority atoms which are pre-consolidated in a consistent mode. After the filling of the majority solid, a perpendicular force is applied to the palpebra which consequences in horizontal shearing force on the brackets that is attached to the palpebra. Shear trial are usually performed on the Jenike examiner with majority samples that are indistinguishable and pre-consolidated under different normal burden ( The establishment of chemical applied scientists, 1989 ) .

The Jenike shear trial was based on the rules of fictile failure with Mohr-Colomb failure standards ( Thomson, 1997 ) . It was observed that free fluxing pulverization encountered a opposition to flux which was due to the clash of the majority pulverization while in cohesive majority pulverizations, the inter-particles forces makes the atom to derive strength which are enhanced by compression ( Peleg, 1983 ) . Bulk particles word picture for assortment of pulverizations are normally achieved with a Jenike examiner ( Ashton et al. , 1965 ; Schra mli, 1967 ; York, 1975 ; Kamath et al. , 1993, 1994 ; Duffy and Puri, 1994, 1999 ; Schwedes, 1996 ; and Fitzpatrick et al. , 2004b ) . The Jenike shear examiner can be used to mensurate bulk belongingss such as the angle of internal clash, wall clash and majority denseness ( Schulze, 1996 ; Rock and Schwedes, 2005 ) .

Fig 2.6 Jenike ‘s Shear Cell ( A: base, B: ring ; C: palpebra ) ( Jorg Schwedes, 1999 )

2.3.2 Disadvantages of Jenike Tester

Requires accomplishments and preparation at a really high degree

Requires more clip when compared to other examiner

The maximal strain is little and sometimes non sufficient

No measuring at little normal emphasis.

2.3.3 Schulze ring examiner

The Schulze ring examiners consist of a ring shear cell which the majority solid sample is poured in and an annulate palpebra attached to the cross beam on top of the sample as shown in figure 2.7. The shear cell of the Schulze examiner is usually driven in an counterclockwise way. The shear cell consist of two tie rod connected to the cross beam which prevents the palpebra from revolving. The majority solid sample is sheared due to the comparative supplanting of the shear cell to the palpebra. The shear cell moving on the sample is normally calculated ( D.Schulze, 1998 ) . The Schulze ring examiner consists of two steering rollers in order to forestall the palpebra from horizontal motion. It is observed that the motion of the palpebra is unhampered which is similar to the screen of the Jenike shear examiners. The weight hanger that is connected to the cross beam exerts a normal force ( D.Schulze, 1998 ) .

The testing process of the Schulze ring examiner is the same as the Jenike shear examiner. The majority solid are usually sheared into two stairss which are the pre-shear and the shear. The pre-shear is done under a normal emphasis up to a steady province flow while shear is done under a normal emphasis up to a peak shear emphasis ( D.Schulze, 1994 ) . The Schulze ring examiner has an automated version which can be operated semi-automatically or to the full automatically. The automatic manner of the Schulze ring examiner has its measuring to the full controlled by a P.C which recognises the steady province flow at pre-shear and shear emphasis extremum at shear while the semi-automatic manner has an operator which Judgess whether a steady province flow or peak emphasis has being attained ( H.wilms and J.Schwedes, 1985 ; D.Schulze, 1996 ) .

Fig 2.7 New Ring Shear Tester of Schulze ( Jorg Schwedes, 1999 )

2.3.4 Differences between the Jenike examiner and the Schulze ring examiner

The chief difference between the Jenike shear examiner and the Schulze examiner is that the Jenike shear examiner uses a new sample of solid when undergoing the pre-shearing and shearing procedure while the Schulze ring examiner uses one sample for the measuring of a complete output venue ( D.Schulze, 1998 ) .

2.3.5 Advantages of the Schulze ring examiner

Does non necessitate much runing accomplishment and clip for it to work decently

Consequences in a low variableness of the majority pulverizations that are measured Results in dependable consequences at a really low normal emphasis for cohesive and free fluxing bulk atoms.

It has an un-limited strain which is an advantage over the translational shear examiner. ( Schulze, 1996 ; Schwedes, 2000 ) .

2.3.6 Disadvantages of the Schulze ring examiner

Does n’t mensurate atoms larger than majority pulverizations. Premise are hence made on other belongings measuring values that are required for since the mercantile establishment dimension is determined from a individual unconfined failure measuring

There is trouble in the extremum shear emphasis due to the influence of the ratio of inner to the outer diameter ( D.Schulze, 1998 ) .

2.3.7 Johanson Indicizer

Figure 2.8 below illustrates the rule of the Johanson indicizer. It consists of cylinder specimen which is compressed axially with a Piston holding two homocentric countries. The interior portion of the upper Piston pushes on the sample until there is an happening of failure when the lower Piston is removed. There is a strength which is usually computed from the failure force ( J.R.Johanson, 1992/1993 ) .The cylinder normally has a wall clash which decreases the perpendicular emphasis during consolidation downwards in a manner which depends on the majority solid and wall belongingss. Bell at Al and Marjonovic et Al performed several comparative trials utilizing the Hang-up Indicizer, Jenike shear examiner and Schulze ring examiner, it was stated clearly that the unconfined output strength gained with the Hang up indicizer will be lower when compared with the Jenike shear examiner and Schulze ring examiner ( J.R.Johanson, 1992/1993 ) .

The Johanson Indicizer follows a simplistic attack in its operation. This made it to have a batch of unfavorable judgment in the field of silo design ( J.W.Carson, 1992 ; J.Schwedes and D.Schulze, 1992 ; G.G.Enstad and L.P.Maltby, 1992 ) . Soon, there is a argument on whether the examiner is suited for silo design. The statement resulted from the hang-up indicizer non shearing the majority solid to the critical province to the measuring of the failure strength.

Fig 2.8 Johanson Hang-up Indicizer ( Jorg Schwedes, 1999 )

2.3.8 Peschl rotational shear cell

The perpendicular axis rotary motion induces the shearing procedure of the examiner. It consists of a roughened screen which is equipped with bars to guarantee that the shear procedure occurs within the majority particles. This helps to forestall an happening of the shear procedure go oning between the majority atom and the screen. The base of the examiner normally operates during operations with the shear minute moving on the screen measured ( S.Kamath, V.M.puri, H.B.Manbeck and R.Hogg, 1993 ) .

2.3.9 Advantages of Peschl rotational shear cell

It has a high possibility of being utilised in an automatic manner due to its simpleness.

It is operator independent

The sample that is being utilized is little due to the fact that the shear cell is little.

The examiner can be used for comparative measuring and quality control such as the betterment of the flow of pharmaceutical pulverizations through the findings of an optimal sum of flow assistance. ( S.Kamath, V.M.puri, H.B.Manbeck and R.Hogg, 1993 )

2.3.10 Decision

If the qualitative measuring of pulverization flow behavior is required so it can scale and utilize to plan handles equipment such as

Hopper or silo or bin or sand traps

Gravity Chows

Feeders for illustration prison guard conveyers, belt conveyer, concatenation conveyer

Then the undermentioned pulverization flow belongingss utilizing a shear examiner will be measured:

Flow map

Internal Clash

Wall clash

Bulk denseness

The shear examiner will be used in this research to analyze the flows of different majority pulverization which will be compared to the flow on the designed base pipe rig used. The pulverization flow belongingss enumerated above will be taken into consideration when analyzing the flow of the majority atoms. The shear examiner normally takes an norm of 30 proceedingss when executing the experiments which is a batch of clip when compared to the simple testing.

2.4 Arching in Hoppers

Arching can be formed through the “ self-generated formation of an arch like supported dead mass of majority stuffs in a bin or hopper when the mercantile establishment is unfastened during gravitative flow. “ ( A.Drescher, A.J.Waters, C.A.Rhoades, 1995 ) It can be caused by two factors which are:

Geometry of the Hopper or bin

The mercantile establishment size.

Arching in hoppers was originated from the survey by Jenike and colleagues ( A.W.Jenike 1961 ; A.W.Jenike, 1964 ; A.W.Jenike and T.Leser, 1963 ) . The weight induced emphasis is normally less than the strength of the member which consequences in stack of stray structural members, arches and domes as assumed by some writers ( D.M.Walker, 1966 ; Z.Mroz and X.Szymanski, 1971 ; P.T.Stainforth and R.C.Ashley, 1973 ; P.C.Arnold and A.G.Mclean, 1976 ; A.Drescher, 1991 ) . Other theories were besides include the force transferred to the top of the arch from the stuff in the hopper above. ( A.Drescher, 1991 ; Z.Mroz and A.Drescher, 1969 ; G.G Enstad, 1975 ; G.G Enstad, 1977 ; G.G.Enstad, 1981 )

2.4.1 Arching Experiments

In order to look into the nexus between the signifier of flow map and the ensuing deduction of curving theories, shear trials were done straight on five different majority stuffs with different degree of wet content added to it which will be conducted to show the status compulsory for the informations decrease algorithms. The majority samples used were limestone, gypsum, coal, Cement and Taconite. The motion of the lower portion were induced when shearing the majority particles alternatively of the upper portion of the shear cell. The lower portion was observed to be resting on the motor-driven sliding tabular array. ( A.Drescher, A.J.Waters, C.A.Rhoades, 1995 ) The perpendicular burden was applied through the hangers which was non laterally displacing. The stationary burden cell placed against the upper portion of the shear cell was used to mensurate the shear force. During the sample readying, concentration were paid to cut down mistakes by avoiding excess burden of the sample when the screen palpebra is being manually twisted with a assistance of a twist which is hard to command. The excess burden atoms were attached wholly to a metal ring, resting on another ring mounted around the shear cell. The two rings entire tallness was somewhat greater than the tallness of the shear cell, and lubrications were done on the borders to understate clash when revolving the twist. The consolidation of the specimen under a changeless perpendicular burden was done during the agreement and the excess burden during distortion was transmitted through the rings. Trials runing from 3-14kpa had a consolidation normal emphasis which was applied for 10 proceedingss and 4 normal emphasiss with a shearing rate of mm/min had a maximal shear emphasis being determined. The following below were determine from the experiment

Bulk unit weight of the stuff

The material/wall interface clash angle with both as a map of the consolidating emphasis by utilizing the cell of the direct cell setup ( A.Drescher, A.J.Waters, C.A.Rhoades, 1995 ) .

2.4.2 Arching Consequences

A graph was plotted with the maximal shear emphasis on the perpendicular axis and the normal emphasis on the horizontal axis to demo the location of the normal and shear emphasis in the Mohr diagram for gypsum, coal, limestone and taconite. The points under consolidating emphasis which was realised during the shearing were marked in full. Coal had its point bunch along a narrow set while limestone and gypsum sets became wider ( A.Drescher, A.J.Waters, C.A.Rhoades, 1995 ) . Taconite had its points for the higher consolidating emphasiss significantly above the lower emphasiss. There were similarity in consequences obtained for the 3.2 % wet content of cement and limestone. The instantaneous output status which consequences in the changing the grade of the consolidation in the confining emphasis or strength of the majority stuffs has no clear indicant which subsequently resulted to a spread diagram. The instantaneous output status which is normally defined as the oncoming of fictile distortion of majority stuffs consolidated to a given denseness were approximated in two ways, which were the additive and non-linear. The Warren-Spring equation was used to depict the flow map of the majority atoms ( A.Drescher, A.J.Waters, C.A.Rhoades, 1995 ) .

2.4.3 Continuance of Arching Experiment

In order to compare the critical mercantile establishment size dividing curving from unobstructed gravitative flow, two types of mid size hopers which are the symmetrical plane ( Wedge form ) and conelike hoppers were used to carry on the experiment. Steel sheet were used to do the sidewall of the plane hopper which was adjustable with an disposition to the perpendicular which varies. To forestall stuffs from sloping, two Plexiglas walls which were midsts and positioned vertically were located at the hopper terminal with a high bin subdivision above it. Thick steel sheet were used to do the perpendicular conelike subdivision which had a half included angle with different mercantile establishment size. The tallness varied with the bin on top. The back uping frame had the perpendicular and symmetrical hopper mounted on it with two symmetrically placed steel hinged home bases functioning as a gate at the mercantile establishment ( A.Drescher, A.J.Waters, C.A.Rhoades, 1995 ) .

Assorted trial stuffs were poured on the hopper which will be delivered by a belt conveyer with a changeless free-fall distance to the mercantile establishment after shuting the gate. The mercantile establishment sizes were varied bit by bit to a larger one after a 10 proceedingss rest period ( A.Drescher, A.J.Waters, C.A.Rhoades, 1995 ) .

2.4.4 Critical Outlet size

The arching theory which predicts the critical mercantile establishment size that prevents curving is based on:

The structural mechanics attack which belongs to the theory of Jenike ( A.W.Jenike, 1961 ) Jenike and Leser ( A.W.Jenike and T.Leser, 1963 ) , Walker ( D.M.Walker, 1966 ) and Szymanski ( Z.Mroz and C.Szymanski, 1971 ) and

The continuum mechanics attack which is the newer theory of Enstad ( G. Enstad, 1981 )

The equality of the compressive uniaxial output strength and the chief emphasis moving on the critical arch span or dome of the stuffs serves as the rudimentss for the structural mechanics attack when obtaining its critical mercantile establishment size. The flow factor line and flow map equation below can be solved analytically to find the chief emphasis.

= ( A.Drescher, A.J.Waters, C.A.Rhoades, 1995 )

Where K and L are changeless

The size of the mercantile establishment diameter can be evaluated from the emphasis finding value.

D = ( A.Drescher, A.J.Waters, C.A.Rhoades, 1995 )

Where = majority unit weight and

= stuff or wall interface clash angle and the

Function g ( i?¦ ) depends on the premise made on the form of the arch in the theory.

The status of no emphasis back uping arch serves as a footing for the continuum based theory in which the critical mercantile establishment is gotten from. The mercantile establishment diameter look for the theory is given below

D = ( A.Drescher, A.J.Waters, C.A.Rhoades, 1995 )

Where = effectual clash angle

= Consolidating independent coherence.

Steep and smooth hoppers with mass flow can use the above equation.

2.4.5Arching Consequences

The mercantile establishment size of the hopper half angle gives an mercantile establishment size much larger than the theory of Jenike Arnold and Mclean when compared to the theory of Walker, Mroz and Szymanski refering the plane and conelike hopper for the Structural mechanics based anticipations. Arching for any mercantile establishment was predicted by the Walker theory for plane hoppers. There were similarity between the Jenike, Arnold and Mclean consequences which was n’t unexpected, because the Arnold and Mclean map g ( i?¦ ) provides Jenike to show a close analytical estimate of map diagrammatically and the flow factor lucifers both the continuum and the structural mechanics theory ( A.Drescher, A.J.Waters, C.A.Rhoades, 1995 ) . The Enstad theory normally ends up with giving an mercantile establishment size near to the tantamount mercantile establishment size of the theory of Jenike, Arnold and Mclean. The theory overestimates the size several times whenever the predicted mercantile establishment size is being compared with the mensural 1. This grounds besides applies for hopper half angle other than 20. The type of flow can non be determined due to the little tallness of the hopper which is a job ( A.Drescher, A.J.Waters, C.A.Rhoades, 1995 ) .

2.5 Jenike Design Method

This design method was used to show the happening of stable arch in sand traps and hoppers. It is based on the theory of gravitation flow in solids which states that ‘Gravity flow of a majority solid in a hopper will take topographic point provided the unconfined failure strength which the solid develops as a consequence of the action of the major chief consolidating emphasis is deficient to back up an obstructor to flux ‘ ( H.Wright, 1970 ) His design method assumed that when flow stops the emptied emphasis distribution during the majority solid discharge will be retained. The arch fails when the consolidating emphasis moving on the hopper exceed the strength of the arch at a critical location.

The Jenike method enables bunker design for two chief types of flows which are:

Mass Flow and

Core Flow ( H.Wright, 1970 )

Mass flow design entails the flows at the wall and the cardinal zone of the sand trap while the Core flow is all about flow that is restricted to the cardinal zone of the sand trap. Jenike characterize the flow of majority atoms through the debut of flow factor which is a ratio of the major chief emphasis at steady province flow ( ) to the unconfined output strength which is illustrated in the expression below ( H.Wright, 1970 ) .

ff =

2.5.1 Evaluation of the Jenike method for the design of mass flow hoppers

The design of storage hoppers for particulate solids normally makes usage of the Jenike method of design so as to forestall the forming of stable pulverization arches across the mercantile establishment. Extensive research has being carried out in this country due to the several designs of hoppers by Jenike method. Valuess that were obtained from the minimal mercantile establishment slot breadth, minimal hopper wall incline for mass flow which was predicted by the Jenike method of design and from full graduated table silo experiment with symmetrical cuneus form hopper were compared. There was an overdesign of the critical hopper in the Jenike method by 8-10 ( R.K.Eckhoff and P.G leverseen, 1974 ) . It was observed that the Jenike method overdesign the critical hopper when the SiC harsh free fluxing pulverization was used to find the critical incline of the hopper wall and the minimal slot breadth informations were obtained for all right SiC pulverization. The slot breadth was overdesigned from 0 to 100 % depending on the failure loci extrapolation into a little normal emphasis. It was found by Walker that the Jenike design overdesigns the hopper mercantile establishment significantly. ( D.M.Walker, 1967 ) .

It was discovered by Wright that there is an overdesign for the Fe ore wall incline required by Jenike method for mass flow by 5-10 and the predicted critical mercantile establishment size is about the same value as the experimental consequence. This led to a farther research on the job since the informations that were published by Wright appears to be contradictory ( R.K.Eckhoff and P.G leverseen, 1974 ) .

2.5.2 Restrictions of the Jenike Design Method

The method does non supply a design that can suit impact make fulling in conelike hoppers which could ensue in curving. This is the cause of the discontinuity of flow that normally occurs in sand traps.

The method does non supply a design which can extinguish curving at the passage of a sand trap with surcharge ( H.Wright, 1970 ) .

2.6 Summary of the consequence of the attack angle measuring in base pipes

The angle of attack is the angle to the vertical of the surface of skiding at the aperture. The angle of attack depends on the followers:

Materials

Geometry of the vas and

Geometry of the aperture through which the stuffs is dispatching

The angle of attack for free fluxing granules in a cylinder consequences in a steep angle of the order of 30 to the perpendicular with a surprising little consequence due to different stuffs ( Brown and Richard, 1965 ) . It was observed during comparing of the attack angle through the cardinal slot and the attack angle towards the border of the slot or cardinal openings that the angle through the border slot is more than the angle through the cardinal slot. There is a much steeper flow towards a cardinal opening along the surface than the flow towards a cardinal slot.

The disposition of the trough walls does non depend on the angle of attack. There is no direct measuring soon being made for the angle of attack ( Brown and Richard, 1965 ) . When an experiment was conducted on the trough holding walls inclining at 75 to the horizontal, it resulted with an angle of attack of 15 which made the surface of skiding co-occuring with the wall. The surface of skiding becomes detach from the wall as the incline of the walls decreased. There is a lessening in mass flow as the wall incline decreases until the critical angle is reached after which it remains changeless. The trough experiment is non satisfactory but seems to hold being equal for polish of the topic. ( Brown and Richard, 1965 )

The is no elaborate account of the angle of attack soon. There is some observation being made because the angle of repose depends on the method of measuring and the majority pulverization belongings. The possible enlightening comparing is the angle of skiding to the horizontal with the angle of internal clash. This is being explained in the Airy and Voellmy computations affecting estimates. The mass flow rate can be gotten through the angle of attack because the mass flow rate varies along the length of the slot. There is a likely possibility that the angle of attack may besides change along the length of the slot ( Brown and Richard, 1965 ) .

2.8 Concluding Remarks

The angle of rest is non a good step of pulverization flow when compared to other basic simple examiner like the Flodex, pulverization rheometers and the tapped denseness examiner. There are a scope of different machines available for flow belongings measuring from simple examiner to shear examiner. The shear examiner will be required to execute a silo design computation for this undertaking. A new shear examiner called the Brookfield PFT which is to the full automated will be used as a tool for mensurating flow belongingss for this undertaking work. The shear examiner gives a more accurate pulverization flow measuring because it takes different parametric quantities into considerations.

The current criterion silo method is that of Jenike. The Jenike mercantile establishment design will be applied in the design of the mercantile establishment for the base pipes so as to forestall the happening of curving. There is no current literature reappraisal on the base pipes outlet design. The Jenike mercantile establishment design method is the most conservative method for silo design when compared to other method by several writers. It outlet were over-design so as to make adequate infinite for the transition of majority atoms. Evaluation in the literature suggests that this significance over predicted experimental mercantile establishment diameters. The experiment looking at attack angles in base pipes shown a probationary nexus between this angle and internal clash. However, all experiment were concerned with the free flowing stuffs where as this undertaking intends to look at the job of curving in base pipes if a cohesive stuffs is used.