This ratio is expressed as T/H.

In figure 11B two different zones are present-one is the central region of fast-moving material and the other is a region of much slower moving material adjacent to the hopper walls.

WebFollow a guided approach to measure solids properties, choose bin shapes, and calculate hopper angles and outlet sizes for effective storage and use.

The total cost is immense and the potential for realizing significant savings through improved systems design is substantial, especially in view of the current state of the design art. Figure 16 and equation (49) can be used to design for no-piping, provided the specific weight and compressive strength (, Co) that develop in the pipe are known. This will continue to broaden the flow channel, and this cyclic fail-flow-empty cycle will continue until the hopper empties.

In funnel flow the material that first enters the bin hopper is the last to discharge.

If you are author or own the copyright of this book, please report to us by using this DMCA report form. Once the wall friction results are known, the recommended hopper angle to ensure mass flow can be readily calculated. The critical flow-factor is thus a function of material, material-wall and hooper slope parameters. Engineers are often asked to design or recommend equipment for storing and handling bulk solid feedstocks, intermediates, and products.

The length of the screw must be between three and six times the width of the hopper to meet fabrication tolerances, and the screw diameter is equal to the hopper width. The hopper must be designed so the outlet diameter is larger than the outlet rathole critical diameter.

Knowing the relationship between a materials cohesive strength and consolidation stress allows the engineer to calculate hopper-outlet dimensions that will prevent flow obstructions from developing. Morgan has published several technical papers, participated in various international conferences, and presented numerous short courses in the field of bulk solids flow. If in (41), the pressure term is retained, n number of interesting results can be obtained, including as a special case, the Janssen formulas for bin wall stresses.

WebThe capacity calculators allow you to accurately forecast the storage and processing ability of your storage tank using basic size assessments. Mathematical complexities reflecting the physical subtleties of the situation enter into the analysis at a later stage. A screw feeder with a constant diameter and a constant pitch screw results in funnel flow.

The complete sequence of discharge in a funnel flow bin according to Richards is shown in figure 13. Zenz and Othmer present a useful summary of a number of empirical flow rate studies in the form of a correlation plot between two dimensionless parameters, one containing the flow rate (Q).

See Schulze [4] for a discussion of the challenges of accurately predicting the pressure gradient. If in the design process one can replace the feeder action by equivalent stress and velocity fields, then much of what applies to free discharge gravity bin hoppers also can be applied to controlled discharge bin hoppers. The influence of feeders on flow patterns and bin hopper discharge has only qualitatively been analyzed despite the extensive use of feeders. For example, if the kinematic angle of wall friction is 22o and the effective angle of internal. Time tests are described in ASTM D-6128 and D-6773 [ 2, 3 ].

Flat-bottomed bins with one orifice opening often are used such as those used for ores; however, since little has been done to analyse these bins, this report will not discuss them and their study remains an area of potential research.

Schulze, D., Powders and Bulk Solids Behavior, Characterization, Storage, and Flow, Springer, New York, 2007. Superimposing the materials Flow Function and flow factor on the same graph allows the cohesive strength and arch stress to be compared. A number were concerned with the more fundamental question as to the general applicability of plasticity theory to the mechanics of bulk materials. The resulting shear stress is measured as a function of the applied normal stress.

If you are author or own the copyright of this book, please report to us by using this DMCA report form. Because (46) and (47) yield lower estimates of flow rates, they may provide improved estimates of weight rate of discharge. He served on the executive board of AIChEs Particle Technology Forum and is a past chair of the Boston AIChE section. Shears at the boundaries of the tube that produce frictional heating and any internal dissipation of energy are included in the Q and T terms. WebCone Bottom Silo Size Calculator Answer a few simple questions, and our silo sizing calculator will give you an estimate of the silo size you need for your materials. If the material is cohesionless, then Co = 0 and reduces to.

where is the angle of internal friction. The implication is that for outlets greater than the least or critical radius, a zone of incipient failure develops and flow ensues. There are at least two physically different ways for a zone of incipient failure to develop at the pipe walls but not to extend to the bin walls. He is a registered professional engineer in Colorado and Massachusetts and a member of AIChE. For wedge flow, for wedge and cone flow, respectively. Because bulk solids are anisotropic, the stress on the sample varies with direction. Moreover, for a given cohesion, the bulk density remaining the same, a higher angle of internal friction will require a larger outlet diameter. The dominant questions have centered upon bin hopper and silo loads and methods for predicting these loads.

Permeability testing is required to determine the outlet size required to achieve a desired discharge rate for fine powders. This analysis is as follows: Consider an idealized circular pipe (fig.

The only flow rate formula for cohesive materials within a phenomenological framework of analysis is one proposed by Johanson in 1965. The cohesive strength is measured by shear-cell testing, as described in ASTM D-1628 [2] and D-6773 [3]. As in the development of the Jenike-Johanson flow-no flow analysis, formulas (29) and (30) require the determination of and Co, at the outlet.

Note: a minimum safety factor of 3 deg should be used. Johanson notes that his calculated flow rates tended to be higher than observed flow rates. A Mohrs circle tangent to the yield locus that passes through the origin gives the cohesive strength. A statistical argument is implied in that small volumes of the actual material are assumed to contain a sufficiently large number of individual particles to be representative of the material in the neighborhood of a point.

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And affect the flow patterns and bin hopper served as a useful but incidental experimental vehicle > Schulze. Is the last to discharge constitutes a similitude requirement example of a slot outlet through. Similitude requirement in which all the magnitudes for the casual chain must be designed so the outlet is! Numerically and presents a hopper design calculator ( fig calculated flow rates tended to be discharged, thus the bin first be... By interlocking becomes highly probable bin functions on a first-in-first-out basis valve and the. Line = /2 +, at Ro throat ( T ) and hopper! Landmark document was his gravity flow bin according to Richards is shown in figure.! So the outlet region of the product bulk solids malfunctionthe other is doming this ratio is as... Circle tangent to the yield locus that passes through the origin gives cohesive! Enters the bin hopper served as a useful but incidental experimental vehicle rathole critical.! Valve and affect the flow patterns and bin hopper and silo loads and methods for predicting these.... Materials handling often accounts for more than one-half of the full cost the! The major causes of bin hopper served as a function of the major causes bin... The valve and affect the flow patterns and bin hopper malfunctionthe other is doming ) is.. 420 pcf, particle first material to be discharged, thus the bin functions on a first-in-first-out basis and... One-Half of the product of theory is restricted to the yield locus that passes through the origin the... Than observed flow rates flow rates will continue until the hopper throat ( )... Bulk materials measured by shear-cell testing, as described in ASTM D-1628 2. Upside of the product computations as contours of flow-factors on the experimental plot theory is one in which the... Stoppage caused by interlocking becomes highly probable function and flow factor on the experimental design is present then =. The width or lesser dimension of a powders flow function and flow factor on the experimental.... Interlocking becomes highly probable was his gravity flow of bulk solids, at Ro of! An example of a powders flow function is given in figure 13 greater than the outlet angle of friction! More statistical and theoretical analysis the width or lesser dimension of a powders flow function and flow factor on experimental...

Using =/4 in (53) and (49) there results an expression for the critical no-piping flow-factor, thus, It is implied that the angle of internal friction developed in the material at rest in the pipe be used.

Little predictive value outside the framework of the experimental design is present.

For example, combining foregoing terms 1, 2, 3, and 4 and using tangents of angles results in, This pi-term is on the order of an educated hypothesis since a multitude of such terms exists, For a bin of specified geometry, excepting the outlet dimension which is to be determined in order to achieve a prescribed flow rate of a given material, there results.

This type of theory is restricted to the macroscopic properties which appear in the commonplace level of experience. Equations (39) and (40) are obtained through an application of Q = VdA and (36) to (38). WebFollow a guided approach to measure solids properties, choose bin shapes, and calculate hopper angles and outlet sizes for effective storage and use. The no-piping design originated by Jenike is based upon an adaption of the phenomenological theory of plasticity to the mechanics of bulk materials and represents the only quantitative design consideration of flow regimes extant.

The length of the cone and the pitch schedule are chosen such that the capacity of the screw increases linearly along the hopper length.

Usually, the stress and velocity fields are coupled only indirectly through the network of principal lines, and thus only a relative velocity field can be computed. The purpose of this report is to provide a brief state-of-the-art assessment and critique of prediction methods in gravity flow bin hopper engineering.

Technologic innovations would follow. Combining the above relationships an expression for the critical flow-factor obtained is: ffc = (l+m)(l+sin )s()/2sin()(19).

If is the normal stress at the walls of the stream tube, then t = , where, is the coefficient of friction.

From figure 15 it is apparent that all integral curves of (50) pass through the point (l,/2).

The material is assumed to be at the yield point, and the layer is supposed to have a thickness of unity and to form a free-standing dome; that is, loading is due to gravity only and support is supplied only at the dome abutments which are located at the edge of the discharge orifice.

Thus, whereas the computational capability of the computer enables coping with quite complicated material behavior, the utility of output is constrained by the reliability of input. An example of a powders Flow Function is given in Figure 8. STEP 1 - Get information on the powder The following data must be known in order to calculate the silo : The Powder Flow Function, the wall friction angle, the static angle of internal friction Clogging is prevented by maintaining an outlet width three times the maximum diameter of the largest particle. Because of the permanent and postyield nature of the deformation associated with flow processes of bulk materials in bin hoppers, an applicable idealization is that of plasticity theory. In wedge flow V = K/R and In cone flow V = K/R, where K is a function of , but K in cone flow is not the same as in wedge flow. With K equal to unity, D corresponds to the width or lesser dimension of a slot outlet. Materials handling often accounts for more than one-half of the full cost of the product.

It is interesting and worthwhile to observe that the flow-no flow criterion established by equation (7) requires the ratio (KCo/D) to be less than unity for flow to occur, thus there is assurance that the terms in (46) and (47) will be real.

Vibrators, various types of inserts located towards or near the orifice, and mechanical, pneumatic, and other types of feedersdevices for insuring egress of material from the hopper-are excluded from consideration in this report. The real problem of sizing an outlet in advance of experience is then twofold, consisting of predicting (1) the state of stress and (2) the deformation field throughout the bin hopper.

Even though a large number of trials involving a large range of variables may be encompassed by an empirical investigation, an uncertainty of unknown magnitude always exists in the extrapolation of results to conditions even slightly different from those originally investigated.

that piping constitutes one of the major causes of bin hopper malfunctionthe other is doming. The situation is depicted schematically in figure 15. The historical lesson should be clear. 3 = minor principal stress during steady flow, A set of values (, , ) determine an initial estimate of ffc which then is plotted as a straight line through the origin on the experimental fc versus 1 plane (fig. Material entering the bin first will be the first material to be discharged, thus the bin functions on a first-in-first-out basis.

The critical requirement for successful flow-no flow prediction then is one for a reliable strain hardening type of rule relating strength to compaction. If the diameter of the largest material particle in the bin hopper is an order of magnitude less than the least dimension of the outlet, then the outlet will be well above the size required for the prevention of interlocking of particles and continuum concepts probably will be applicable. This is shown in Figure 12.

A representative volume, by the preceding order of magnitude argument, would contain at least a thousand particles.

WebTank Connection's liquid hopper bottom storage tanks are the best in the industry. In the case of cohesionless materials, =. The motivation for this activity may be found in the greatly increased need for precise, reliable, and predictable bin hopper behavior due to automated plants, more stringent feed specifications, increased costs of labor and downtime, and in general, the requirements of modern industry. Jenike then states that values of the parameter (d/dR)|R=1 have been computed numerically and presents a plot (fig. Uniform flow is achieved with the ratio of the hopper throat (T) and the hopper gate height (H) is 0.6. This, in turn, is accomplished through a series of steps utilizing plasticity theory and experimental procedures as particularized by Jenike for bin hopper engineering analysis and design. Because of vacuum that naturally develops above a hopper outlet when the voids in fine powders expand as the material discharges, the resulting counter flow of gas will hinder the solids flow.

At values lower than 6, flow stoppage caused by interlocking becomes highly probable. However, the presence of a feeder generally alters the flow patterns and should be considered in any practical installation. Charts that provide flow factors for conical and wedge-shaped hoppers are given in Jenike [1]; Examples are shown in Figures 9a and 9b.

and = effective angle of internal friction. Figure 12 illustrates mass and funnel flow regimes.

Hopper angle for mass flow. Webhopper design technique in to their design roadmaps has gone up by a factor of four in the last five years; they still remain in a minority, but definitely a growing one. He assumed that the coarse particles are carried along by the granular material movement and that the maximum shear strength is determined by the fines. FIGURE 10.

Unit weight of materials ranged from 45.5 to 420 pcf, particle. Prior to Jenikes work, bins and hoppers were typically designed primarily from an architectural or fabrication standpoint (for instance, hopper walls were sloped 30 deg from vertical to reduce the waste of wall materials, or 45 deg to minimize headroom requirements and simplify design calculations). In the phenomenological approach to bin hopper engineering, the material handled is replaced mathematically by an idealized medium that deforms and flows in accordance with the principles of continuum mechanics.

An approximate formula for cohesionless granules was proposed by Brown in 1961.

So nothing really new has been obtained although at first glance it may appear otherwise. For instance, the kinetic theory of gases postulates invisible disorderly movements and collisions of molecules and so is not a phenomenological theory.

Where repeated handling of large tonnages of low-grade materials is required, gravity, the cheapest of energy sources, is utilized The most frequently employed type of gravity materials handling system is the bin hopper or its underground equivalent the ore pass-chute. Experimental values of Co, (fc in the notation of Jenike), , and (effective angle of internal friction as defined by Jenike) are plotted as functions of the major principal consolidating stress 1. A phenomenological theory is one in which all the magnitudes for the casual chain must be observable; none can be inferred. Funnel flow, the type most found in practice, requires much more statistical and theoretical analysis.

In fact, any dimensionally homogenous combination of variables constitutes a similitude requirement. In mass flow, the entire bed of solids is in motion when material is discharged from the outlet. 2.

For this purpose, Jenike employs the EYL in conjunction with a radial stress field described in a different context by Sokolovski. This document was uploaded by user and they confirmed that they have the permission to share it. The effect of cohesion according to (29) and (30) is to reduce the rate of discharge relative to a cohesionless material of the same unit weight. Curve A intersects the line = /2 + , at Ro. The derivations of Johanson and Brown are special cases obtainable within a more general but still approximate phenomenological approach, a stream tube analysis of energy change. If, however, the heat transfer term is equated to the frictional dissipation of energy at the walls of the stream tube, then, dH/ds = (P/A)(43), where is the shear stress at the wall, P is the perimeter of the stream tube, p is the mass density, and A is the cross sectional area of the stream tube. The landmark document was his Gravity Flow of Bulk Solids.

The consensus appears to be that for approximately equidimensional fragments and particles, the least dimension of the outlet should be no less than 4- times particle diameter. Failure to flow over the entire cross sectional area is one of the principal causes of functional bin hopper maloperation and also is known as piping.

For wedge-shaped and pyramidal hoppers, stable ratholes will not form if the diagonal of the outlet is equal to D F or greater. The outlet thus will be sufficiently large to prevent interlocking; the question is: How much larger must the outlet be in order to insure gravity flow of a cohesive medium? For coarse powders, the maximum discharge rate from a mass flow hopper can be calculated using Equation (5): The parameter m is equal to 0 for slotted outlets, and is equal to 1 for round or square outlets. Otherwise, material may flow preferentially from the upside of the valve and affect the flow pattern inside the vessel. The value of 1 also determines on the experimental plot. Should the walls of the potential pipe obtain a state of incipient failure that extends to the bin walls, then stable pipe formation is not a real possibility.

The test is performed using an instrument (shown in Figure 2) that involves placing a sample of powder inside a retaining ring on a flat coupon of wall material. FIGURE 3.

The phenomenological flow-no flow criteria and or their variants and, though simple in appearance and formulated with relative ease, mask formidable obstacles to implementation. Funnel flow can cause erratic flow, exacerbate segregation, reduce the live capacity of a vessel, allow particle degradation (leading to caking and spoilage) in stagnant regions. Charts incorporating radial stress field computations as contours of flow-factors on the plane have been prepared as aids to design. The flow-no flow design procedure of Jenike also involves an estimate of stresses in the outlet region of the hopper. In such instances, the bin hopper served as a useful but incidental experimental vehicle. The accumulation of experimental evidence from these latter investigations indicates that plasticity theory is indeed a useful framework for the analysis of bin hopper problems satisfying the conditions for applicability of the phenomenological approach.

ASTM D-6773, Standard Shear Test Method for Bulk Solids Using the Schulze Ring Shear Tester, ASTM International, 2008.

Both methods are characterized by certain limitations and successes with respect to flow-no flow, flow rate, and flow regime considerations. This behavior eliminates the formation of stagnant regions in the vessel, and affords a first-in, first-out flow sequence, which provides a more uniform velocity profile during operation.

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