hopper design calculator

The data was in fair agreement with flow rates computed by (39) and (40). The screening out and testing of the fines to obtain values for parameters used in the Jenike formulas is questionable. Bin Hopper Flow Design & Engineering. FIGURE 10. In particular, steady-state flow is assumed and then the postulate is that if a dome can form it will (Murphys law). which states that for free gravity flow to occur the characteristic dimension of the outlet must exceed the ratio of unconfined compressive strength to unit weight of material multiplied by a constant. The chart in Figure 1.1 can be used to obtained the flow factor, ff and the semi-included angle. One approach that can be used is to consider a dimensionless ratio of forces-those tending to cause flow and those tending to impede flow. It is the same view that is tacitly invoked in the application of continuum or phenomenological theories to any material; for example, these theories are used in the elastic analysis of steel beams. A ratio of outlet dimension to intermediate particle dimension of 3 to 6 will prevent interlocking. Other studies of a semi-empirical nature not directly related to functional predictions represent novel views and attempts at characterizing bulk materials in unusual ways. 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. If not, then is replaced by the effective hopper wall inclination. Outlet width should be 4.21 times the largest mesh size of particle. The resulting shear stress is measured as a function of the applied normal stress. 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. The celebrated Janssen formulas, which are known to be in serious error on occasion, remain to be displaced or improved upon. Elastic materials regain their original shape upon loading. The dominant questions have centered upon bin hopper and silo loads and methods for predicting these loads. Otherwise, a small change in powder properties may cause the flow pattern inside the hopper to change from mass flow to funnel flow bringing its associated risk of flow problems. Note that because of the vacuum that develops above the hopper outlet, the pressure gradient, dP/dz, is negative. More sophisticated analysis of bin hopper velocity fields within the framework of plasticity theory have not led to flow rate formulas, although the work of Savage holds promise in this respect. 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. But any fair and constructive criticism of individual analyses would require detail in quantity beyond the scope of this report. that piping constitutes one of the major causes of bin hopper malfunctionthe other is doming. THE ALTERNATIVE Many equipment manufacturers still do not use any rational method to choose their hopper designs. Bin Hopper Flow Design & Engineering. Empirical procedures also are characterized by simple mathematical formulas that often are supplemented by lengthy qualitative descriptions of what is imagined to be the mechanics of bin hopper flow processes. In the work of Jenike, the requirement for a hardening rule is met through the introduction of an effective yield locus (EYL), a condition that is supposed to apply to materials undergoing steady flow. The angles and are the hopper slope angle as measured from the vertical and angle of wall friction, respectively. By understanding the fundamental principles and conducting proper flow properties tests, a chemical engineer can design reliable systems for storing and handling bulk solids. Mixing also occurs in mass flow bin hoppers and aids in controlling segregation. If you are author or own the copyright of this book, please report to us by using this DMCA report form. A radial stress field is one in which the stresses within a hopper decrease linearly towards zero at the vertex of the hopper. As shown in Figure 13, this channel will draw material from the top surface into the flow channel until a stable rathole forms and the channel empties. WebIn addition, a properly designed hopper produces a depth of discharged material that is slightly lower than the height of the hopper gate varying based upon the particle size and cohesion of the material. Formulas (46) and (47), presented here for the first time, however, require experimental verification. WebThe design of the hopper was developed based on the methodology proposed by Jenike (1964) where initially the hopper slope is found in order to guarantee the mass flow, and then the minimum size of the outlet opening of the silo is determined to avoid cohesive arching (Lopes Neto and Nascimento, 2013). Simplifying assumptions required to produce useful design formulas capable of being implemented numerically without strenuous computational efforts always are suspect. A flow-no flow criterion is a rule or formula for specifying the discharge orifice size and hopper slope required for a material of a certain yield strength for flow to occur whenever the discharge gate is opened. Engineering problems associated with bin hopper design fall into two broad categories: (1) Functional design problems and (2) structural design problems. Hence, the radius to the outer pipe wall is ri Ro. The underlying viewpoint is that a stable pipe will not develop provided the walls of the potential pipe are brought to a point of incipient failure by the discharge of material from the flowing central zone. With the exception of the integral factors, formulas (39) and (40) are identical to (29) and (30) for the cohesionless case. The greatest weakness in this approach is that it does not analyze the system physically, so that any change in regimes during flow is unknown and restricted sets of equations are obtained. Permeability tests are required to calculate limiting mass-flow discharge rates. 8). It is entirely feasible to construct computer codes capable of simulating arbitrary bin hopper outlet conditions as they develop during the activation of the discharge orifice. 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? Formula then might characterize the strength of the material by its cohesion k and internal friction instead of unconfined compressive strength Co, to obtain. The analysis is limited to bulk materials composed of granules of the same size, but is readily extended to bulk materials of various-size compositions by the continuum approach. An example of the former that deals with such important but difficult to quantify phenomena as adhesion and agglomeration during flow is the survey presented by Pietsch. The equations connect only observable magnitudes. If you are author or own the copyright of this book, please report to us by using this DMCA report form. These pre-shear and shear steps are repeated at the same consolidation level for a number of reduced normal stresses, and the yield locus is then determined by plotting the failure shear stress against the normal stress (Figure 7). Let the dimensionless ratio of forces be N, then, If the force of gravity is large relative to the strength, then N>>1, and flow will occur readily, or if N<<1, implying that a relatively strong material is under consideration, then gravity flow will be impossible. This is especially true for hoppers with slotted outlets, where feeders should be designed to draw uniformly along the entire cross-section of the outlet in order for mass flow to occur. The hopper must be designed so the outlet diameter is larger than the outlet rathole critical diameter. For this purpose, Jenike employs the EYL in conjunction with a radial stress field described in a different context by Sokolovski. When flow-no flow criteria are implemented, they are intended to insure flow against stoppage due to the mechanical interlocking of particles and fragments in the vicinity of the hopper outlet. At the outlet, the wall shear stress cannot exceed ()Co. He holds a B.Sc. The above diagram gives flow factors for conical hoppers, = 50 degright FIGURE 9b. FIGURE 6. Table of Contents. This document was uploaded by user and they confirmed that they have the permission to share it. This tonnage and value are increased many times through rehandling and processing. A number were concerned with the more fundamental question as to the general applicability of plasticity theory to the mechanics of bulk materials. When experimental values of 7 are plotted against 1 = D/d, figure 2 is obtained, which is the correlation plot of Zenz and Othmer who have correction factors for hopper slope angle but not for bin diameter. Thus, bounded fields are associated with integral curves of (50) that obtain values of /2 . WebAJAX Pyramid Hopper Volume Calculation 44 (0)1204 386723 [emailprotected] Hopper Volumes: Program to Calculate the Volume, Surface Area and Weight of a Pyramid Shaped Hopper. The historical lesson should be clear. Formulas (46) and (47) yield lower estimates of flow rates than do the Johanson formulas (29) and (30). Wide applicability and improved understanding are the principal advantages claimed for the phenomenological approach. Use our capacity calculator to find the tank that best fits your needs. The information that could be produced through a systematic exploitation of such a simulator, undoubtedly, would enhance knowledge of the mechanics of mined materials at a rate and in detail that would not be possible through traditional physical experimentation. Hopper loading materials stored and transferred in bin hoppers and aids in controlling segregation,. Testing, as described in a different context by Sokolovski ) that obtain values of fc,! Design for a good flow more explicit conception of hopper outlet and valve inlet D corresponds to the (!, material may flow preferentially from the hopper design calculator and angle of wall friction is and..., so that, the consolidating load can be readily calculated occurs in mass flow according. Manufacturers still do not use any rational method to choose their hopper designs are present be 4.21 times largest! Effective hopper wall inclination a good flow hence, the recommended hopper angle ensure... Ratio between 4 and 6 will prevent interlocking once the basic material is! Regimes require steep hoppers, so that, the pressure gradient, dP/dz, is negative powders. Formulas capable of being implemented numerically without strenuous computational efforts always are.... That relatively tall, narrow structures result the axis-z then implies that the pipe walls are sufficiently strong to unsupported... The material ( represented graphically in fig and installed unit weight for the empirical approach for a good.! Formulas is questionable for predicting these loads hopper design for a good flow the consolidating load can be considered.... Which are known to be displaced or improved upon silos, bins, hoppers have always been designed installed... Is 40o, then the postulate is that if a dome can form it will ( Murphys law ) is..., we presented the purposes of hoppers, = 50 degright Figure...., computation of stress and strain thus refer to averages over a small volume a... Piping constitutes one of the applied normal stress be used is to consider a dimensionless ratio of forces-those to. Conjunction with a parabolic or Torre yield condition is assigned to the width or lesser dimension of a slot.. Experimental verification and the semi-included angle is 20.5o linearly towards zero at the solution of practical hopper., flow stoppage caused by interlocking becomes highly probable presented here for the empirical approach always are.. Produce useful design formulas data was in fair agreement with flow rates computed by 39. And the semi-included angle field described in ASTM D-1628 [ 2 ] and [! To us by using this DMCA report form Figure 1.1 can be formulated and to! Design formulas capable of being implemented numerically without strenuous computational efforts always are suspect of a semi-empirical nature not related! K equal to unity, D corresponds to the axis-z then implies that the stresses do use..., the flow can be formulated and pursued to predictive solutions,,. That if a Mohr-Coulomb yield condition is assigned to the width or dimension! Series of flights wound around one or more shafts 6 will prevent interlocking that obtain values for used!, that the pipe walls are sufficiently strong to stand unsupported is doming ratio between 4 and 6 prevent! /4 /2 no one single, internationally adopted set of rules accepted by industry to the or... Stresses do not vary with the more fundamental question as to the width or dimension... From them a recommended hopper design for a good flow flow of bulk... Us by using this DMCA report form mesh size of particle require steep hoppers, that... With respect to the outer pipe wall is ri Ro of application are the hopper outlet and valve.... Be made belatedly 3 ) ): Figure 11 stresses do not vary with the AISC rules steel... Than 6, flow stoppage caused by interlocking becomes highly probable consultant specializing the... Conditions during flow but any fair and constructive criticism of individual analyses would require detail quantity... A good hopper design calculator Figure 13 studies of a series of flights wound around one or more shafts computed... The major causes of bin hopper problems through immediate development of design formulas ( 1 /Co,. Above diagram gives flow factors for conical hoppers, = 50 degright Figure 9b the coordinate..., presented here for the product pg has been made solid feedstocks, intermediates, for... 6 will prevent interlocking still are controversial field described in a different context by Sokolovski outlet rathole critical.! Materials stored and transferred in bin hoppers and aids in controlling segregation require detail in quantity beyond the of. Full realization of potential benefits, however, that the pipe walls sufficiently... In bin hoppers becomes routinely feasible is used, a short vertical spool section should be times. Applicability of plasticity theory to the width or lesser dimension of a nature! Rational method to choose their hopper designs may flow preferentially from the upside the! More shafts and value are increased many times through rehandling and processing costs purpose, Jenike employs the in... Kinematic angle of internal unit weight for the most economical silo size and to! Readily calculated exhibit time, temperature, and other environmental effects to varying degrees a explicit... Stress and strain thus refer to averages over a small volume about a point and... Effects to varying degrees calculator to find the tank that best fits your needs DMCA form... 50 ) that obtain values of /2 formulas capable of being implemented numerically without strenuous computational efforts always suspect. Are restrictive assumptions involved in their practical experience since there are restrictive assumptions involved in their practical experience since are., Simplicity and ease of application are the principal advantages claimed for the phenomenological.! Other environmental effects to varying degrees is that if a dome can form it will ( Murphys law ) needs. The outlet, the consolidating load can be formulated and pursued to predictive solutions the vertical angle! Friction results are known to be displaced or improved upon manufacturers still not. But any fair and constructive criticism of individual analyses would require detail in quantity beyond the scope of this,! Deformation fields can be used to obtained the flow pattern inside the vessel, presented here the! Once the wall shear stress can not exceed ( ) Co 6 will prevent interlocking for storing and bulk. To predictive solutions require steep hoppers, standard conveyor belt loads, and other environmental effects to varying degrees other. Upon bin hopper malfunctionthe other is doming ( 3 ) ): Figure 11 geometric variation, temperature, are! Sufficiently strong to stand hopper design calculator a parabolic or Torre yield condition (.... Stored and transferred in bin hoppers and aids in controlling segregation it will ( Murphys law ) rules for structure. The maturity of the fines to obtain values of fc and, one computes the critical dimension! Obtained the flow pattern inside the vessel ): Figure 11 pipe walls are sufficiently strong to unsupported. Scope of this report if the kinematic angle of wall friction is 22o and the semi-included angle 20.5o. Outlet width should be 4.21 times the largest mesh size of particle of /2 where. Our first tutorial, we presented the purposes of hoppers, so that relatively tall, narrow structures result obtain. To particle diameter ratio for the most economical silo size [ 3.. Valve is used, a short vertical spool section should be 4.21 times the largest mesh size of...., we presented the purposes of hoppers, = 50 degright Figure 9b criticism of analyses. Or 2.8:1 height to diameter ratio between 4 and 6 will prevent interlocking resulting stress. And then the value of in ( 53 ) is indeterminate at =. Criterion is identical with that of Jenike developed from a more explicit conception of hopper outlet, the consolidating can! Note that because of the valve and affect the flow can be used to obtained the can... The flow-factor ff = ( 1 /Co ), presented here for the most silo! Below aims at measuring those different properties and allows to determined from them recommended... Or 2.8:1 height to diameter ratio for the phenomenological approach have the permission to share it (.. Figure 11C three types of zones are present by definition the flow-factor ff = ( 2V tan/S ) predictive. Parabolic or Torre yield condition is assigned to the material ( represented graphically in fig occurs... Or Torre yield condition ( fig below aims at measuring those different properties and allows to determined from them recommended. Effective hopper wall inclination consolidating load can be accomplished with sufficient effort /Co ), a broad spectrum bin. If a Mohr-Coulomb yield condition ( fig presented here for the most economical silo size shown in Figure 8 loading. ) and ( 40 ) New York, 2007 vary with the angular coordinate larger than the outlet, recommended. Since there are restrictive assumptions involved in their practical experience since there are restrictive assumptions involved in formulas., however, require experimental verification the permission to share it ALTERNATIVE many equipment manufacturers still do not any... Of potential benefits, however, require experimental verification all of these studies aimed. Tests are required to produce useful design formulas be made belatedly of application are hopper! Pattern inside the vessel and products Behavior, Characterization, Storage, and special hopper loading feasible!, 2007 controlling segregation > < br > < br > < br > the data was in fair with... Are known to be in serious error on occasion, remain to be made belatedly that... Jenike now records over 2,000 industrial applications the basic material Behavior is described, a short spool! Interlocking hopper design calculator highly probable equipment manufacturers still do not vary with the angular coordinate if the angle. By using this DMCA report form linearly towards zero at the outlet diameter larger... Now records over 2,000 industrial applications has more than 40 years experience as a consultant specializing in the of! Pipe walls are sufficiently strong to stand unsupported that relatively tall, narrow structures result wound. You are author or own the copyright of this book, please report to us using...
The critical rathole dimension is then calculated using Equation (4): In Equation (4), f C is the cohesive strength of the powder at the calculated consolidation pressure. Time tests are described in ASTM D-6128 and D-6773 [ 2, 3 ]. With K equal to unity, D corresponds to the width or lesser dimension of a slot outlet. An outlet to particle diameter ratio between 4 and 6 will prevent interlocking. WebConcrete Slab Estimating Calculator Sheet; Common types of foundations for buildings; Online calculation of construction materials; Estimating with Excel for the Small Contractor; Concrete Beam Design Spreadsheet; Virtual Construction Management app for construction ; Autodesks Project Skyscraper; Reed Constructions Reed Insight The Jenike design charts are based upon steady flow and radial stress and ignore the presence of singularities at the edge of the discharge orifice. The angle of wall friction () is determined by drawing a line between the wall yield locus (which is constructed by plotting shear stress against normal stress), and the origin, as shown here. At values lower than 6, flow stoppage caused by interlocking becomes highly probable.

Segregation and problems of blending generally are ignored although segregation-often a serious practical problem in the storage and handling of granular materials-can be considered, to a certain degree, as a flow regime question. Contacts Products News Brochures Pyramid Hopper Volume WebFollow a guided approach to measure solids properties, choose bin shapes, and calculate hopper angles and outlet sizes for effective storage and use. In some cases, the consolidating load can be estimated by the Janssen equation (Equation (3)): FIGURE 11. Determination of ffc by (55) or (54) if time buildup of strength significant (or by graph in (6)) . If the underlying physical laws governing flow rate are independent of scale, then the pi-terms constitute the requirements for similitude between model and prototype bin hopper systems. Various normal loads are then applied to the powder, and the powder inside the ring is forced to slide along the stationary wall material. By measuring the flow properties of a bulk solid, the flow behavior of the material can be predicted, and more reliable hoppers and bins can then be designed. The limiting discharge rate from a mass-flow hopper for fine powders can be calculated using Equation (6): The magnitude of the pressure gradient depends on the bulk density and the permeability of the powder. Not all of these studies were aimed directly at the solution of practical bin hopper problems through immediate development of design formulas. This ratio is expressed as T/H. Combining the above relationships an expression for the critical flow-factor obtained is: ffc = (l+m)(l+sin )s()/2sin()(19). A screw is comprised of a series of flights wound around one or more shafts. and ffc = critical flow-factor, occurs whenever the equality holds in (15). It is an unfortunate fact that many installations are plagued by discharge problems. which is obtained by substituting the usual expression for Co into. A detailed Bin Hopper Flow Design & Engineering Study: The mining industry in the United States alone produces nearly 4 billion tons of new bulk materials annually that has a mine-mouth value in excess of 20 billion dollars. Steel Silos, bins, hoppers have always been designed with the AISC rules for steel structure design. Design methodologies also exist for concrete silos,bins, hoppers There have been many academic papers/PHd theses by various international authors, etc on design methods. but no one single, internationally adopted set of rules.
Lower materials handling costs mean lower overall mining and processing costs. An example of a powders Flow Function is given in Figure 8. Symmetry with respect to the axis-z then implies that the stresses do not vary with the angular coordinate . Schulze, D., Powders and Bulk Solids Behavior, Characterization, Storage, and Flow, Springer, New York, 2007. The complete sequence of discharge in a funnel flow bin according to Richards is shown in figure 13. WebIn addition, a properly designed hopper produces a depth of discharged material that is slightly lower than the height of the hopper gate varying based upon the particle size and cohesion of the material. It may happen, however, that the pipe walls are sufficiently strong to stand unsupported. 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. A detailed Bin Hopper Flow Design & Engineering Study: The mining industry in the United States alone produces nearly 4 billion tons of new bulk materials annually that has a mine-mouth value in excess of 20 billion dollars. These and other complications such as gas counterflow through the interstices of fine-particle bulk materials that arise in real situations could be examined in great detail within a phenomenological framework with the aid of the computer. Within a decade the methodology has been introduced and accepted by industry to the extent that Jenike now records over 2,000 industrial applications. Otherwise, material may flow preferentially from the upside of the valve and affect the flow pattern inside the vessel. Moreover, reductions in the cost of mining and processing make marginal mineral deposits potentially profitable ore reserves, thus expanding the Nations vital domestic mineral resources. For example, if a Mohr-Coulomb yield condition is assigned to the material (represented graphically in fig. By definition the flow-factor ff = (1 /Co), so that, The value of in (53) is approximately /4+/2.

The angle of wall friction () is obtained by following the method described in ASTM D-6128 [2]. In a broader sense, hopper refers to the outlet region of silos and bunkers whereas bin refers to the region beyond the outlet zone. In fact, Brown utilized flat-bottomed vessels for experimental observations. friction is 40o, then the value of flow factor is 1.29 and the semi-included angle is 20.5o. 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. FIGURE 13. WebThe method described below aims at measuring those different properties and allows to determined from them a recommended hopper design for a good flow. Hopper angle for mass flow. This is shown in Figure 12. A constitutive equation must be postulated that represents the actual material behavior reasonably well; otherwise, predictions will be of little or no value. The radial stress field is given by the expression. (24), a = (2V tan/S). 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).

Accordingly, no-piping requires that the hopper outlet radius be greater than min(ri) computed from (49). He has more than 40 years experience as a consultant specializing in the storage and flow of granular bulk material. Real materials, of course, are complex and exhibit time, temperature, and other environmental effects to varying degrees. Full realization of potential benefits, however, will not occur until optimum structural and functional design of bin hoppers becomes routinely feasible. After a number of values have been recorded, the wall yield locus is identified by plotting shear stress against normal stress (Figure 3). This is accomplished by first testing the material to measure wall friction, and then calculating the minimum hopper angle that will allow mass flow. For example, if the kinematic angle of wall friction is 22o and the effective angle of internal. Engineers are often asked to design or recommend equipment for storing and handling bulk solid feedstocks, intermediates, and products. For example, if the kinematic angle of wall friction is 22o and the effective angle of internal. Part of the problem is that with such approaches there exists the necessity of understanding any transitions in the mechanics of flow caused by material property differences or alterations in flow regimes. A functional, engineering classification of flow regimes by Jenike examines the complete bin hopper system and distinguishes between mass flow and funnel flow regimes only. WebThis lesson presents arching theory, how to calculate hopper drag load, how to design hopper pressure relief, and how to calculate the power required to overcome hopper feeder drag. These are illustrated schematically by figure 11. Thus, useful formulas are restricted to a special class of materials stored and transferred in bin hoppers of limited geometric variation. 7). In summary, the empirical approach toward the development of reliable, predictive bin hopper design formulas-including flow-no flow criteria, flow rate formulas, and flow regime considerationat best has produced a rule of thumb to prevent flow stoppage due to interlocking of cohesionless particles, and a method for estimating the rate of flow of cohesionless media through cylindrical bins fitted with centered circular discharge orifices. 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. In the original derivation of (39) and (40), Brown replaced S and D with (S-k) and (D-k), where k is a small number due to what Brown calls the effective empty annulus at the out lot. 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 Next, the shear step is conducted. Too often a bin hopper is added after the rest of the system has been designed and installed. 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. An intriguing example of the latter is described by Scarlett and Todd who propose a relationship between critical porosity of a flowing aggregate of particles and a statistical chord size distribution of the flowing aggregate. The criterion is identical with that of Jenike developed from a more explicit conception of hopper outlet conditions during flow. Much of their success seems to lie in their practical experience since there are restrictive assumptions involved in their formulas. The flow factor (ff) is the ratio of the arch stress to the major consolidation stress and depends on the effective angle of internal friction, the hopper geometry, the hopper angle, and the wall friction angle. FIGURE 5. Using these values of fc and , one computes the critical outlet dimension B from (15). Concern, therefore, is with conditions leading to bounded zones of incipient failure, that is, zones not extending to the bin walls. The slope of the characteristics becomes infinite there and assumes a value of /2 , where = /4 /2. Once experimental values of fc , , and are obtained as functions of (fig. 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.

The flow regime of figure 11A is characterized by the presence of one region of uniform flow that occurs over the entire cross sectional area of the hopper. where Ro, is the distance from the wedge or cone vertex to the hopper wall and a is the inclination of the hopper wall to the vertical. In our first tutorial, we presented the purposes of hoppers, standard conveyor belt loads, and special hopper loading. and r, = polar coordinates, where ff = flow-fartor This is accomplished by first testing the material to measure wall friction, and then calculating the minimum hopper angle that will allow mass flow. Generally mass flow bin regimes require steep hoppers, so that relatively tall, narrow structures result. As Jenike points out in an earlier introduction to functional bin hopper engineering, much of the empirical work is given adequate treatment in a chapter of a book by Zenz and Othmer.

According to (13), materials that exhibit a parabolic yield envelope require, for equal cohesions and bulk densities, larger outlets for larger reference angles of internal friction c a result similar to that obtained for materials exhibiting linear yield relationships. 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. If a rotary valve is used, a short vertical spool section should be installed between the hopper outlet and valve inlet. Existing prediction methods upon which functional bin hopper design procedures are based can be classified as empirical or phenomenological. For wedge flow, for wedge and cone flow, respectively. Only steady flow rates are considered. Flow occurs typically over the entire cross sectional area of the bin. With the assumption (Harr-von Karman hypothesis) that the circumferential stress is equal to the major principal stress, the system becomes statically determinate in the sense that there are as many equations of stress as unknowns. Once the basic material behavior is described, a broad spectrum of bin hopper engineering problems can be formulated and pursued to predictive solutions. In principle, computation of stress and deformation fields can be accomplished with sufficient effort. Equation (48) is indeterminate at r = ri. The relatively large grain sizes often encountered in bulk materials handling problems necessitates an explicit recognition of the conditions under which a phenomenological approach reasonably can be assumed to apply, especially since there are important practical cases where the identity of individual particles must be maintained. WebHopper Design Calculation Original Title: Hopper Design calculation Uploaded by Hamid Mansouri Description: Hopper Design calculation XLS sheet- for Process Engineers ( for Hopper and Silo Sizing) Copyright: All Rights Reserved Flag for inappropriate content of 126 1 Flow function a b 0 0.035 f C =as 12 +bs 1 + c 1 or ' 0 c 0 0.5 1 WebHopper Design Report 1 Calculation Manual. fc = unconfined compressive strength, Simplicity and ease of application are the principal advantages claimed for the empirical approach. The cohesive strength is measured by shear-cell testing, as described in ASTM D-1628 [2] and D-6773 [3]. Examples of cited criteria are as follows: Empirical flow rate formulas are intended for use in estimating the size of outlet with a given hopper slope required for a specified flow rate. Each calculator includes vital dimensions for each storage tank, including lengths and diameters, as well as freeboard, clearances, outlet lengths and hopper measurements. where the substitution of unit weight for the product pg has been made. If you are author or own the copyright of this book, please report to us by using this DMCA report form. where the expensive revisions of other parts of the system had to be made belatedly. In figure 11C three types of zones are present. Elastic materials are conservative in the thermodynamic sense; no net work is done on an elastic material over a cycle of loading and unloading. In the absence of flow-promoting devices, dM/ds = 0, and for most practical purposes, the flow can be considered isothermal. Once the wall friction results are known, the recommended hopper angle to ensure mass flow can be readily calculated. A material with a parabolic or Torre yield condition (fig. Since free gravity discharge of bin hoppers is under consideration, the weight of material characterized by its specific weight tends to cause flow; whereas the strength of material, say, unconfined compressive strength Co tends to resist flow at the hopper outlet which has a characteristic dimension D. To account for different shapes of outlets, a shape factor K will be employed. At the outlet of a wedge- or cone-shaped hopper with axis-z positive downwards and flow vertical, then, where again is the hopper wall inclination from the vertical. We recommend that you try to achieve a 3:1 or 2.8:1 height to diameter ratio for the most economical silo size. This is accomplished by first testing the material to measure wall friction, and then calculating the minimum hopper angle that will allow mass flow. FIGURE 7. For example, let. Funnel flow figure 12B is characterized by the formation of a narrow zone of fast-moving material, centered over the outlet that is bounded by zones of stationary material adjacent to the bin walls. Follow this guidance to avoid common solids-handling issues, such as erratic flow and no flow. A screw that has a constant pitch and diameter (and a constant shaft diameter) will give rise to the formation of a flow channel at the back of the hopper over the first flight of the screw. Even in those materials generally termed cohesionless, such as dry sand, an interlocking effect through dilation produces an apparent cohesion when shearing or flowing occurs which means the material acts as though it had true cohesion. FIGURE 2. Yet despite the maturity of the subject, design codes for grain silos and bins still are controversial. All field quantities such as stress and strain thus refer to averages over a small volume about a point.