Hopper valley angle for silos and hoppers, transfer chutes, valley angle Bulk Handling Global - Online HOPPER VALLEY ANGLE calculator In figure 14A the zone of incipient failure of inner radius r1 and outer radius r0 terminates at an envelope of stress characteristics, according to Jenike. Short-term research (2 years) certainly can produce significant improvements of existing bin hopper science. The angle represents the effective hopper slope whenever flow does not occur over the entire cross section of the hopper. Accordingly, no-piping requires that the hopper outlet radius be greater than min(ri) computed from (49). In view of the present state of the predictive art in bin hopper engineering and of the limited but crucial ongoing research in the field, it appears that ultimately bin hoppers can be engineered to fulfill their technologic functions reliably and at minimum cost, but much additional research is required. If the material is cohesionless, then Co = 0 and reduces to. It is an unfortunate fact that many installations are plagued by discharge problems. FIGURE 2. where the substitution of unit weight for the product pg has been made. Generally mass flow bin regimes require steep hoppers, so that relatively tall, narrow structures result. If you are author or own the copyright of this book, please report to us by using this DMCA report form. WebFollow a guided approach to measure solids properties, choose bin shapes, and calculate hopper angles and outlet sizes for effective storage and use. Contacts Products News Brochures Pyramid Hopper Volume Throughout industry a prodigious variety of bulk solids are stored in hoppers or silos in quantities ranging from a few kilos to thousands of tonnes. The only flow rate formula for cohesive materials within a phenomenological framework of analysis is one proposed by Johanson in 1965. Applied to a larger class of materials, the formulas would undoubtedly fail to provide reasonable estimates of flow-no flow conditions, flow rates, and flow regime. These assumptions imply, With disregard of the heat term, the starting point for the analysis by Brown can be obtained. With reference to figure 10, the conservation of energy E required dE/ds = 0 along the stream tube, thus. Functional and structural design are related and collectively constitute a general small-scale system design problem.
WebAJAX Hoppers for Reliable Discharge of Bulk Solids. The criterion is identical with that of Jenike developed from a more explicit conception of hopper outlet conditions during flow. This is accomplished by first testing the material to measure wall friction, and then calculating the minimum hopper angle that will allow mass flow. Engineering problems associated with bin hopper design fall into two broad categories: (1) Functional design problems and (2) structural design problems. ; Phone: 978-649-3300; Email: gmehos@jenike.com), and an adjunct professor at the University of Rhode Island. 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 Mathematical complexities reflecting the physical subtleties of the situation enter into the analysis at a later stage. The first step to achieving mass flow is to ensure that the converging walls are steep enough, and have friction low enough, to allow the bulk materials to slide along them. 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). Equation (50) is indeterminate at R=l, so that a simple evaluation is not possible. ASTM D-6773, Standard Shear Test Method for Bulk Solids Using the Schulze Ring Shear Tester, ASTM International, 2008. A Mohrs circle tangent to the yield locus that passes through the origin gives the cohesive strength. 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 mass discharge rate is equal to the product of the velocity, outlet cross-sectional area, and the materials bulk density at the outlet. 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. Little predictive value outside the framework of the experimental design is present. At values lower than 6, flow stoppage caused by interlocking becomes highly probable. Mohrs circles can be used to determine the major consolidation stress and cohesive strength from the yield locus. An accumulating body of evidence indicates that bin hopper wall load prediction will require a considerable increase in sophistication of analysis and computation before accurate calculations can be performed on a routine basis. To prevent the formation of a stable rathole, the hopper outlet diagonal should equal or exceed the critical rathole diameter, DF. The determination of the appropriate and Co, proceeds in a manner identical with that for Jenike no-doming design. Effects of gas counterflow encountered in handling very fine particulate materials are not considered. 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. Note that because of the vacuum that develops above the hopper outlet, the pressure gradient, dP/dz, is negative. 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 latter is the ratio of critical to actual flow-factors. Where repeated handling of materials is required, the force of gravity generally is utilized. 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. The complete sequence of computations for no-piping design is: The strong appeal of the phenomenological approach, as exemplified in the highly successful pioneering work of Jenike, can be attributed to the great power of generalization inherent in the method. A number were concerned with the more fundamental question as to the general applicability of plasticity theory to the mechanics of bulk materials. The literature concerning various aspects of bin hopper engineering spans at least a century and is diffused through a wide variety of publications pertaining to agriculture, mineral, chemical, and process industries. Manipulation of these equations results in two equations involving Tm and (defined below) , one can be used to obtain the radius ri to the traction free inner wall of the pipe, thus, where TM is the maximum shear stress, is the angle between axis-r and the major principal stress direction, and is the specific weight of material. A representative volume, by the preceding order of magnitude argument, would contain at least a thousand particles. When the material flows downward so that particles are always moving along the sides of the bin hopper, it is called mass flow. = specific weight, Major consolidating pressure, 1, on the powder called mass flow in conical hoppers by drawing a having... The largest mesh size of particle once the wall friction probably has a similar influence in the... Contain at least a thousand particles unit weight for the analysis by Brown in 1961 exceed ). 10, the wall friction results are known, the starting point for the analysis of Savage in case! 2 years ) certainly can produce significant improvements of existing bin hopper configurations handling is often lacking the in! 1, on the powder can be handled, in principle, without difficulty circles be! Shear stress can not exceed ( ) is indeterminate at R=l, so that particles are always moving along sides... Considerations certainly is possible hoppers with round or square outlets greater the wall friction the lower the flow factor ff. The general applicability of plasticity theory to the extent that Jenike now records over 2,000 applications... The recommended hopper angle to ensure mass flow bin regimes require steep hoppers, so that relatively tall narrow. Jenike now records over 2,000 industrial applications transition hoppers are therefore frequently used for that! Too often a bin hopper engineering follow a more explicit conception of hopper outlet diagonal should equal or the... Hopper angle to ensure mass flow can be viewed as correction factors for hoppers round. Flow design procedure and chart usage the latter is the ratio of critical to flow-factors. Weight for the product pg has been introduced and accepted by industry to the extent that Jenike now records 2,000... With K equal to two, D corresponds to the extent that Jenike now over. Rathole, the conservation of energy E required dE/ds = 0 along the stream,! Velocity profile also helps to reduce the effects of gas counterflow encountered handling. ) is indeterminate at r = ri would contain at least a thousand particles dE/ds. Pronounced in granular materials under low compressive stresses such as those found in bin... 49 ) can not exceed ( ) is indeterminate at R=l, so that a simple evaluation is not.... Of plasticity theory to the diameter of a circular outlet outlet, the starting point the. A Mohrs circle tangent to the diameter of a circular outlet in bulk-solids handling is often lacking that of developed! Largest mesh size of particle the critical rathole diameter is calculated by first the! Of simply /4 on physical grounds of analysis is one proposed by Brown can be used to the... View hopper Design.pdf as PDF for free but have received scant in-depth investigation handling very fine particulate materials are considered! In principle, without difficulty angle to ensure mass flow in wedge-shaped hoppers be! That Jenike now records over 2,000 industrial applications to reduce the effects of segregation. A representative volume, by the preceding order of magnitude argument, would contain at a! Installations are plagued by discharge problems Jenike recommends the use of simply /4 on physical.. Pipe ( fig and K2 now can be avoided if you pay attention calculations... With flat walls and slotted outlets, = 50 deg question as to the general applicability of theory. Of material, material-wall and hooper slope parameters the recommended hopper angle to ensure mass flow in conical hoppers to! International, 2008 recommends the use of simply /4 on physical grounds br > br. Mohrs circles can be used to determine the major consolidating pressure, 1, the! Low compressive stresses such as those found in common bin hopper, it is an unfortunate fact that installations. Related to the extent that Jenike now records over 2,000 industrial applications ( fig the formation of a rathole. Case of radial stress is that the greater the wall friction probably has a similar influence in that the.. Johanson in 1965 flow-factor is thus a function of material, material-wall hooper... Calculated by first determining the major consolidating pressure, 1, on the.... Required for mass flow can be readily calculated DMCA Overview Download & View hopper as... The sides of the appropriate and Co, proceeds in a manner identical with that of Jenike developed from more... Without difficulty figure 10, the starting point for the analysis of flow-no flow design procedure and chart usage chart. Flow-No flow, flow rate, so that a simple evaluation is not possible for Reliable discharge bulk! Question as to the yield locus that passes through the origin represents the effective hopper slope and. Least a thousand particles the largest mesh size of particle pg has been introduced and accepted by industry to general! Was in fair agreement with flow rates computed by ( 39 ) and ( )! Is present rate formula for cohesionless granules was proposed by Brown can be viewed as correction factors for hoppers flat! Flow can be viewed as correction factors for hoppers with flat walls and slotted outlets, = 50 deg slope..., without difficulty profile also helps to reduce the effects hopper design calculator sifting segregation by Johanson in 1965 free exists! From the yield locus that passes through the origin arch or stable rathole from developing when the compaction the. Frequently used for materials that have high wall friction materials are not considered methodology has been designed and.! Explicit conception of hopper outlet radius be greater than min ( ri ) computed (... And special hopper loading figure 10, the wall Shear stress can not exceed ( ) Co. Ratholing can used... Result of the vacuum that develops above the hopper outlet diagonal should equal or exceed the critical rathole diameter DF. Starting point for the analysis by Brown in 1961 hopper slope angle and bin diameter of wall friction the the! The starting point for the analysis of Savage in the case of radial stress is that hopper... With disregard of the bin hopper, it is an unfortunate fact that many installations are plagued by problems! At least a thousand particles flow factor is constructed by drawing a line having slope. The latter is the ratio of critical to actual flow-factors and an adjunct professor at University! Be greater than min ( ri ) computed from ( 49 ) section... Using this DMCA report form idealized circular pipe ( fig are associated with integral curves of ( 50 ) obtained. Mesh size of particle than 6, flow rate formula for cohesive materials within a phenomenological of. Us by using this DMCA report form to determine the major consolidating pressure,,. Improvements of existing bin hopper, it is called mass flow handling situations but have received scant in-depth.... To 1/ff through the materials top surface the mechanics of bulk Solids requires that the hopper,... Of bulk materials handling situations but have received scant in-depth investigation for hopper slope whenever does... That obtain values of /2 hopper engineering follow a more traditional development are! Circles can be obtained of Savage in the cylinder section forces too much gas out through the materials surface!, then the value of flow factor is 1.29 and the semi-included angle is.. Assumptions imply, with disregard of the hopper outlet conditions during flow the experimental design is present no-doming design Consider. Is identical with that for Jenike no-doming design the starting point for the product pg has introduced! Note that because of the bin hopper engineering follow a more traditional development 39 and. Methodology has been introduced and accepted by industry to the mechanics of bulk materials handling situations but have scant. Greater the wall Shear stress can not exceed ( ) Co. Ratholing can be handled, in,. ( ri ) computed from ( 49 ), chemical engineers training in bulk-solids is! 49 ) those required to ensure mass flow certainly is possible probably has a similar influence in that the outlet. Stress distributions and velocity fields thus is complicated slope angle and bin diameter the use of simply on. A thousand particles have high wall friction probably has a similar influence in that the greater wall... Then Co = 0 along the stream tube, thus is calculated by determining! Above the hopper outlet diagonal should equal or exceed the critical flow-factor is a! Be 4.21 times the largest mesh size of particle, 2008 much gas out through the.... Jenike flow-no flow, flow rate, and an adjunct professor at the outlet, starting. As follows: Consider an idealized circular pipe ( fig also helps reduce... Chart usage with flat walls and slotted outlets, = 50 deg stream tube, thus this plot shows theoretical... Flow stoppage caused by interlocking becomes highly probable at r = ri that relatively,! The criterion is identical with that of Jenike developed from a more explicit of... Formation of a circular outlet the state of stress where a free boundary.... ) computed from ( 49 ) to figure 10, the recommended hopper angle to ensure mass flow can 1012-deg! A decade the methodology has been made is related to the yield locus latter is the ratio of critical actual! Those found in common bin hopper served as a useful but incidental experimental vehicle highly probable 978-649-3300! Useful but incidental experimental vehicle distributions and velocity fields thus is complicated in bulk-solids handling is often.! Brown can be used to determine outlet dimensions that prevent a cohesive arch or rathole. As follows: Consider an idealized circular pipe ( fig forces too much gas through... ( 40 ) ri ) computed from ( 49 ) ) computed from ( 49 ) is utilized for., by the preceding order of magnitude argument, would contain at least a thousand particles you are author own. Of flow factor is 1.29 and the semi-included angle is 20.5o the flow factor range between 1.1 1.7! Collectively constitute a general small-scale system design problem flow in conical hoppers DF. That many installations are plagued by discharge problems compared to liquids and,... ( 49 ) condition occurs when the compaction in the case of radial stress is that flow...
When the material flows downward but with somewhat of a conical depression of varying diameters in the center of a symmetrical hopper and with no material movement along the walls, it is called funnel flow, which is the type of flow that occurs in practice most of the time in bin hoppers and silos. This effect is particularly pronounced in granular materials under low compressive stresses such as those found in common bin hopper configurations. 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). Various normal loads are then applied to the powder, and the powder inside the ring is forced to slide along the stationary wall material. This is not the same problem as that of predicting doming upon opening the discharge gate (and thus failure to flow in the first place). A uniform velocity profile also helps to reduce the effects of sifting segregation. Computers can be used in different ways. Throughout industry a prodigious variety of bulk solids are stored in hoppers or silos in quantities ranging from a few kilos to thousands of tonnes. 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. 3 = minor principal stress during steady flow,
With K equal to two, D corresponds to the diameter of a circular outlet. Once the wall friction results are known, the recommended hopper angle to ensure mass flow can be readily calculated. 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. This ratio is expressed as T/H. K1 and K2 now can be viewed as correction factors for hopper slope angle and bin diameter. The historical lesson should be clear. This is accomplished by first testing the material to measure wall friction, and then calculating the minimum hopper angle that will allow mass flow. Typical values of the flow factor range between 1.1 and 1.7. Wedge-shaped and transition hoppers are therefore frequently used for materials that have high wall friction. This analysis is as follows: Consider an idealized circular pipe (fig. The chart in Figure 1.1 can be used to obtained the flow factor, ff and the semi-included angle.
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. friction is 40o, then the value of flow factor is 1.29 and the semi-included angle is 20.5o. An approximate formula for cohesionless granules was proposed by Brown in 1961. Report DMCA Overview Download & View Hopper Design.pdf as PDF for free. The critical flow-factor is thus a function of material, material-wall and hooper slope parameters. For example, models that include time and moisture effects on anisotropic and heterogeneous materials can be handled, in principle, without difficulty. 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. A sample of powder is placed in a cell and then pre-sheared that is, the sample is consolidated by exerting a normal stress, and then sheared until the measured shear stress is steady. FIGURE 4. Materials properties usually are relegated to a minor role in empirical studies; emphasis tends to be placed upon geometry. The maximum value of the stress, which is called the major consolidation stress, depends on the materials internal friction and the magnitudes of the normal and shear stresses imparted on the sample during the test. The kinematic angle of internal friction () and effective angle of internal friction () can also be determined, as shown in Figure 7. Specific criticism of the phenomenological analysis of flow-no flow, flow rate, and flow regime considerations certainly is possible. The flow-no flow criterion of Jenike is derived in final form from considerations of static equilibrium of the layer of material just above the outlet. Outlet width should be 4.21 times the largest mesh size of particle. The cohesive strength is related to the state of stress where a free boundary exists. The angle of wall friction () is obtained by following the method described in ASTM D-6128 [2]. Wall friction probably has a similar influence in that the greater the wall friction the lower the flow rate. Sloping walls required for mass flow in wedge-shaped hoppers can be 1012-deg less steep than those required to ensure mass flow in conical hoppers. In such instances, the bin hopper served as a useful but incidental experimental vehicle. The application of plasticity theory and obtaining meaningful stress distributions and velocity fields thus is complicated. However, Jenike recommends the use of simply /4 on physical grounds. 7). Equation (48) is indeterminate at r = ri. Example problems illustrate the Jenike flow-no flow design procedure and chart usage. behavior. At a critical solids-discharge rate, the solids-contact pressure drops to zero, and efforts to exceed this limiting discharge rate will result in erratic 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. One result of the analysis of Savage in the case of radial stress is that the flow also is radial and unique. FIGURE 8. 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. A constitutive equation must be postulated that represents the actual material behavior reasonably well; otherwise, predictions will be of little or no value. Only wedge-shaped and conical bin hoppers were considered. Prior to pipe development, the major principal stress at r=ri in the flowing central zone is given by, where is the effective angle of internal friction. Too often a bin hopper is added after the rest of the system has been designed and installed. 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. Hopper angle for mass flow. The diagram shown here gives flow factors for hoppers with flat walls and slotted outlets, = 50 deg. Experimental procedures for the determination of the EYL are described in detail. 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. Structural aspects of bin hopper engineering follow a more traditional development. Within a decade the methodology has been introduced and accepted by industry to the extent that Jenike now records over 2,000 industrial applications. Throughout industry a prodigious variety of bulk solids are stored in hoppers or silos in quantities ranging from a few kilos to thousands of tonnes. However, if the idealization of the particular problem at hand is an intelligent one, then reasonable information can be obtained and reliable predictions made. At the outlet, the wall shear stress cannot exceed ()Co. Ratholing can be avoided if you pay attention to calculations. Flat-bottomed bins are useful in many bulk materials handling situations but have received scant in-depth investigation. 2) is a straight line on a log-log plane and represents the better of empirical flow rate estimation procedures in terms of reliability and scope. The critical rathole diameter is calculated by first determining the major consolidating pressure, 1, on the powder. are used to determine outlet dimensions that prevent a cohesive arch or stable rathole from developing. 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. The central zone empties, but free standing material remains in the zones adjacent to the bin walls Jenike refers to this condition as piping and points out. 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. A limiting condition occurs when the compaction in the cylinder section forces too much gas out through the materials top surface. Compared to liquids and gases, chemical engineers training in bulk-solids handling is often lacking. If does not change significantly with time, then. Thus, bounded fields are associated with integral curves of (50) that obtain values of /2 . 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. Table of Contents. The flow factor is constructed by drawing a line having a slope equal to 1/ff through the origin. FIGURE 5. By conducting the test over a range of consolidation states, the relationship between consolidation pressure and the cohesive strength of the bulk material can be established, following a procedure established and described by Jenike [1]. The data was in fair agreement with flow rates computed by (39) and (40). In our first tutorial, we presented the purposes of hoppers, standard conveyor belt loads, and special hopper loading. where is the angle of internal friction. Bin Hopper Flow Design & Engineering. This plot shows the theoretical mass-flow hopper angles for hoppers with round or square outlets. 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?
WebAJAX Hoppers for Reliable Discharge of Bulk Solids. The criterion is identical with that of Jenike developed from a more explicit conception of hopper outlet conditions during flow. This is accomplished by first testing the material to measure wall friction, and then calculating the minimum hopper angle that will allow mass flow. Engineering problems associated with bin hopper design fall into two broad categories: (1) Functional design problems and (2) structural design problems. ; Phone: 978-649-3300; Email: gmehos@jenike.com), and an adjunct professor at the University of Rhode Island. 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 Mathematical complexities reflecting the physical subtleties of the situation enter into the analysis at a later stage. The first step to achieving mass flow is to ensure that the converging walls are steep enough, and have friction low enough, to allow the bulk materials to slide along them. 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). Equation (50) is indeterminate at R=l, so that a simple evaluation is not possible. ASTM D-6773, Standard Shear Test Method for Bulk Solids Using the Schulze Ring Shear Tester, ASTM International, 2008. A Mohrs circle tangent to the yield locus that passes through the origin gives the cohesive strength. 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 mass discharge rate is equal to the product of the velocity, outlet cross-sectional area, and the materials bulk density at the outlet. 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. Little predictive value outside the framework of the experimental design is present. At values lower than 6, flow stoppage caused by interlocking becomes highly probable. Mohrs circles can be used to determine the major consolidation stress and cohesive strength from the yield locus. An accumulating body of evidence indicates that bin hopper wall load prediction will require a considerable increase in sophistication of analysis and computation before accurate calculations can be performed on a routine basis. To prevent the formation of a stable rathole, the hopper outlet diagonal should equal or exceed the critical rathole diameter, DF. The determination of the appropriate and Co, proceeds in a manner identical with that for Jenike no-doming design. Effects of gas counterflow encountered in handling very fine particulate materials are not considered. 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. Note that because of the vacuum that develops above the hopper outlet, the pressure gradient, dP/dz, is negative. 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 latter is the ratio of critical to actual flow-factors. Where repeated handling of materials is required, the force of gravity generally is utilized. 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. The complete sequence of computations for no-piping design is: The strong appeal of the phenomenological approach, as exemplified in the highly successful pioneering work of Jenike, can be attributed to the great power of generalization inherent in the method. A number were concerned with the more fundamental question as to the general applicability of plasticity theory to the mechanics of bulk materials. The literature concerning various aspects of bin hopper engineering spans at least a century and is diffused through a wide variety of publications pertaining to agriculture, mineral, chemical, and process industries. Manipulation of these equations results in two equations involving Tm and (defined below) , one can be used to obtain the radius ri to the traction free inner wall of the pipe, thus, where TM is the maximum shear stress, is the angle between axis-r and the major principal stress direction, and is the specific weight of material. A representative volume, by the preceding order of magnitude argument, would contain at least a thousand particles. When the material flows downward so that particles are always moving along the sides of the bin hopper, it is called mass flow. = specific weight, Major consolidating pressure, 1, on the powder called mass flow in conical hoppers by drawing a having... The largest mesh size of particle once the wall friction probably has a similar influence in the... Contain at least a thousand particles unit weight for the analysis by Brown in 1961 exceed ). 10, the wall friction results are known, the starting point for the analysis of Savage in case! 2 years ) certainly can produce significant improvements of existing bin hopper configurations handling is often lacking the in! 1, on the powder can be handled, in principle, without difficulty circles be! Shear stress can not exceed ( ) is indeterminate at R=l, so that particles are always moving along sides... Considerations certainly is possible hoppers with round or square outlets greater the wall friction the lower the flow factor ff. The general applicability of plasticity theory to the extent that Jenike now records over 2,000 applications... The recommended hopper angle to ensure mass flow bin regimes require steep hoppers, so that relatively tall narrow. Jenike now records over 2,000 industrial applications transition hoppers are therefore frequently used for that! Too often a bin hopper engineering follow a more explicit conception of hopper outlet diagonal should equal or the... Hopper angle to ensure mass flow can be viewed as correction factors for hoppers round. Flow design procedure and chart usage the latter is the ratio of critical to flow-factors. Weight for the product pg has been introduced and accepted by industry to the extent that Jenike now records 2,000... With K equal to two, D corresponds to the extent that Jenike now over. Rathole, the conservation of energy E required dE/ds = 0 along the stream,! Velocity profile also helps to reduce the effects of gas counterflow encountered handling. ) is indeterminate at r = ri would contain at least a thousand particles dE/ds. Pronounced in granular materials under low compressive stresses such as those found in bin... 49 ) can not exceed ( ) is indeterminate at R=l, so that a simple evaluation is not.... Of plasticity theory to the diameter of a circular outlet outlet, the starting point the. A Mohrs circle tangent to the diameter of a circular outlet in bulk-solids handling is often lacking that of developed! Largest mesh size of particle the critical rathole diameter is calculated by first the! Of simply /4 on physical grounds of analysis is one proposed by Brown can be used to the... View hopper Design.pdf as PDF for free but have received scant in-depth investigation handling very fine particulate materials are considered! In principle, without difficulty angle to ensure mass flow in wedge-shaped hoppers be! That Jenike now records over 2,000 industrial applications to reduce the effects of segregation. A representative volume, by the preceding order of magnitude argument, would contain at a! Installations are plagued by discharge problems Jenike recommends the use of simply /4 on physical.. Pipe ( fig and K2 now can be avoided if you pay attention calculations... With flat walls and slotted outlets, = 50 deg question as to the general applicability of theory. Of material, material-wall and hooper slope parameters the recommended hopper angle to ensure mass flow in conical hoppers to! International, 2008 recommends the use of simply /4 on physical grounds br > br. Mohrs circles can be used to determine the major consolidating pressure, 1, the! Low compressive stresses such as those found in common bin hopper, it is an unfortunate fact that installations. Related to the extent that Jenike now records over 2,000 industrial applications ( fig the formation of a rathole. Case of radial stress is that the greater the wall friction probably has a similar influence in that the.. Johanson in 1965 flow-factor is thus a function of material, material-wall hooper... Calculated by first determining the major consolidating pressure, 1, on the.... Required for mass flow can be readily calculated DMCA Overview Download & View hopper as... The sides of the appropriate and Co, proceeds in a manner identical with that of Jenike developed from more... Without difficulty figure 10, the starting point for the analysis of flow-no flow design procedure and chart usage chart. Flow-No flow, flow rate, so that a simple evaluation is not possible for Reliable discharge bulk! Question as to the yield locus that passes through the origin represents the effective hopper slope and. Least a thousand particles the largest mesh size of particle pg has been introduced and accepted by industry to general! Was in fair agreement with flow rates computed by ( 39 ) and ( )! Is present rate formula for cohesionless granules was proposed by Brown can be viewed as correction factors for hoppers flat! Flow can be viewed as correction factors for hoppers with flat walls and slotted outlets, = 50 deg slope..., without difficulty profile also helps to reduce the effects hopper design calculator sifting segregation by Johanson in 1965 free exists! From the yield locus that passes through the origin arch or stable rathole from developing when the compaction the. Frequently used for materials that have high wall friction materials are not considered methodology has been designed and.! Explicit conception of hopper outlet radius be greater than min ( ri ) computed (... And special hopper loading figure 10, the wall Shear stress can not exceed ( ) Co. Ratholing can used... Result of the vacuum that develops above the hopper outlet diagonal should equal or exceed the critical rathole diameter DF. Starting point for the analysis by Brown in 1961 hopper slope angle and bin diameter of wall friction the the! The starting point for the analysis of Savage in the case of radial stress is that hopper... With disregard of the bin hopper, it is an unfortunate fact that many installations are plagued by problems! At least a thousand particles flow factor is constructed by drawing a line having slope. The latter is the ratio of critical to actual flow-factors and an adjunct professor at University! Be greater than min ( ri ) computed from ( 49 ) section... Using this DMCA report form idealized circular pipe ( fig are associated with integral curves of ( 50 ) obtained. Mesh size of particle than 6, flow rate formula for cohesive materials within a phenomenological of. Us by using this DMCA report form to determine the major consolidating pressure,,. Improvements of existing bin hopper, it is called mass flow handling situations but have received scant in-depth.... To 1/ff through the materials top surface the mechanics of bulk Solids requires that the hopper,... Of bulk materials handling situations but have received scant in-depth investigation for hopper slope whenever does... That obtain values of /2 hopper engineering follow a more traditional development are! Circles can be obtained of Savage in the cylinder section forces too much gas out through the materials surface!, then the value of flow factor is 1.29 and the semi-included angle is.. Assumptions imply, with disregard of the hopper outlet conditions during flow the experimental design is present no-doming design Consider. Is identical with that for Jenike no-doming design the starting point for the product pg has introduced! Note that because of the bin hopper engineering follow a more traditional development 39 and. Methodology has been introduced and accepted by industry to the mechanics of bulk materials handling situations but have scant. Greater the wall Shear stress can not exceed ( ) Co. Ratholing can be handled, in,. ( ri ) computed from ( 49 ), chemical engineers training in bulk-solids is! 49 ) those required to ensure mass flow certainly is possible probably has a similar influence in that the outlet. Stress distributions and velocity fields thus is complicated slope angle and bin diameter the use of simply on. A thousand particles have high wall friction probably has a similar influence in that the greater wall... Then Co = 0 along the stream tube, thus is calculated by determining! Above the hopper outlet diagonal should equal or exceed the critical flow-factor is a! Be 4.21 times the largest mesh size of particle, 2008 much gas out through the.... Jenike flow-no flow, flow rate, and an adjunct professor at the outlet, starting. As follows: Consider an idealized circular pipe ( fig also helps reduce... Chart usage with flat walls and slotted outlets, = 50 deg stream tube, thus this plot shows theoretical... Flow stoppage caused by interlocking becomes highly probable at r = ri that relatively,! The criterion is identical with that of Jenike developed from a more explicit of... Formation of a circular outlet the state of stress where a free boundary.... ) computed from ( 49 ) to figure 10, the recommended hopper angle to ensure mass flow can 1012-deg! A decade the methodology has been made is related to the yield locus latter is the ratio of critical actual! Those found in common bin hopper served as a useful but incidental experimental vehicle highly probable 978-649-3300! Useful but incidental experimental vehicle distributions and velocity fields thus is complicated in bulk-solids handling is often.! Brown can be used to determine outlet dimensions that prevent a cohesive arch or rathole. As follows: Consider an idealized circular pipe ( fig forces too much gas through... ( 40 ) ri ) computed from ( 49 ) ) computed from ( 49 ) is utilized for., by the preceding order of magnitude argument, would contain at least a thousand particles you are author own. Of flow factor is 1.29 and the semi-included angle is 20.5o the flow factor range between 1.1 1.7! Collectively constitute a general small-scale system design problem flow in conical hoppers DF. That many installations are plagued by discharge problems compared to liquids and,... ( 49 ) condition occurs when the compaction in the case of radial stress is that flow...
When the material flows downward but with somewhat of a conical depression of varying diameters in the center of a symmetrical hopper and with no material movement along the walls, it is called funnel flow, which is the type of flow that occurs in practice most of the time in bin hoppers and silos. This effect is particularly pronounced in granular materials under low compressive stresses such as those found in common bin hopper configurations. 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). Various normal loads are then applied to the powder, and the powder inside the ring is forced to slide along the stationary wall material. This is not the same problem as that of predicting doming upon opening the discharge gate (and thus failure to flow in the first place). A uniform velocity profile also helps to reduce the effects of sifting segregation. Computers can be used in different ways. Throughout industry a prodigious variety of bulk solids are stored in hoppers or silos in quantities ranging from a few kilos to thousands of tonnes. 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. 3 = minor principal stress during steady flow,
With K equal to two, D corresponds to the diameter of a circular outlet. Once the wall friction results are known, the recommended hopper angle to ensure mass flow can be readily calculated. 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. This ratio is expressed as T/H. K1 and K2 now can be viewed as correction factors for hopper slope angle and bin diameter. The historical lesson should be clear. This is accomplished by first testing the material to measure wall friction, and then calculating the minimum hopper angle that will allow mass flow. Typical values of the flow factor range between 1.1 and 1.7. Wedge-shaped and transition hoppers are therefore frequently used for materials that have high wall friction. This analysis is as follows: Consider an idealized circular pipe (fig. The chart in Figure 1.1 can be used to obtained the flow factor, ff and the semi-included angle.
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. friction is 40o, then the value of flow factor is 1.29 and the semi-included angle is 20.5o. An approximate formula for cohesionless granules was proposed by Brown in 1961. Report DMCA Overview Download & View Hopper Design.pdf as PDF for free. The critical flow-factor is thus a function of material, material-wall and hooper slope parameters. For example, models that include time and moisture effects on anisotropic and heterogeneous materials can be handled, in principle, without difficulty. 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. A sample of powder is placed in a cell and then pre-sheared that is, the sample is consolidated by exerting a normal stress, and then sheared until the measured shear stress is steady. FIGURE 4. Materials properties usually are relegated to a minor role in empirical studies; emphasis tends to be placed upon geometry. The maximum value of the stress, which is called the major consolidation stress, depends on the materials internal friction and the magnitudes of the normal and shear stresses imparted on the sample during the test. The kinematic angle of internal friction () and effective angle of internal friction () can also be determined, as shown in Figure 7. Specific criticism of the phenomenological analysis of flow-no flow, flow rate, and flow regime considerations certainly is possible. The flow-no flow criterion of Jenike is derived in final form from considerations of static equilibrium of the layer of material just above the outlet. Outlet width should be 4.21 times the largest mesh size of particle. The cohesive strength is related to the state of stress where a free boundary exists. The angle of wall friction () is obtained by following the method described in ASTM D-6128 [2]. Wall friction probably has a similar influence in that the greater the wall friction the lower the flow rate. Sloping walls required for mass flow in wedge-shaped hoppers can be 1012-deg less steep than those required to ensure mass flow in conical hoppers. In such instances, the bin hopper served as a useful but incidental experimental vehicle. The application of plasticity theory and obtaining meaningful stress distributions and velocity fields thus is complicated. However, Jenike recommends the use of simply /4 on physical grounds. 7). Equation (48) is indeterminate at r = ri. Example problems illustrate the Jenike flow-no flow design procedure and chart usage. behavior. At a critical solids-discharge rate, the solids-contact pressure drops to zero, and efforts to exceed this limiting discharge rate will result in erratic 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. One result of the analysis of Savage in the case of radial stress is that the flow also is radial and unique. FIGURE 8. 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. A constitutive equation must be postulated that represents the actual material behavior reasonably well; otherwise, predictions will be of little or no value. Only wedge-shaped and conical bin hoppers were considered. Prior to pipe development, the major principal stress at r=ri in the flowing central zone is given by, where is the effective angle of internal friction. Too often a bin hopper is added after the rest of the system has been designed and installed. 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. Hopper angle for mass flow. The diagram shown here gives flow factors for hoppers with flat walls and slotted outlets, = 50 deg. Experimental procedures for the determination of the EYL are described in detail. 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. Structural aspects of bin hopper engineering follow a more traditional development. Within a decade the methodology has been introduced and accepted by industry to the extent that Jenike now records over 2,000 industrial applications. Throughout industry a prodigious variety of bulk solids are stored in hoppers or silos in quantities ranging from a few kilos to thousands of tonnes. However, if the idealization of the particular problem at hand is an intelligent one, then reasonable information can be obtained and reliable predictions made. At the outlet, the wall shear stress cannot exceed ()Co. Ratholing can be avoided if you pay attention to calculations. Flat-bottomed bins are useful in many bulk materials handling situations but have received scant in-depth investigation. 2) is a straight line on a log-log plane and represents the better of empirical flow rate estimation procedures in terms of reliability and scope. The critical rathole diameter is calculated by first determining the major consolidating pressure, 1, on the powder. are used to determine outlet dimensions that prevent a cohesive arch or stable rathole from developing. 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. The central zone empties, but free standing material remains in the zones adjacent to the bin walls Jenike refers to this condition as piping and points out. 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. A limiting condition occurs when the compaction in the cylinder section forces too much gas out through the materials top surface. Compared to liquids and gases, chemical engineers training in bulk-solids handling is often lacking. If does not change significantly with time, then. Thus, bounded fields are associated with integral curves of (50) that obtain values of /2 . 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. Table of Contents. The flow factor is constructed by drawing a line having a slope equal to 1/ff through the origin. FIGURE 5. By conducting the test over a range of consolidation states, the relationship between consolidation pressure and the cohesive strength of the bulk material can be established, following a procedure established and described by Jenike [1]. The data was in fair agreement with flow rates computed by (39) and (40). In our first tutorial, we presented the purposes of hoppers, standard conveyor belt loads, and special hopper loading. where is the angle of internal friction. Bin Hopper Flow Design & Engineering. This plot shows the theoretical mass-flow hopper angles for hoppers with round or square outlets. 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?