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Bulk Solids Flow by the Numbers

Storing and discharging powders and pellets: density, friction, silo pressures, flow patterns, outlets and discharge rates, worked through one compounding plant

Why powders and pellets behave unlike liquids, and how to size and run bins and silos so they hold what they should, discharge reliably and do not arch, rathole or segregate.

11 chapters · About 110 minutes · Free to read · Intermediate mechanical and process engineering

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KEVOS® LibraryENGINEERINGBulk Solids Flowby the NumbersKEVOS® ORIGINAL BOOK11 CHAPTERS

About this book

A bin of pellets or powder looks like a tank of liquid that happens to be dry. It is not. A bulk solid holds itself up by friction, so the pressure at the bottom of a tall silo stops rising after a few diameters of depth. It can stand in a steep heap, bridge across an outlet or leave a stable hole down its middle. It flows out of an outlet at a rate that hardly depends on how full the bin is. It sorts itself by size when it is poured, shaken or discharged. Each of these behaviours has caused stopped production lines, damaged silos and injuries, and each can be predicted with a few measurements and some straightforward arithmetic.

This book teaches that arithmetic for practical use. It starts with the physical reasons a granular material behaves as it does, then works through bulk density and compaction, the angle of repose, internal and wall friction, and the Janssen pressures in a silo. It then covers the two flow patterns, mass flow and funnel flow, and the checks that decide whether a hopper will arch or rathole. It ends with discharge rates, segregation and the safe running of a storage system.

It is for mechanical, process and plant engineers, production and maintenance supervisors, and students who specify, buy, modify or run bins and silos. It assumes algebra, basic statics and friction, and the idea of stress as force per area. Each chapter works the running case with real numbers, includes one plausible mistake and how it was found, and ends with an exercise and its worked answer.

The running case

Every chapter follows one fictional plant. This is an illustration. Plant C compounds polypropylene with up to 30% calcium carbonate filler and sells the result as pellets to injection moulders. Two stores feed its extrusion line.

  • Silo S1, polypropylene pellets. A 304 stainless steel silo with a mill (2B) finish: 3.2 m diameter, a 9.0 m cylinder and a conical hopper 2.6 m high, at 60° to the horizontal, down to a 200 mm outlet with a slide gate and rotary valve. It is filled by blowing pellets from road tankers into a central inlet in the roof. The pellets are cylinders about 3.5 mm long weighing 24 mg each, with a particle density of 905 kg/m³ and a measured poured bulk density of 545 kg/m³.
  • Bin B2, calcium carbonate filler. A 304 stainless bin, 1.6 m in diameter, with a 1.5 m cylinder and a 60° cone to a 150 mm outlet over a screw feeder. It is filled from one-tonne bulk bags. The filler is a ground calcium carbonate with a median particle size of about 3 µm, a poured bulk density of 650 kg/m³ and a tapped bulk density of 1,000 kg/m³.

S1 has worked well since it was installed. B2 has not: it stops feeding several times a shift and is cleared by an operator hitting the cone with a mallet. The plant’s engineer is asked to explain both and to fix B2.

The plant, its equipment and every measurement and test result are invented. None describes KEVOS® work, a real plant or a real supplier’s product.

How to use the book

Read Chapters 1 to 5 in order: they set out the properties every later chapter uses, and the pressures in a silo. Chapters 6 to 9 cover flow: the two flow patterns, arching, ratholes and flow aids, and discharge rates. Chapter 10 deals with segregation and Chapter 11 with the inspection and safe running of bins and silos.

KEVOS® tools are linked where they perform a step of the method, with a note of exactly what each one calculates and where its model stops. Where a tool solves a related problem rather than the chapter’s own, the text says so.

Source limits and professional responsibility

The relations in this book are the standard engineering models of bulk solids: Janssen’s pressure equation, Jenike’s arching method and Beverloo’s discharge correlation. They are well tested within their assumptions and each chapter states those assumptions. Hopper design charts, flow factors and silo load factors belong to the original methods and to standards such as AS 3774. They are named here, not reproduced, and the illustrative test results in the running case are not values for any real material.

Silos fail structurally, collapse when a rathole or arch gives way, engulf people who enter them and can contain explosive dust clouds. The design, modification, inspection and entry of real bins and silos are matters for competent engineers and trained people under the relevant standards, the equipment maker’s instructions and Australian work health and safety law. This book is educational. It explains how bulk solids behave and how the standard checks work; it is not a design for any bin or silo or a substitute for testing a real material.

Who this book is for

Mechanical, process and plant engineers, production and maintenance supervisors, and students who specify, buy, modify or run bins, hoppers and silos for powders, pellets and granules.

What you will learn

  • Explain why a bulk solid carries load by friction and force chains, so its pressures and discharge rate do not follow liquid rules.
  • Use poured, tapped and consolidated bulk density correctly for capacity, and read the Hausner ratio as a first flowability check.
  • Read shear and wall friction test results and use them to calculate Janssen pressures in a silo.
  • Tell mass flow from funnel flow, and check a hopper's wall angle and outlet size against arching and ratholing.
  • Estimate the discharge rate of a coarse material through an outlet, and know why fine powders discharge more slowly.
  • Recognise segregation, flow aid misuse and the safety hazards of silos, and plan inspections and corrections.

Inside this book

Chapters

  1. 01Bulk solids are not liquidsWhy a powder or pellet store carries load by friction and force chains, so its pressures level off with depth and its discharge rate does not depend on how full it is.
  2. 02Bulk density, voids and compactionParticle density, poured, tapped and consolidated bulk density, voidage and the Hausner ratio, and how each is used for capacity, level-to-mass conversion and a first flowability check.
  3. 03Angle of repose, heaps and avalanchesWhat the angle of repose measures, why heaps grow and fail in avalanches of every size, how the heap in a silo costs capacity and fools level sensors, and why repose is not a hopper angle.
  4. 04Internal and wall friction: what a shear test tells youYield loci, effective angle of internal friction, unconfined yield strength and the flow function from a shear test, wall friction and the tilt test, and why the wall coupon must match the wall.
  5. 05Pressures in a silo: the Janssen equationDerive the Janssen equation from a slice balance, apply it to Plant C's pellet silo, see how wall friction shifts weight from the floor to the walls, and know what static pressures leave out.
  6. 06Mass flow and funnel flowThe two ways a bin discharges, what each means for first-in-first-out, ratholes, segregation and live capacity, what decides between them, and how to check a hopper and prove its flow pattern.
  7. 07Arching and the smallest outlet that will not blockWhy cohesive powders arch over an outlet, Jenike's comparison of the stress in an arch with the powder's strength, and how the flow function, flow factor and time consolidation set the outlet size.
  8. 08Ratholes, flow aids and vibrationHow a cohesive powder leaves a stable hole in a funnel-flow bin, what vibrators, air pads, air cannons and agitators can and cannot fix, and how a vibrator run at the wrong time makes a bin worse.
  9. 09Discharge rate and the hourglass lawWhy a coarse material's discharge rate depends on outlet size to the power 2.5 and not on the head, the Beverloo correlation and its limits, why fine powders are slower, and chutes below outlets.
  10. 10Segregation in storageHow bins and silos sort particles by size during filling and discharge, how the flow pattern decides what comes out when, and how to measure segregation and tell it apart from attrition.
  11. 11Running bins and silos safelyThe hazards of storing bulk solids, an inspection and monitoring plan, dust control at a bag station checked with the extraction duct tool, and a final review of Plant C's silo and bin.

Apply This in Practice

Use these KEVOS® tools to try the method from this reading with your own numbers.

References and source notes

The manuscript and worked examples are original KEVOS® writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 31 October 2026.

  • L. P. Kadanoff, World Scientific, Singapore (ISBN 981 02 3758 8). Statistical Physics: Statics, Dynamics and Renormalization (2000). Supplied source, in copyright. Read only as a subject map: many-particle systems, fluctuations, self-organised criticality and the experimental studies of granular materials it reprints. It is a physics text; no text, equations, figures, examples or exercises are reproduced or adapted, and the engineering treatment, running case and numbers in this book are original.
  • H. M. Jaeger, S. R. Nagel and R. P. Behringer, Reviews of Modern Physics, vol. 68, pp. 1259–1273. Granular solids, liquids, and gases (1996). Review of the physics of granular materials: force chains, dilatancy, pressure saturation in containers, discharge through an orifice and segregation. Used for the physical explanations in Chapters 1, 3 and 10; described, not quoted.
  • P. Bak, C. Tang and K. Wiesenfeld, Physical Review Letters, vol. 59, pp. 381–384. Self-organized criticality: an explanation of the 1/f noise (1987). The sandpile model of avalanches, used in Chapter 3 to explain why a heap fails in slips of every size. Described, not quoted.
  • J. B. Knight, C. G. Fandrich, C. N. Lau, H. M. Jaeger and S. R. Nagel, Physical Review E, vol. 51, pp. 3957–3963. Density relaxation in a vibrated granular material (1995). Experiments showing that a tapped granular column compacts slowly, roughly with the logarithm of the number of taps. Used qualitatively in Chapter 2.
  • M. Sperl, Granular Matter, vol. 8, pp. 59–65. Experiments on corn pressure in silo cells: translation and comment of Janssen's paper from 1895 (2006). English translation and commentary of H. A. Janssen's 1895 paper on grain pressures in silos, the origin of the pressure equation derived independently in Chapter 5.
  • W. A. Beverloo, H. A. Leniger and J. van de Velde, Chemical Engineering Science, vol. 15, pp. 260–269. The flow of granular solids through orifices (1961). Origin of the discharge-rate correlation used in Chapter 9. The commonly cited constants (C about 0.58, k about 1.4 and up to about 3 depending on particle shape) are used as stated there, with the correlation's limits.
  • A. W. Jenike, Utah Engineering Experiment Station, University of Utah. Storage and Flow of Solids, Bulletin 123 (1964). The founding method for mass-flow hopper design, flow functions, flow factors and critical outlet dimensions. Its design charts are not reproduced; Chapters 6 to 8 explain the method and use illustrative test-report values.
  • D. Schulze, Springer, Berlin. Powders and Bulk Solids: Behavior, Characterization, Storage and Flow (2008). Textbook reference for shear testing, flowability classification by the ratio of consolidation stress to unconfined yield strength, wall friction, flow patterns and flow aids. Used for orientation; nothing is reproduced.
  • J. Jáky, Journal of the Society of Hungarian Architects and Engineers. The coefficient of earth pressure at rest (1944). Origin of the approximation K = 1 − sin φ for the ratio of horizontal to vertical stress in a granular fill, used for the Janssen calculations in Chapter 5.
  • H. H. Hausner, International Journal of Powder Metallurgy, vol. 3, no. 4, pp. 7–13. Friction conditions in a mass of metal powder (1967). Origin of the ratio of tapped to poured bulk density used as a flowability indicator in Chapter 2.
  • Standards Australia. AS 3774, Loads on bulk solids containers (Current edition). Named by number and scope only, as the Australian standard for structural loads on bins and silos, including filling, discharge and eccentric discharge loads. No values or factors from it are quoted.
  • European Committee for Standardization. EN 1991-4, Eurocode 1: Actions on structures, Part 4: Silos and tanks (Current edition). Named by number and scope only, as a widely used code for silo loads. No values or factors from it are quoted.
  • ASTM International. ASTM D6128 (Jenike shear tester) and ASTM D6773 (Schulze ring shear tester), standard test methods for shear testing of bulk solids (Current editions). Named by number and scope only, as the test methods behind the flow function and wall friction results discussed in Chapters 4 and 7.
  • ASTM International. ASTM D6940 and ASTM D6941, standard practices for measuring sifting and fluidization segregation tendencies of bulk solids (Current editions). Named by number and scope only in Chapter 10, as laboratory tests that rank a material's tendency to segregate. No procedures or values are quoted.
  • J. C. Williams, Powder Technology, vol. 15, pp. 245–251. The segregation of particulate materials. A review (1976). Review of segregation mechanisms (sifting, trajectory, air entrainment and others) used for the classification in Chapter 10. Described, not quoted.
  • International Organization for Standardization. ISO 60, Plastics: Determination of apparent density of material that can be poured from a specified funnel (Current edition). Named by number and scope only in Chapter 2, as a standard method for the poured bulk density of plastics granules. No values are quoted.
  • Safe Work Australia. Model Code of Practice: Confined spaces (2020). Cited in Chapter 11 because the inside of a bin or silo is typically a confined space. The book does not set out entry procedures; this code, the site's procedures and competent people do.
  • Standards Australia and Standards New Zealand. AS/NZS 60079.10.2, Explosive atmospheres: Classification of areas, Explosive dust atmospheres (Current edition). Named by number and scope only, as the standard for classifying areas where combustible dust can form an explosive atmosphere, discussed in Chapter 11. No values are quoted.
  • Standards Australia and Standards New Zealand. AS/NZS 4024 series, Safety of machinery (Current editions). Named by number and scope only in Chapter 11, as the standards covering guarding and safety-related controls for feeders and rotary valves. Nothing is quoted.

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