BIZOMAT MAKEOS · Fabrication
Hopper and Bin Design (Capacity, Wall Angle, Plate Mass)
How much material will this round bin with a conical hopper hold, is the cone steep enough for the material to flow, and what will the shell plate weigh?
Design check of a round bin with a cylindrical section over a conical hopper: hopper volume, slant area and wall angle from horizontal (as the frustum volume tool), cylinder volume, mass held at the bulk density and fill level against the mass needed, the wall angle against the angle your material needs to flow, and the plate area and mass of the shell for the plate thickness.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bin diameter (top of the cone) | mm | Inside diameter of the bin and the top of the cone. |
| Cylindrical section height | mm | Height of the straight cylindrical section. |
| Outlet diameter | mm | Diameter of the outlet at the bottom of the cone. |
| Cone height | mm | Vertical height of the cone. |
| Material and plate | ||
| Bulk density of the material | kg/m³ | Loose bulk density of the stored material. |
| Fill level (share of total volume) | % | How full the bin is normally filled. |
| Mass to be held | kg | Mass the bin must hold. |
| Least wall angle from horizontal for flow | ° | Least cone wall angle from horizontal the material needs to flow (from flow testing or experience). |
| Plate thickness | mm | Thickness of the shell plate. |
| Plate density | kg/m³ | Density of the plate material. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Bin diameter (top of the cone)
- What it is
- The inside diameter of the round bin, which is also the diameter at the top of the conical hopper.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Cylinder volume rises with the square of the diameter.
What this means: Cylindrical section height
- What it is
- The vertical height of the straight cylindrical section above the cone.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Cylinder volume and its plate area rise in proportion.
What this means: Outlet diameter
- What it is
- The diameter of the outlet at the bottom of the cone, where the material discharges.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger outlet makes the cone walls steeper for the same cone height.
- Get it right
- It must be smaller than the bin diameter.
What this means: Cone height
- What it is
- The vertical height of the conical hopper from the outlet up to where it meets the cylinder.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A taller cone makes the walls steeper and adds volume.
- Get it right
- Use the vertical height, not the slant length of the cone wall.
Material and plate
What this means: Bulk density of the material
- What it is
- The loose bulk density of the stored material, including the air between particles, from testing or the material supplier.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 20000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1400 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Mass held is proportional to it.
- Get it right
- Use bulk density, not the density of the solid particles.
What this means: Fill level (share of total volume)
- What it is
- How full the bin is normally filled, as a share of its total volume (cone plus cylinder).
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Mass held is proportional to it.
- Get it right
- Type the percentage itself, not a fraction.
What this means: Mass to be held
- What it is
- The mass of material the bin must be able to hold for the process. It is compared with the mass held at the fill level.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 100000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8000 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Least wall angle from horizontal for flow
- What it is
- The least angle of the cone wall from horizontal at which your material will flow out without hanging up, from flow testing or experience with it.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 89°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- This is measured from horizontal, not from the vertical axis.
What this means: Plate thickness
- What it is
- The thickness of the plate used for the cone and cylinder shell.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Plate mass is proportional to thickness.
What this means: Plate density
- What it is
- The mass per unit volume of the shell plate material, from the supplier data sheet.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 20000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type kg/m³, not g/cm³ (multiply g/cm³ by 1000).
Method and formulas
- Cone volume = π h (D² + D d + d²) ÷ 12; slant area = π (R + r) × slant height; wall angle = tan⁻¹[h ÷ (R − r)] (as the frustum volume tool).
- Cylinder volume = π D² ÷ 4 × height; mass held = total volume × fill × bulk density.
- Plate area = slant area + π D × cylinder height; plate mass = area × thickness × density.
- Example: the bin holds 6.5541 m³, 8,258.2 kg at 90% fill; the cone walls are at 60.461°; the shell weighs 614.41 kg.
Limitations
- Level fill; a heaped top adds volume and a surcharge.
- Flow depends on the material’s friction on the wall; the angle needed must come from tests or experience.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a feed hopper or storage bin
- Check a hopper angle for a new material
- Estimate plate for fabrication
Who it is for
- Fabrication supervisors
- Process engineers
- Design engineers
What you get
- Cone, cylinder and total volume
- Mass held and wall angle
- Plate area and mass
Interpreting the result
- Steeper cones flow better but give less volume for the same height.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 82–87, 66. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Bulk solids are not liquids
In Bulk Solids Flow by the Numbers
What it covers: Why 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.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Hopper and Bin Design (Capacity, Wall Angle, Plate Mass) calculator