KEVOS® 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. |
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.
WORKOS 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
