Silo + Hopper Capacity (3D)
Compute cylinder bin plus conical hopper capacity with an interactive 3D silo.
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
Textbook physics/chemistry, SI-friendly. The Silo + Hopper Capacity (3D) on MyCalcsWorld is for homework checks and first-cut estimates under idealized assumptions unless noted. What it does: Cylinder bin plus conical hopper capacity and lateral area โ with interactive 3D silo. Typical inputs: Cylinder radius (m), Cylinder height (m), Hopper height (m), Hopper outlet radius (m). Demo defaults (cylinder radius 2 m, cylinder height 8 m, hopper height 3 m, hopper outlet radius 0.2 m) currently resolve to Total capacity 114.4796 in the live panel โ change any field to explore sensitivity. Who it helps: lab students, makers, and engineers doing first-cut checks with textbook identities before applying real tolerances.
When to use / who it helps
- Grain or pellet bin volume.
- Comparing hopper angles via height/outlet.
- Teaching cylinder + cone volume.
- Use the Silo + Hopper Capacity (3D) for homework checks and first-cut design estimates under textbook assumptions.
- Keep SI (or the formโs stated units) consistent โ a wrong unit ruins precision.
How to use
Steps
- Enter cylinder radius/height and hopper height/outlet radius.
- Read total capacity.
- Orbit the 3D silo.
- Open the Silo + Hopper Capacity (3D) on MyCalcsWorld and skim the labeled fields before you type.
- Set Cylinder radius (m) โ demo default is 2 m.
- Set Cylinder height (m) โ demo default is 8 m.
How to interpret results
- Total capacity is geometric volume.
- Convert to mass with bulk density separately.
- Outlet radius 0 is a pointed cone.
- Each result is driven only by the labeled inputs (Cylinder radius (m), Cylinder height (m), Hopper height (m), Hopper outlet radius (m)); anything not on the form (fees, holidays, clinical adjustments) is outside this estimate.
- Results assume the idealized model stated in the formula notes (constant parameters, ohmic behavior, etc.).
Common mistakes & gotchas
- Using diameter as radius.
- Ignoring packing density for mass.
- Assuming perfect cone discharge.
- Mixing SI and customary units across: Cylinder radius (m), Cylinder height (m), Hopper height (m), Hopper outlet radius (m).
- Ignoring that textbook models omit friction, temperature drift, or non-ohmic behavior.
Worked example
Worked example โ R=2, Hc=8, Hh=3, r=0.2
- Cylinder = ฯร4ร8 โ 100.53.
- Hopper โ ฯร3ร(4+0.4+0.04)/3 โ 13.95.
- Total โ 114.5.
- Open the Silo + Hopper Capacity (3D) (silo hopper 3d) and note the starting defaults (cylinder radius 2 m, cylinder height 8 m, hopper height 3 m, hopper outlet radius 0.2 m).
Result: With defaults (cylinder radius 2 m, cylinder height 8 m, hopper height 3 m, hopper outlet radius 0.2 m), the Silo + Hopper Capacity (3D) shows: Total capacity 114.4796.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
Cylinder V = ฯRยฒHc. Hopper frustum V = ฯHh(Rยฒ+Rr+rยฒ)/3. Science tools apply textbook relationships (Ohmโs law, density, kinematics, waves, energy) with SI units unless the form asks otherwise. Idealized assumptions (constant g, ohmic resistors, frictionless motion) apply unless noted โ real lab or field conditions need your own corrections. For the Silo + Hopper Capacity (3D), the labeled fields (Cylinder radius (m), Cylinder height (m), Hopper height (m), Hopper outlet radius (m)) drive the live result panel.
Frequently asked questions
Tons of grain?
Multiply volume by bulk density for your commodity.
Roof volume?
Not included โ body + hopper only.
Metric?
Any consistent length unit works.
Why 3D?
To see cylinder-to-hopper proportions.
What does the Silo + Hopper Capacity (3D) on MyCalcsWorld actually compute?
Cylinder bin plus conical hopper capacity and lateral area โ with interactive 3D silo. You enter Cylinder radius (m), Cylinder height (m), Hopper height (m), Hopper outlet radius (m), and the result panel updates in your browser.
What inputs does the Silo + Hopper Capacity (3D) need?
The Silo + Hopper Capacity (3D) asks for: Cylinder radius (m); Cylinder height (m); Hopper height (m); Hopper outlet radius (m).
What results does the Silo + Hopper Capacity (3D) show?
The panel reports Total capacity. Each figure is recalculated whenever you change an input, so you can compare scenarios side by side.
Does this include real-world losses and tolerances?
Usually not. Textbook identities assume ideal conditions unless a field asks for efficiency, friction, or tolerance. Apply your own safety factors for designs that affect safety or compliance.
Textbook formulas under ideal assumptions. For safety-critical, structural, or regulated work, verify with a qualified engineer and the governing standards. Full disclaimer