Silo Volume and Bulk Solids Weight Calculator
Calculate the volume and weight of bulk solids in a cylindrical silo with a conical hopper, from the material level. The top heap formed at the angle of repose can be added.
- Hopper frustum: V = πh/3 × (r² + rR + R²) = 13.58 m³
- Cylinder part: πR² × (level − hopper height)
- Heap cone: π × rs² × rs tan(α) ÷ 3 = 4.837 m³
- Weight = volume × bulk density = 51.51 t
Silo Volume Formulas
Cylinder: V = π × R² × h
Heap: V = π × R² × (R × tan α) ÷ 3
R is the silo radius, r the outlet radius, h the height of the section, α the angle of repose of the material and bulk density the poured density. Material level is measured to the flat surface at the wall; a level sensor at the centre sees the heap peak instead.
Worked example
A 4 m silo with a 3 m hopper (0.3 m outlet) and solids 7 m above the outlet, with a 30° heap: volume ≈ 68.7 m³, or 51.5 t at 750 kg/m³ (the heap adds 4.8 m³).
Frequently Asked Questions
What is angle of repose?
The steepest angle at which a heap of bulk material stays stable. It sets the shape of the heap on top of the material.
Why does the level sensor position matter?
A radar at the centre sees the heap peak; one near the wall sees a lower surface. Convert to volume using the same reference as the sensor.
Which bulk density should I use?
Use the loose or poured bulk density for filling and a compacted value for long storage. Material suppliers publish both.
Learn more on the blog
Types of level transmitters
A practical, field focused guide on instrumentationblog.in that explains the theory behind this calculator and how engineers apply it on real plants.
Read Full Article