M.08Silo and Hopper Volume

Calculate the volume and capacity of a cylinder-plus-cone silo.

Use 85–95% to allow for headspace and fill heap.

Results

Capacity
—
Usable volume
—
Total volume
—
Cylinder volume
—
Hopper volume
—
Hopper height
—
Total height
—

    This tool is for preliminary sizing. Final design must be verified with material tests, the relevant standards and equipment manufacturer data.

    Formulas

    Hopper height
    h = (r − r₀) · tan θ
    Frustum volume
    V_h = π · h · (r² + r·r₀ + r₀²) / 3
    Cylinder volume
    V_c = π · r² · H
    Capacity
    m = (V_c + V_h) · φ · ρ

    Note

    The result is the geometric volume. Actual capacity varies with the heap formed at the top, compaction and density change under pressure. The hopper angle required for mass flow depends on the material’s wall friction angle.

    Mechanical Engineering Tools

    Other tools