Cylindrical Silo Capacity
Calculate the storage capacity (mass) of a silo's cylindrical part, M = ρ · (π·D²/4) · H, from the product bulk density ρ (kg/m³), the silo inner diameter D (m) and the cylindrical body height H (m). The calculation combines the cylinder volume (section area times height) with the product's bulk density — the product mass per unit apparent volume, which includes the voids between particles and differs from the solid particle density. Bulk density varies with product and state: soybeans ~720 kg/m³, corn ~720, wheat ~770, cement ~1500, and it also changes with moisture and compaction. Capacity is a silo's most basic commercial and operational parameter: it sets how much product it stores, and thus the logistics of receiving, dispatch and stock turnover. This computes the cylindrical part; total capacity also includes the lower hopper volume and, in grain silos, the upper product cone above the transition line (formed by the angle of repose during filling). Correctly estimating capacity is essential in designing storage units, cooperatives and grain terminals. Enter the bulk density, diameter and cylindrical body height.
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Cylindrical silo capacity
The storage capacity (by mass) of the cylindrical section of a silo is M = ρ · (π·D²/4) · H, combining the volume of the cylinder (cross-sectional area times height) with the bulk density of the product. Bulk density is the mass of product per unit of apparent volume — it includes the voids between the particles and is therefore lower than the density of the solid particle itself. It varies a great deal with the product and its condition: soybeans ~720 kg/m³, maize ~720, wheat ~770, cement ~1500 — and it shifts further with moisture content and compaction. Capacity is the most basic commercial and operational parameter of a silo: it sets how much product the structure holds and therefore the whole logistics of intake, outloading and stock turnover (critical in commodities, where grain cannot sit idle for long without aeration and control of pests and moisture). The calculation here covers the cylindrical section; the total capacity of a grain silo also includes the volume of the lower hopper and the upper cone of product that piles up above the transition line during filling (set by the angle of repose). Estimating capacity correctly is essential in the design of storage plants, farm cooperatives and bulk terminals, and in harvest planning. Enter the bulk density, the inside diameter and the height of the cylindrical body.
Related Tools
Silo Vertical Pressure (Janssen)
Calculate the vertical pressure of stored product at a silo cross-section by the Janssen equation, p_v = (γ·D)/(4·μ·K)·(1 − e^(−4·μ·K·z/D)), from the product unit weight γ (N/m³), silo diameter D (m), product-wall friction coefficient μ, lateral pressure ratio K and depth z (m). The Janssen equation (1895) is the basis of silo structural design and reveals a counterintuitive, fundamental fact: pressure at the bottom of a silo does NOT grow indefinitely with product height like a liquid (p = γ·h). Instead it tends to a LIMIT (asymptotic) value. This is because granular product (grain, cement, ore) transmits part of its weight LATERALLY to the walls, and product-wall friction 'holds' that load, relieving the bottom. The deeper it goes, the larger the fraction of weight carried by wall friction, until all added weight is absorbed by the walls and bottom pressure stabilizes. So silos can be very tall without bottom pressures proportional to height. This arching and wall-friction effect is the heart of silo design. Enter the unit weight, diameter, friction coefficient, lateral pressure ratio and depth.
Silo Horizontal Pressure (Janssen)
Calculate the horizontal pressure the stored product exerts on a silo wall by the Janssen equation, p_h = (γ·D)/(4·μ)·(1 − e^(−4·μ·K·z/D)), from the unit weight γ, diameter D, product-wall friction coefficient μ, lateral pressure ratio K and depth z. Horizontal pressure is the outward thrust grains apply against the silo walls — the load that sizes the wall for hoop tension (in cylindrical silos, the wall acts as a ring under internal pressure). It relates to vertical pressure by the lateral pressure ratio K (p_h = K·p_v), typically 0.3-0.6 for granular products and depending on the product's internal friction angle. Like vertical pressure, horizontal pressure tends to an asymptotic value with depth, by the same wall-friction effect of Janssen theory. Horizontal pressure is decisive for the thickness and reinforcement of concrete silo walls and the plating of steel silos, and rises significantly during DISCHARGE (dynamic overpressure), which codes handle with amplification factors. Enter the unit weight, diameter, friction coefficient, lateral pressure ratio and depth.
Silo Emptying Time
Calculate the time to empty a silo by gravity discharge, t = M ÷ W, from the stored product mass M (kg) and the mass discharge rate W (kg/s). Since the discharge rate of a granular material through an orifice is practically CONSTANT (independent of the product height above, by the Janssen effect and per the Beverloo equation), the emptying time is simply total mass divided by rate — a direct relation, unlike a liquid's emptying, which slows as the level falls. This time is an important operational parameter in silo, hopper and storage-unit design and operation: it sets the dispatch capacity (how fast a truck, rail car or ship is loaded), sizes the downstream conveying systems (belts, bucket elevators, screws) that must match the discharge rate, and frames shift logistics and vehicle queues at grain terminals. The discharge rate W can be estimated by the Beverloo equation from the outlet diameter, closing the calculation: larger outlets discharge faster (W ∝ D₀^2.5), reducing emptying time. Enter the stored mass and the discharge rate.
Granular Discharge Rate (Beverloo)
Calculate the mass discharge rate of a granular material through a bottom orifice by the Beverloo equation, W = C·ρ·√g·(D₀ − k·d)^2.5, from the discharge coefficient C (~0.58), the bulk density ρ (kg/m³), the orifice diameter D₀ (m), the particle diameter d (m) and the shape factor k (~1.4). The empirical Beverloo equation describes a fascinating behavior distinct from liquids: the grain discharge rate through an orifice does NOT depend on the product height above it (unlike a liquid, whose flow grows with head). This is due to the Janssen arching effect — bottom pressure saturates, so flow depends essentially on orifice size, not the amount of product above. That is why an hourglass keeps time steadily: sand flows at the same rate whether the top bulb is full or nearly empty. Flow is proportional to (D₀ − k·d)^2.5 — note the 2.5 exponent (not 2, of area) and the k·d term, an effective 'empty annulus' near the orifice edge where grains do not pass. Beverloo is fundamental in designing silos, hoppers, feeders and dosers in grain, cement, pharmaceutical and mining industries. Enter the coefficient, density, orifice diameter, particle diameter and shape factor.
Silo Asymptotic Pressure
Calculate the asymptotic (saturation) vertical pressure of a deep silo, p_∞ = (γ·D) ÷ (4·μ·K), from the product unit weight γ, diameter D, product-wall friction coefficient μ and lateral pressure ratio K. This is the LIMIT value the Janssen vertical pressure tends to at great depth — the maximum bottom pressure a silo can reach, however tall the stored product. It is Janssen's most striking result: while in a liquid pressure would grow without limit with height (p = γ·h), in granular product WALL FRICTION absorbs all added weight beyond a certain depth, making bottom pressure SATURATE. So a 30 m silo of grain may have a bottom pressure equal to only a few metres of product column. This asymptotic pressure is fundamental in design: it sets the maximum bottom and wall load the structure must bear, regardless of height, and explains why silos can be built slender and tall with relatively modest foundations. Note it is proportional to diameter and inversely proportional to friction — wide, smooth-walled silos generate higher pressures. Enter the unit weight, diameter, friction coefficient and lateral pressure ratio.
Grain Conical Pile Volume
Calculate the volume of a conical pile of granular material formed by free pouring, V = (π/3)·r³·tan(θ), from the pile base radius r (m) and the material's angle of repose θ (degrees). When granular material is freely poured onto a surface, it naturally forms a CONE whose side slope is the angle of repose — a characteristic property of each material (dry sand ~30-35°, grain ~25-30°, crushed stone ~37-40°) reflecting inter-particle friction. Since the cone height is h = r·tan(θ), the cone volume (1/3·π·r²·h) becomes (π/3)·r³·tan(θ), a function of radius and angle of repose only. This is widely used in practice to estimate, from a survey or base-radius measurement, the volume (and with density, the mass) of open stockpiles — piles of grain, sand, crushed stone, coal, ore, fertilizer in yards and warehouses. It is the basis of bulk-material inventory in piles, a quick alternative to weighing. It also guides stockyard area and height sizing and bulk-warehouse design. For elongated piles (prismatic with conical ends), add the central part. Enter the base radius and the angle of repose.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.