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.
Result
—
Capacidade de silo cilíndrico
A capacidade de armazenamento (em massa) da parte cilíndrica de um silo é M = ρ · (π·D²/4) · H, combinando o volume do cilindro (área da seção vezes a altura) com a densidade aparente (bulk density) do produto. A densidade aparente é a massa de produto por unidade de volume aparente — ela inclui os vazios entre as partículas e é, portanto, menor que a densidade da partícula sólida. Ela varia bastante com o produto e seu estado: grãos de soja ~720 kg/m³, milho ~720, trigo ~770, cimento ~1500 — e ainda muda com a umidade e a compactação do produto. A capacidade é o parâmetro comercial e operacional mais básico de um silo: define quanto produto ele armazena e, portanto, toda a logística de recebimento, expedição e giro de estoque (importante em commodities, onde o produto não pode ficar parado tempo demais sem ventilação e controle de pragas e umidade). O cálculo aqui considera a parte cilíndrica; a capacidade total de um silo graneleiro inclui ainda o volume da tremonha (funil) inferior e o cone superior de produto que se forma acima da linha de transição durante o enchimento (definido pelo ângulo de repouso). Estimar corretamente a capacidade é essencial no projeto de unidades armazenadoras, cooperativas e terminais graneleiros, e no planejamento da safra. Informe a densidade aparente, o diâmetro interno e a altura do corpo cilíndrico.
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.
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.