Silo Discharge Overpressure
Calculate the DISCHARGE horizontal pressure in a silo, p_d = C_d · p_h, from the discharge overpressure coefficient C_d and the static horizontal pressure p_h (from Janssen for the full silo at rest). One of the most important phenomena — historically responsible for many silo failures — is that wall pressures during DISCHARGE are SIGNIFICANTLY HIGHER than static pressures with the silo merely full. When the product starts flowing toward the outlet, flow zones and dynamic arches form, and stress redistribution generates pressure peaks (overpressures) on the wall, especially at the transition from the cylindrical body to the hopper. The overpressure coefficient C_d (typically 1.3-2.0 or more, per the code, flow type — mass or funnel — and geometry) amplifies the static pressure to cover these dynamic peaks. Silo design codes (such as EN 1991-4 / Eurocode and ANSI) prescribe these factors precisely because designing a silo only for static loads, ignoring discharge overpressure, is a classic cause of structural collapse. Enter the overpressure coefficient and the static horizontal pressure.
Result
—
Sobrepressão de descarga de silo
A pressão horizontal de descarga em um silo é p_d = C_d · p_h, a partir do coeficiente de sobrepressão C_d e da pressão horizontal estática p_h (calculada por Janssen para o silo cheio em repouso). Um dos fenômenos mais importantes — e historicamente responsável por muitas rupturas de silos — é que as pressões nas paredes durante a descarga do produto são significativamente maiores que as pressões estáticas com o silo simplesmente cheio. Quando o produto começa a fluir para a boca de saída, formam-se zonas de fluxo e arcos dinâmicos, e a redistribuição de tensões gera picos de pressão (sobrepressões) na parede, especialmente na transição do corpo cilíndrico para a tremonha (funil), onde muitos colapsos se iniciam. O coeficiente C_d — tipicamente de 1,3 a 2,0 ou mais, conforme a norma, o tipo de fluxo (mássico, em que todo o produto se move, ou de funil, em que só uma coluna central escoa) e a geometria — majora a pressão estática para cobrir esses picos dinâmicos. As normas de projeto (a europeia EN 1991-4 / Eurocódigo, a americana ANSI/ASAE, e outras) prescrevem esses fatores justamente porque dimensionar um silo apenas para as cargas estáticas, ignorando a sobrepressão de descarga, é uma causa clássica e bem documentada de colapso estrutural. Informe o coeficiente de sobrepressão e a pressão horizontal estática.
Related Tools
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 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 Slenderness Ratio
Calculate a silo's slenderness ratio, λ = H ÷ D, from the stored product height H (m) and the silo diameter D (m). This simple ratio is the fundamental criterion that CLASSIFIES silos and determines how their pressures behave and how codes treat them. Silos with HIGH slenderness (typically H/D ≥ 1.5-2, called slender or 'tall') are dominated by the Janssen wall-friction effect: pressure saturates quickly, most weight transfers to the walls, and the bottom receives a much lower pressure than the product column would suggest. Silos with LOW ratio (H/D < 1.0-1.5, called squat) behave intermediately between Janssen and a tank: wall friction has less extent to act, and a larger fraction of weight reaches the bottom. This distinction changes the applicable pressure formulas, the discharge overpressure factors and even the expected flow type. The slenderness ratio is thus the first decision in silo analysis — it sets which load model to use and influences the whole structural concept, from foundation to walls. Enter the product height and the silo diameter.
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.