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.
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Tempo de esvaziamento de silo
O tempo para esvaziar um silo por descarga gravitacional é t = M ÷ W, a partir da massa de produto armazenada M e da vazão mássica de descarga W. Como a vazão de descarga de um material granular por um orifício é praticamente constante — independente da altura de produto acima, pelo efeito de Janssen e conforme a equação de Beverloo —, o tempo de esvaziamento é simplesmente a massa total dividida pela vazão, uma relação direta e linear. Isso é diferente do esvaziamento de um líquido, que desacelera à medida que o nível cai (a vazão diminui com a carga). Esse tempo é um parâmetro operacional importante no projeto e na operação de silos, moegas e unidades armazenadoras: define a capacidade de expedição (quão rápido se carrega um caminhão, um vagão ferroviário ou um navio graneleiro), dimensiona os sistemas de transporte a jusante (correias transportadoras, elevadores de canecas, roscas) que precisam acompanhar a vazão de descarga sem criar gargalos, e baliza a logística de turnos e filas de veículos em terminais graneleiros (onde o tempo de carregamento define a rotatividade do pátio). A vazão de descarga W pode ser estimada pela equação de Beverloo a partir do diâmetro da boca de saída, fechando o cálculo de forma integrada: orifícios maiores descarregam muito mais rápido (W ∝ D₀^2,5), reduzindo o tempo de esvaziamento. Informe a massa armazenada e a vazão de descarga.
Related Tools
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.
Reservoir Emptying Time
Calculate the time to empty a constant-surface-area reservoir through a bottom orifice, t = 2·A_s·√H ÷ (C_d·A_o·√(2g)), from the water-surface area A_s (m²), the outlet orifice area A_o (m²), the initial head H (m, water height above the orifice) and the discharge coefficient C_d (≈ 0.6 for orifices). The formula integrates Torricelli's equation over the drawdown: as orifice flow drops while the level (and head) falls, emptying decelerates, and total time results from integrating dH/dt. It is useful for designing dam bottom outlets (used to lower the reservoir in emergencies or for maintenance), emptying industrial tanks and basins. Time grows with reservoir area and the square root of head, and falls with orifice area — emptying large reservoirs takes a long time, a real limitation in dam emergency management. It assumes constant A_s; real reservoirs vary with elevation. Enter the surface area, orifice area, initial head and discharge coefficient.
Janssen Characteristic Depth
Calculate a silo's Janssen characteristic depth, z₀ = D ÷ (4·μ·K), from the diameter D, product-wall friction coefficient μ and lateral pressure ratio K. The characteristic depth governs how fast silo pressures approach their asymptotic (limit) value: in the Janssen equation, it is the depth at which pressure reaches about 63% (1 − 1/e) of the maximum. Depths of a few times z₀ practically reach the limit pressure. Conceptually, z₀ shows how 'deep' the silo must be for wall friction to dominate: silos with small z₀ (small diameter, high friction) quickly reach the constant-pressure regime and behave as slender (tall) silos; silos with large z₀ (large diameter) saturate slowly and behave more like squat silos, where much of the weight still reaches the bottom. The characteristic depth is thus a natural measure of the vertical 'scale' of the silo's pressure behavior, useful to classify it and understand its load profile. Enter the diameter, friction coefficient and lateral pressure ratio.
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