Solids Mass Flow (Dredge)
Calculate the mass flow of solids transported by a dredge or pipeline, ṁ_s = Q·C_v·ρ_s, from the total slurry flow Q (m³/s), the solids volumetric concentration C_v (fraction) and the solids density ρ_s (kg/m³). Solids mass flow is the MASS of useful material transported per unit time (kg/s, or tonnes per hour), the production indicator used when TONNAGE matters — the typical case of ore transport by pipeline (measured in t/h of dry ore) and mineral processing. It is the product of three factors: the slurry flow (pump capacity), the solids concentration (how 'loaded' the slurry is) and the solids density (iron ores, for example, are very dense, ~5000 kg/m³, so little volumetric concentration already gives high tonnage). Mass flow, integrated over time, gives the total transported tonnage, the basis of billing and operational mass balance. Optimizing it — maximizing tonnage per unit pumping energy — is the central goal of pipeline operation, which moves hundreds of millions of tonnes of ore per year over long distances far more energy-efficiently than trucks or trains. Enter the slurry flow, the volumetric concentration and the solids density.
Result
—
Vazão mássica de sólidos (draga)
A vazão mássica de sólidos transportados por uma draga ou mineroduto é ṁ_s = Q·C_v·ρ_s, a partir da vazão total da polpa Q, da concentração volumétrica C_v e da densidade dos sólidos ρ_s. É a massa de material útil transportado por unidade de tempo (kg/s, ou toneladas por hora), o indicador de produção usado quando o que importa é a tonelagem — caso típico do transporte de minério por mineroduto (medido em t/h de minério seco) e do processamento mineral. É o produto de três fatores: a vazão da polpa (capacidade da bomba), a concentração de sólidos (quão 'carregada' está a polpa) e a densidade dos sólidos (minérios de ferro, por exemplo, são muito densos, ~5000 kg/m³, então pouca concentração volumétrica já dá alta tonelagem). A vazão mássica, integrada no tempo, dá a tonelagem total, base do faturamento e do balanço de massa. Otimizá-la — maximizando a tonelagem por unidade de energia de bombeamento — é o objetivo central da operação de minerodutos, que transportam centenas de milhões de toneladas de minério por ano por longas distâncias com eficiência energética muito superior à de caminhões ou trens. Informe a vazão da polpa, a concentração volumétrica e a densidade dos sólidos.
Related Tools
Dredge Solids Production
Calculate the volumetric solids production of a dredge or pipeline, Q_s = Q·C_v, from the total slurry flow Q (m³/s) and the solids volumetric concentration C_v (fraction). Solids production is the volume of useful material (sand, sediment, ore) effectively transported per unit time — the direct measure of dredging or slurry-pumping PRODUCTIVITY, and what really matters commercially (a dredge is paid per cubic metre dredged, not per pumped water). It is the product of the total slurry flow and the solids fraction: increasing production means increasing the flow (bigger pumps, more power) OR increasing the solids concentration (excavating denser material, optimizing the suction). There is a fundamental trade-off: pumping very concentrated slurry raises production per cubic metre of slurry but raises mixture density, head loss and deposition/clogging risk. Solids production, integrated over time, gives the total dredged volume (for measurement and payment) and frames planning (how many hours/days to dredge a channel, fill a pit, move overburden). It is the key operational indicator. Enter the slurry flow and the volumetric concentration.
Slurry Mass Concentration
Calculate the solids mass (weight) concentration in a slurry, C_w = C_v·(ρ_s ÷ ρ_m)·100, from the volumetric concentration C_v (fraction), the solids density ρ_s and the mixture density ρ_m (kg/m³); the result is a percentage. Mass concentration is the fraction of the total slurry MASS that is solid (kg of solid per kg of slurry), different from volumetric concentration (volume fraction). Both measure the same thing differently, and their relation depends on the solids density: since solids are DENSER than water (sand ~2.65×), mass concentration is always GREATER than volumetric (a slurry with 20% solids by volume has about 40% by mass). Mass concentration (% solids by weight) is the form most used in the mineral industry and ore processing, since it relates directly to the tonnage of solids processed and is what is controlled in thickeners, mills and flotation. Converting between mass and volumetric concentration is a daily operation in processing-plant mass balance and pipeline and dredging control. Enter the volumetric concentration, the solids density and the mixture density.
Critical Deposition Velocity (Durand)
Calculate the critical deposition velocity in hydraulic solids transport by Durand's equation, V_c = F_L·√(2·g·D·(s − 1)), from the Durand factor F_L (dimensionless, a function of grain size and concentration), the pipe inner diameter D (m) and the solids relative density s = ρ_s/ρ_w. Critical velocity is the MOST important parameter in designing pipelines and dredge discharge lines: it is the MINIMUM flow velocity below which solids start to DEPOSIT on the pipe bottom, forming a bed that reduces the section, raises head loss and can lead to total CLOGGING of the line (a very costly, slow accident to clear). Above the critical velocity, turbulence keeps the particles suspended and moving. Operation must keep the velocity ALWAYS above critical (with safety margin), but not too far above, since excessive velocities waste pumping energy and cause accelerated abrasive wear of pipe and pumps. Determining the critical velocity sets the operating velocity, the pipe diameter and the pumping power. Durand's correlation (1953), with the tabulated F_L factor, is the classic basis of this calculation. Enter the Durand factor, the pipe diameter and the solids relative density.
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.