Grinding Energy (Bond Work Index)
Calculate the specific comminution (grinding/crushing) energy by Bond's law, W = 10 × Wi × (1/√P₈₀ − 1/√F₈₀), from the ore's Bond work index Wi (kWh/t), and the particle sizes passing 80% of the product (P₈₀) and feed (F₈₀), in micrometers. The result, in kWh per tonne, is the energy needed to reduce the ore from feed to product size. Comminution is mining's largest energy consumer (up to 50% of the plant). The Wi index characterizes the ore's resistance to fragmentation. It is the basis for sizing mills and energy consumption. Enter the Wi, P₈₀ and F₈₀.
Resultado
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Energia de moagem (lei de Bond)
A cominuição — britar e moer o minério para liberar os minerais valiosos — é o maior consumo de energia de uma planta de mineração, podendo representar 30 a 50% de toda a eletricidade usada. Estimar essa energia é, portanto, crucial, e a referência clássica é a lei de Bond: W = 10 × Wi × (1/√P₈₀ − 1/√F₈₀). Aqui Wi é o índice de trabalho de Bond (kWh/t), uma propriedade do minério determinada em laboratório que mede sua resistência à fragmentação (minérios duros como quartzitos têm Wi alto, ~15-20; minérios brandos, baixo); F₈₀ e P₈₀ são os tamanhos pelos quais passam 80% da alimentação e do produto, em micrômetros (a granulometria de referência). O resultado, em kWh por tonelada, é a energia específica de moagem. A lei de Bond expressa uma verdade física importante: a energia para moer cresce desproporcionalmente à medida que se busca finura — moer até partículas muito finas (P₈₀ pequeno) consome muito mais energia (o termo 1/√P₈₀ dispara). Por isso a moagem fina é tão cara, e há um equilíbrio entre liberar bem o mineral (moer fino) e gastar energia razoável. A lei de Bond é uma das três 'leis da cominuição' (com Kick, para britagem grosseira, e Rittinger, para moagem fina); Bond é a mais usada na faixa intermediária e industrial. É a base do dimensionamento de moinhos (potência instalada), da estimativa de custo operacional e da comparação de circuitos. Informe o Wi, o P₈₀ e o F₈₀.
Related Tools
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Calculate the total reduction ratio of a three-stage comminution circuit, RR_total = RR₁ × RR₂ × RR₃, multiplying the reduction ratios of each crusher/mill in series. The dimensionless result is the circuit's overall size reduction — from bench rock blocks (hundreds of mm) to fine particles (mm or µm). Since each stage has a limited reduction ratio (4 to 10 for crushers), large total reductions (100, 1000 or more) require several stages in series: primary, secondary, tertiary crushing and milling. Enter the reduction ratios of the three stages.
Punching Work
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Crushing Reduction Ratio
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Calculate the WBGT (wet bulb globe temperature) for indoor environments without solar load, WBGT = 0.7·t_nw + 0.3·t_g, from the natural wet-bulb temperature t_nw and the globe temperature t_g (°C). The result, in °C, is the heat stress index used to assess heat exposure: compared with tolerance limits according to the activity's metabolic rate, it sets the allowed work-rest regime. For environments with solar load, the dry-bulb temperature is also included. Enter the natural wet-bulb and globe temperatures.
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Zeldovich Number
Computes the Zeldovich number of a flame, β = E_a·(T_b − T_u) ÷ (R·T_b²), the activation energy made dimensionless by the temperature rise across the flame front. It measures how sensitive the reaction rate is to a small temperature change: a high β (typically 8 to 12 for hydrocarbons) means the reaction is concentrated in a very thin layer near the flame temperature, which justifies the large-activation-energy assumption of asymptotic flame theory and the extinction and cellular-instability criteria. The universal gas constant R = 8.314 J/(mol·K) is adopted, with activation energy in J/mol and temperatures in kelvin. Enter the activation energy, the burned gas temperature and the unburned gas temperature.
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