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.
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Velocidade crítica de deposição (Durand)
A velocidade crítica de deposição no transporte hidráulico de sólidos, pela equação de Durand, é V_c = F_L·√(2·g·D·(s − 1)), a partir do fator de Durand F_L (função da granulometria e da concentração), do diâmetro interno da tubulação D e da densidade relativa dos sólidos s = ρ_s/ρ_w. É o parâmetro mais importante do projeto de minerodutos e linhas de recalque de dragas: a velocidade mínima abaixo da qual os sólidos começam a se depositar no fundo da tubulação, formando um leito que reduz a seção, aumenta a perda de carga e pode levar ao entupimento total da linha (um acidente caríssimo e demorado de desobstruir). Acima da velocidade crítica, a turbulência mantém as partículas em suspensão e em movimento. A operação precisa manter a velocidade sempre acima da crítica (com margem de segurança), mas não muito acima, pois velocidades altas demais desperdiçam energia de bombeamento e causam desgaste abrasivo acelerado da tubulação e das bombas. Determinar a velocidade crítica define a velocidade de operação, o diâmetro da tubulação e a potência de bombeamento. A correlação de Durand (1953), com o fator F_L tabelado, é a base clássica desse cálculo. Informe o fator de Durand, o diâmetro da tubulação e a densidade relativa dos sólidos.
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