Particle Reynolds Number
Calculate the particle Reynolds number in settling, Re_p = (ρ_w·v_s·d) ÷ μ, from the fluid density ρ_w (kg/m³), the settling velocity v_s (m/s), the particle diameter d (m) and the dynamic viscosity μ (Pa·s). The particle Reynolds number characterizes the flow regime around a particle settling (or being transported) in a fluid, comparing inertial and viscous forces. Its value sets WHICH settling-velocity formula is valid: for Re_p < ~1, the flow around the particle is LAMINAR and Stokes' Law holds (drag proportional to velocity); for Re_p > ~1000, the flow is TURBULENT and Newton's law holds (drag proportional to velocity squared); in the intermediate range, transition correlations are used (such as Allen's or drag-coefficient expressions vs Re_p). So when computing a settling velocity by Stokes' Law, it is ESSENTIAL to verify afterwards that Re_p < 1 — if not, the Stokes result is wrong and the correct regime's formula must be used. The particle Reynolds number is thus the 'checker' that validates the settling calculation, and it is central in designing settling tanks, classifying particles and hydraulic solids transport. Enter the fluid density, the settling velocity, the particle diameter and the viscosity.
Result
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Número de Reynolds da partícula
O número de Reynolds da partícula em sedimentação é Re_p = (ρ_w·v_s·d) ÷ μ, a partir da densidade do fluido ρ_w, da velocidade de sedimentação v_s, do diâmetro da partícula d e da viscosidade dinâmica μ. Ele caracteriza o regime do escoamento ao redor de uma partícula que sedimenta (ou é transportada) em um fluido, comparando as forças de inércia com as viscosas. Seu valor define qual fórmula de velocidade de sedimentação é válida: para Re_p < ~1, o escoamento ao redor da partícula é laminar e vale a Lei de Stokes (arrasto proporcional à velocidade); para Re_p > ~1000, o escoamento é turbulento e vale a lei de Newton (arrasto proporcional ao quadrado da velocidade); na faixa intermediária, usam-se correlações de transição. Por isso, ao calcular uma velocidade de sedimentação pela Lei de Stokes, é essencial verificar a posteriori se Re_p < 1 — se não for, o resultado de Stokes está errado e é preciso usar a fórmula do regime correto. O Reynolds de partícula é, portanto, o 'verificador' que valida o cálculo de sedimentação, e é central no projeto de decantadores, na classificação de partículas e no transporte hidráulico de sólidos. Informe a densidade do fluido, a velocidade de sedimentação, o diâmetro da partícula e a viscosidade.
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