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.
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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.
Related Tools
Settling Velocity (Newton)
Calculate the settling (terminal) velocity of a particle in turbulent regime by Newton's law, v_t = √(4·g·d·(s − 1) ÷ (3·C_d)), from the particle diameter d (m), the solids relative density s = ρ_s/ρ_w and the drag coefficient C_d (dimensionless, ≈ 0.44 for spheres in turbulent regime). While Stokes' Law holds for SMALL particles (laminar regime, particle Reynolds < 1), Newton's law holds for LARGE, dense particles — gravel, crushed stone, coarse sand — that sink fast, generating TURBULENT flow around them (particle Reynolds > ~1000). In this regime, drag is no longer proportional to velocity (Stokes) but to its SQUARE, and the terminal velocity grows with the SQUARE ROOT of diameter (not the square, as in Stokes) — large particles sink fast, but the size dependence is milder. The drag coefficient C_d ≈ 0.44 is roughly constant in this range (the 'Newton region' of the sphere drag curve). This calculation is fundamental in designing coarse-particle classifiers and separators, sizing settling basins for coarse solids, coarse-sediment transport and hydraulic transport of gravel and granular ore. For the intermediate range between Stokes and Newton, transition correlations are used. Enter the diameter, the relative density and the drag coefficient.
Settling Velocity (Stokes)
Calculate the settling (terminal) velocity of a particle in laminar regime by Stokes' Law, v_s = g·d²·(ρ_s − ρ_w) ÷ (18·μ), from the particle diameter d (m), the solids ρ_s and water ρ_w densities (kg/m³) and the fluid dynamic viscosity μ (Pa·s). The settling velocity is the speed at which an isolated particle SINKS in a still fluid, when weight (minus buoyancy) balances drag. Stokes' Law (1851) holds for the LAMINAR regime (small particles, particle Reynolds < ~1) — fine sand, silt, clay — and has the remarkable property that velocity grows with the SQUARE of diameter: particles twice as large sink four times faster. This calculation is fundamental in many fields: particle settling and separation (settling tanks, thickeners, water and effluent clarifiers), grain-size classification by sedimentation (pipette or hydrometer test), sediment transport in rivers and reservoir deposition, and hydraulic transport (the particle settling velocity sets the critical deposition velocity in the pipe). For large particles (higher Reynolds), Stokes' Law fails and Newton's terminal velocity (turbulent regime) is used. Enter the particle diameter, the densities and the viscosity.
Reynolds Number Calculator
Compute Reynolds number Re = ρ·v·D/μ.
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.