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Particle settling velocity and removal in an ideal basin

A particle settles at the speed where drag balances its weight in water. An ideal basin then removes every particle faster than its overflow rate and a proportional share of the slower ones.

Particle diameterµm

Particle densitykg/m³Sand 2,650; alum floc about 1,010 to 1,050.

Water temperature°C

Basin flowm³/h

Basin surface aream²

Settling-velocity distribution (optional): velocity in m/h and count per bin, one pair per lineUse the bin midpoint velocity. Leave empty to skip.

Single particle

Settling velocity

70.06m/h

Settling velocity

19.46mm/s

Reynolds number

2.68

Regime

transition

Ideal basin

Overflow rate

2.50m/h

This particle in the basin

fully removed

Removal of the distribution

66.4%

How it works

Force balance on a sphere, with the drag coefficient by regime:

v_{s} = \sqrt{\frac{4 g (ρ_{p} - ρ_{w}) d}{3 C_{d} ρ_{w}}} R e = \frac{ρ_{w} v_{s} d}{μ}

(1)

v_{s} = \frac{g (ρ_{p} - ρ_{w}) d^{2}}{18 μ} (R e < 2) v_{s} = {[\frac{g (ρ_{p} - ρ_{w}) d^{1.6}}{13.9 ρ_{w}^{0.4} μ^{0.6}}]}^{1 / 1.4} (2 \leq R e \leq 500)

(2)

Above a Reynolds number of 500 the drag coefficient is 0.44. In an ideal rectangular basin the critical velocity equals the overflow rate, and a slower particle is removed in proportion:

v_{c} = \frac{Q}{A} f = \min (1, \frac{v_{s}}{v_{c}})

(3)

where

$v_{s}$: terminal settling velocity, m/s
$g$: gravity, 9.81 m/s²
$ρ_{p}, ρ_{w}$: particle and water density, kg/m³
$d$: particle diameter, m
$C_{d}$: drag coefficient
$R e$: particle Reynolds number
$μ$: water viscosity, kg/m·s
$v_{c}$: critical settling velocity, m/h
$Q$: basin flow, m³/h
$A$: basin surface area, m²
$f$: fraction of a particle class removed

Depth and detention time do not enter. Real suspensions flocculate as they settle and real basins have non-ideal flow, so this is the floor for a discrete suspension. Below about 1 µm Brownian motion dominates and particles do not settle in practical times.

Particle settling velocity and removal in an ideal basin

How it works

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