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Clean-bed head loss through a granular filter

The head a clean bed consumes is the floor under the run: whatever is left of the available head goes to the solids the filter captures.

Medium

Filtration ratem/h5 to 15 typical; up to 25 with strong floc.

Effective sizemm

Bed depthm

PorositySand about 0.42, anthracite about 0.50.

Water temperature°C

Available headm

Clean-bed head loss

0.50m

Share of available head

20%

Clean-bed loss of about 20% of the available head leaves the rest for solids capture.

Viscous term

0.44m

Inertial term

0.06m

Head loss per metre of bed

0.277m/m

Grain Reynolds number

3.47

How it works

The Ergun equation with the medium's own coefficients, which absorb grain shape when the sieve effective size is used as the diameter:

h_{L} = κ_{V} \frac{(1 - ε)^{2}}{ε^{3}} \frac{μ L v}{ρ_{w} g d^{2}} + κ_{I} \frac{1 - ε}{ε^{3}} \frac{L v^{2}}{g d}

(1)

where

$h_{L}$: clean-bed head loss, m
$κ_{V}, κ_{I}$: viscous and inertial coefficients of the medium
$ε$: bed porosity
$μ$: water viscosity, kg/m·s
$L$: bed depth, m
$v$: filtration rate, m/s
$ρ_{w}$: water density, kg/m³
$g$: gravity, 9.81 m/s²
$d$: effective size of the grains, m

Coefficients: sand κ_V 110 to 115 and κ_I 2.0 to 2.5; anthracite 210 to 245 and 3.5 to 5.3 (midpoints used). Layers of a dual or tri-media bed add. Head loss roughly doubles when the effective size falls from 1.2 to 0.8 mm and is 60 to 70% higher at 5 °C than at 25 °C. Clean bed only: the loss grows through the run as solids deposit.

Clean-bed head loss through a granular filter

How it works

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