Rapid Sand Filtration — Headloss & Backwash Cycle

Filter Parameters

Influent turbidity 25 NTU

Filtration rate 10.0 m/h

Sand effective size 0.60 mm

Operation

Auto-backwash at limit

Live Readouts

0 cmlimit 250 cm

Headloss

— cm

Effluent turbidity

— NTU

Run time

0 min

Bed clogging

How it works

The bed is split into 10 depth layers. Turbidity removal follows the Iwasaki depth-filtration law, and as each layer traps solids its filter coefficient falls while its local headloss rises — a clogging front that migrates downward with time:

dC/dz = −λ·C            (Iwasaki)
λ_i = λ0·(1 − s_i)       (removal fades as layer i clogs)
s_i += k·(C_in − C_out)·v·dt   (specific deposit accumulates)

Headloss per layer comes straight from the Carman–Kozeny equation, with the layer's effective porosity shrinking as deposit s_i fills its pores (ε_i = ε0·(1 − s_i)):

hL/L = 180·ν·(1−ε)² / (g·ε³·d²) · v

Influent turbidity / filtration rate — more solids or faster flow load the bed harder, speeding up both headloss growth and breakthrough.
Sand effective size — finer sand removes more per layer (higher λ0) but clogs and loses head faster; coarser sand runs longer between washes but passes more turbidity.
Backwash — fluidizes the bed (upward flow expands and scours the grains), resetting every layer's deposit to zero and headloss back to the clean-bed value.
A run ends when headloss reaches the terminal limit or effluent turbidity breaks through the treatment goal — whichever comes first, exactly as on a real rapid gravity filter.

Real-world relevance: this is the run-limiting mechanism engineers size every rapid sand/anthracite filter around — trading grain size and loading rate against run length and backwash-water demand.

Clean sand Clogged (high deposit) Turbidity in raw water

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