Sand Filter Design Example — Worked Sizing Steps

This worked example sizes a surface sand filter treating runoff from a 3-acre civic-center site. Sand filters are the practice of choice where space is tight, soils will not infiltrate, and the drainage area is small and highly impervious. The sequence below — head check, peak discharge, diversion, filter bed, sedimentation chamber, volume check — mirrors a real submittal. Applicability and maintenance are covered in the sand filter fact sheet.

Site data

Existing ground at the facility location: elevation 22.0 ft
Seasonally high water table: 13.0 ft
Adjacent creek invert: 12.0 ft
Water quality volume WQ_v: 6,752 cubic feet (see the sizing criteria guide)

Step 1 — Confirm the water quality volume

WQ_v = 6,752 cf, carried over from the site hydrology. The pond design calculator reproduces this derivation from drainage area, impervious cover and rainfall depth.

Step 2 — Determine available head

Head is the budget every filter design spends. Work from the hydraulic high point down:

From above

Parking low point 23.5 − 2.0 (pass Q10) − 0.5 (channel to facility) = 21.0 ft

From below

Stream invert 12.0 + 2.0 (outfall above invert) + 0.5 (drain) + 0.67 (gravel blanket) + 1.5 (sand bed) = 16.67 ft

Available head

21.0 − 16.67 = 4.33 ft → average head over filter h_f = 4.33 / 2 = 2.17 ft

Step 3 — Recharge volume

The sedimentation basin is built with an open bottom so the recharge volume — 1,688 cubic feet — infiltrates through the sediment chamber floor. The chamber dimensions in Step 7 provide more than this volume.

Step 4 — Water quality peak discharge

TR-55 underpredicts runoff from small storms, so a modified curve number is back-computed from the water-quality storm:

Modified CN

P = 1.0 in, Q = 0.62 in
CN = 1000 / [10 + 5P + 10Q − 10·(Q² + 1.25·Q·P)^0.5] = 95.6 → use CN = 96

Peak discharge

Tc = 0.16 hr, Ia/P = 0.083 → qu = 900 csm/in
qp = 900 · 0.62 · (3.0 / 640) = 2.6 cfs

Step 5 — Size the flow diversion

Structure	Design flow	Equation	Result
Low-flow orifice	2.6 cfs @ 1.5 ft head	Q = C·A·√(2gh), C = 0.6	A = 0.44 sf → d = 8 in
10-yr overflow weir	14.0 cfs @ 2.0 ft head	Q = C·L·H^1.5, C = 3.1	L = 1.6 ft → use 2.0 ft

The weir wall sits at elevation 19.0; the low-flow invert lands at 17.17 after subtracting the head and half the orifice diameter.

Step 6 — Size the filter bed (Darcy’s Law)

Equation

A_f = WQv · d_f / [k · (h_f + d_f) · t_f]

d_f = 18 in sand depth, k = 3.5 ft/day sand permeability, h_f = 2.17 ft average head, t_f = 40 hr drawdown

Result

A_f = 6,752 · 1.5 / [3.5 · (2.17 + 1.5) · (40/24)] = 473 sf → bed 15.5 × 30.5 ft (2:1)

Step 7 — Size the sedimentation chamber

For sites under 75% impervious cover the Camp-Hazen settling relationship reduces to A_s = 0.066 · WQ_v:

Chamber area

A_s = 0.066 · 6,752 = 446 sf → 15.5 × 28.75 ft at the shared wall width

Step 8 — Minimum storage check

Filter systems may store less than the full WQ_v within the practice; the floor is typically three quarters of it:

Required

V_min = 0.75 · WQv = 5,064 cf

Provided

V_filter-bed voids = 473 · 1.5 · 0.4 = 284 cf
+ temporary ponding above the bed + sedimentation chamber volume ≥ V_min

The balance is provided as ponding above the filter surface and storage in the sedimentation chamber; the final grading confirms the stack-up.

field note

The 40-hour drawdown assumption is a design value for clean sand. Filters slow down as they load — a bed that draws down in 40 hours when new may take twice that after two years, which is exactly when the surface needs raking or replacement of the top few inches.

Design summary

Element	Value
Water quality volume	6,752 cf
Available head	4.33 ft (h_f = 2.17 ft)
WQv peak discharge	2.6 cfs (CN 96)
Filter bed	473 sf — 15.5 × 30.5 ft, 18 in sand
Sedimentation chamber	446 sf — 15.5 × 28.75 ft, open bottom
Diversion	8 in orifice / 2.0 ft weir
Minimum storage	5,064 cf (0.75 · WQv)

Frequently asked questions

When is a sand filter the right stormwater practice?

Small, highly impervious drainage areas — typically under 5 acres for surface filters and under 2 acres for underground and perimeter variants — where soils will not infiltrate and space for a pond does not exist. The BMP selector screens these conditions automatically.

How much head does a surface sand filter need?

Around 5 feet is comfortable; this example works with 4.33 feet. Perimeter sand filters can operate with as little as 2 feet.

Why use a modified curve number for the water quality storm?

Standard TR-55 curve numbers underpredict runoff from small events. Back-computing the CN from the known water-quality runoff (here CN 96 for a 1-inch storm) gives a realistic peak for sizing the diversion.

What sand permeability should be assumed?

Clean concrete sand is conventionally assigned k = 3.5 ft/day for design. Field permeability declines as the filter loads, which the 40-hour drawdown allowance accounts for.

Does a sand filter provide groundwater recharge?

Only if a chamber is built with an open bottom over suitable soils, as in this example’s sedimentation basin. The filter bed itself discharges through an underdrain.

What maintenance does a sand filter need?

Remove accumulated sediment from the sedimentation chamber roughly annually, rake the filter surface when drawdown slows, and replace the top several inches of sand when raking no longer restores the rate.

Can the filter store less than the full water quality volume?

Yes — filter designs conventionally require at least 75% of WQ_v within the practice (V_min), because treatment continues while the volume passes through the bed during the storm.

What pollutant removal can a sand filter achieve?

Monitored medians are about 86% for sediment, 59% for total phosphorus and 38% for total nitrogen — per-study records are in the pollutant removal database.