3 acres commercial bioretention North Carolina

Sizing a bioretention cell from the Water Quality Volume: a 3-acre commercial site in NC

A 3-acre commercial infill needs a stormwater control measure to treat the water quality storm. This walks the standard chain: the runoff coefficient from percent impervious, the Water Quality Volume from the 1-inch design storm, then the bioretention surface area from the Darcy filter-bed equation, checked against ponding storage and the required drawdown time. Real numbers, every step.

Result: Runoff coefficient R_v = 0.635; Water Quality Volume = 6,900 ft³ (1-inch storm). A 3-ft media bed at k = 1 in/hr with 9 in of ponding sizes to a filter-bed surface area of ~1,540 ft² to pass the WQV in a 48-hour drawdown — about 1.2% of the contributing area. Step-by-step formulas below.

Site inputs

Parameter	Value	Source
Contributing area, A	3.0 ac (130,680 ft²)	SCM drainage boundary
Impervious fraction, I	65%	Site plan (roofs, pavement)
Water-quality design storm, P	1.0 in	NCDEQ SCM design storm
Media depth, d_f	3.0 ft	Bioretention media spec
Media permeability, k	1.0 in/hr (2.0 ft/day)	Sand-based media, design value
Max ponding depth	9 in (0.75 ft)	NCDEQ MDC, ≤ 12 in
Target drawdown, t_f	48 hr (2 days)	NCDEQ MDC, drains within 2–5 days

Step 1 — Runoff coefficient

The volumetric runoff coefficient from percent impervious (Schueler, 1987):

$R_v = 0.05 + 0.009\,I = 0.05 + 0.009(65) = 0.635$

So 63.5% of the rain on this site runs off — the rest is intercepted, stored in depressions, or infiltrates before reaching the SCM.

Step 2 — Water Quality Volume

The WQV is the runoff generated by the design storm over the contributing area:

$WQV = \frac{P \cdot R_v \cdot A}{12} \;\;(\text{ft, ac}) \;\;\equiv\;\; P \cdot R_v \cdot A_{ac} \times 3{,}630 \;\;(\text{ft}^3)$

With P = 1.0 in, R_v = 0.635, A = 3.0 ac (1 ac-in = 3,630 ft³):

$WQV = 1.0 \times 0.635 \times 3.0 \times 3{,}630 = 6{,}915 \approx 6{,}900 \text{ ft}^3$

WQV = 6,900 ft³. This is the volume the bioretention cell must capture and treat.

Step 3 — Bioretention surface area (Darcy filter-bed equation)

Size the filter bed so the WQV passes through the media within the target drawdown. Darcy's law, integrated over the draining ponded head, gives the filter-bed surface area:

$A_f = \frac{WQV \cdot d_f}{k \,(h_f + d_f)\, t_f}$

where h_f is the average head over the bed during drawdown (half the max ponding, ≈ 0.375 ft), d_f = 3.0 ft, k = 2.0 ft/day, and t_f = 2 days:

$A_f = \frac{6{,}900 \times 3.0}{2.0 \,(0.375 + 3.0)\, 2} = \frac{20{,}700}{13.5} = 1{,}533 \approx 1{,}540 \text{ ft}^2$

Use 1,540 ft² of filter-bed surface — about 1.2% of the 130,680 ft² contributing area, a typical bioretention footprint ratio.

Note: the Darcy equation is sensitive to k. The 1 in/hr here is a design (long-term, partly-clogged) value, not the as-built media test value — using a fresh-media k of 3–6 in/hr would undersize the cell for its service life. NCDEQ expects the conservative design k.

Step 4 — Ponding and storage check

At 1,540 ft² with 0.75 ft of ponding, the surface storage is:

$V_{pond} = A_f \cdot h_{max} = 1{,}540 \times 0.75 = 1{,}155 \text{ ft}^3$

Plus the media void storage (porosity n ≈ 0.30 over a typical 0.5-ft saturated working depth) and the underdrain gravel adds more. The cell does not hold the entire 6,900 ft³ at once — it captures the first flush in ponding and treats the full WQV by filtration over the drawdown period. Inflow beyond the ponding volume during the peak is bypassed by the overflow/outlet structure, which is why the WQV (not the peak rate) governs SCM sizing.

Step 5 — Pollutant treatment context

Bioretention earns pollutant-removal credit in the NCDEQ MDC framework — on the order of ~85% TSS, with lower but meaningful nutrient removal that depends on media and an internal water storage (IWSZ) zone for denitrification. The WQV sizing above is the hydraulic prerequisite; the removal credits then feed the site's nutrient or TSS load-reduction accounting.

What changes if you tweak the inputs

If you change…	The result moves…
Impervious 65% → 85%	R_v → 0.815; WQV → 8,870 ft³; A_f → ~1,980 ft²
Design storm 1.0 → 1.5 in	WQV → 10,400 ft³ (1.5×); filter bed scales up proportionally
Media k 1.0 → 2.0 in/hr	A_f halves to ~770 ft² — but only if NCDEQ accepts the higher design k
Drawdown 48 → 72 hr	A_f drops ~33% — smaller footprint, slower drain (still within MDC)
Media depth 3 → 4 ft	A_f rises slightly (more head to push through), deeper excavation

Open this SCM in HydroComplete

The Water Quality (IDEAL) engine computes the runoff coefficient, WQV, and Darcy filter-bed sizing, then routes the treatment train. Change the impervious fraction, media depth, or drawdown target and watch the cell re-size.

Open in app 14-day free trial

Sources and further reading

NCDEQ. Stormwater Design Manual — Minimum Design Criteria (MDC) for bioretention; design storm and WQV.
Schueler, T. (1987). Controlling Urban Runoff. Metropolitan Washington COG — runoff coefficient R_v = 0.05 + 0.009·I.
Maryland Dept. of the Environment. Stormwater Design Manual. Darcy filter-bed surface-area equation.
Claytor, R. & Schueler, T. (1996). Design of Stormwater Filtering Systems. Center for Watershed Protection.

— Michael Flynn, PE
This worked example uses HydroComplete's Water Quality (IDEAL) engine for the Rv, WQV, and Darcy filter-bed sizing. Open the scenario in the app to verify or modify any input.

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