Storm Drainage Toolkit

Q (cfs) = C · i · A Tc (min) = 0.0078 · L^0.77 · S^−0.385 (Kirpich; S in ft/ft)

Variables & units: C — runoff coefficient (dimensionless); i — rainfall intensity, in/hr, from the local IDF curve at the design return period and Tc; A — drainage area, acres; L — longest flow path, ft; S — mean flow-path slope, ft/ft.

Typical C values (Industry Approximation — Verify with PE)	C
Pavement / asphalt / concrete	0.85–0.95
Roofs	0.85–0.95
Gravel	0.40–0.70
Lawn, flat (sandy → heavy soil)	0.10–0.25
Lawn, steep (sandy → heavy soil)	0.15–0.35
Composite site — area-weight the parts	ΣCᵢAᵢ / ΣAᵢ

Assumptions & limitations: small, hydrologically simple areas (commonly capped near 100–200 acres by agency policy); uniform rainfall over the whole area for a duration ≥ Tc; C constant over the storm. Intensity–duration–frequency data are regional — this tool does not hardcode an IDF curve, so i must be read from the governing agency's curves at the computed Tc. Many agencies apply a Tc floor of 5–10 min. Kirpich was calibrated on small rural Tennessee watersheds; check the governing manual's preferred Tc method for paved sites.

Source: Rational Method per FHWA HEC-22 (Urban Drainage Design Manual), Ch. 3; Kirpich (1940). C values are generic textbook ranges (e.g. HEC-22 Table 3-1) — use the governing agency's table.

Q (cfs) = (1.49/n) · A · R^(2/3) · S^(1/2), R = D/4 (full circular) D_req (ft) = [ Q·n / (0.4644·√S) ]^(3/8)

Variables & units: Q — design flow, cfs; n — Manning roughness (dimensionless, empirical); S — pipe slope, ft/ft; D — inside diameter, ft; A — flow area, ft²; R — hydraulic radius, ft. Standard sizes carried: 12, 15, 18, 24, 30, 36, 42, 48, 54, 60 in.

Manning's n guidance: concrete 0.013; PVC 0.010–0.011; HDPE (smooth interior) 0.012–0.013; CMP 0.024. The dropdown carries one representative value per material — confirm against the manufacturer and the governing manual.

Assumptions & limitations: gravity flow, uniform (normal) depth, barrel not surcharged. The d/D readout solves partial circular flow at the design Q by the same equation. Storm drains are commonly designed near d/D ≤ 0.8–1.0 for the design storm — the governing standard controls. Junction, bend, and inlet losses (hydraulic grade line) are not modeled; check minimum self-cleansing velocity (typ. ≥ 2–3 fps).

Source: Manning's equation per FHWA HEC-22 Ch. 5 and standard hydraulics practice. n values: Industry Approximation — Verify with PE.

Grate, weir: Q = Cw · P · d^1.5 (Cw ≈ 3.0) Grate, orifice: Q = Co · A · √(2g·d) (Co ≈ 0.67; d ≳ 0.4 ft) Curb, weir: Q = Cw · L · d^1.5 (Cw ≈ 3.0–3.6)

Variables & units: d — ponding depth at the inlet, ft (over the grate; to the curb-opening lip); P — grate perimeter available to flow, ft, excluding the side against the curb; A — clear (open) grate area, ft²; L — curb opening length, ft; g = 32.174 ft/s².

Assumptions & limitations: sag/sump locations only — all approaching flow ponds at the inlet, so interception is a capacity problem, not an efficiency problem. Grate capacity is reported as the lesser of the weir and orifice values, which is conservative through the transition zone (d ≈ 0.4–1.4 ft for typical grates). Capacities are unclogged; HEC-22 recommends designing sag grates for ~50% clogging (curb openings are less clogging-prone). Curb openings transition to orifice flow when depth exceeds ~1.4 × the opening height — outside this calculator's range.

Source: FHWA HEC-22 (Urban Drainage Design Manual), Ch. 4, inlets in sag locations. Coefficients are HEC-22 defaults: Industry Approximation — Verify with PE.

Vs (cf) = (Qin − Qout) · Td · 60 / 2 (per trial duration; largest governs)

Variables & units: Qin — peak inflow, cfs, from the Rational Method at the IDF intensity for each trial duration; Qout — allowable release rate, cfs (the downstream or pre-development constraint); Td — trial storm duration, min.

Why several durations: shorter storms are more intense (higher Qin) but briefer; longer storms are weaker but deliver volume for longer. The critical duration is the one that maximizes Vs, so this simple method requires checking several — enter one Qin per duration (re-run calculator 01 with the IDF intensity at each Td). A single Qin may be broadcast across all durations for a quick upper-bound pass, but it makes the longest duration govern by construction.

Assumptions & limitations: triangular inflow and outflow approximation with release at a constant Qout; no routing, stage-storage, or outlet rating. Small-site preliminary sizing only — not a substitute for full hydrograph routing (TR-55/TR-20 or continuous simulation) on larger or complex sites, and many agencies mandate a specific method.

Source: Modified Rational Method, standard drainage-manual practice built on the Rational Method of FHWA HEC-22 Ch. 3. Industry Approximation — Verify with PE.

Orifice: Q = Cd · A · √(2g·h) → A = Q / (Cd·√(2g·h)) Weir: Q = Cw · L · H^1.5 → L = Q / (Cw·H^1.5)

Variables & units: Cd — orifice discharge coefficient (≈ 0.6 for a sharp-edged orifice); h — head from the design water surface to the orifice centroid, ft; Cw — rectangular sharp-crested weir coefficient (3.0–3.33); H — head above the weir crest, ft; L — weir length, ft; g = 32.174 ft/s².

Assumptions & limitations: free (unsubmerged) discharge on both elements; end contractions and velocity of approach ignored; single-stage release at the design water surface. Multi-stage outlets need a rating curve across the full stage range. Small orifices clog — many agencies set a minimum orifice size and require a trash rack.

Source: standard orifice and sharp-crested weir equations per FHWA HEC-22 and hydraulics texts (e.g. Brater & King). Coefficients: Industry Approximation — Verify with PE.

F = Q / (A·D^0.5) Inlet, unsubmerged (F ≤ 3.5): HW/D = Hc/D + K·F^M + cs·S Inlet, submerged (F ≥ 4.0): HW/D = c·F² + Y + cs·S Outlet (full flow): H = [1 + ke + 29·n²·L / R^(4/3)] · V²/2g HWo = max(TW, (dc+D)/2) + H − S·L

Variables & units: D — barrel diameter, ft; A — barrel area, ft²; dc — critical depth in the barrel, ft (computed); Hc — specific head at critical depth, ft; K, M, c, Y — HDS-5 inlet-control constants by entrance type; cs — slope-term coefficient (−0.5 standard; +0.7 mitered); ke — entrance loss coefficient; n — barrel Manning roughness (concrete 0.012, CMP 0.024); TW — tailwater above the outlet invert, ft. Between F = 3.5 and 4.0 the two inlet equations are interpolated linearly.

Assumptions & limitations: single circular barrel, no inlet depression, no skew. Outlet control uses the full-barrel-flow approximation, which is conservative for partly full barrels at low headwater. The inlet-control fits apply to roughly HW/D ≤ 3 (the nomograph range). The larger of the two headwaters governs. Roadway overtopping, buoyancy/uplift, and scour are not checked.

Source: FHWA HDS-5 (Hydraulic Design of Highway Culverts) — inlet-control nomograph-fit constants per Appendix A and entrance-loss coefficients per the outlet-control tables; simplified per screening practice (FHWA's HY-8 implements the full method). Constants: Industry Approximation — Verify with PE.

Fd (—) = Q / (√g · D^2.5) (discharge intensity) d50 (ft) = 0.2 · D · Fd^(4/3) · (D / TW) La (ft) = D · (8 + 17 · log10 Fd), min 4·D W (ft) = 3·D + (2/3)·La

Variables & units: D — outlet pipe diameter, ft; Q — design discharge, cfs; TW — tailwater depth used in the stone-size relation, ft (minimal/unknown → 0.4·D; adequate → 1.0·D); g = 32.174 ft/s².

Assumptions & limitations: minor circular outlet discharging onto a flat apron with no defined downstream channel; apron level, flared to the width W at its downstream end; riprap layer thickness typically 2×d50 over filter fabric or granular filter. High discharge intensity (Fd ≳ 2.5), drop outlets, steep or confined receiving channels, and supercritical approach flow are outside the simplified method — use a full HEC-14 energy-dissipator design. Round d50 up to the nearest local riprap class.

Source: FHWA HEC-14 (Hydraulic Design of Energy Dissipators), riprap apron design, simplified. Tailwater-condition assumptions: Industry Approximation — Verify with PE.