Culvert Headwater Quick-Check (Inlet/Outlet Control)

Culvert Headwater Quick-Check

Circular culvert headwater per the FHWA HDS-5 method: inlet control from the nomograph regression equations, outlet control assuming full flow, and whichever governs. Runs entirely offline; inputs persist in this browser via localStorage.

Use limits: This is the HDS-5 hand method for a single circular barrel — the right tool for "will this crossing pass the design storm without drowning the road," not a replacement for HY-8 or the drainage report. Outlet control here assumes the barrel flows full (conservative and standard for the hand check; partially full outlet-control profiles need water-surface computations). Box culverts, multiple barrels, improved inlets, and fish passage are HY-8 territory. Regression coefficients are the standard HDS-5 Appendix A values for common circular inlets — verify against the current edition for anything contractual.

Culvert

Diameter (in) Material / inlet configuration

Length (ft) Slope (ft/ft)

Hydraulics

Design flow Q (cfs)

Tailwater depth above outlet invert (ft)

Allowable headwater depth (ft) — optional

—

Inlet control HW	—
Outlet control HW (full flow)	—
Governing headwater	—
HW/D ratio	—
Critical depth	—
Full-flow velocity (outlet scour check)	—

How the Numbers Are Derived

Inlet control (the nomograph equations)

Inlet control means the entrance is the bottleneck — the barrel could carry more than the inlet lets in. HDS-5 fits two regression forms to the lab data behind the nomographs, using the discharge parameter Q/(A·D^0.5):

Unsubmerged (≤ 3.5): HW/D = H_c/D + K·[Q/(A·D^0.5)]^M − 0.5·S, where H_c is critical depth plus critical velocity head.

Submerged (≥ 4.0): HW/D = c·[Q/(A·D^0.5)]² + Y − 0.5·S — the inlet acting as an orifice.

Between 3.5 and 4.0 the tool interpolates linearly, per standard practice. Mitered inlets use +0.7·S instead of −0.5·S. K, M, c, Y are inlet-specific (HDS-5 Appendix A); a grooved concrete end genuinely outperforms a square edge, which is why the coefficient table matters.

Outlet control (full flow)

Outlet control means the barrel plus the downstream water surface is the bottleneck. Assuming full flow: HW = H + h_o − S·L, where the head loss H = [1 + K_e + 29·n²·L / R^4/3] · V²/2g (entrance + friction + exit, English units), and h_o = max(TW, (d_c+D)/2) approximates the effective downstream head. The governing headwater is simply the larger of inlet and outlet control — the culvert doesn't get to choose the easier one.

Critical depth

Solved for the circular section by bisection on Q²·T / (g·A³) = 1 with A = (θ−sin θ)·D²/8 and T = D·sin(θ/2), capped just below the crown. It feeds both the unsubmerged inlet form (through H_c) and the outlet-control h_o term.

Field/reviewer notes

Typical criteria allow HW/D of 1.2–1.5 at the design storm; the tool flags beyond 1.5. Overtopping checks compare governing HW against the road profile, not just a ratio.
An inlet-controlled culvert wastes its barrel — if inlet control governs by a wide margin, an improved inlet (beveled/grooved end, headwall) buys capacity far cheaper than a bigger pipe.
Full-flow outlet velocity above ~10 ft/s wants energy dissipation or riprap sizing at the outlet (HEC-14).
Debris and sediment don't appear in these equations, and they're how real culverts actually fail. Maintenance access beats another six inches of diameter.

References

FHWA HDS-5, Hydraulic Design of Highway Culverts — the governing method, coefficient tables, and nomographs. https://www.fhwa.dot.gov/engineering/hydraulics/

FHWA HY-8 — free culvert analysis software for anything past a hand check.

FHWA HEC-14 — outlet energy dissipators.