Culvert calculator

Using the calculator above

The calculator opens on the first site of the worked example further down this page, so you can check its numbers against the text.

• Barrel. Choose pipe or box, then the diameter, or the span and rise. Barrels is the number of identical barrels side by side; the flow is split equally between them.
• Material and Manning’s n. The material fills a typical n, which you can overwrite. The inlet list shows the entrance details the calculator has coefficients for with that shape and material, with the entrance loss coefficient Ke in each label.
• Profile. Barrel length and the inlet and outlet invert levels. The barrel slope comes from these.
• Flow and tailwater. The design flow and the tailwater depth above the outlet invert.
• Road over the culvert. Crest level, the length of road that would overtop, and the road width. If headwater rises above the crest, the calculator balances the flow between the barrel and the road.
• Inlet-control method. FHWA HDS-5 / HY-8 by default, or the SANRAL Drainage Manual (6th ed.) relations for South African submissions that cite them.

Inlet control vs outlet control

A culvert runs under inlet control when the entrance cannot admit water as fast as the barrel could carry it. Headwater then depends on the inlet alone: its shape, its edge and a small slope correction. Barrel length, roughness and tailwater make no difference. Short, smooth, steep barrels with a free outlet usually behave this way.

It runs under outlet control when the barrel is the bottleneck: a long or rough barrel, a flat slope, or tailwater backing up from downstream. Headwater then depends on everything between the pond and the outlet pool.

You rarely know in advance which applies, so HDS-5 computes both and the higher headwater governs. The governing regime can change with flow, which is why the calculator plots both curves on the performance chart.

Inlet control equations

HDS-5 fits inlet control with one regression for an unsubmerged entrance, which behaves like a weir, and one for a submerged entrance, which behaves like an orifice:

The unsubmerged form applies up to a flow intensity $K_u Q / A D^{0.5}$ of about 3.5 and the submerged form above about 4.0. Mitred inlets take $+0.7S$ in place of $-0.5S$. Where HY-8 publishes a fifth-degree polynomial fit to the HDS-5 nomographs for the inlet, the calculator uses that polynomial, as HY-8 does, and falls back to these regressions otherwise.

Outlet control equations

Outlet control is an energy balance from the outlet back to the headwater pond:

In US customary units the friction term is $29\,n^2 L / R^{1.33}$. $V$ and $R$ are full-barrel values, $K_e$ is the entrance loss coefficient, the 1 is the exit loss, and $TW$ is the tailwater depth. When the barrel runs part full on a mild slope with a free outlet, the calculator steps the water surface up the barrel from the outlet (direct step) in place of the full-barrel equation, which is the approach HY-8 takes.

Worked example: one pipe, two sites

A 1200 mm precast concrete pipe (n = 0.012) with a square-edged inlet in a headwall ($K_e$ = 0.5) carries a design flow of 3.0 m³/s. Full-barrel area is 1.131 m² and full-barrel velocity 2.65 m/s.

Site A: 30 m barrel at 2%, tailwater 0.60 m (inverts 100.00 m and 99.40 m).

• Inlet control: $K_u Q / A D^{0.5}$ = 1.811 × 3.0 / (1.131 × 1.2^0.5) = 4.39, so the entrance is submerged. HW/D = 0.0398 × 4.39² + 0.67 − 0.5 × 0.02 = 1.43, giving 1.71 m. The HY-8 polynomial the calculator uses gives 1.706 m.
• Outlet control: critical depth is 0.95 m and normal depth 0.60 m, so the barrel is steep with a free outlet. $h_o$ = max(0.60, (0.95 + 1.20)/2) = 1.08 m. With $V^2/2g$ = 0.359 m, entrance loss is 0.18 m, friction 0.15 m and exit 0.36 m, so $H$ = 0.69 m and $HW_o$ = 1.08 + 0.69 − 0.60 = 1.17 m.
• Result: inlet control governs. Headwater 1.71 m (level 101.71 m), HW/D 1.42, outlet velocity 5.29 m/s at normal depth, HY-8 type 5-S2n. The SANRAL solver gives 1.60 m for the same inlet.

Site B: same pipe and flow, 60 m barrel at 0.5%, tailwater 1.40 m.

• Inlet control barely moves: 1.72 m.
• Outlet control: tailwater is above the crown, so the barrel runs full. $H$ = 0.18 + 0.30 + 0.36 = 0.84 m and $HW_o$ = 1.40 + 0.84 − 60 × 0.005 = 1.94 m.
• Result: outlet control governs. Headwater 1.94 m, HW/D 1.62, outlet velocity 2.65 m/s, HY-8 type 4-FFf.

The two sites call for different fixes. At site A a groove-end inlet cuts headwater from 1.71 m to 1.53 m without changing the pipe. At site B the same inlet saves only 0.11 m (to 1.83 m), while the next pipe size, 1350 mm, brings headwater down to 1.60 m and HW/D to 1.18. A corrugated metal barrel (n = 0.024) at site B would raise outlet-control headwater to 2.85 m.

Entrance loss coefficients (Ke)

$K_e$ multiplies the velocity head in the outlet-control equation. These are the HDS-5 values the calculator applies:

HDS-5 has no rows for plastic pipe. Smooth HDPE and PVC pipes take the concrete-pipe values for a square edge (0.5) or groove end (0.2) and 0.9 when projecting, the values HY-8 lists for them.

$K_e$ only enters outlet control. Under inlet control the same choice of inlet works through the HY-8 polynomial for that inlet, or the HDS-5 constants $K$, $M$, $c$ and $Y$ where HY-8 has none.

Manning’s n for culvert barrels

Roughness only affects outlet control. For a barrel with a long design life, or one likely to carry sediment, test the upper value as well.

Limitations

• Inlet control is only as good as the match between your entrance and a tabulated HDS-5 inlet. Side-tapered and slope-tapered improved inlets are not in the list.
• All barrels at a crossing must be identical. A crossing that combines different barrels needs HY-8.
• Pipe and box barrels only. Pipe-arch, elliptical and open-bottom arch sections are not available yet.
• The Studio Culvert Designer takes SI inputs only (m, mm, m³/s). This calculator converts US customary inputs to SI before running the same engine.
• The analysis is steady flow at a peak discharge. If the pond upstream stores enough water to cut the peak, route the hydrograph with the detention pond calculator instead.
• The design flow comes from elsewhere: the rational method calculator for small catchments, or design flood estimation for South African sites.
• The calculator reports outlet velocity but does not design protection. Size the apron with the riprap sizing calculator.
• For tailwater, the normal depth of the downstream channel comes from the Manning’s equation calculator.

What a free Studio account adds

A free Delta Hydro Studio account includes the full Culvert Designer, which runs the same engine with more of the inputs exposed:

• Save the crossing to a project and export a Word, Excel or PDF report with the side view, longitudinal profile, performance curve and summary table.
• A sizing assistant that ranks commercial barrel sizes against your limits on HW/D, headwater level, freeboard to the road, outlet velocity and cover, and keeps the near misses in view with the failing constraint named.
• Batch import of many crossings from one CSV or Excel file, each analysed and saved as its own design.
• Tailwater computed as normal depth in the downstream channel section.
• A summary table across a range of flows, and a report table with the USGS flow type beside the HY-8 code.