Culvert Designer

Open Culvert Designer

Design and analyse culvert crossings using the FHWA HDS-5 methodology. Evaluate inlet and outlet control headwater, compare performance across return periods, and generate professional longitudinal profiles for circular, box, and arch culverts.

Overview

The Culvert Designer tool sizes and evaluates culvert crossings for road drainage and river crossings. It implements the Federal Highway Administration (FHWA) Hydraulic Design Series No. 5 (HDS-5) methodology — the same approach used in the well-known HY-8 software — adapted for South African conditions and metric units.

Given a design flow, culvert geometry, and site conditions, the tool determines whether the culvert operates under inlet control or outlet control and calculates the resulting headwater elevation. It evaluates performance across multiple flow rates to generate performance curves and a longitudinal profile through the barrel.

When to use this tool

Use the Culvert Designer for any pipe or box structure conveying water beneath a road, railway, or embankment. It is suitable for single-barrel culverts with uniform slope and cross-section. For multi-barrel installations, analyse each barrel individually with the apportioned flow.

Culvert Shapes & Materials

The tool supports the three culvert shapes commonly specified in South African road drainage practice: circular pipes, rectangular (box) culverts, and arch culverts. Each shape has its own geometry relationships and its own set of FHWA inlet-control regression coefficients.

Circular

Circular culverts are the most commonly used shape in South Africa. They are available in standard precast concrete and corrugated steel pipe sizes ranging from 300 mm to 2100 mm diameter. Circular pipes are structurally efficient and are well-suited where the allowable headwater is at least 1.2 times the pipe diameter.

$$A_\text{full} = \frac{\pi D^2}{4} \qquad P_\text{full} = \pi D \qquad R_\text{full} = \frac{D}{4}$$

Full-flow geometry — circular culvert

Standard SA pipe diameters (mm): 300, 375, 450, 525, 600, 675, 750, 900, 1050, 1200, 1350, 1500, 1650, 1800, 1950, 2100.

Box (Rectangular)

Box culverts are reinforced concrete structures defined by a span $B$ (width) and rise $D$ (height). They are preferred when vertical clearance is limited and a low-profile structure is required, or when the natural channel is wide and shallow. Box culverts can accommodate larger flows with lower headwater depths compared to circular pipes of equivalent area.

$$A_\text{full} = B \cdot D \qquad P_\text{full} = 2(B + D) \qquad R_\text{full} = \frac{B D}{2(B + D)}$$

Full-flow geometry — box culvert

Box vs circular

For the same cross-sectional area, a box culvert produces lower headwater under inlet control because its wider opening accepts flow more efficiently. Consider box culverts when the allowable headwater-to-rise ratio (HW/D) must remain below 1.0.

Materials & Manning’s n

The Manning’s roughness coefficient $n$ determines friction losses through the barrel. Select the value that best represents the culvert material and expected condition over its design life.

Material	Manning’s n	Notes
Concrete (precast)	0.012	Most common in SA; smooth interior finish
Concrete (cast-in-place)	0.013	Slightly rougher due to formwork marks
Corrugated steel (68 mm × 13 mm)	0.024	Standard annular corrugation
Corrugated steel (helical)	0.019	Helical corrugation; smoother flow path
HDPE (smooth interior)	0.012	Smooth-lined corrugated exterior pipes
HDPE (corrugated interior)	0.020	Single-wall corrugated pipe
PVC	0.010	Smooth bore; limited to smaller diameters

Aging and sediment

Manning’s n values increase over the culvert’s life due to corrosion, sediment deposits, and biological growth. Consider using a value 10–20% higher than the published value for conservative design, particularly for culverts with a 50+ year design life.

Inlet Configurations

The inlet is where flow contracts from the upstream channel or ponded approach into the barrel. Because the contraction geometry controls how efficiently the culvert can accept flow, the choice of inlet type has a direct and often dominant effect on the required headwater.

Inlet Types & Ke Values

The inlet configuration determines the entrance loss coefficient $K_e$ and the inlet control regression coefficients ($K_1$, $M_1$, $c$, $Y$, $K_2$). A more hydraulically efficient inlet reduces headwater by smoothing the flow contraction at the entrance.

Inlet type	Ke	Description
Square edge, headwall	0.50	Pipe cut flush with a vertical concrete headwall
Groove end, headwall	0.20	Socket (bell) end of pipe in headwall; hydraulically efficient
Groove end, projecting	0.20	Socket end extends beyond the embankment face
Projecting (square cut)	0.70	Pipe projects from fill with no headwall; worst efficiency
Mitered to slope	0.70	Pipe end cut to match the embankment slope
Beveled ring (33.7°)	0.25	Beveled edge at inlet; improved flow entry
Wingwall flare (30–75°)	0.20	Box culvert with angled wingwalls to guide flow
Wingwall parallel (0°)	0.70	Box culvert with walls parallel to flow; poor efficiency

Inlet selection impact

The difference between a square-edge projecting inlet ($K_e = 0.70$) and a groove-end headwall ($K_e = 0.20$) can reduce headwater by 20–30% for the same flow rate. Always consider upgrading the inlet before increasing the culvert size.

Inlet Depression

An inlet depression (or fall) is a deliberate lowering of the culvert entrance below the natural streambed level. This increases the effective head at the inlet and improves hydraulic performance under inlet control, particularly for smaller culverts operating in the unsubmerged range.

The depression is typically formed by placing the inlet invert 150–300 mm below the upstream channel bed. The tool accounts for inlet depression when computing inlet control headwater by adjusting the upstream invert elevation accordingly.

Flow Control Analysis

A culvert can operate under one of two control regimes. The regime that produces the higher headwater governs the design. Understanding control type is fundamental to proper culvert sizing.

Inlet Control

Under inlet control, the culvert barrel has more capacity than the inlet can deliver. The headwater is determined entirely by the inlet geometry — the barrel length, slope, and roughness do not affect the headwater depth. The culvert entrance acts as a weir (unsubmerged flow) or an orifice (submerged flow).

Inlet control typically occurs when:

• The barrel slope is steep (supercritical flow in the barrel),
• The barrel is short, or
• The barrel has a smooth interior with low friction.

Inlet control indicator

If the barrel flows partially full with a free water surface and supercritical conditions, the culvert is almost certainly under inlet control. Improving the inlet edge condition (e.g. adding a headwall or beveled edge) is the most effective way to reduce headwater.

Outlet Control

Under outlet control, the barrel capacity limits the flow. Headwater depends on all losses through the system: entrance loss, friction loss through the barrel, and exit loss. Tailwater conditions downstream also influence the headwater elevation.

Outlet control typically occurs when the barrel slope is mild (subcritical flow), the barrel is long, or the barrel has high friction (e.g. corrugated steel). High tailwater further promotes outlet control.

$$H_L \;=\; K_e \cdot \frac{V^2}{2g} \;+\; \frac{n^2 \cdot L \cdot V^2}{R^{4/3}} \;+\; \frac{V^2}{2g}$$

Outlet-control head loss — sum of entrance, friction, and exit losses

Where $H_L$ is the total head loss comprising entrance loss, friction loss (Manning’s equation form), and exit loss (one velocity head). The factor of $V^2/2g$ on the exit term assumes the full velocity head is lost to the downstream pool.

Determining Control Type

The tool calculates headwater for both inlet and outlet control independently. The controlling regime is the one that produces the higher headwater elevation:

$$HW_\text{design} \;=\; \max\!\left(HW_\text{inlet},\; HW_\text{outlet}\right)$$

Controlling headwater is the greater of inlet and outlet control

Note that the controlling regime can change with flow rate. A culvert may be under inlet control at low flows but switch to outlet control at high flows, or vice versa. The performance curve shows this transition clearly.

Always check both

Never assume one control type governs for all flows. The tool evaluates both for every flow rate in the performance curve. A culvert that switches control type at the design flow may exhibit unexpected behaviour — for example, a sudden jump in headwater as flow increases past the crossover.

USGS Flow Types

The USGS classifies culvert flow into distinct types based on whether the inlet and outlet are submerged and whether the barrel flows full or partially full. The tool identifies the flow type for each computed condition. The key types are summarised below.

Inlet Control Types

Type	Inlet	Outlet	Barrel	Description
1	Unsubmerged	Unsubmerged	Partially full	Weir flow at inlet; steep slope with supercritical flow
2	Unsubmerged	Unsubmerged	Partially full	Weir flow at inlet; mild slope with subcritical flow
5	Submerged	Unsubmerged	Full near inlet	Orifice flow at inlet; barrel flows full near entrance, free surface downstream

Outlet Control Types

Type	Inlet	Outlet	Barrel	Description
4	Submerged	Submerged	Full	Classic full-flow pipe; pressure flow throughout
6	Submerged	Unsubmerged	Full	Full barrel flow with free outfall
7	Unsubmerged	Unsubmerged	Partially full	Subcritical flow throughout; backwater from outlet controls

Flow type reporting

The summary table reports the USGS flow type code for each return period. This helps verify that the analysis is physically reasonable. For example, if a steep culvert reports Type 4 (full flow, outlet control), check whether the tailwater is unusually high.

Headwater Calculations

The tool computes headwater from first principles for both control regimes. For inlet control it applies the FHWA regression equations from HDS-5; for outlet control it applies an energy balance from tailwater to headwater through the barrel.

Inlet Control Equations

Inlet control headwater is calculated using the FHWA regression equations from HDS-5. The equations use shape-specific and inlet-type-specific coefficients ($K_1$, $M_1$, $c$, $Y$, $K_2$).

Unsubmerged (weir) condition — applies when the inlet is not drowned:

$$\frac{HW}{D} \;=\; K_1 \left(\frac{Q}{A \, D^{0.5}}\right)^{M_1} \;+\; K_2 \, S \;-\; 0.5 \, S^2$$

Inlet control — unsubmerged (weir) equation

Submerged (orifice) condition — applies when the inlet is drowned:

$$\frac{HW}{D} \;=\; c \left(\frac{Q}{A \, D^{0.5}}\right)^{\!2} \;+\; Y \;+\; K_2 \, S \;-\; 0.5 \, S^2$$

Inlet control — submerged (orifice) equation

Where:

• $HW/D$ = headwater depth divided by culvert rise (or diameter)
• $Q$ = design flow (m³/s)
• $A$ = full cross-sectional area of the culvert (m²)
• $D$ = interior height / diameter (m)
• $S$ = barrel slope (m/m)
• $K_1$, $M_1$, $c$, $Y$, $K_2$ = regression coefficients from FHWA tables (vary by shape and inlet type)

Transition zone

The transition from unsubmerged to submerged flow typically occurs near $HW/D = 1.5$ for circular culverts. The tool uses a smooth interpolation between the two equations in this transition zone to avoid discontinuities in the performance curve.

Outlet Control Equations

Outlet control headwater is computed from an energy balance between the upstream headwater pool and the downstream tailwater, accounting for all losses through the culvert:

$$HW \;=\; h_o \;+\; H_L \;-\; L \cdot S$$

Outlet control — energy balance from tailwater to headwater

Where:

• $h_o$ = outlet depth — the greater of tailwater depth and $(d_c + D)/2$, where $d_c$ is the critical depth
• $H_L$ = total head loss = entrance + friction + exit losses
• $L \cdot S$ = elevation difference between inlet and outlet inverts (barrel drop)

Total head loss components:

$$H_e \;=\; K_e \cdot \frac{V^2}{2g}$$

Entrance loss

$$H_f \;=\; \frac{n^2 \cdot L \cdot V^2}{R^{4/3}}$$

Friction loss — Manning's equation form

$$H_x \;=\; 1.0 \cdot \frac{V^2}{2g}$$

Exit loss — one full velocity head

The velocity $V = Q/A_\text{full}$ when the barrel flows full. For partially full flow in mild-slope culverts, the tool steps backwater along the barrel from the outlet to determine the water surface profile.

Performance Curves

A performance curve plots headwater elevation (or HW/D ratio) against discharge for both inlet and outlet control. The upper envelope of the two curves defines the actual culvert performance. Where the curves cross, the controlling regime changes.

The tool generates performance curves across a range of flows from zero to 1.5 times the maximum design flow. This allows you to assess the culvert’s behaviour across all anticipated conditions, including events exceeding the design storm.

Reading performance curves

Look for the crossover point between inlet and outlet control curves. If the design flow is near this crossover, the culvert is sensitive to both inlet geometry and barrel properties — consider optimising both the inlet type and the barrel size.

Tailwater Analysis

Tailwater (TW) is the water depth immediately downstream of the culvert outlet, measured from the outlet invert. It directly affects outlet control headwater and must be estimated accurately. The tool supports two approaches:

• Direct input: Enter a known tailwater depth (m) for each design flow. Use this when downstream water levels are controlled by a dam, confluence, or other known condition.
• Channel-computed: The tool computes normal depth in the downstream channel using Manning’s equation, based on the channel geometry, slope, and roughness you provide. This is appropriate when the downstream channel is long and uniform enough for normal depth to develop.

Normal depth is the depth at which the downstream channel conveys the design flow uniformly — it solves the Manning equation iteratively for the free surface depth that balances area, hydraulic radius, slope, and roughness. See the Channel Analysis guide for the full treatment of normal and critical depth in open channels.

Tailwater sensitivity

Outlet control headwater is very sensitive to tailwater. An error of 0.3 m in tailwater can change the headwater by a similar amount. When in doubt, use a conservatively high tailwater estimate. Always verify tailwater conditions in the field — for example, check whether a downstream confluence, weir, or flat reach could back water up to the outlet.

Design Process

A defensible culvert design follows a deliberate sequence: establish the design flow, set the allowable headwater, trial a size and inlet, and iterate until both control regimes are satisfied. The steps below mirror the FHWA HDS-5 design procedure adapted to the tool’s workflow.

Step-by-Step Procedure

1. Determine the design flow (Q): Use the appropriate flood estimation method (Rational, SCS, Unit Hydrograph, etc.) to establish the peak flow for each design return period. The culvert must convey the design flow without exceeding the allowable headwater.
2. Set the allowable headwater ($HW_\text{allow}$): Typically limited by the road embankment height. The headwater should not overtop the road. A common criterion is $HW/D \le 1.2$ for circular culverts or $HW/D \le 1.0$ for box culverts.
3. Select culvert shape and material: Choose circular or box based on site constraints and headwater requirements. Select the material and corresponding Manning’s $n$.
4. Select initial size: Start with a trial diameter or span–rise dimension. For circular culverts, begin with $D \approx 1.2 \times (Q/2.5)^{0.4}$ as an initial estimate, then round up to the next standard size.
5. Check inlet control headwater: Calculate $HW$ for inlet control. If $HW$ exceeds the allowable, either increase the culvert size or improve the inlet type.
6. Check outlet control headwater: Calculate $HW$ for outlet control including friction and tailwater effects. If $HW$ exceeds the allowable, increase the culvert size.
7. Select the controlling headwater: The design headwater is the greater of inlet and outlet control headwater. Verify it is within the allowable limit.
8. Check overtopping: Verify that the headwater does not reach the road overtopping level. Assess the overtopping flow if the design is exceeded.
9. Check outlet velocity: Verify that the outlet velocity does not exceed the erosion resistance of the downstream channel. Provide energy dissipation (riprap apron, stilling basin) if needed.

Worked Example

Design a culvert crossing for the following conditions:

Parameter	Value
Design flow (Q)	5.0 m³/s
Culvert shape	Circular
Material	Precast concrete (n = 0.012)
Diameter (D)	900 mm (0.9 m)
Barrel length (L)	30 m
Barrel slope (S)	1% (0.01 m/m)
Inlet type	Square edge with headwall (Ke = 0.50)
Tailwater depth (TW)	0.5 m
Allowable HW	1.5 m (HW/D = 1.67)

Step 1 — Full-flow properties

$$A \;=\; \frac{\pi (0.9)^2}{4} \;=\; 0.636 \ \mathrm{m^2} \qquad R \;=\; \frac{0.9}{4} \;=\; 0.225 \ \mathrm{m} \qquad V \;=\; \frac{5.0}{0.636} \;=\; 7.86 \ \mathrm{m/s}$$

Step 2 — Inlet control headwater

Compute the flow parameter:

$$\frac{Q}{A \, D^{0.5}} \;=\; \frac{5.0}{0.636 \times 0.9^{0.5}} \;=\; 8.29$$

Since this exceeds the transition threshold, use the submerged equation with FHWA coefficients for concrete circular pipe, square edge headwall ($c = 0.0398$, $Y = 0.67$):

$$\begin{aligned} \frac{HW}{D} &\;=\; 0.0398 (8.29)^2 + 0.67 + 0 \\[4pt] &\;=\; 3.41 \\[4pt] HW_\text{inlet} &\;=\; 3.41 \times 0.9 \;=\; 3.07 \ \mathrm{m} \end{aligned}$$

Step 3 — Outlet control headwater

$$\begin{aligned} \tfrac{V^2}{2g} &\;=\; \tfrac{7.86^2}{19.62} \;=\; 3.15 \ \mathrm{m} \\[2pt] H_e &\;=\; 0.50 \times 3.15 \;=\; 1.57 \ \mathrm{m} \\[2pt] H_f &\;=\; \tfrac{0.012^2 \times 30 \times 7.86^2}{0.225^{4/3}} \;=\; 1.88 \ \mathrm{m} \\[2pt] H_x &\;=\; 3.15 \ \mathrm{m} \\[2pt] H_L &\;=\; 1.57 + 1.88 + 3.15 \;=\; 6.60 \ \mathrm{m} \\[2pt] h_o &\;=\; \max(0.5,\; (d_c + 0.9)/2) \;=\; 0.5 \ \mathrm{m} \ \text{(assuming $d_c < 0.1$ m)} \\[2pt] HW_\text{outlet} &\;=\; 0.5 + 6.60 - 30(0.01) \;=\; 6.80 \ \mathrm{m} \end{aligned}$$

Step 4 — Determine control

$HW_\text{outlet}$ (6.80 m) > $HW_\text{inlet}$ (3.07 m) → Outlet control governs.

Culvert undersized

The headwater of 6.80 m far exceeds the allowable 1.5 m. A 900 mm culvert is grossly undersized for 5.0 m³/s. The designer would need to increase the diameter significantly (likely to 1500–1800 mm) or use multiple barrels. This example illustrates the importance of checking both control types and iterating on the design.

Interpreting Results

The tool produces a summary table for each analysed return period plus a longitudinal profile plot. Read them together — the numbers tell you whether the design works, and the profile shows you why.

Summary Table

The summary table presents key results for each return period. Understanding each column is essential for evaluating the design:

Column	Description
Q (m³/s)	Design peak flow for the return period
HW_inlet (m)	Headwater depth under inlet control
HW_outlet (m)	Headwater depth under outlet control
HW_design (m)	Governing headwater (maximum of inlet and outlet)
HW/D	Headwater-to-rise ratio; target ≤ 1.2 for circular, ≤ 1.0 for box
Control	Governing control type (Inlet or Outlet)
V_out (m/s)	Outlet velocity; check against downstream channel capacity
Flow Type	USGS flow type code identifying the hydraulic regime

Longitudinal Profile

The longitudinal profile shows a section through the culvert from inlet to outlet, including:

• Barrel invert: The bottom of the culvert from inlet to outlet, showing the slope
• Barrel crown: The top of the culvert (invert + diameter/rise)
• Headwater elevation: The upstream pool level at the inlet face
• Hydraulic grade line (HGL): The pressure head through the barrel under outlet control
• Energy grade line (EGL): The total energy line (HGL + velocity head)
• Tailwater elevation: The downstream water level at the outlet

Profile interpretation

Under inlet control, the HGL drops below the barrel crown shortly after the inlet — you can see the flow surface inside the barrel. Under outlet control with full flow, the HGL stays at or above the crown throughout the barrel length.

Common Mistakes

The failure modes below crop up repeatedly in culvert design reviews. Screen for each one before finalising the structure.

• Undersizing the culvert. Selecting a culvert based on inlet control alone without checking outlet control. A culvert that appears adequate under inlet control may produce unacceptable headwater when friction and tailwater effects are included.
• Ignoring embedment. Failing to account for culvert embedment (burying the invert below the streambed). When a culvert is embedded 10–20% of its diameter for fish passage or scour protection, the effective opening area is reduced, increasing headwater. Adjust the calculations accordingly.
• Wrong inlet type selection. Using “groove end, headwall” coefficients when the actual installation is a projecting pipe with no headwall. This can underestimate headwater by 20–30%. Always match the inlet type to what will actually be constructed.
• Ignoring tailwater conditions. Assuming zero tailwater when a downstream confluence, dam, or flat channel creates significant backwater. This underestimates outlet control headwater and may result in road overtopping.
• Not checking overtopping. Designing only for the 1:50 year event without assessing what happens at the 1:100 year flow. Even if the culvert is designed for a specific return period, the overtopping level and flow should be computed to ensure the road and embankment can withstand the occasional exceedance.
• Neglecting outlet velocity. High outlet velocities (often 3–6 m/s) can cause severe scour downstream. Always check the outlet velocity and provide appropriate energy dissipation such as a riprap apron, gabion mattress, or concrete stilling basin.

Glossary

Term	Definition
Headwater (HW)	The depth of water upstream of the culvert inlet, measured from the inlet invert to the upstream water surface.
Tailwater (TW)	The depth of water downstream of the culvert outlet, measured from the outlet invert to the downstream water surface.
HW/D	Headwater-to-diameter (or rise) ratio. A dimensionless measure of how high the upstream pool is relative to the opening.
Critical depth (d_c)	The depth at which specific energy is minimum for a given discharge. Controls the transition between sub- and supercritical flow.
Normal depth (d_n)	The uniform-flow depth that balances the Manning equation for a given channel, slope, and roughness.
Froude number (Fr)	Ratio of flow velocity to wave celerity ($Fr = V/\sqrt{g D_h}$). Fr < 1 is subcritical, Fr > 1 is supercritical.
Inlet control	Condition where the culvert entrance geometry limits the flow capacity; barrel properties do not affect headwater.
Outlet control	Condition where barrel friction, length, and tailwater determine the headwater; the barrel operates at or near full.
Performance curve	A plot of headwater vs discharge showing culvert capacity under both inlet and outlet control across a range of flows.
Ke	Entrance loss coefficient, quantifying the energy loss as flow contracts to enter the culvert barrel.
Manning’s n	Roughness coefficient describing the frictional resistance of the culvert barrel interior surface.
HDS-5	FHWA Hydraulic Design Series No. 5 — the definitive reference for culvert hydraulic design methodology.
HGL	Hydraulic Grade Line — the line representing pressure head along the culvert barrel length.
EGL	Energy Grade Line — the total energy line (HGL + velocity head) along the culvert barrel length.
Barrel	The main body of the culvert between the inlet and outlet faces, through which water flows.
Overtopping	Flow over the road surface when headwater exceeds the road crest elevation.
Embedment	The practice of burying the culvert invert below the natural streambed for environmental or scour reasons.

References

• FHWA. (2012). Hydraulic Design of Highway Culverts (Hydraulic Design Series No. 5, 3rd ed., Publication No. FHWA-HIF-12-026). Federal Highway Administration, U.S. Department of Transportation, Washington, D.C. (HDS-5 — the primary reference for the methodology implemented in this tool.)
• FHWA. (2012). HY-8 Culvert Hydraulic Analysis Program (User Manual). Federal Highway Administration. (Reference implementation of the HDS-5 methodology.)
• SANRAL. (2013). Drainage Manual (6th ed.). South African National Roads Agency, Pretoria. Chapter 7 — Hydraulic design of culverts and bridges.
• AASHTO. (2020). LRFD Bridge Design Specifications (9th ed.). American Association of State Highway and Transportation Officials, Washington, D.C. Section 2 — Hydraulic and hydrologic considerations; Section 12 — Buried structures.
• Chow, V.T. (1959). Open-Channel Hydraulics. McGraw-Hill, New York. Chapter 17 — Hydraulic design of culverts.
• Normann, J.M., Houghtalen, R.J. & Johnston, W.J. (2001). Hydraulic Design of Highway Culverts (HDS-5, 2nd ed.). Federal Highway Administration. (Earlier edition retained for historical reference and regression coefficient derivations.)

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Open Culvert Designer