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Introduction to Highway Hydraulics

CHAPTER 9 - Closed-Conduit Applications - Culvert Design

9.1 General Design Concepts

Typical closed-conduit facilities in highway drainage include culverts and storm drains. A storm drain facility can be a much more extensive closed-conduit system than a cross drainage system such as a culvert. In some respects, a storm drain is simply a long culvert. Storm drain systems consist of inlets connected to an underground pipe and an outlet facility. Storm drain systems are often used when the capacity of the roadway (established by the allowable spread) is exceeded or for the collection and diversion of median drainage when the capacity of the swale is exceeded. A storm drain system may also be used in high gradient situations where erosion control is a concern.

Culverts are commonly used for cross drainage and can range in size from a single small culvert draining an isolated depression to multiple barrel designs and/or very large culverts for passing major stream channels under a roadway. Small culverts are also used for downdrains to protect fill slopes or to divert roadway water from a bridge deck.

Typical pipe materials used in storm drains include reinforced concrete pipe (RCP), corrugated metal pipe (CMP) and plastic pipe. These same materials are common for culverts, however, culverts are available in a variety of cross section shapes and often a shape other than circular is desirable. Conduit and culvert material are typically available in standard (nominal) sizes. Conduit size should not be decreased in the downstream direction, even if hydraulic calculations suggest this is possible due to maintenance issues such as deposition and clogging.

Energy dissipation is often required at the outlet of a storm drain or culvert to prevent erosion. Chapter 10 provides information on energy dissipators based on HEC-14 (Thompson and Kilgore 2006). Debris control structures may be required at the entrances of some culverts. HEC-9 provides guidance on debris control structures for culvert and bridges (Bradley et al. 2005). Maintenance is required for any closed-conduit facility. Sediment deposition within the conduit and debris removal at the entrances are typical maintenance items.

9.2 Culvert Design Approach

A culvert is a conduit that conveys flow through a roadway embankment or past some other type of flow obstruction. Culverts are typically constructed of concrete (reinforced and nonreinforced), corrugated metal (aluminum or steel) and plastic in a variety of cross sectional shapes. The most common cross sectional shapes for culverts are illustrated in Figure 9.1a and typical entrance conditions are shown in Figure 9.1b. The selection of culvert material depends on structural strength, hydraulic roughness, durability, and corrosion and abrasion resistance.

Flow conditions in a culvert may occur as open-channel flow, gravity full flow or pressure flow, or in some combination of these conditions. A complete theoretical analysis of the hydraulics of culvert flow is time-consuming and difficult. Flow conditions depend on a complex interaction of a variety of factors created by upstream and downstream conditions, barrel characteristics and inlet geometry. For purposes of design, standard procedures and nomographs have been developed to simplify the analysis of culvert flow. These procedures are detailed in Hydraulic Design Series Number 5 (HDS-5) entitled "Hydraulic Design of Highway Culverts." (Normann et al. 2005). The following information summarizes the basic design concepts and principles for culverts.

Sketch of six common culvert shapes - circular, box, elliptical, pipe arch, metal box, and arch
Figure 9.1a. Commonly used culvert shapes.

Sketches of two culvert entrances showing contraction of flow. Square edge entrance shows large contraction of flow reducing effective barrel size, while the beveled edge entrance shows minimal contraction of flow and maximizes effective barrel size
Figure 9.1b. Entrance contraction (schematic).

9.3 Types of Culvert Inlets and Outlets

A culvert typically represents a significant contraction of flow over conditions in the upstream and downstream channels and often is a hydraulic control point in the channel. Provision of a more gradual flow transition at the inlet of a culvert can improve the discharge capacity of the culvert by reducing the energy losses associated with flow contraction. Culvert inlets are available in a variety of configurations and may be prefabricated or constructed in place. Commonly used inlet configurations include projecting culvert barrels, cast-in-place concrete headwalls, precast or prefabricated end sections, and culvert ends mitered to conform to the fill slope (Figure 9.2). Structural stability, aesthetics, erosion control, fill retention, economics, safety, and hydraulic performance are considerations in the selection of an inlet.

Sketches of four types of inlets, projecting barrel, cast-in-place concrete headwall and wingwalls, end mitered to the slope and precast end section mitered to the slope and beveled
Figure 9.2. Four standard inlet types (schematic).

Hydraulic performance is improved by use of beveled edges rather than square edges, as illustrated in Figure 9.1b. Side-tapered and slope-tapered inlets, commonly referred to as improved inlets, can significantly increase culvert capacity. Figure 9.3 illustrates side-tapered and slope-tapered inlet conditions. A side-tapered inlet provides a more gradual contraction of flow and reduces energy losses. A slope-tapered inlet, or depressed inlet, increases the effective head on the control section and improves culvert efficiency.

Culvert outlet configuration can be similar to any of the typical inlet configurations; however, hydraulic performance of a culvert is influenced more by tailwater conditions in the downstream channel than by the type of outlet. Outlet design is important for transitioning flow back into the natural channel, since outlet velocities are typically high and can cause scour of the downstream streambed and bank.

Two sketches side-by-side showing a side tapered inlet and a slope tapered inlet in both elevation and plan views. Locations of the face section, throat section and for the sloped tapered inlet, the bend section, are shown.
Figure 9.3. Side- and slope-tapered inlets.

9.4 Culvert Flow Conditions

A culvert may flow full over all its length or partially full. Full flow throughout a culvert is rare, and generally some portion of the barrel flows partly full. A water surface profile analysis is the only way to determine accurately how much of the barrel flows full. Pressure flow conditions in a culvert can be created by either high downstream or upstream water surface elevations. Regardless of the cause, the capacity of a culvert operating under pressure flow is affected by up- and downstream conditions and by the hydraulic characteristics of the culvert.

Partly full flow, or open-channel flow, in a culvert may occur as subcritical, critical or supercritical flow. Gravity full flow, where the pipe flows full with no pressure and the water surface just touches the crown of the pipe, is a special case of free surface flow and is analyzed in the same manner as open-channel flow.

9.5 Types of Flow Control

Based on a variety of laboratory tests and field experience, two basic types of flow control have been defined for culverts: (1) inlet control, and (2) outlet control. Inlet control occurs when the culvert barrel is capable of conveying more flow than the inlet will accept. The hydraulic control section of a culvert operating under inlet control is located just inside the entrance. Critical depth occurs at or near this location and the flow regime immediately downstream is supercritical. Hydraulic characteristics downstream of the inlet do not affect culvert capacity. Upstream water surface elevation and inlet geometry are the primary factors influencing culvert capacity.

Figure 9.4 illustrates typical inlet control conditions. The type of flow depends on the submergence of the inlet and outlet ends of the culvert; however, in each case the control section is at the inlet end of the culvert. For low headwater conditions the entrance of the culvert operates as a weir, and for headwaters submerging the entrance the entrance operates as an orifice. Figure 9.4a depicts a condition where neither the inlet nor the outlet end of the culvert are submerged. The flow passes through critical depth just downstream of the culvert entrance and the flow in the barrel is supercritical. The barrel flows partly full over its length, and the flow approaches normal depth at the outlet end.

Figure 9.4b shows that submergence of the outlet end of the culvert does not assure outlet control. In this case, the flow just downstream of the inlet is supercritical and a hydraulic jump forms in the culvert barrel.

Figure 9.4c is a more typical design situation. The inlet end is submerged and the outlet end flows freely. Again, the flow is supercritical and the barrel flows partly full over its length. Critical depth is located just downstream of the culvert entrance, and the flow is approaching normal depth at the downstream end of the culvert.

Figure 9.4d is an unusual condition illustrating the fact that even submergence of both the inlet and the outlet ends of the culvert does not assure full flow. In this case, a hydraulic jump will form in the barrel. The median inlet provides ventilation of the culvert barrel. If the barrel were not ventilated, sub-atmospheric pressures could develop which might create an unstable condition during which the barrel would alternate between full flow and partly full flow.

Outlet control occurs when the culvert barrel is not capable of conveying as much flow as the inlet opening will accept. The control section for outlet control is located at the barrel exit or further downstream. Either subcritical or pressure flow exists in the culvert under outlet control. All the geometric and hydraulic characteristics of the culvert play a role in determining culvert capacity. Figure 9.5 illustrates typical outlet control conditions. Condition 9.5a represents the classic full flow condition, with both inlet and outlet submerged. The barrel is in pressure flow throughout its length.

Condition 9.5b depicts the outlet submerged with the inlet unsubmerged. For this case, the headwater is shallow so that the inlet crown is exposed as the flow contracts into the culvert.

Condition 9.5c shows the entrance submerged to such a degree that the culvert flows full throughout its entire length while the exit is unsubmerged. This is a rare condition, it requires an extremely high headwater to maintain full barrel flow with no tailwater. Outlet velocities are unusually high under this condition.

Condition 9.5d is more typical. The culvert entrance is submerged by the headwater and the outlet end flows freely with a low tailwater. For this condition, the barrel flows partly full over at least part of its length (subcritical flow) and the flow passes through critical depth just upstream of the outlet.

Condition 9.5e is also typical, with neither the inlet nor the outlet end of the culvert submerged. The barrel flows partly full over its entire length, and the flow profile is subcritical.

Four types of inlet control illustrated by sketches labeled a, b, c and d from top-to-bottom operating as described in the above text.
Figure 9.4. Types of inlet control.

Five types of outlet control illustrated by sketches labeled a, b, c, d and e from top-to-bottom operating as described in the above text.
Figure 9.5. Types of outlet control.

9.6 Headwater and Tailwater Considerations

Energy is required to force flow through the constricted opening represented by a culvert. This energy occurs as an increased water surface elevation on the upstream side of the culvert. The headwater depth (HW) is defined as the depth of water at the culvert entrance. In areas with flat ground slope or high fills a considerable amount of ponding may occur upstream of the culvert. If significant, this ponding can attenuate flood peaks and may justify a reduction in the required culvert size.

Tailwater is defined as the depth of water downstream of the culvert, measured from the outlet invert. Tailwater is an important factor in determining culvert capacity under outlet control conditions. Tailwater conditions are most accurately estimated by water surface profile analysis of the downstream channel; however, when appropriate, tailwater conditions may be estimated by normal depth approximations.

9.7 Performance Curves

A performance curve is a plot of headwater depth or elevation versus flow rate. A performance curve can be used to evaluate the consequences of higher flow rates, such as the potential for overtopping the roadway if the design event is exceeded or to evaluate the benefits of inlet improvements. In developing a performance curve both inlet and outlet control curves must be plotted, since the dominant control is hard to predict and may shift over a range of flow rates.

Figure 9.6 illustrates a typical culvert performance curve. Below a headwater elevation of 4.3, the culvert operates under inlet control suggesting that inlet improvements might increase the culvert capacity and take better advantage of the culvert barrel capacity. A culvert that operates with inlet control over the range of design conditions could also be designed with additional barrel roughness to reduce outlet velocities, should downstream erosion be a concern.

9.8 Culvert Design Method

The basic design method is based on the location of the control (inlet or outlet). Although control may oscillate from inlet to outlet, the concept of "minimum performance" is applied meaning that while the culvert may operate more efficiently at times, it will never operate at a lower performance than calculated. The design procedure then is to assume a pipe size and material and calculate the headwater elevation for both inlet and outlet control. The higher of the two is designated as the controlling headwater elevation. The controlling headwater elevation is compared to the desired design headwater, usually governed by overtopping considerations, to determine if the assumed culvert size is acceptable.

Outlet velocity should then be considered to evaluate the need for outlet protection. If the controlling headwater is based on inlet control, determine the normal depth and velocity in the culvert barrel. Velocity at normal depth is assumed to be the outlet velocity. If the controlling headwater is based on outlet control, determine the area of flow at the outlet based on the barrel geometry and the following: (1) critical depth if the tailwater is below critical depth, (2) tailwater depth if the tailwater is between critical depth and the top of the barrel, and (3) height of the barrel if the tailwater is above the top of the barrel.

Culvert performance curve with y axis as headwater elevation and the x axis as discharge with an inlet control curve, outlet control curve and overall performance curve plotted. Overall performance curve is inlet controlled at low headwater and outlet controlled at higher headwater.
Figure 9.6. Culvert performance curve.

Evaluation of headwater conditions and outlet velocity is repeated until an acceptable culvert configuration is determined. To facilitate the design process, a Culvert Design Form is provided in HDS-5. Once the barrel is selected, it must be fitted into the roadway cross section. The culvert barrel must have adequate cover, the length should be close to the approximate length, and the headwalls and wingwalls must be dimensioned.

An exact theoretical analysis of culvert flow is extremely complex because the flow is usually nonuniform with regions of both gradually varied and rapidly varied flow. An exact analysis would involve backwater and drawdown calculations, energy and momentum balance and applications of the results of hydraulic model studies. Flow conditions in a given culvert will change as the flow rate and tailwater elevations change, and hydraulic jumps often form inside or downstream of the barrel.

To avoid the analytical complexities created by this wide range of flow conditions, HDS-5 (Normann et al. 2005) provides a culvert design method based on design charts and nomographs. These same procedures are implemented by the FHWA computer program HY-8. The design equations used to develop the nomograph and HY-8 procedures were based on extensive research. This research included quantifying empirical coefficients for various culvert conditions. Inlet and outlet control nomographs for reinforced concrete pipe (RCP) are provided in Figures 9.7 and 9.8, respectively. HDS-5 (Normann et al. 2005) provides nomographs for other pipe materials and shapes and a number of examples on the application of the design method. While it is possible to use the design method nomographs in HDS-5 and particularly the HY-8 computer program, without a thorough understanding of culvert hydraulics, this is not recommended.

Example Problem 9.1 (SI and English Units)

Given: A culvert at a new roadway crossing must be designed to pass the 25-year flood. Hydrologic analysis indicates a peak flow rate of 6.0 m3/s (212 ft3/s). The approximate culvert length is 60 m (197 ft) and the natural stream bed slope approaching the culvert is 1 percent. The elevation of the culvert inlet invert is 600 m (1968.5 ft) and the roadway elevation is 603 m (1978.35 ft). To provide some capacity in excess of the design flood, the desired headwater elevation should be at least 0.5 m (1.64 ft) below the roadway elevation. The tailwater for the 25-year flood is 1 m (3.28 ft).

Find: The size of RCP culvert necessary for the 25-year flood.

  1. The design will be completed using the nomographs in Figures 9.7 and 9.8. The Culvert Design Form will be used to facilitate the trial and error design process. The Culvert Design Form provides a summary of all the pertinent design data, and a small sketch with important dimensions and elevations.
  2. The critical depth required as part of the outlet control computation was evaluated using Figures 4.10a and b.
  3. The outlet velocity can be computed by calculating the full flow discharge (Equation 7.1) and full flow velocity (from continuity) and then using the part-full flow relationships (Figure 7.1) to find V/Vf ratio given Q/Qf.
  4. The completed Culvert Design Form (see following page) indicates that a 1,500-mm (60 in.) RCP with a projecting groove end entrance, operating under inlet control, will result in a headwater elevation that is 0.9 m (2.95 ft) below the roadway. The computed outlet velocity is relatively high and protection should be provided at the outlet.

The completed Culvert Design Form with English and SI units

9.9 Improved Inlet Design

Culvert outlet control capacity is governed by headwater depth, tailwater depth, entrance configuration and barrel characteristics. The entrance condition is defined by the barrel cross-sectional area, shape and edge condition, while the barrel characteristics are area, shape, slope, length and roughness. Inlet improvements on culverts functioning under outlet control will reduce entrance losses, but these losses are only a small portion of the total headwater requirement. Therefore, only minor modifications of the inlet geometry which result in little additional cost are justified.

Culvert inlet control capacity is governed only by entrance configuration and headwater depth. Barrel characteristics and tailwater depth are normally of little consequence since culverts with inlet control typically flow only partly full. Entrance improvements can result in full, or nearly full flow, thereby increasing culvert capacity significantly.

As discussed in Section 9.3 inlet improvements consist of bevel-edged inlets, side-tapered inlets and slope-tapered inlets. Beveled edges reduce the contraction of flow by effectively enlarging the face of the culvert. Bevels are plane surfaces, but rounded edges that approximate a bevel and the socket end of RCP are also effective. Bevels are recommended on all headwalls.

A second degree of improvement is a side-tapered inlet. Tapered inlets improve culvert performance by providing a more efficient control section (the throat). The inlet has an enlarged face area with the transition to the culvert barrel accomplished by tapering the sidewalls. The inlet face has the same height as the barrel, and its top and bottom are extensions of the top and bottom of the barrel. The intersection of the sidewall taper and barrel is defined as the throat section. Two control sections occur on a side-tapered inlet: at the face and throat. Throat control reduces the contraction at the throat.

Chart 1A: Nomograph for designing round concrete pipe culverts with inlet control in SI units. Given diameter of culvert in mm and discharge in cubic meters per second the nomograph predicts the headwater depth to diameter ratio for 3 types of inlets, square edge with headwall, groove end projecting, groove end with headwall.
Figure 9.7a. RCP inlet control culvert nomograph - SI units (from HDS-5).

Chart 1B: Nomograph for designing round concrete pipe culverts with inlet control in English units. Given diameter of culvert in inches and discharge in cubic feet per second the nomograph predicts the headwater depth to diameter ratio for 3 types of inlets, square edge with headwall, groove end projecting, groove end with headwall.
Figure 9.7b. RCP inlet control culvert nomograph - English units.

Nomograph for designing round concrete pipe culverts with outlet control in SI units. Given diameter of culvert in mm, discharge in cubic meters per second, the length of the barrel in meters and the entrance loss coefficient, the nomograph predicts the head loss H through the culvert which can be used to calculate the headwater depth HW.
Figure 9.8a. RCP outlet control culvert nomograph - SI units (from HDS-5, Normann et al. 2005).

Nomograph for designing round concrete pipe culverts with outlet control in English units. Given diameter of culvert in inches, discharge in cubic feet per second, the length of the barrel in feet and the entrance loss coefficient, the nomograph predicts the head loss H through the culvert which can be used to calculate the headwater depth HW.
Figure 9.8b. RCP outlet control culvert nomograph - English units (from HDS-5, Normann et al. 2005).

A third degree of improvement is a slope-tapered inlet. The advantage of a slope-tapered inlet over a side-tapered inlet without a depression is that more head is applied at the control (throat) section. Both face and throat control are possible in a slope-tapered inlet; however, since the major cost of a culvert is in the barrel portion and not the inlet structure, the inlet face should be designed with greater capacity at the allowable headwater elevation than the throat. This will ensure flow control will be at the throat and more of the potential capacity of the barrel will be used.

9.10 Culvert Design Using HY 8

The FHWA culvert program HY-8 is an interactive culvert analysis program that uses the HDS-5 analysis methods. The program will compute the culvert hydraulics and water surface profiles for circular, rectangular, elliptical, pipe arch, metal box and user-defined geometry. Additionally, improved inlets can be specified and the user can analyze inlet and outlet control for full and partially full culverts, analyze the tailwater in trapezoidal and coordinate defined downstream channels, analyze flow over the roadway embankment, and balance flows through multiple culverts.

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Veronica Ghelardi
Resource Center (Lakewood)

Updated: 04/07/2011

United States Department of Transportation - Federal Highway Administration