Culvert Hydraulics

5/25/2018 Culvert Hydraulics

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Culvert Hydraulics:Basic Principles By Philip A. Creamer, P.E.

December 2007


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2 PDH Special Advertising Section CONTECH Bridge Solutions

Aculvert is a relatively short segment of conduit that

is typically used to transport water underneath aroadway or other type of earthen embankment.

There is some common terminology that is used

in culvert hydraulics that can best be presented by referring

to Figure 1. The culvert itself consists of an entrance, an

outlet, and a culvert barrel. Common culvert shapes include

circular pipes, rectangular boxes, ellipses, and arches.

Noncircular culverts are generally described by their size in

terms of a culvert rise (D ) and a culvert span (B). The size of

a circular culvert is usually expressed in terms of the culvert

diameter (D ).

There is a wide variety of entrance conditions found at

culverts, including square edge, angled wingwalls, beveled

edges, entrance mitered to slope, et cetera. Some of these

common culvert end treatments are shown in Figure 2. It is

not uncommon for the opening of a culvert to be smaller

than the original channel cross-section prior to the culvert

installation. All else being equal, a smaller waterway open-

ing will result in a lower channel conveyance, that is, a

lower carrying capacity of the channel. For the same flow,

a lower conveyance will, in turn, result in a higher depth of

water upstream of the structure, called the headwater.

In todays environment of floodplain management and

regulations, the increase in water surface upstream of

culverts is often limited. Therefore, culvert designs that

convey water under roadways with minimal headwater

buildup are becoming more common. The hydraulic solu-tion to minimize the head loss would be to not constrict

the flow by spanning the entire conveyance channel.

However, economic considerations many times prohibit

this approach. While some increase in water level upstream

of the culvert may be tolerated, the basic principle behind

culvert design is to ensure that the water level increase is

not unacceptably high. The headwater can be estimated

using well-established design methodologies.

Historically, most culverts were closed conduits, where

the same material is found on the top, bottom, and sides

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Learning ObjectivesThis article presents a brief

summary of culvert hydraulic design

procedures. The reader will learn the

concepts of culvert inlet and outlet

control and the various equations

that describe each. The article also

introduces techniques to more accu-

rately model culvert hydraulics of the

large size natural bottom culverts that

are commonly required.

Professional DevelopmentSeries Sponsor

CONTECH Bridge Solutions Inc.

Culvert Hydraulics: Basic PrinciplesBy Philip A. Creamer, P.E.

Professional Development Series

Figure 1: Culvert geometry


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Special Advertising Section CONTECH Bridge Solutions PDH 3

Culvert Hydraulics: Basic Principles

of the culvert, for example, a corrugated metal pipe culvert.

With environmental regulations becoming more stringent,

many culvert installations utilize three-sided culverts. A

three-sided culvert is a structure that has the same material

on the top and sides of the structure. The bottom of the

culvert is typically the natural channel bottom.

The most commonly used culvert materials are concrete,

corrugated metal, and plastic. Usually, the internal rough-ness of a culvert is a function of the culvert material.

However, for a three-sided culvert, where the bottom of the

installation is the natural channel, the internal roughness is

a function of the culvert material and the roughness of the

channel itself.

Culverts are usually laid on a slope, which can be found

by dividing the elevation difference between the upstream

and downstream ends of the culvert (Z) by the culvert

length (L ). Typically, the slope is downward such that the

outlet elevation is lower than the inlet elevation. In some

cases, culverts may be laid horizontal or on an adverse

slope where the downstream elevation is higher than the

upstream elevation.

The tailwater at a culvert is the depth of water at the

downstream end of the culvert, as measured from the

downstream invert of the culvert. The tailwater must be

known or estimated prior to performing the culvert hydrau-

lic calculations. There are various methods to estimate the

tailwater at a culvert. One method is to estimate a down-

stream channel shape and use Mannings equation to calcu-

late a tailwater depth. Another method is to conduct a

water surface profile analysis of the steam reach down-

stream of the culvert.

For a given design discharge (Q), there will be a corre-

sponding headwater depth (HW) upstream of the culvert

entrance. In fact, it is the headwater depth that pushes or

forces the design discharge through the culvert opening.

For a given culvert opening, a higher discharge will typically

result in a higher headwater depth since more energy is

needed to force the flow through the culvert. In open-chan-

nel hydraulics, energy is synonymous with water depth asshown in Equation 1.

where Eis specific energy (feet); Yis depth of water (feet);

2g

V2

E= Y + (Equation 1)

Figure 2: Common culvert end treatments

Many installations use three-sided culverts, where the bottom of the culvert is typically the natural channel bottom.


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Vis mean water velocity (feet per second);

and gis acceleration due to gravity (feet per

second per second).

Culverts are frequently designed to pass some

specified design discharge without creating an unaccept-

ably high headwater depth. Thus, for an engineer to design

a culvert successfully, the headwater depth for the designdischarge must be reliably predicted. For many applications,

the culvert design discharge is frequently associated with

the 1-percent, 2-percent, or 4-percent annual chance storm

event. Knowledge of the headwater depth associated with a

particular flow condition will reveal to the engineer whether

or not the culvert will pass the design flow safely with-

out overtopping the embankment or violating applicable

regulations. The definition of an unacceptable headwater

depth may vary among sites, but typically, the maximum

headwater elevation should be about 1 or 2 feet lower than

the roadway shoulder elevation to minimize the potential

for roadway flooding. Of course, other factors, including site

conditions and construction schedules, contribute to the final

culvert design specifications. Nonetheless, it is important for

engineers and others involved with culverts to be able to

predict the hydraulic performance of these structures accu-

rately so that they operate without any undesirable effects.

Standard FHWA culvert design approachAccording to research sponsored by the Federal Highway

Administration (FHWA), culvert operation is governed at

all times by one of two conditions: inlet control or outlet

control (Normann, et al, 1985). Inlet control is a common

governing situation for culvert design, characterized by

the fact that the tailwater or culvert barrel conditions allowmore flow to be passed through the culvert than the inlet

can accept. The inlet itself acts as a controlling or governing

section of the culvert, restricting the passage of water into

the main barrel.

Outlet control is different from inlet control in that the

barrel or tailwater cannot accept as high a flow as the

inlet may allow. This may occur with a high tailwater or

a long culvert with a rough interior. Outlet control may

be mathematically modeled using water surface profile

methods or by an energy balance. Because outlet control

conditions in culverts can be calculated with open-channel

hydraulic principles, there is no need for empirical test-

ing and regression formulas to describe the relationship

between the flow through the culvert and the headwater.

However, testing on scale models can provide valuable

information about the head loss coefficients associated with

the culvert entrance. Once the outlet control situation has

been modeled as accurately as possible based on known

information, the headwater may be calculated to evaluate

the culvert design.

The FHWA has standardized the manner by which

culverts are examined and designed. The design approach

involves first computing the headwater elevation upstream

of the culvert assuming that inlet control governs. The

headwater elevation is then also found assuming that outlet

control governs. The two headwater values are compared

with one another and the higher of the two is selected as

the basis of the culvert design.

Generally speaking, the procedure described above is

repeated for different types of culvert shapes, sizes, andentrance conditions. The least expensive culvert that

produces an acceptable headwater elevation is typically

chosen for the final design. Of course, site conditions,

structural considerations, permit requirements, or aesthetic

appeal may also influence the choice of culvert design.

Inlet controlInlet control represents a much more complex hydraulic

environment than outlet control, and it cannot be strictly

mathematically modeled to obtain headwater depths.

Under inlet control, the flow patterns at the entrance to

the culvert may be three dimensional with vortices or other

unpredictable features. These patterns are influenced by

a number of factors, the most important of which are

inlet geometry, wingwall configuration, culvert shape, and

degree of beveling. Fortunately, culverts operating under

inlet control can be modeled using regression equations.

For many years, inlet control culverts modeled using the

methodology outlined in the FHWA Hydraulic Design Series

No. 5 (HDS-5) Hydraulic Design of Highway Culverts have

successfully withstood both extensive laboratory tests as well

as the test of time in field installations. Empirical measure-

ments on small-scale models of varying inlet geometries and

wingwall configurations led to derivation of unique regression

coefficients for each case. These models possess remarkablysimilar hydraulic characteristics to their full-size counterparts

and provide the best approximation of how a particular culvert

shape will perform in the field (Normann, et al, 1985).

Because inlet control represents the case where the culvert

barrel will convey more flow than the inlet will accept, the

culvert normally will not flow full for its full length, thereby

resulting in a free water surface that exists along the length

of the structure. Under inlet control, the culvert entrance

may either be unsubmerged or submerged. Figure 3 shows

the latter case.

At low flows, the culvert entrance is unsubmerged and

the discharge through the culvert entrance behaves like

weir flow. A weir is a flow control cross-section where the

discharge and depth of water are related to one another

through some predictable relationship. At much higher

flows, the culvert entrance is submerged and the flow

through the entrance acts like orifice flow. Orifice flow

represents the case where an opening is submerged and

the discharge through the opening increases as the depth

or head above the opening increases.

One example of where inlet control occurs is when

there is a mild channel slope upstream of the culvert that

transitions to a steep culvert slope (Norman, et al, 1985).


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The transition from a mild slope to a steep slope causes a

change in the flow regime from subcritical to supercriti-

cal flow. The change from subcritical to supercritical flow

results in critical depth occurring at or near the entrance to

the culvert. In some cases, such as short, smooth culverts,

the nature of the culvert entrance can cause inlet control to

occur even if the culvert slope is mild or flat.

While the behavior of flow at the entrance to a culvert

is extremely complex, the primary influencing factors for

headwater depths are the type of opening (pipe, box,

arch, et cetera), the size or area of the culvert opening, and

the entrance conditions. Commonly found entrance condi-

tions include square edge with headwall, end mitered to

the slope, projecting barrel, and beveled entrance. Culvert

inlets may also utilize wingwalls placed at an angle from

the culvert barrel. Not only do wingwalls provide struc-

tural stability to the culvert and act as retaining walls for

fill slopes, they can also perform a hydraulic function by

funneling flow into the culvert opening.Recall that the complexity of the hydraulics associated

with inlet control, when combined with the large number

of different shapes, sizes, and entrance conditions available

for culverts, make it nearly impossible to develop a single

formula capable of describing the hydraulic behavior of

culverts operating under inlet control. As a result, empirical

methods are typically used to evaluate inlet control.

Inlet control equations are presented in HDS-5 that

describe unsubmerged and submerged inlet control

(Normann, et al, 1985). For the unsubmerged case, two

expressions can be used as shown in Equations 2 and 3.

While both expressions provide acceptable results, Equation

2 is theoretically more accurate, while Equation 3 is easier to

apply. Additionally, the latter equation is easier to use when

developing regression coefficients from observed headwater

depths and discharges or when the critical depth through a

structure is not easily determined.

where HWis headwater depth at the culvert

entrance (feet); HCis specific energy at criti-

cal depth (feet); Q is discharge through the

culvert (cubic feet per second (ft3/s)); A is full

open area of the culvert (square feet); Dis culvert rise (feet);

Sis the slope of the culvert barrel (feet/foot); and Kand M

are inlet control regression coefficients for unsubmergedconditions.

Either form of the two equations above will produce

acceptable results (Normann, et al,1985). For model stud-

ies, quantities measured in the lab are typically the head-

water (HW) and the discharge (Q). Other known quantities

include the area of the model (A ), the model rise (D)

and the slope of the channel. When developing regres-

sion coefficients using Equation 2, the specific energy at

critical depth must be computed and used in the regression

analysis. Use of Equation 3 avoids the need to make these

additional calculations.

When the culvert entrance is submerged, a different

equation must be applied to find the headwater depth

under inlet control (see Equation 4). As with the case of

unsubmerged inlet control, model studies are typically used

to develop the inlet control regression coefficients.

where HW, Q, A, D, and S are as previously defined; and c

and Y are inlet control regression coefficients for submerged

conditions.

Outlet control culvert flowing fullIn HDS-5 design methodology, outlet control is deter-

mined assuming that the culvert is flowing full. The headwa-

ter due to outlet control is found from Equation 5, which is

an energy balance between the upstream and downstream

ends of the culvert.

where HWis headwater depth above the inlet invert (feet);

EL0is the elevation of the culvert invert at the outlet; H0is

the governing tailwater (feet); and hLis head loss through

the culvert (feet).

To find the governing tailwater, H0 , the critical depth in

the culvert must first be determined. The critical depth is

then used with the culvert size and compared to the speci-

fied tailwater as shown in Equation 6.

where TW is the tailwater at the downstream end of the

culvert (feet); DCis critical depth in the culvert (feet); and D

is culvert diameter or rise (feet).

D

HW

AD0.5Q

D

Hc= + K 0.5S (Equation 2)

M

D

HW

AD0.5Q

=K (Equation 3)M

D

HW

AD0.5Q

= c +Y 0.5S (Equation 4)2

2

Dc+ DH0= MAX TW, (Equation 6)

HW= EL0+ H0+ hL (Equation 5)

Figure 3: Example of submerged inlet control


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The head loss through the culvert, hL,

is found by considering all losses, including

entrance losses, exit losses, and friction losses.

Mannings equation is rearranged to quantify

friction losses. Equation 7 can be used to determine the

head loss through a culvert. If bends occur along the length

of the culvert, then these losses must also be included inEquation 7.

where Kx is an exit loss coefficient; n is Mannings rough-

ness coefficient; Lis the length of the culvert (feet); Ris the

hydraulic radius of the culvert (feet); Keis an entrance loss

coefficient; V is velocity in the culvert (feet per second);

and g is the gravitational constant (feet per second per

second).

Values for the entrance loss coefficient, Ke, are avail-

able in various hydraulic texts including HDS-5, and values

range from 0.20 to 0.80, depending on the inlet type and

configuration. Values for exit loss coefficients, Kx, can vary

between 0.3 and 1.0. For a sudden expansion of flow, the

exit loss coefficient is set to 1.0. The exit loss coefficient

should be reduced as the transition becomes less abrupt

(HEC-RAS Hydraulic Reference Manual, 2002).

For culvert applications where a natural bottom is used,

a composite Mannings roughness coefficient must be

computed. There are several assumptions that can be used

to determine a composite roughness value. One common

assumption is that each part of the area has the same aver-

age velocity, which is equal to the average velocity of thewhole section (Chow, 1959). With this assumption, the

composite Mannings roughness, nc, may be obtained by

Equation 8:

where Ps&tis the wetted perimeter of culvert sides and top

(feet); Pch is the wetted perimeter of the natural channel

(feet); ns&tis Mannings roughness for the culvert sides and

top culvert; and nchis Mannings roughness for the natural

channel.

Outlet control culvert flowing partially fullThe methodology in HDS-5 using the equations from

the procedure outlined above assumes that the culvert

is flowing full along the entire length. A common design

case occurs when it is necessary to minimize the head loss

through a culvert. The minimal headwater rise, small slope,

and high relative tailwaters associated with these condi-

tions usually result in outlet control. In this outlet control

case, the culvert is most likely to be flowing partially full.

In this case, a water surface profile analysis is necessary to

determine the losses through the culvert accurately. The

profile analysis is conducted from the downstream end to

the upstream end of the culvert.

For culverts flowing partially full, the most efficient

method to compute the water surface profile in the culvert

is the direct step method. The direct step method computes

the water surface profile at increments of known depths.The first step is to compute the exit loss and establish a

starting water surface inside the culvert at the downstream

end. The starting water surface will either be critical depth

or the result of an energy balance between the tailwater

and a cross section just inside the culvert on the down-

stream end. Once a water surface is computed inside the

culvert at the downstream end, the designer performs the

direct step calculations along the length of the culvert. After

the depth of water is determined at the upstream end, the

entrance loss is added in to compute the headwater depth.

SummaryA successful culvert design depends on accurately predict-ing the effect that a culvert will have on the surrounding

area. Typically, culverts can be expected to cause changes

in the water surface elevation upstream. The designer must

estimate these effects to ensure that the change to water

elevation upstream headwater will not adversely affect the

surrounding community. The techniques to design culverts

hydraulically were developed more than four decades ago.

More stringent floodplain and environmental regulations

are changing the types of culverts design engineers are

specifying today. However, these traditional culvert hydrau-

lic design procedures are still applicable when used with

modifications to reflect the current culvert crossing charac-teristics.

Philip A. Creamer, P.E., is director of Bridge Design Services

with CONTECH Bridge Solutions Inc. He can be contacted at

[email protected].

References

Chase, Donald V., Hydraulic Characteristics of CON/SPAN

Bridge Systems, University of Dayton, 1999.

Normann, J.M., Houghtalen, R. J., and Johnston, W.J.,

Hydraulic Design of Highway Culverts, Hydraulic Design

Series No. 5, Federal Highway Administration, Sept. 1985.

HEC-RAS River Analysis System, Hydraulic Reference Manual,

U.S. Army Corps of Engineers, Hydrologic Engineering

Center, Nov. 2002.

Chow, V.T., Open Channel Hydraulics, McGraw-Hill, 1959.

R1.3329n2L

2g

V2hL= Kx+ + Ke (Equation 7)

(PS&Tn1.5 + Pchnch )

nc= (Equation 8)s&t

1.5

(PS&T + Pch)

2/3

2/3


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1. A culvert that lowers a channel conveyance typically results in:

a) Increased roughness values.

b) Decreased downstream velocity.

c) Increased headwater elevation.

d) Decreased head loss.

2. A culvert on a steep slope:

a) Will always be in outlet control.

b) Could be in inlet or outlet control.

c) Will always be in inlet control.

d) Will have subcritical flow through the entire length.

3. Which variable affects outlet control headwater?

a) Culvert inlet configuration

b) Culvert outlet configuration

c) Mannings roughness value of the culvert

d) All of the above

4. A common assumption for the tailwater elevation is:

a) One-half the culvert rise/diameter.

b) Ordinary high water surface elevation. c) 1 foot to 2 feet below the roadway shoulder elevation.

d) Normal depth based on Mannings equation and the downstream

channel characteristics.

5. What are typical minimum values for entrance loss and exit loss

coefficients?

a) 0.2 and 0.3

b) 0.3 and 0.1

c) 0.5 and 0.2

d) 0.1 and 0.5

6. Which variable does not affect inlet control

headwater?

a) Wingwall configuration

b) Headwall type

c) Mannings roughness value of the culverts

d) Culvert opening area

7. What situation warrants that a water surface profile through the

culvert be calculated?

a) When the culvert is in outlet control

b) When the tailwater is higher than the culvert height

c) When the culvert is in inlet control

d) When the culvert is flowing partially full

8. When is it necessary to compute a composite Mannings value?

a) When the culvert is flowing partially full

b) When the culvert has a natural bottom

c) Multiple cell culverts

d) When the culvert is in outlet control

9. Why does FHWAs HDS-5 outlet control methodology assume that

the culvert is flowing full?

a) It simplifies the calculations.

b) Most culverts flow full.

c) Most culverts are closed conduits.

d) None of the above

10. What is the primary goal of culvert hydraulic design?

a) To ensure that the water level increase due to the culvert is not

unacceptably high

b) To determine the least expensive culvert that meets all the design

requirements

c) To accurately predict the hydraulic performance of the culvert

d) All of the above

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