
This section introduces the basic concepts of culvert hydraulics, which are
used in the HECRAS culvert routines.
Introduction to Culvert Terminology

A culvert is a relatively short length of closed conduit, which connects two
open channel segments or bodies of water.
 Two of the most common types of
culverts are: circular pipe culverts, which are circular in cross section, and
box culverts, which are rectangular in cross section.
 Figure 6.6 shows an
illustration of circular pipe and box culverts.
Figure 6.7
Full flowing culvert with energy and hydraulic gradelines.

 In addition to box and pipe
culverts, HECRAS has the ability to model arch; pipe arch; low profile arch;
high profile arch; elliptical; semicircular; and ConSpan culvert shapes.

Culverts are made up of an entrance where water flows into the culvert, a
barrel, which is the closed conduit portion of the culvert, and an exit, where
the water flows out of the culvert (see Figure 6.7).
Figure 6.8 Culvert performance curve with roadway overtopping.

 The total flow capacity of
a culvert depends upon the characteristics of the entrance as well as the
culvert barrel and exit.

The Tailwater at a culvert is the depth of water on the exit or downstream
side of the culvert, as measured from the downstream invert of the culvert
(shown as TW on Figure 6.7).
 The invert is the lowest point on the inside of
the culvert at a particular cross section.
 The tailwater depth depends on the
flow rate and hydraulic conditions downstream of the culvert.

Headwater (HW on Figure 6.7) is the depth from the culvert inlet invert to
the energy grade line, for the cross section just upstream of the culvert
(Section 3).
 The Headwater represents the amount of energy head required to
pass a given flow through the culvert.

The Upstream Water Surface (WS_{U} on Figure 6.7) is the depth of water on
the entrance or upstream side of the culvert (Section 3), as measured from the
upstream invert of Cross Section 3.

The Total Energy at any location is equal to the elevation of the invert plus
the specific energy (depth of water + velocity heady) at that location.
 All of
the culvert computations within HECRAS compute the total energy for the
upstream end of the culvert.
 The upstream water surface (WS_{U}) is then
obtained by placing that energy into the upstream cross section and
computing the water surface that corresponds to that energy for the given
flow rate.
Flow Analysis for Culverts

The analysis of flow in culverts is quite complicated.
 It is common to use the
concepts of inlet control and outlet control to simplify the analysis.
 Inlet
control flow occurs when the flow capacity of the culvert entrance is less
than the flow capacity of the culvert barrel.
 The control section of a culvert
operating under inlet control is located just inside the entrance of the culvert.

The water surface passes through critical depth at or near this location, and
the flow regime immediately downstream is supercritical.
 For inlet control,
the required upstream energy is computed by assuming that the culvert inlet
acts as a sluice gate or as a weir.
 Therefore, the inlet control capacity
depends primarily on the geometry of the culvert entrance.
 Outlet control
flow occurs when the culvert flow capacity is limited by downstream
conditions (high tailwater) or by the flow carrying capacity of the culvert
barrel.
 The HECRAS culvert routines compute the upstream energy required
to produce a given flow rate through the culvert for inlet control conditions
and for outlet control conditions (Figure 6.8).
 In general, the higher upstream
energy "controls" and determines the type of flow in the culvert for a given
flow rate and tailwater condition.
 For outlet control, the required upstream
energy is computed by performing an energy balance from the downstream
section to the upstream section.
 The HECRAS culvert routines consider
entrance losses, friction losses in the culvert barrel, and exit losses at the
outlet in computing the outlet control headwater of the culvert.
Figure 6.9 Flow chart for outlet control computations.


During the computations, if the inlet control answer comes out higher than the
outlet control answer, the program will perform some additional computations
to evaluate if the inlet control answer can actually persist through the culvert
without pressurizing the culvert barrel.
 The assumption of inlet control is that
the flow passes through critical depth near the culvert inlet and transitions
into supercritical flow.
 If the flow persists as low flow through the length of
the culvert barrel, then inlet control is assumed to be valid.
 If the flow goes
through a hydraulic jump inside the barrel, and fully develops the entire area
of the culvert, it is assumed that this condition will cause the pipe to
pressurize over the entire length of the culvert barrel and thus act more like an
orifice type of flow.
 If this occurs, then the outlet control answer (under the
assumption of a full flowing barrel) is used instead of the inlet control answer.
Computing Inlet Control Headwater

For inlet control conditions, the capacity of the culvert is limited by the
capacity of the culvert opening, rather than by conditions farther downstream.

Extensive laboratory tests by the National Bureau of Standards, the Bureau
of Public Roads, and other entities resulted in a series of equations, which
describe the inlet control headwater under various conditions.
 These
equations form the basis of the FHWA inlet control nomographs shown in the
Hydraulic Design of Highway Culverts publication [FHWA, 1985].
 The
FHWA inlet control equations are used by the HECRAS culvert routines in
computing the upstream energy.
 The inlet control equations were developed
for submerged and unsubmerged inlet conditions.
 These equations are:
Unsubmerged Inlet:
HW_{i} /D = H_{c}/D + K [ Q/(AD^{1/2}) ]^{M}  0.5 S
(61)
HW_{i} /D = K [ Q/(AD^{1/2}) ]^{M} (62)
Submerged Inlet:
HW_{i} /D = c [ Q/(AD^{1/2}) ]^{M} + Y  0.5 S (63)
where
 HW_{i} = Headwater energy deoth above the invert of the culvert inlet, feet
 D = interior height of the culvert barrel, feet
 H_{c} = specific head at critical depth, feet
 Q = discharge through the culvert, cfs
 A = full crosssectional area of the culvert barrel, square feet
 S = culvert barrel slope, fett/feet
 K, M, c, and Y = equation constants, which vary depending on culvert shape and entrance conditions

Note that there are two forms of the unsubmerged inlet equation.
 The first
form (equation 61) is more correct from a theoretical standpoint, but form
two (equation 62) is easier to apply and is the only documented form of
equation for some of the culvert types.
 Both forms of the equations are used
in the HECRAS software, depending on the type of culvert.

The nomographs in the FHWA report are considered to be accurate to within
about 10 percent in determining the required inlet control headwater [FHWA,
1985].
 The nomographs were computed assuming a culvert slope of 0.02 feet
per foot (2 percent).
 For different culvert slopes, the nomographs are less
accurate because inlet control headwater changes with slope.
 However, the
culvert routines in HECRAS consider the slope in computing the inlet
control energy.
 Therefore, the culvert routines in HECRAS should be more
accurate than the nomographs, especially for slopes other than 0.02 feet per
foot.
Computing Outlet Control Headwater

For outlet control flow, the required upstream energy to pass the given flow
must be computed considering several conditions within the culvert and
downstream of the culvert.
 Figure 6.9 illustrates the logic of the outlet
control computations.
Figure 6.10 Culvert with multiple Manning's n values.


HECRAS uses Bernoulli's equation in order to
compute the change in energy through the culvert under outlet control
conditions.
 The outlet control computations are energy based.
 The equation
used by the program is the following:
FHWA Full Flow Equations
Direct Step Water Surface Profile Computations

For culverts flowing partially full, the water surface profile in the culvert is
computed using the direct step method.
 This method is very efficient,
because no iterations are required to determine the flow depth for each step.

The water surface profile is computed for small increments of depth (usually
between 0.01 and 0.05 feet).
 If the flow depth equals the height of the culvert
before the profile reaches the upstream end of the culvert, the friction loss
through the remainder of the culvert is computed assuming full flow.

The first step in the direct step method is to compute the exit loss and
establish a starting water surface inside the culvert.
 If the tailwater depth is
below critical depth inside the culvert, then the starting condition inside the
culvert is assumed to be critical depth.
 If the tailwater depth is greater than
critical depth in the culvert, then an energy balance is performed from the
downstream cross section to inside of the culvert.
 This energy balance
evaluates the change in energy by the following equation.
xxx

Once a water surface is computed inside the culvert at the downstream end,
the next step is to perform the direct step backwater calculations through the
culvert.
 The direct step backwater calculations will continue until a water
surface and energy are obtained inside the culvert at the upstream end.
 The
final step is to add an entrance loss to the computed energy to obtain the
upstream energy outside of the culvert at Section 3 (Figure 6.7).
 The water
surface outside the culvert is then obtained by computing the water surface at
Section 3 that corresponds to the calculated energy for the given flow rate.
Normal Depth of Flow in the Culvert
Critical Depth of Flow in the Culvert

Critical depth occurs when the flow in a channel has a minimum specific
energy.
 Specific energy refers to the sum of the depth of flow and the
velocity head.
 Critical depth depends on the channel shape and flow rate.

The depth of flow at the culvert outlet is assumed to be equal to critical depth
for culverts operating under outlet control with low tailwater.
 Critical depth
may also influence the inlet control headwater for unsubmerged conditions.

The culvert routines compute critical depth in the culvert by an iterative
procedure, which arrives at a value satisfying the following equation:

xxx

Critical depth for box culverts can be solved directly with the following
equation [AISI, 1980]:
xxx
Horizontal and Adverse Culvert Slopes

The culvert routines also allow for horizontal and adverse culvert slopes.
 The
primary difference is that normal depth is not computed for a horizontal or
adverse culvert.
 Outlet control is either computed by the direct step method
for an unsubmerged outlet or the full flow equation for a submerged outlet.
Weir Flow

The first solution through the culvert is under the assumption that all of the
flow is going through the culvert barrels.
 Once a final upstream energy is
obtained, the program checks to see if the energy elevation is greater than the
minimum elevation for weir flow to occur.
 If the computed energy is less
than the minimum elevation for weir flow, then the solution is final.
 If the
computed energy is greater than the minimum elevation for weir flow, the
program performs an iterative procedure to determine the amount of flow
over the weir and through the culverts.
 During this iterative procedure, the
program recalculates both inlet and outlet control culvert solutions for each
estimate of the culvert flow.
 In general the higher of the two is used for the
culvert portion of the solution, unless the program feels that inlet control
cannot be maintained.
 The program will continue to iterate until it finds a
flow split that produces the same upstream energy (within the error tolerance)
for both weir and culvert flow.
Supercritical and Mixed Flow Regime Inside of
Culvert

The culvert routines allow for supercritical and mixed flow regimes inside the
culvert barrel.
 During outlet control computations, the program first makes a
subcritical flow pass through the culvert, from downstream to upstream.
 If
the culvert barrel is on a steep slope, the program may default to critical depth
inside of the culvert barrel.
 If this occurs, a supercritical forewater
calculation is made from upstream to downstream, starting with the
assumption of critical depth at the culvert inlet.
 During the forewater
calculations, the program is continually checking the specific force of the
flow, and comparing it to the specific force of the flow from the subcritical
flow pass.
 If the specific force of the subcritical flow is larger than the
supercritical answer, the program assumes that a hydraulic jump will occur at
that location.
 Otherwise, a supercritical flow profile is calculated all the way
through and out of the culvert barrel.
Multiple Manning's n Values Inside of Culvert

This version of HECRAS allows the user to enter two Manning's n values
inside of the culvert, one for the top and sides, and a second for the culvert
bottom.
 The user defines the depth inside the culvert to which the bottom n
value is applied.
 This feature can be used to simulate culverts that have a
natural stream bottom, or a culvert that has the bottom portion rougher than
the top, or if something has been placed in the bottom of the culvert for fish
passage.
 An example of this is shown in Figure 6.10.
Figure 6.11 Partially Filled or Buried Culverts.

 When multiple Manningâ€™s n values are applied to a culvert, the computational
program will use the bottom n value until the water surface goes above the
specified bottom n value.
 When the water surface goes above the bottom n
value depth the program calculates a composite n value for the culvert as a
whole.
 This composite n value is based on an equation from Chow's book on
Open Channel Hydraulics (Chow, 1959) and is the same equation we use for
computing a composite n value in open channel flow (see equation 2 6, from
chapter 2 of this manual).
Partially Filled or Buried Culverts

This version of HECRAS allows the user to fill in a portion of the culvert
from the bottom.
 This option can be applied to any of the culvert shapes.

The user is only required to specify the depth to which the culvert bottom is
filled in.
 An example of this is shown in figure 6.11.
 The user can also
specify a different Manning's n value for the blocked portion of the culvert
(the bottom), versus the remainder of the culvert.
 The user must specify the
depth to apply the bottom n value as being equal to the depth of the filled
portion of the culvert.
Figure 6.12 Geometric Interpolation of ConSpan Culvert for Non
Standard Widths (Span)

