Culverts in H2OCalc, background to Culverts in #InfoSWMM and #SWMM5

Culverts in H2OCalc, background to Culverts in #InfoSWMM and #SWMM5

Introduction: H2OCalc is a hydrology and hydraulics calculator sold by Innovyze that has many of the equations and calculation methods used in InfoSWMM, ICM and SWMM5. This is the H2OCalc information for the FHWA Culvert Equations.

A culvert is a pipe that carries water under or through some feature (usually a road or highway) that would otherwise block the flow of water. The culvert acts as an open channel as long as the flow is partly full. The characteristics of the flow are very complicated because the flow is controlled by many variables, including the inlet geometry, slope, size, roughness, approach and tailwater conditions, etc. Therefore, an adequate determination of the flow through a culvert is generally made by laboratory or field investigation.

Culverts are classified according to which of their ends controls the discharge capacity: inlet control or outlet control. If water can flow through and out of the culvert faster than it can enter, the culvert is under inlet control. If water can flow into the culvert faster than it can flow through and out, the culvert is under outlet control. Culverts under inlet control will always flow partially full. Culverts under outlet control can flow either partially full or full. H2OCalc analyzes culverts using two different approaches: a simplified culvert analysis method and the Federal Highway Administration’s (FHWA) HDS No. 5 method (Normann et al, 1985). Both techniques are described below.

Simplified Method

The simplified method classifies culvert flow into six different types on the basis of the type of control, the steepness of the barrel, the relative tailwater and headwater heights, and in some cases, the relationship between critical depth and culvert size. These parameters are quantified through the use of the ratios in Table 3.4. The six types are illustrated in the following figure.

For culverts flowing full, the friction loss (hf) can be determined using the Darcy formula. For partial flow, the Manning equation can be used. The friction head loss between sections 1 and 2 (see the figure below), for example, can be calculated from Manning’s equation as

where L = the culvert length

K = Conveyance factor and equals

R = hydraulic radius (m, ft); R = A/P

A = cross-sectional area of flow section (m2, ft2)

P = wetted perimeter (m, ft)

N = Manning’s coefficient

Table 3-4: Culvert Flow Classification Parameters

Flow type (h1–z)/D h4/hc h4/D Culvert slope Barrel flow Location of control Kind of control
1 < 1.5 < 1.0 ≤ 1.0 steep partial Inlet critical depth
2 < 1.5 < 1.0 ≤ 1.0 mild partial outlet critical depth
3 < 1.5 > 1.0 ≤ 1.0 mild partial outlet backwater
4 > 1.0 > 1.0 any full outlet backwater
5 ≥ 1.5 ≤ 1.0 any partial inlet entrance geometry
6 ≥ 1.5 ≤ 1.0 any Full outlet entrance geometry

Adapted from Lindeburg (2003)

The total hydraulic head available, H, is divided between the velocity head in the culvert, the entrance loss (if considered), and the friction loss as follows

where ke is the local loss for entrance.

Re-arranging Equations (46) and (48), velocity through the culvert can be given as

A. Type-1 Flow

Water passes through the critical depth near the culvert entrance, and the culvert flows partially full. The slope of the culvert barrel is greater than the critical slope, and the tailwater elevation is less than the elevation of the water surface at the control section.

where Q = discharge from the culvert (m3/s, ft3/s)

Cd = discharge coefficient

v1 = average velocity of the water approaching the culvert entrance

α = velocity-head coefficient (i.e., assumed as 1.0)

dc = the critical depth

Ac = flow area at the critical section, not the culvert area

B. Type-2 Flow

As in Type-1 flow, flow passes through the critical depth at the culvert outlet, and the barrel flows partially full. The slope of the culvert is less than critical, and the tailwater elevation does not exceed the elevation of the water surface at the control section.

C. Type-3 Flow

When backwater is the controlling factor in culvert flow, the critical depth cannot occur. The upstream water surface elevation for a given discharge is a function of the height of the tailwater. For Type-3 flow, flow is subcritical for the entire length of the culvert, with the flow being partial. The outlet is not submerged, but the tailwater elevation does exceed the elevation of critical depth at the terminal section.

where A3 is the flow area at section 3 (i.e., the exit).

D. Type-4 Flow

As in Type-3 flow, the backwater elevation is the controlling factor in this case. Critical depth cannot occur, and the upstream water surface elevation for a given discharge is a function of the tailwater elevation. Discharge is independent of barrel slope. The culvert is submerged at both the headwater and the tailwater.

where Ao is the culvert area. The complicated term in the denominator corrects for friction. For rough estimates and for culverts less than 50 ft long, the friction loss can be ignored.

E. Type-5 Flow

Partially full flow under a high head is classified as Type-5 flow. The flow pattern is similar to the flow downstream from a sluice gate, with rapid flow near the entrance. Usually, Type-5 flow requires a relatively square entrance that causes contraction of the flow area to less than the culvert area. In addition, the barrel length, roughness, and bed slope must be sufficient to keep the velocity high throughout the culvert.

F. Type-6 Flow

Type-6 flow, like Type-5 flow, is considered a high-head flow. The culvert is full under pressure with free outfall.

Note that distance h3is undefined. For conservative first approximations, h3 can be taken as the barrel diameter.

The FHWA Method

The Federal Highway Administration (FHWA) offers equations as well as nomographs that can be used for analysis and design of culverts. Different equations and nomographs are developed for inlet controlled culvert flows and outlet controlled culvert flows. Only equation based analysis and design approaches are described in this section. Readers interested in the FHWA nomographs, for both control types, may refer to Normann et al. (1985).

Culvert design according to FHWA involves analyzing the culvert under both inlet control and outlet control conditions and selecting the control type that yields the worst condition (i.e., larger headwater depth). The design would be acceptable if the governing headwater depth is less than the maximum allowable headwater to avoid flooding of streets and property. Otherwise, the design needs to be revised (e.g., culvert size is increased) to reduce the headwater depth.

Inlet Control

The objective is to determine the headwater depth based on predetermined design discharge and a trial culvert size. The design equation used to determine headwater depth for inlet controlled culvert vary depending on the flow condition at the inlet of the culvert. If the inlet is submerged, the flow type would be orifice flow. Unsubmerged conditions will behave as a weir flow.

If the inlet is submerged (orifice flow), the equation to determine the headwater depth will be

where HWi = headwater depth above the inlet control section invert (ft)

D = diameter of the culvert (ft)

Q = discharge (ft3/s)

A = full cross-sectional area of the culvert (ft2)

c, Y = constant from Table 3.5

Z = culver barrel slope term (ft/ft).

For mitered inlets,

and for all other conditions (i.e., inlet types other than mitered inlets),

The unsubmerged flow (weir flow) condition can be evaluated using one of the following two approaches:

1) Based on specific head (Hc) at critical depth

where Hc= specific head at critical depth (ft)

K and M = constants from Table 3.5

dc = critical depth (ft)

Vc =critical velocity (ft/sec)

2) A simpler form that ignores specific head (Hc) at critical depth

Table 3-5: Constants for Inlet Control Design Equations

Shape and material Inlet Edge Description K M c Y
Circular Concrete Square edge w/ headwall 0.0098 2.000 0.0398 0.67
Groove end w/ headwall 0.0078 2.000 0.0292 0.74
Groove end projecting 0.0045 2.000 0.0317 0.69
Circular CMP Headwall 0.0078 2.000 0.0379 0.69
Mitered to slope 0.0210 1.330 0.0463 0.75
Projecting 0.0340 1.500 0.0553 0.54
Circular Ring Beveled ring, 450 bevels 0.0018 2.500 0.0300 0.74
Beveled ring 33.70 bevels 0.0018 2.500 0.0243 0.83
Rectangular Box 300 – 750 wingwall flares 0.0260 1.000 0.0385 0.81
900 and 150 wingwall flares 0.0610 0.750 0.0400 0.80
00 wingwall flares 0.0610 0750 0.0423 0.82
Rectangular Box 450 wingwall flare 0.5100 0.667 0.0309 0.80
180 – 33.70 wingwall flare 0.4860 0.667 0.0249 0.83
Rectangular Box 900 headwall w/¾ in chamfers 0.5150 0.667 0.0375 0.79
900 headwall w/ 450 bevels 0.7950 0.667 0.0314 0.82
900 headwall w/33.70 bevels 0.4860 0.667 0.0252 0.87
Rectangular Box ¾ in chamfers, 450 skewed headwall 0.5220 0.667 0.0402 0.73
¾ in chamfers, 300 skewed headwall 0.5330 0.667 0.0425 0.71
¾ in chamfers, 150 skewed headwall 0.5450 0.667 0.0451 0.68
450 bevels, 10-450 skewed wall 0.4980 0.667 0.0327 0.75
Rectangular Box, ¾ in. chamfers 450 non offset wingwall flares 0.4970 0.667 0.0339 0.80
18.40 non offset wingwall flares 0.4930 0.667 0.0361 0.81
18.40 non offset wingwall flares, 300 skewed barrel 0.4930 0.667 0.0386 0.71
Rectangular Box, top bevels 450 wingwall flares-offset 0.4970 0.667 0.0302 0.84
33.70 wingwall flares – offset 0.4950 0.667 0.0252 0.88
18.40 wingwall flares – offset 0.4930 0.667 0.0227 0.89
Corrugated Metal Boxes 900 headwall 0.0083 2.000 0.0379 0.69
Thick wall projecting 0.0145 1.750 0.0419 0.64

Adapted from Normann et al. (1985)

Outlet Control

Headwater for outlet control conditions can be determined using energy equation based on tailwater depth and head loss through the culvert considering entrance loss, exit loss, and friction loss.

where H = total head loss (ft)

ke = entrance loss coefficient (see Table 3.6)

ho = water depth at the outlet of the culvert (ft)

dc = critical depth (ft)

q = unit discharge (discharge per unit width of the culvert) (ft3/s/ft)

Table 3-6: Entrance Loss Coefficients-Outlet Control, Full or Partly Full

Type of Structures and Design of Entrance Coefficient ke
Pipe, Concrete Mitered to conform to fill slope 0.7
End-section conforming to fill slope 0.5
Projecting from fill, square cut end 0.5
Headwall or headwall and wingwalls

Square Edge

Rounded( radius= 1/12 Culvert Diameter

Socket End of Pipe ( groove-end)

Projecting from fill, socket end (groove-end) 0.2
Beveled edges, 33.70 or 450 bevels 0.2
Side- or slope-tapered inlet 0.2
Pipe, or Pipe-Arch, Corrugated Metal Projecting from fill ( no metal) 0.9
Mitered to conform to fill slope, paved or unpaved slope 0.7
Headwall or headwall and wingwalls square-edge 0.5
End-section conforming to fill slope 0.5
Beveled edges, 33.70 or 450 bevels 0.2
Side- or slope-tapered inlet 0.2
Box, Reinforced Concrete Wingwalls parallel ( extension of sides)

Square edge at crown

Wingwalls at 100-250 or 300-750 to barrel

Square-edged at crown

Headwall parallel to embankment (no wingwalls)

Square-edged on three edges

Rounded on three edges to radius of 1/12

barrel dimension, or beveled edges on three sides



Wingwalls at 300-750 to barrel

Crown edge rounded to radius of 1/12 barrel

dimension, or beveled to edges

Side- or slope-tapered inlet 0.2

Adapted from Normann et al. (1985)

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