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TK 1425 .58 F472 no.2565d
SUSITM 1I!J)1OILECDIC 'lOner
DRAINAGE STRUCTUU AND WATERWAY DESIGN GUIDELINES
Report by Rarza-Ebasco Suaitna Joint Venture
Prepared for Alaaka Pover Authority
Draft Report September 1984
0r-
OoLOLOr-,MM
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SUSITBA HYDROELEctRIC PROJECT
DRAINAGE STRUCTURE AND WATERWAY DESIGN GUIDELINES
Report byHarza-Ebasco Susitna Joint Venture
Prepared forAlaska Power Authority
Draft ReportSeptember 1984
AlaskaResources & InformationLibrary Suite 111
3211Providence DriveAnchorage, AK 99508-4614
TABLE OF COIITEJiTS
SECTION/TITLE
1.0 INTRODUCTION
1.1 Setting1.2 Scope1.3 Project Description
PAGE
1-1
1-11-11-2
1.3.11. 3. 2
GeneralWatana Dam and Reservoir
1-21-3
1.3.2.11.3.2.21.3.2.31.3.2.4
Dam SiteTransmission FacilitiesAccess PlanSite Facilities
1-31-41-41-4
1.3.3 Devil Canyon Dam and Reservoir 1-4
1.3.3.11.3.3.21.3.3.31.3.3.4
Dam SiteTransmission FacilitiesAccess PlanSite Facilities
1-41-51-51-6
1.4 Stage 1 Pre-Project Field Investigations 1-6
1.4.11.4.2
Engineering ActivitiesEnvironmental Science Activities
1-61-7
1.5 Stage II Project Construction
2.0 FLOW DETERMINATION
2.1 General2.2 Gaged Watercourses2.3 Ungaged Watercourses
1-8-
2-1
2-12-12-3
2.3.12.3.22.3.32.3.4
GeneralRunoff CoefficientDraining AreaRainfall Intensity
2-32-42-52-i
2.4 Example Peak Discharge Determination 2-10
TABLE OF CONTEBTS (cont'd)
SECTION/TITLE
3.0 HYDRAULIC DESIGN
3.1 Introduction3.2 Fish Passage Problems
PAGE
3-1
3-13-1
3.2.13.2.23.2.33.2.4
Excessive Water VelocityInadequate Water DepthExcessive Hydraulic JumpGuidelines for Structures
3-23-23-43-4
3.3 Drainage Structure Design Criteria3.4 Waterway Hydraulics
3-53-7
3.4.13.4.2
GeneralWaterways
3-73-7
3.4.2.1
3.4.2.2
Permissible Non-erodibleVelocity MethodTractive Force Method
3-123-15
3•4 • 3 Cu 1ve rt s 3-24
3.4.3.13.4.3.23.4.3.33.4.3.43.4.3.53.4.3.63.4.3.73.4.3.83.4.3.93.4.3.103.4.3.113.4.3.12
3.4.4 Bridges
3.4.4.13.4.4.2
3.4.4.33.4.4.4
Fish Passing RequirementsScope of GuidelinesCulvert HydraulicsCulverts Flowing with Inlet ControlCulverts Flowing with Outlet ControlComputing Depth of TailwaterVelocity of Culvert FlowInlets and Culvert CapacityProcedure for Selection of Culvert SizeInlet Control NanographsOutlet Control NanographsPerformance Curves
GeneralHydraulics of Constrictions inWatercoursesProcedure for Design of Bridge WaterwayExample
3-243-253-263-273-293-393-403-423-453-503-593-75
3-81
3-81
3-813-893-102
30221/TOC840922
TABLE OF COJiTEliITS (conttd)
SECTION/TITLE
REFERENCES
APPENDIX A PROJECT DRAWINGS
APPENDIX B RAINFALL FREQUENCY DATA FOR ALASKA
-iii-
PAGE
4-1
A-I
B-2
3022l!TOC840922
No.
2.3.1
2.3.2
3.2.1
3.4.1
3.4.2
3.4.3
3.4.4
3.4.5
TABLES
TITLE Page
Values of Relative Imperviousness 2-5
Runoff Coefficients "C" 2-6
Average Cross Sectional Velocities in Feet/SecondMeasured at the Outlet of the Culvert 3-3
Typical Channel Roughness Coefficients 3-10
Channel Roughness Determination 3-11
Recommended Permissible Velocities for Unlined Channels 3-13
Entrance Loss Coefficients 3-33
Key to Tables for Cland k Values for Each ConstrictionType 3-87
-~v-
No.
2.3.1
2.3.2
2.3.3
2.3.4
3.4.1
3.4.2
3.4.3
3.4.4
3.4.5
3.4.6
3.4.7
3.4.8
3.4.9
3.4.10
3.4.11
3.4.12
3.4.13
3.4.14
3.4.15
3.4.16
3.4.17
302211TOC840922
FIGUUS
TITLE
Tc Nomograph for Small Watersheds
Tc Nomograph for Large Watersheds
Upland Method Velocity Determination
Time of Concentration vs Intensity
Waterway Cross Section Measurement
Recommend Permissible Unit Tractive Force for Canalsin Noncohesive Material
Permissible Tractive Force for Coarse NoncohesiveMaterial
Angles of Repose of Noncohesive Material
Tractive Force Ratio K vs Side Slope
The Maximum Tractive Force on a Bed and Sides
Inlet Control
Outlet Control
Culvert Hydraulics Diagram
Culvert Outlet Diagram
Culvert Outlet Submerged
Hydraulic Performance Curves for 48-Inch C.M. PipeCulvert with Projecting Inlet
Definition Sketch of Flow through Constriction
Constriction Types
Type I Opening, Vertical Embankment Vertical Abutment
Subrupts kW & k Curves for Vertical Embankmentand Abutment of Type I Opening
Type II Opening, Embankment Slope 1 to 1, VerticalAbutment
-v-
2-8
2-8
2-9
2-11
3-8
3-19
3-20
3-21
3-22
3-23
3-28
3-30
3-35
3-38
3-39
3-77
3-82
3-83
3-92
3-94
30221/TOC840922
No.
3.4.18
3.4.19
3.4.20
3.4.21
3.4.22
3.4.23
3.4.24
3.4.25
FIGURES (cout'd)
TITLE
Type II Opening Embankment and Abutment Slope 2 to 1Vertical Abutment
Type III Opening, Embankment and Abutment Slope 1 to 1
Type III Opening, Embankment and Abutment Slope 2 to 1
Type IV Opening, Embankment Slope 1 to 1, VerticalAbutment with Wing Walls
Type IV Opening, Embankment Slope 2 to 1, VerticalAbutment with Wing Walls
Types I-IV Openings, ke, kt and k j cures
The Effect of Channel Roughness on the Backwater Ratiofor Basic - Type Constrictions
The Effect of Constriction on the Backwater Ratio
-V:L-
3-95
3-96
3-97
3-98
3-99
3-100
3-101
3-101
DESIGN CHAR.TS
CHART NO. TITLE
1 Headwater Depth for Box Culverts with Inlet Control
2 Headwater Depth for Concrete Pipe Culverts with InletControl
3 Headwater Depth for Oval Concrete Pipe Culverts withLong Axis Horizontal with Inlet Control
4 Headwater Depth for Oval Concrete Pipe Culverts withLong Axis Vertical with Inlet Control
5 Headwater Depth for C.M. Pipe Culverts with InletControl
6 Headwater Depth for C.M. Pipe Arch Culverts withInlet Control
7 Headwater Depth for Circular Pipe Culverts withBevelled Ring Inlet Control
8 Head for Concrete Box Culverts Flowing Full n=.012
9 Head for Concrete Pipe Culverts Flowing Full n=.012
10 Head for Oval Concrete Pipe Culverts Long AxisHorizontal or Vertical Flowing Full n=.Ol2
11 Head for Standard C.M. Pipe Culverts FlowingFull n=.024
12 Head for Standard C.M. Pipe Arch Flowing Full n=.024
13 Head for Structural Plate C.M. Pipe Culverts FlowingFull n=0.03028 to 0.0302
3-52
3-53
3-54
3-55
3-56
3-57
3-58
3-62
3-63
3-64
3-65
3-66
3-67
14 Head for Structural Plate C.M. Pipe Arch Culverts 18 in.Corner Radius Flowing Full n=0.0327 to 0.0306 3-68
3022l!TOC840922
15
16
17
Q/B vs dc
Critical Depth Circular Pipe
Critical Depth Oval Concrete pipe Long Axis Horizontal
-vu.-
3-69
3-70
3-71
3022l!TOC840922
DESIGN CHARTS (cont'd)
CHART NO. TITLE Page
18 Critical Depth Oval Concrete Pipe Long Axis Vertical 3-72
19 Critical Depth Standard C.M. Pipe-Arch 3-73
20 Critical Structural Plate C.M. Pipe-Arch 18 inch CornerRadius 3-74
-viii-
DRAINAGE ST1WCTU'iE AID WAIEi.WAY DESIGN GUIDELINES
1.0 INTRODUCTION
1.1 SETTING
This manual is intended to be used by design engineers during the
preparation of contract plans and specifications for Alaska Power Authority
projects. The guidelines ~n the manual incorporate State-of-the-Art
Engineering Practices and procedures, and also incorporate Alaska Department
of Fish and Game 1981 proposed habitat regulations where appropriate.
Although the manual is organized in such a way that it is applicable to any
Alas ka Power Authority project in ge ne r a L, nevertheless it contains much
detailed information which can be used directly ~n the preparation of
contract documents for any specific project.
1.2 SCOPE
The purpose of these best practices guidelines i s to establish the proper
procedures for drainage structures and waterways required tor implementation
of a major construction project using-the Susitna Project as an example.
Drainage structures considered in these guidelines will consist of culverts,
waterways, and the waterways beneath bridges which are required to implement
temporary or permanent access to project features. The drainage structures
and pertinent waterway work will be classi fied by the type of fish
utilization that occurs in the watercourse where the project feature is
proposed. These types are:
Type A: Watercourse that i s used by anadromous f ish during any period
of the year.
3022l/l840922
1-1
Type B: Watercourse that is utilized by resident fish during any
period of the year.
Type C: Watercourse that has no history of being used by anadromous or
re s ident fi sh ,
Waterway work for Type A and B watercourses will be limited to the necessary
adjustments in the watercourse at the inlet and out let of the drainage
structure to assure efficient hydraulic condi tions, fish movement, and to
preclude deleterious sediment transport or deposition in or around the
drainage structure. Waterway work for Type C watercourses can in some cases
be more extensive in that a collector system may be required to channel
surface runoff to the watercourse in question. A typical example of this is
an interceptor ditch along a roadway or waterway work associated with
diverting the watercourse during the construction of the drainage
structure.
The watercourse work will be divided into two distinct stages. Stage I will
be the field investigations and design. During this stage, site specific
investigation results and design criteria will be presented to secure the
necessary permits from the Alaska Department of Fish and Game and any other
permits ie., CIRI, State of Federal. Stage II would be the construction of
the drainage structure of waterway.
1.3 PROJECT DESCRIPTION (Example)
1.3.1 General
The Susitna Hydroelectric Project, located on the Susitna River
approximately 60 miles northeast of Anchorage, will consist of two dams and
reservoirs and ancillary features necessary for field investigation, design,
site access, construction, operation and transmission of energy to the
30221/1840922
1-2
l
centers of Anchorage and Fairbanks. The Federal Energy Regulatory
Ccmmission License Application Project No. 7114-000 as accepted July 29,
1983 included both Watana and Devil Canyon. Watana is located at river mile
184 on the Susitna River and 1S to be initiated first. Devil Canyon,
located at r1ver mile 152 is scheduled to begin seven years after
commencement of Watana Construction.
1 .3.2 Watana Dam and Reservoir
1.3.2.1 Dam Site The Watana Dam, Figure A-I Appendix A, will create a
reservoir approximately 48 miles long, with a surface area of 38,000 acres,
and a gross storage capacity of 9,500 acre-feet at Elevation 2185, the
normal maximum operating level.
The dam will contain a rolled embankment, earth and rock fill structure,
with a central impervious core. The design crest elevation of the dam will
be 2205, which results in a max unum height of 885 feet above the foundation
and a crest length of 4,100 feet. During construction, the river will be
diverted through two concrete-lined diversion tunnels, each 36 feet 1n
diameter and 4,100 feet long, on the north bank of the river.
The power intake will also be located on the north bank with a bi-level
approach channel excavated in rock, serving it and the spillway. Turbine
discharge will flow through six draft tube tunnels to surge chambers
downstream from the powerhouse. The surge chambers will discharge to the
river through two concrete-lined tailrace tunnels. The spillway located to
the north of the power intake will consist of an upstream ogee control
structure with three radial gates and an inclined concrete chute and flip
bucket.
Emergency release facilities will be located in one of the diversion tunnels
to allow lowering of the reservoir over a period of time to permit emergency
inspection or repair of impoundment structures.
30221/1840922
1-3
1.3.2.2 Transmission Facilities. The project transmission facilities will
deliver power fran the Susi tna River basin generating plants to the major
load centers at Anchorage and Fairbnks in an economical and reliable manner.
The facilities will consist of overhead transmission lines, underwater
cables, switchyards, substations, a load dispatch center, and a
communications system.
1.3.2.3 Access Plan. Access to the project site (See Figure A-3, Appendix
A) will connect with the existing Alaska Railroad at Cantwell where a
railhead and storage facility occupying 40 acres will be constructed.
1.3.2.4 Site Facilities. Included among the site facilities will be a
combination camp and village that will be constructed and maintained at the
project site. The camp/village will be a largely self-sufficient community
housing 3300 people during construction of the project.
Permanent facilities required will include a permanent town or
community for approximately 130 staff members and their families.
permanent facilities will include a maintenance building for use
subsequent operation of the power plant.
small
Other
during
A plan showing the location of the campi vi llage and the permanent town 1.S
shown on Figure A-I, Appendix A.
1.3.3 Devil Canyon Dam and Reservoir
1.3.3.1 Dam Site. The Devil Canyon dam and surrounding area in relation
to main access facilities and camp facilities are shown on Figure A-4,
Appendix A.
The Devil Canyon Dam will form a reserV01.r approximately 26 miles long with
a surface area of 7,800 acres and a gross storage capacity of 1,000,000
acre-feet at Elevation 1455, the normal maximum operating level.
30221/1840922
1-4
The dam will be a thin-arch concrete structure with a crest elevation of
1463 (not including a three-foot parapet) which results 1n a maximum height
of 646 feet. An earth-and rockfill saddle dam will provide closure to the
south bank. The saddle dam will be a central core type earth and over fill
similar in cross section to the Watana Dam. The dam will have a nominal
crest elevation of 1469. The maximum height above foundation level of the
dam is approximately 245 feet.
During construction, the river will be diverted by means of a single 30-foot
diameter concrete-lined diversion tunnel on the south bank of the river.
A power intake on the north bank will consist of an approach channel
excavated in rock leading to a reinforced concrete gate structure. The
turbines will discharge to the river by means of a single 38-foot diameter
trailrace tunnel leading from a surge chamber downstream from the powerhouse
cavern.
Outlet facilities consisting of seven individual outlet conduits will be
located in the lower part of the main dam. The spillway will also be
located on the north bank. As at Watana, this spillway will consist of an
upstream ogee control structure with three radial gates and an inclined
concrete chute and flip bucket.
1.3.3.2 Transmission Facilities.
Transmission lines will be built between the Devil Canyon switchyard and the
Gold Creek switching station.
1.3.3.3 Access Plan. Access to the Devil Canyon site (See Figure A-3,
Appendix) will consist primarily of a rai lroad ex tension from the ex isting
Alaska Railroad at Gold Creek to a railhead and storage facility adjacent to
the Devil Canyon camp area.
30221/1840922
1-5
1.3.3.4 Site Facilities. The construction of the Devil Canyon Dam will
require various facilities to support the construction activities throughout
the entire construction period.
As described for Watana, a construction camp will be constructed and
maintained at the project site. The camp/village will provide housing and
living facilities for 1,800 people during construction. Electric power will
be provided from Watana. A plan showing the location of the camp/village is
shown on Figure A-4, Appendix A.
1.4 STAGE I PRE-PROJECT FIELD INVESTIGATIONS
During the feasibility and licensing phase of the Susitna Project
investigations in the areas described in section 1.3 "Project Description",
will be necessary to design and construct the Project. This time frame is
defined herein as Stage I and involves activities i n the engineering and
environmental sciences. All such activities would be conducted under the
applicable technical and regulatory permits required by Federal, State,
and/or local authorities.
1.4.1 Engineering Activities
The principal activity during this stage would be subsurface exploration for
the major project features at Watana including improvements to the present
camp site which could also include the development of a temporary airstrip.
The geotechnical explorations will include damsite subsurface drilling,
monitoring, dozer or backhoe excavation of inspection trenches, geophysical
surveys and investigation of quarry materials and borrow materials. The
above activities (except for quarry and borrow area development) can be
accomplished with light equipment, helicopter transport or with special
ground transport equipment. Whereas quarry and borrow_area development may
require heavier equipment and access crossing natural waterways or earthwork
which could impede drainage courses. In these instances drainage structures
30221/1840922
1-6
will be designed and constructed using the criteria established Ln Section
2.0 and 3.0 of these guidelines.
The temporary ai.r field will require the design and construction of a
drainage collector system and perhaps drainage structures to insure that
surface runoff will reach the existing drainage features. Criteria for this
design is presented in sections 2.0 and 3.0.
The preceeding is an estimate of what will be the Stage I engineering work
requiring drainage and waterway design.
1.4.2 Environmental Study Activities
Environmental science activities will consist of aquatic, terrestrial, and
cultural resource field investigations.
Environmental science activities involve most areas of the Susitna Project.
The biological studies encompass both aquatic and terrestrial programs. The
aquatic studies are concentrated on the mainstem Susitna River from the
Oshetna River (the upstream boundary of the reservoir impoundment) to Cook
Inlet. In addition, tributaries within this reach, lakes within the
proposed impoundment areas and streams along the proposed access road are
being studied. The primary terrestrial study area includes that portion of
the Susitna Basin that lies within about 15 miles of the Susitna River from
Gold Creek to the Oshetna River mouth. In addition, studies are being
conducted within the Susitna River floodplain between Gold Creek and Cook
Inlet. Cultural resource studies would be conducted primarily in the
vicinity of the impoundment areas, along the access roads, railway and
transmission line routes.
These activities will not involve ground distrubance nor require culvert or
bridges; hence waterways and drainage courses will not-be affected.
30221/1840922
1-7
1.5 STAGE II PROJECT CONSTRUCTION
The Alaska Power Authority and their engineering consultant will prepare
engineering design memoranda, construction drawings and specifications for
the features described in 1.3.2 Watana Dam and Reservoir. In project
features requiring drainage structures or waterways, the technical criteria
presented in these guidelines will be incorporated, and used in the design
memoranda, and construction contract documents.
3022111840922
1-8
2.0 FLOW DETEKKlHAIIOI
2.1 GENERAL
In this section. the methodologies for determining the flow i.n a waterway
for a specified recurrence frequency are discussed.
2.2 GAGED WATERCOURSES
The U.S. Geological Survey, in cooperation with the Alaska Department of
Transportation and Public Facilities and other State and Federal Agencies.
maintains a network of stream gaging stations and crest gages throughout the
State of Alaska. The data obtained from these programs is published in
Water Resources Data for Alaska. Part 1. Surface Water Records. The U.S.
Geological Survey has published computer print-outs of frequency-discharge
curves for all stations with satisfactory length of record. Data obtained
from the stream gaging program has been used to formulate· a report that
presents regional flood frequency curves for most sites in Alaska. The
publication contains Magni tude and Frequency of Floods in Alaska South of
the Yukon River, Geological Survey Circular 493.
In the case where a site 1.S being investigated on a waterway that has a gage
and historical records of flow. the drainage area above the site will be
compared with that above the gage to determine if there is compatibility 1.n
the factors that affect runoff for the two areas. Factors that affect
runoff can be grouped into two major categories; climatic. which for the
purposes of these guidelines may have little or no incidence. and physio
graphic. Climatic factors mainly include the effects of rain. temperature.
and evapotranspiration. all of which exhibit seasonal changes in accordance
with the climatic environment. Physiographic factors may be further
classified into two kinds: basin characteristics and channel
characteristics. Basin characteristics include such factors as size, shape.
30221/2840922
2-1
drainage area, permeability and capacity of groundwater reservoirs, presence
of lakes and swamps, land use, etc. Channel characteristics are related
30221/2840922
mostly to hydraulic properties of the channel which govern the movement and
configuration of flood waves and develop the storage capacity. It should be
noted that the above classification of factors are interdependent to a cer
tain extent. For clarity, the following is a list of the major factors:
Meteorologic factors
1) Rainfall
a) Intensity
b) Duration
c) Time distribution
d) Areal distribution
e) Frequency
f) Geographic location
2) Snow
3) Temperature
4) Evapotranspiration
Physiographic factors
1) Basin Characteristics
a) Geometric factors
i , Drainage area
2. Shape
3. Slope
4. Stream density
5. Mean Elevation
b) Physical factors
1. Land use or cover
2. Surface infiltration condition
3. Soil type
4. Geological condition, such as the permeability and
capacity of groundwater reservoir
5. Topographical condition, such as the presence of lakes,
swamps, and glaciers.
2-2
2) Channel characteristics
a) Carrying capacity, considering size and shape of cross sec
tion, slope, and roughness
b) Storage capacity
If there is no significant difference i n these factors for both drainage
areas above the site or above the existing gage, the flow at the site can be
computed for the specified frequency by multiplying the gaged flow by the
ratio of the squares of drainage areas.
Qs = Qg(A )1/2
s
(A )1/2g
Qs = Site flow
Qg = Gage flow
As = Site drainage area
Ag = Gaged drainage area
In cases where compatibility in the factors cannot be readily ascertained,
the staff hydrologist should be consulted or the flow determination be made
using the methodology for ungaged watercourses outlined in the succeeding
paragraph.
2.3 UNGAGED WATERCOURSES
2.3.1 General
The relation between rainfall and peak runoff has been represented by many
empirical and semiempirical formulas. The rational formula which will be
30221/2840922
used in these guidelines can be taken as representative of these formulas.
The rational formula is:
2-3
Q = CIA
where Q is the peak discharge in cubic feet per second (cf s ) , C a runoff
coefficient dependent on the physiographic conditions of the drainage area,
the average rainfall intensity (I) in inches per hour and A is the drainage
area in acres.
In using the rational formula it is assumed that the maximum rate of flow,
due to a rainfall intensity over the drainage area, is produced by that
rainfall intensity being maintained for a time equal to the period of con
centration of flow at the point under consideration (Tc).
The elements involved in runoff are far more complicated than the rational
formula indicates. In larger drainage areas the temporary storage of storm
water in overland travel toward stream channels and in these channels them
selves accounts for a considerable reduction in the peak discharge rate. It
is for this reason the Alaska Department of Highways recommends that use of
this method be restricted to drainage areas less than 200 acres unless no
other method is available to estimate discharges.
The remainder of this section will be dedicated to quantifying the para
meters used in the rational formula.
2.3.2 Runoff Coefficient
The rational formula runoff coefficient (C) is the ratio of runoff to the
average rate of rainfall at an average intensity when all the drainage area
is contributing. Since this is the only manipulative parameter in the
rational formula, judgement in its selection should reflect the physiogra
phic factors listed in paragraph 2.2.
30221/2840922
2-4
Table 2.3.1 presents values of relative imperviousness for various surfaces.
In Table 2.3.2 the runoff coefficient C can be determined by weighting
physiographic factors (watershed characteristics) and summing them.
Table 2.3.1 Values of Relative Imperviousness
Type of Surface
For.all watertight roof surfacesFor asphalt runway pavementsFor concrete runway pavementsFor gravel or macadam pavements
*For impervious soils (heavy)*For impervious soils, with turf*For slightly pervious soils*For slightly pervious soils, with turf*For moderately pervious soils*For moderately pervious soils, with turf
*For slopes from 1% to 2%
Factor C
0.75 to 0.950.80 to 0.950.70 to 0.900.35 to 0.700.40 to 0.650.30 to 0.550.15 to 0.400.10 to 0.300.05 to 0.200.00 to 0.10
To account for antecedent precipitation conditions, as reflected by the fre
quency of the selected rainfall intensity, a correction factor Ca should
be multiplied with the runoff coefficient C. Values of Ca for various re
currence intervals are listed below:
RecurrenceInterval
(Years)
2 to 102550
100
.fa
1.01.11.21.25
30221/284U922
In no case should the product C x Ca exceed 1.
2.3.3 Drainage Area
The drainage area, in acres, which contributes to the site for which the
discharge is to be determined, can be calculated from~ topographic map or
2-5
Thble 2.3.2 RUNOFF COEFFICIENTS "c"
Runoff Producing Characteristics of Watershed With ODrresponding Weights
Z,I
G",
Designation ofWatershed
Characteristics
Relief
Soil
Vegetal cover
Surface Storage
Extreme75 to 100%
(40)St e e p , rugged terrain,with average slopesgenerally above 30%.
(20)No effective soil cover;either rock or thin soilmantle of negligible infiltration capacity.
(20)No effective plant cover; bare or very sparsecover.
(20)Negligible, surface depressions few and shallow; drainageways steepand small; no ponds ormarshes.
High50 to 75%
(30)Hilly, with averageslopes of 10 to 30%.
(15)Slow to take up water;clay or other soil lowinfiltration capacity.
(15)Poor to fair; cleancultivated crops orpoor natural cover;less than 10% ofdrainage area undergood cover.
(15)Low; well-defined system of small drainageways; no ponds ormarshes.
Normal30 to 50%
(20)Rolling, with averageslopes of 5 to 10%.
(10)Normal; deep permeablesoils.
(10)Fair to good; about50% of drainage areain good grassland,woodland, or equivalent cover; not morethan 50% of area inclean-cultivated crops.
(10)Normal; considerablesurface depressionstorage; drainage system similar to that oftypical prairie lands;lakes, ponds, andmarshes less than 2%of drainage area.
Low25 to 30%
(10)Relatively flat land, withaverage slopes of 0 to 5%.
(5 )Hlgh; sands, loamy sandsand other loose, opensoils.
(5)Good to excellent; about90% of drainage area ingood grassland, woodland,or equivalent cover.
(5)High; surface depressionstorage high; drainagesystem not sharply defined;large floodplain storageor a large number of lakes,ponds, or marshes.
from measurements taken in the field. If the former is used, a site visit
should be programmed to gather information to be used in determining the
runoff coefficient C and the parameters that will affect the value of the
selected rainfall intensi ty , Also, the si te visi t , literature review and
discussions with fisheries resource managers should be used to ascertain the
type of water course. (see 1.2 Scope).
2.3.4 Rainfall Intensity
Rainfall intensity, for the drainage area in question can be estimated for
specific recurrence intervals (frequency) from the isohyetal maps 1n
Appendix B. The average rainfall I used t n the rational formula depends
upon size and shape of the drainage area, the land slope, type of surface,
whether flow is overland or channelized as'well as the rainfall intensity.
The former factors are instrumental in determining the time of concentration
(T c) for the drainage area.
The theory underlying the developnent of the rational formula 1S that the
maximum discharge at any point in a drainage system occurs when:
1. The entire area tributary to the point 1S contributing to the
flow.
2. The average rainf all intensi ty producing such flow is based upon
the rainfall which can be expected to fall in the time req uired
for water to flow from the most remote point of the area to the
point being investigated. The "most remote point II is the point
from which the time of flow is greatest. It may not be at the
greatest linear distance from the point under investigation.
Nanographs .for the determination of time of concentration Tc for small and
large drainage areas are presented in Figures 2.3.1 and 2.3.2 respectively.
These nomographs utilize the length of travel (L) in feet and the difference
in elevation (H) in feet between the beginning and end point.
30221/2840922
2-7
150
Tc,min200
150
100
80L,ft
10,000 6050
405,000
30
c 25~O .2 20........ "§2,000 -... C 15
II1,500 v
e0
U 101,000 '0 8- II
Ei= 6
500 5
4300
3200
150 2
100
EXAMPLEHeiQht =100ftLenQth ~ 3,OOOftTime of concentration -14 Min
10
2
3
100................
................E~PlE-...
................ -II>
Note: ~
Use nomograph Tc for natural ....basins with well defined chonnels, 0
for overlond flow on bar. ~.arth,ond for mowed ora.. road- ~
side channels ....For overland flow, orau.d sur- 5
foe.., multiply Tc by 2__ .55 For overland flow, cmrc'r.te or ~
.. - OiPhciit surfac.. , multiply Tc ~by 0.4
For concrete channels, multiplyTc by 0.2
'"o~
c'0CL.
II
'0EII
'"
,]:;oII>o
.I:J-c
Ba.ed an .tudy by P.Z. Kirpich,Civil £ngin-.ring, Vol. 10, No.6, Jun. 1940, p.~62
Fig. 2.3.1 Tc Nomograph for Small Watersheds
10
40,000 108
30,000 6
420
20,000 330
2 Ul.. 40;:,
10,0000s:
1.0 .s8,000 .8 o 60
I-- __ .6806,000
~- - - - - __f::~,"!,~e100 =4,000 3 --. '3£=..i 3,000 .2
200
2,000 0.1300
400
1,000
800 Example 600L = 7,250 It
800600 H=130ftthen Tc = 0.57 hr 1,000
Fig. 2.3.2 Tc Nomograph for Large Watersheds
2-8
The time of concentration of the preceeding nomographs may be calculated by
the following equation:
T ~ .0078 (L )0.77c l' H/L"""'
where Tc is in minutes. The Tc calculated by the preceeding methods
assumes a natural drainage basin with well defined channels, for overland
flow on bare earth, and for mowed grass road side channels. If the overland
flow is on grassed surfaces multiply the Tc by 2. For overland flow on
concrete or asphalt surfaces multiply Tc by 0.4. For concrete channels,
multiply Tc by 0.2.
Alternatively travel times for overland flow in watersheds with a variety of
land covers can be calculated by the Uplands Method. (See Figure 2.3.3).
The individual times are calculated from the velocity for each ground cover
and the summation of the time giving the time of concentra-
40
30
20
i:•u..10•"" 9.s 8
• 7j 6en 5
4
3
2
1.0
0.5..Nc::i
tion Tc'
Figure 2.3.3 Upland Method Velocity Determination
2-9
With the time of concentration calculated and the rainfall intensity for the
area selected (Appendix B) the average rainfall intensity for the drainage
area may be determined using Figure 2.3.4. The curve for the selected one
hour rainfall is followed to the right or left until reaching the calculated
time of concentration and the average rainfall intensity (I) can be
determined.
2.4 EXAMPLE PEAK DISCHARGE DETERMINATION
As an example of the use of the Rational Method, a hypothetical drainage
area and its characteristics are used.
A drainage area of 40 acres with a distance from its most remote point being
measured as 2500 feet of which 500 feet is overland flow in forests with
heavy ground litter having an average slope of 5%. The remaining 2000 feet
can be classified as in a natural basin with well defined channels with a
drop in elevation of 150 feet.
Watershed characteristics: Reference Table 2.3.2
Relief; Flat to rolling land averageslope approximately 7 percent 0.15
Soil; Medium soil permeabilities 0.18
Vegetal cover; 25% of the area undergood cover 0.13
Surface Storage; Well defined systemof drainage ways on50% of area, negligibleon remainder
Sum C =
0.17
0.63
30221/2840922
It is required to determine the runoff for recurrence periods of 2, 10 and
50 years for a location 100 miles north of Anchorage. Referring to Appendix
2-10
,...•• 0
,
'1 !T,
1.41·11.2I .110090.80.70.6
0.5
041
2
Iii'
';.....I .s::. _;
-0-< -:a ~-itlitttttitttiJtt-
2oommm
f) 0-
19
b
~ll JillIf II
EWtt#llll
._-
.4£J:::i::i::HttH
.It I I I I II" '1'1"'"11
,-Fig. 2.3.4
" l
B Figures B2, B4 and B6 we estimate 0.4, 0.6 and 0.7 inches per hour
respectively.
Time of concentration Tc)
Overland flow Figure 2.3.3 yields a velocity of 0.6 ft/sec.
The Remaining route of 2000 feet and 150 feet of drop from Figure 2.3.1 give
9 minutes.
Time of concentration
= 22.9 minutes500 ftT c = 9 + _
0.6 ft/sec 60 sec
Average Rainfall Intensity (I)
Referring to Figure 2.3.4 with the given rainfall intensities the average
rainfall intensities (I) can be derived as follows:
FrequencyOne hourRainfall
AverageRainfall
Intensity (1)
2 year10 year50 year
0.4 in.O. 6 m ,O. 7 m ,
0.72 i n ,1.25 in.1.48 i.n ,
Runoff Calculations
Two year frequency
Q = CIA = 0.63 x 0.72 x 40 = 18.14 ft 3jsec
30221/2840922
2-12
Ten year freq uency
Q = CIA = 0.63 x 1.25 x 40 = 31.50 ft 3/sec
Fifty year frequency
Q = C Ca* I A = 0.63 x 1.2 x 1.48 x 40 = 44.76 ft 3/sec
*Antecedent precipitation correction factor see paragraph 2.3.2.
30221/2840922
2-13
3.0 HYDRAULIC DESIGN
3.1 INTRODUCTION
An effective drainage structure and waterway design process involves many
factors. principal of which are hydraulic performance. structural adeq uacy
and overall construction and maintenance costs. The design process will
incl ude an assessment by a fisheries biologist to determine whether the
water course is a fish stream. Type A or Type B. (see section 1.2-Scope).
A fish stream is defined as any water flow that is accessible to fish and
capable of supporting aquatic life. This would include. but is not limited
to. all Alaska Department of Fish and Game designated streams and all their
tributaries up to impassab l e natural barriers. Type A freshwater systems
above blockages may also support resident fish stocks. Evaluation and
recommendations will be made by a fisheries biologist during site location
to determine the presence of fish stocks.
If the waterway is classified as either Type A or Type B the following cri
teria should be included in the design process.
3.2 FISH PASSAGE PROBLEMS
The efficient passage of fish through a drainage structure req U1 res close
attention to the resolution of three problems:
1. Excessive water velocity
2. Inadequate water depth
30221/3840922
3-1
3. Excessive hydraulic jump
3.2.1 Excessive Water Velocity
Excessive water velocities can block fish movement simply by exceeding the
swimming ability of fish. Swimming ability varies with species, size and
age of fish, and length of drainage structure (culvert). Studies of fish
movement have provided the information presented on Table 3.2.1.
Slope is the most important factor determining velocity in culverts. Slopes
steeper than 0.5 percent (1/2 foot drop in 100 feet) generally create exces
sive velocities for fish passage.
3.2.2 Inadequate Water Depth
Fish require sufficient water depth to attain maxunum swimming abilities.
The depth required is directly related to fish size with larger fish requir
ing deeper water. When insufficient depths are encountered, fish are unable
to produce full propulsion.
Causes of inadequate depth. The two most frequently encountered reasons for
insufficient water depth are steep slope and a wide, flat channel bottom (no
low flow channel).
a. All other factors being constant, the steeper the slope of a structure
the shallower the water depth.
b. All other factors being constant, the wider the structure bottom the
shallower the water depth.
30221/3840922
3-2
Table 3.2.1
AVERAGE CROSS SECTIONAL VELOCITIES IN FEET/SECOND MEASUREDl/AT THE OUTLET OF THE CULVERT
Length ofCulvertin Feet
Group I
Upstream migrant salmonfry and fingerlings whenups team migration takesplace at meanannual flood
Group II
Adult and juvenileslow swimmers:grayling, longnosesuckers, whitefish,burbot, sheefish,Northern pike,Dolly Varden/ArcticChar, upstreammigrant salmon fryand fingerlings whenmigration not a~
mean annual flood
Group III
Adult moderate swimmers: pinksalmon, chumsalmon, rainbow trout,cutthroattrout
Group IV
Adult highperformanceswimmers:king salmon,coho salmon,sockeye salmon, steelhead
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1/
30 1.0 4.6 6.8 9.9
40 1.0 3.8 5.8 8.5
50 1.0 3.2 5.0 7.5
60 0.9 2.8 4.6 6.6
70 0.8 2.6 4.2 6.0
80 0.8 2.3 3.9 5.5
90 0.7 2.1 3.7 5.1
100 0.7 2.0 3.4 4.8
150 0.5 1.8 2.8 3.7
200 0.5 1.8 2.4 3.1
200 0.5 1.8 2.4 3.0
Title 5 Fish and Game Part 6 Protection of Fish and Game HabitatChapter 95 - Alaska Department of Fish and Game
3-3
Minimum water depths required for instream movement of juveniles will vary
with species and size of fish present. Generally, 0.2 foot (2.4 inches) ~s
sufficient for passage. Minimum water depths for adult fish are: lJ
King Salmon-0.8 feet
Other salmon and trout over 20 inches-0.6 feet
Trout under 20 inches-0.4 foot
3.2.3 Excessive Hydraulic Jump
The two basic causes for a hydraulic jump at the downstream end of a
structure are bed scour and slope of structure placement.
a. Degradation of the streambed below the. structure can result in lowering
the water surface below the downstream end of the structure. This
occurs most frequently in steep gradient streams with erodible bottom
materials. Degradation of a receiving waterway can create a hydraulic
jump at a downstream end of the structure.
tributary.
b. Placement of a flat sloped structure on a steep sloped waterway builds
in a jump.
3.2.4 Guidelines for Structures
Location: The guidelines for locating structures for fish passage are also
coincidental with those for hydraulic design.
1. There should not be a sudden increase i.n velocity immediately above,
below, or at the crossing.
2. Structures should not be located on a sharp bend ~n the stream channel.
1/ Lauman, J.E. Salmonid Passage at Stream - Road Crossings: A Reportwith Department Standards for Passage of Salmonids. 1976 Department ofFish and Wildlife Portland Oregon.
30221/3840922
3-4
3. Structures should be designed to fit the stream channel alignment.
They should not necessitate a channel change to fit a particular cross
ing design.
3.3 DRAINAGE STRUCTURE DESIGN CRITERIA
All drainage structures in waterways an which fish are known to freq uent
(Type A or B) shall be designed in accordance with the following criteria:
Water-
course Flood
Type Frequency
A
B
C
2 year
10 years
50 years*
Maximum velocity per Table 3.2.1 group and twice the
depth of flow per paragraph 3.2.2
No static head at culvert entrance
Allowable pondage at site
* In the case that the drainage structure is at a primary road or railway
the flood frequency is to be 100 years.
Drainage structures 1.n waterways where there are no anadromous fish will be
designed for criteria Band C above. Drainage structures that are
classified as temporary, meaning that they will be removed and the habitat
rehabi l i tated wi thin a 10 year period wi 11 be designed for the preceedi ng
criteria except that the flood frequency of criteria C will be 25 years.
Drainage structures in fishery streams shall be placed with the waterway
substrate in its invert. In the case of culverts, at least one fifth of the
diameter of each round culvert and at least 6 inches of the height of each
elliptical or arch type culvert is to be set below the stream bed at both
the inlet and outlet of the culvert. The above is not applicable to bottom
less arch type culverts. In the case of a rock substrate, a request for
30221/3840922
3-5
variance should be submitted to the Alaska Department of Fish and Game
(ADF&G) for approval.
A drainage structure design data sheet, tabulating information for each
site, prepared by a fisheries biologist and a design engineer will be sub
mitted to ADF&G for approval and approved prior to undertaking any construc
tion. (See end of 3.4.3.8, Inlets and Culvert Capacity.)
The drainage structure design will require the following conditions to be
adhered to during its construction.
a. All bank cuts, slopes, fills and exposed earth work attributable to
installation in a waterway must be stabilized to prevent erosion during
and after construction.
b. The width and depth of the temporary diverison channel must equal or
exceed 7S percent of the width and the depth, respectively, of that
portion of the waterway which is covered by ordinary high water at the
diversion site, unless a lesser width or depth is specified by the
ADF&G on the permit for activities undertaken during periods of lower
flow;
c. During excavation or construction, the temporary diversion channel must
be isolated from water of the waterway, to be diverted, by natural
plugs left ~n place at the upstream and downstream ends of the
diversion channel.
d. The diversion channel must be constructed so that the bed and banks
will not significantly erode at expected flows.
e. Diversion of water f low into the temporary diversion channel mus t be
conducted by first removing the downstream plug then removing the up
stream plug, then closing the upstream end and then the downstream end,
respectively, of the natural channel of the diverted waterway.
30221/3840922
3-6
f. Rediversion of flow into the natural stream must be conducted by remov
ing the downstream plug from the natural channel and then the upstream
plug, then closing the upstream end and then the downstream end, re
spectively, of the diversion channel.
g. After use, the diversion channel and the natural waterway must be
stabilized and rehabilitated as may be specified by permit conditions.
3.4 WATERWAY HYDRAULICS
3.4.1 General
A field inspection is basic to the design of diversion channels, culverts,
and bridge encroachment into waterways, all of which encompass the drainage
structures to which these guidelines are addressed.
For the design of drainage structures, the hydraulic condi tion of the
prepared structure will be similar to the natural waterway upstream and
downstream of the proposed structure site must be known. The parameters for
a typical section will be measured in the field. During this inspection a
check should be made of downstream controls. At times the tailwater
is controlled by a downstream obstruction or by water stages in another
waterway.
3.4.2 Waterways
This section describes the techniques for investigation of the waterway on
which a drainage structure is to be constructed and the construction
activities for a new waterway such as a temporary diverison channel.
Hydraulic investigation and design of waterways will be based upon Manning's
formula for uniform flow unless existing site conditions indicate that flows
will be non uniform. A full treatment of this subject may be found i.n
30221/3840922
3-7
treatment of this subject may be found in Open-Channel Hydraulics by Ven Te
Chow, Mc Graw Hill 1959.
The Manning formula:
v • 1.49 R2/3 Sl/2n
Where: V is the mean velocity in fps;
R is the hydraulic radius ft;
S is the slope of the waterway, and
n is the coefficient of roughness, specifically known as
Manning's n
The discharge in the waterway may be determined by multiplying by "A" the
area of the water prism in the formula.
a. Waterway Investigation
A hydraulic rating curve of the waterway should be determined by measuring
the waterway cross section between highwater marks on both sides of the
waterway. If these marks are not visible a high water level should be esti
mated. Figure 3.4.1 is an example of a waterway cross section measurement.
8' /0' 6' 1" 6' /2' 5'
Figure 3.4.1 Waterway Cross Section Measurement
3-8
30221/2840922
From the cross section the area and wetted perimeter should be calculated
for at least 3 levels, or more if the waterway is deep, including the maxi
mum level.
From the measured slope of the waterway and a determination of waterway
roughness n, the discharges for the selected levels (depth of flows) can be
calculated using Manning's formula. The n values for typical channel condi
tions are presented in Table 3.4.1 and a method used by the U.S. Soil Con
servation Service for computing an n value taking into consideration factors
that affect n is presented in Table 3.4.2.
b. Waterway Design
The required capacity of the waterway should be determined by the method
indicated in Section 2.0-Flow Determination. If the waterway IS to be de
signed for fish passage, the group (Table 3.2.1) and the minimum depth of
flow for instream movement (paragraph 3.2.2) snould be determined.
3-9
Table 3.4.1 Typical Channel Roughness Coefficientsl/
Value of n Channel Condition
0.016-0.017
0.020
0.0225
Smoothest natural earth channels, free from growth, withstraigth alignment.
Smooth natural earth channel, free from growth, little curvature.
Small earth channels in good condition, or large earth channels with some growth on banks or scattered cobbles in bed.
0.030 Earth channels with considerable growth.with good alignment, fairly constant section.channels, well maintained.
Natural streamsLarge floodway
0.035 Earth channels considerably covered with small growth.Cleared but not continuously maintained floodways.
0.040-0.050 Mountain streams in clean loose cobbles.able section and some vegetation growingchannels with thick aquatic growths.
Rivers within banks.
variEarth
0.060-0.075 Rivers with fairly straightbadly obstructed by smallaquatic growth.
alignment and cross section,trees, very little underbrush or
0.100
0.125
0.150-0.200
Rivers with irregular alignment and cross section, moderatelyobstructed by small trees and underbrush. Rivers with fairlyregular alignment and cross section, heavily obstructed bysmall trees and underbrush.
Rivers with irregular alignment and cross section, coveredwith growth of virgin timber and occasional dense patcnes ofbushes and small trees, some logs and dead fallen reese
Rivers with very irregular alignment and cross section, manyroots, trees, bushes, large logs, and other drift on bottom,trees continually falling into channel due to bank caving.
30221/2840922
1/ Design of Small Dams, U.S. Bureau of Reclamation, 1977.
3-10
Table 3.4.2 Channel Roughness Determinationl1
Steps
1. Assume basin n2. Select modifying n for roughness or degree of irregularity3. Select modifying n for variation in size and shape of cross section4. Select modifying n for obstructions such as debris deposits, stumps, exposed
and fallen logs5. Select modifying n for vegetation6. Select modifying n for meandering7. Add items 1 through 6
Aids in Selecting Various n Values
1. Recommended basic in valuesChannels in earth------------O.OlOChannels in rock-------------0.015
Channels ln fine gravel------------0.014Channels ln coarse gravel----------0.028
2. Recommended modifying n value for degree of irregularitySmooth-----------------------O.OOO Moderate---------------------------O.OlOMinor------------------------0.005 Severe-----------------------------0.020
3. Recommended modifying n value for changes in size and shape of cross &ectionGradual----------------------O.OOO Frequent------------------O.OlO to 0.015Occasional-------------------0.005
4. Recommended modifying n value for obstruction such as debris, roots, etc.Negligible effect------------O.OOO Appreciable effect-----------------0.030Minor effect-----------------O.OlO Severe effect----------------------0.060
5. Recommended modifying n values for vegetationLow effect----------0.005 to 0.010 High effect---------------0.025 to 0.050Medium effect-------O.OlO to 0.025 Very high effect----------0.050 to 0.100
6. Recommended modifying n value for channel meander
Ls=Straight length of reach ~=Meander length of reach
Lm/Ls n
1.0-1.2 0.000
1.2-1.5 0.15 times n,s
>1.5 0.30 times ns
where ns=items 1+2+3+4+5
II Design of Small Dams, U.S. Bureau of Reclamation, 1977.
30221/3840922
3-11
30221/2840922
The design of a stable channel 1S accomplished by trial and error. It is
reasonable to expect a channel to suffer some damage during a 50-year flood
event, but one would desire a stable channel for the la-year flood event.
Therefore as a trial starting point, the channel section will be des igned
for maximum discharge with a velocity approximately 20% higher than the
velocity that would be permissible in the channel during the la-year flood
event.
Two methods will be presented for channel design; the Permissible Velocity
Method and the Tractive Force Method. Examples of their use will also be
presented.
3.4.2.1. Permissible Non-erodible Velocity Method
The maximum permissible velocity, or non-erodible velocity is the greatest
mean velocity that will not cause erosion of the channel body. In general,
old and well-seasoned channels will stand much higher velocities than new
ones, because the old channel bed is usually better stabilized, particular
ly with the deposition of colloidal matter. When other conditions are the
same, a deeper channel will convey water at a higher mean velocity without
erosion than a shallower one.
Table 3.4.3. lists the maX1mum permissible velocity for cnannels with erod
ible linings based on uniform flow in continuously wet, aged channels.
3-12
30221/2840922
Table 3.4.3*
RECOMMENDED PERMISSIBLE VELOCITIES (ft./sec.) FOR UNLINEDCHANNELS
Type of Material for Excavated Section Clear Water Silt - Carrying Water
Fine Sand (non colloidal) 1.5 2.5Sandy Loam (non colloidal) 1.7 2.5Silt Loam (non colloidal) 2.0 3.0Ordinary Firm Loam 2.5 3.5Volcanic Ash 2.5 3.5Fine Gravel 2.5 4.0Stiff Clay (colloidal) 3.7 5.0
Graded Material:Loam to Gravel 3.7 5.0Silt to Gravel 4.0 5.5Gravel 5.0 6.0Coarse Gravel 5.5 6.5Gravel to Cobbles «6") 6.0 7.0Gravel to Cobbles ()6") 7.0 8.0Shales and Hardpans 7.0 8.0
* State of California, Dept. of Public Works, Division of Highways,"Planning Manual of Instructions, Part 7, Design," 1963.
Using permissible velocity as a criterion, the design procedure for an un
lined cnannel section, assumed to be trapezoidal, is as follows:
1. For the given kind of material forming the channel body, estimate
the roughness coefficient n, side slope z, and the maximum per
missible velocity, V (Table 3.4.3).
2. Compute the hydraulic radius R by use of the Manning formula.
3. Compute the water area required by the given discharge and per
missible velocity, i.e.: A = Q/(1.2V).
4. Compute the wetted perimeter, P = A/R.
3-13
5. Solve simultaneously for band y (base and depth of flow).
6. With the given section, by iteration, calculate with varying
depths of flow, the depth and velocity for the 10-year flood dis
charge. Check if velocity is equal or less than the permissible.
If not, change slope if possible or lower velocity and repeat 1.
7. For fish streams, repeat 6 for the 2-year flood discharge to
check if velocity is equal to or less than permissible fish pass
age velocity for the designated group (Table 3.2.1) and the depth
of flow is at least 50% greater than that indicated in paragraph.
3.2.2 for the fish type. If the above are not met, a further
channel revision may be required necessitating recalculation be
ginning with 1 or the incorporation of a low flow section in the
invert of the channel.
A calculation example follows in steps 1 through 6
Compute the bottom width and depth of flow of a trapezoid channel laid
on a slope of .0016 and carrying a design discharge of 400 c f s , The
channel a s to be excavated in earth containing non-colloidal gravelly
silt.
Solution:
For the given conditions, the following are estimated: n = 0.025, side
slope z = 2:1, and maximum permissible velocity = 3.75 x 1.2 = 4.5 fps.
1. Using the Manning Formula, solve for R
4.5 = 1.49 R2/3 (.0016)1/20.025
R = 2.60 ftThen A = 400/4.5 = 88.8 ft 2, and P = AIR = 88.8/2.60 = 34.2
30221/3840922
3-14
2. A ~ (b + zy)y = (b + 2y)y = 88.8 ft 2and P = b + 2 (1 + z2)1/2y = [b + 2(5)1/2y ] = 34.2 ft.
3. Solving the two equations simultaneously:(b + 2y) y = 88.8(b + 4.47y) = 34.288.8 - 2y2 = 34.2y - 4.47 y22.47y2 - 34.2y + 88.8 = 0
y = 3.46 ftb = 18.7 ft
3.4.2.2 Tractive Force Method
The tractive force method takes into account physical factors of bed ma
terial, channel section, depth of flow and velocity. This method will be
confined to non cohesive materials for which the permissible tractive force
is related to particle size and shape, and sediment load in the water. The
tractive force is the unit force tending to cause erosion of the material
forming the channel. Figure 3.4.2 shows curves for recommended values of
permissible unit tractive force for particles up to about 4 inches in diame
ter. For coarser material, the permissible tractive force in psf is eq ual
to 0.4 times the diameter in inches as shown in Figure 3.4.3. The diameter
is that of a particle of equivalent spherical volume. The curves in Figures
3.4.2 and 3.4.3 are based on particle sizes of which 25% by weight are larg-
er.
The limiting condi tion for permissible tractive force i s governed by the
particles on the sides rather than those on the bottom of the channel. The
resistance of the material on the sides is reduced by the sliding force down
the sides due to gravity. The effect of side sLopes is expressed as factor
K, which is the ratio of the tractive force required to initiate motion of a
particle on the sloping sides to that on a level bottom. The equation is:
( 1 - sin2 0 1/2K = sin2 0 )
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3-15
30221/2840922
o = side slope angle
e = angle of repose of the material which varies with particle sizeand shape as shown in Figure 3.4.4.
The solution of this equation is given in Figure 3.4.5.
The formula for maximum tractive force is:
TO = 62.4 R8
8 = energy gradient ~n ft/ft (channel slope for uniform flow)
R = hydraulic radius
In a wide open channel, the hydraulic radius ~s approximately equal to the
depth of flow y; hence, TO = 62.4 y8.
Channels in fine material less than 5 mm ~n diameter are designed by using
the recommended values of tractive force ploted in Figure 3.4.2. In this
case, "d " is the mean diameter for which 50% by weight are larger. The
sliding effect of the particles down the channel sides due to their own
weight is neglected.
An example using values for; a 10-year flood design, a trapezoidal channel
laid on a slope of .0016, and carrying a discharge of 400 cfs. The channel
is to be excavated in earth containing noncolloidal coarse gravels and peb
bles, 25% of which is 1.25 in or over in diameter. Manning's n = 0.025.
For trapezoidal channels, the maxamum unit tractive force on the sloping
sides is usually less than that on the bottom (Figure 3.46); hence, the side
force ~s the controlling value ~n the analysis. The design of the channel
should therefore include: (a) the proportioning of the section dimensions
for the maximum unit tractive force on the sides and (b) checking the
proportioned dimensions for the maximum unit tractive force on the bottom.
3-16
a. Proportioning the Section Dimensions:
1. Assuming side slopes of 2: 1 and a b/y ratio =5, the maximum
unit tractive force on the sloping sides (Figures 3.4.6) is
.775 x 62.4 yS = .775 x 62.4 x .0016y = 0.078y psf.
2. Considering a very rounded material 1.25 in. in diameter, the
angle of repose (Figure 3.4.4) is 9 = 33.5. With 9 = 33.5
and SS = 2.1, the permissible tractive force ratio on the
sloping sides (Figure 3.4.5) is K = 0.6. For a size of 1.25
in., the permissible tractive force on a level bottom is T =
0.4 x 1.25 = 0.5 psf (this can also be obtained from Figure
3.4.2) and the permissible tractive force on the sides is
equal to 0.6 x 0.5 = 0.3 psf.
3. For a state of impending motion of the particles on side
slopes, .078y = 0.3 or y = 3.88 ft. Accordingly, the bottom
width b = 5 x 3.85 = 19.3 ft. For this trapezoidal section,
A = 104 sq ft and R = 2.85.
4. By the Manning equation Q = 1.486 AR2/3S1/2n
= 1.486 (104) (2.85)2/3 (.0016)1/2 = 491 cfs.025
Further computation will show that for a side slope of 2: 1
and b/y ratio of 4.1, b = 15.8 ft., Q = 425 cfs, which is
close to the design discharge.
30221/2840922
b. Checking the proportioned dimensions:
With S8 = 2:1 and b/y = 4.1, the maximum unit tractive force on
the channel bottom (Figure 3.4.6) is 0.97 x 62.4 x 3.85 x .0016
0.374 psf < 0.5 psf (permissible tractive force on the bottom).
3-17
30221/2840922
5.
6.
Determining maximum flow conditions: with base width and
side slopes determined, the depth of flow required for the
maximum flow conditions can be determined using the Manning
formula.
For fish streams, repeat paragraph 5 for the 2-year flood
discharge to check if velocity i s equal to or less than
permissible fish passage velocity for the designated group
(Table 3.2.1) and the depth of flow is at least 50% greater
than that indicated in paragraph 3.2.2 for the fish type. If
the above are not met, a further channel revision may be
required, necessitating recalculation beginning with 1 or the
incorporation of a low flow section in the invert of the
channel.
3-18
2.0
4.0
OA
0002
..... t,.
'7
7/
/
/Hi9f\ content of
V ~ I.lI.i~Coarse noncahesivefine sed iment '" V material
I '" ~ ~ ,II.~ ~ 7
~ '":--"" ,/
-- /, ./\ .....10-- ..-1\\ - ........
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I
lj.4 0.6 081.0 2 4 6810 20 40 60 80 IOJ
O.~
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0.10.08
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Mean Diameter - mm.
Figure 3.4.2
RECOMMEND PERMISSIBLE UNIT TRACTIVE FORCE
FOR CANALS IN NONCOHESIVE MATERIAL
3-19
••4
2
N.:-~•..a0.8
.s8 O.i
!QI 0.4>.--c.J0'"~~..a~
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11.
0.1
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//
/V
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0.1 0.2 0.4 0.' 0.8 I 2 4. e 10Diameter In IneMI t 2!5'*a larger
Figure 3.4.3
PERMISSIBLE TRACTIVE FORCE FOR COARSE NONCOHESIVE MATERIAL
3-20
42
"i 40-c:0...
38-'"0J::
J:: 36-.-,lit 34Qc»"" 32CI'c»'0. 30~0Q, 28~-0 26•e;. 24.i
22
20
Particle size in inches0.2 0.4 o.sO.8 LO 2.0 3.0 4.0
1 I 't'« I I I
112 11'1'2.
.,- ,..-~
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o o~ ~/ II..,0; bI~~ ~b~11.~ c0 oJi I
~" ~ ~ II~ ..~~ ...~~/
" ..0 ~I A§j~ Vt.s:I~I
Figure 3.4.4
ANGLES OF REPOSE OF
NONCOHESlVE MATERIAL
3-21
Repose
Side Slopes
j SIII. z ,Based on 8qu~tlon K- 1- SIII.~ ...
40-11,44:1-
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>-3 CD25-
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U.I 0.2 0.3 0.4· 0..5 Q.6 0.7 o.a 0.9 .0K = Permissible Tractive Farce on Side. in fraction of Volue for level Bottom for Nancaheslve Mote,••'
0' J_ I
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Fig
ure
3.4
.6
THEM
AXIMUM
TRACTIV
EFORCE
ONBED
ANDSID
ES
3-2
3
30221/2840922
3.4.3 Culverts
3.4.3.1 Fish Passing Requirements. The following presentation on culvert
design is essentially a repitition of the Hydraulic Engineering Circular
No.5 pepared by the Bureau of Public Roads, U.S. Department of Commerce.
As such the design criteria established are for the design of highway
culverts and includes no provisions of fish passage criteria. Therefore,
this paragraph will ammend the following in the instances that the culvert
is to be placed on a waterway that has been established to have resident
fish or used by anadromous fish.
In Sections 3.2, Fish Passage Problems and 3.3 Drainage Structure Design
Criteria, the basic requirements were presented for the successful design of
a culvert for passing fish. They were:
1. Velocity requirement per fish group (Specified in Table 3.2.1)
2. Place invert below waterway bed by at least 0.2 diameter
3. Maintain depth of flow requirement for fish type per paragraph 3.2.2
Inadequate Water Depth.
It can be shown that concrete culvert characteristics with full flow, when
the lower 20% of the diameter is filled with the streambed substrate, are
modified as follows:
Area reduced by 14.5%
Hydraulic radius reduced by 11%
Average roughness coefficient n
increased by 30%
3-24
These changes in parameters will reduce the culvert capacity by about 39%.
Therefore the selection of the culvert s i ze as presented in the following
text will require a correction. This correction is achieved by increasing
the design discharge (full pipe flow only) by 63% before starting the design
procedure indicated in 3.4.3.11 Outlet Control Nomographs.
For low flow design, as in the case of the 2 year flood, the culvert will
flow partially full and the discharge depth for runoff discharge can be
computed taking into consideration the culvert section with fill material
using Manning's formula. The hydraulic radius is accounted for by weighting
the perimeter with the n's of the culvert and the substrate material as per
the following equation.
P n 1.5)2/3s s
n =
"Important"
Per the preceeding, culverts meeting the requirements prescribed herein
should be designed for a maximum capacity equivalent to: 1.63 x the cal
culated design discharge.
3.4.3.2 Scope of Guidelines. The following text contains a brief discus
sion of the hydraulics of conventional culverts and charts for selecting a
culvert size for a given set of conditions. Instructions for using the
charts are provided. Sane approx imations are made in the hydraulic design
procedure for simplicity. These approximations are discussed at appropriate
points throughout the text.
30221/3840922
3-25
30221/2840922
For this discussion, conventional culverts include those commonly installed,
such as circular, arch and oval pipes, both metal and concrete box culverts.
All such conventional culverts have a uniform barrel cross section through
out. The culvert inlet may consist of the culvert barrel projected from
the roadway fill or mitered to the embankment slope. Sometimes inlets have
headwalls, wingwalls and apron slabs, or standard end sections of concrete
or metal. The more common types of conventional culverts are considered in
these guidelines.
3.4.3.3 Culvert Hydraulics. Laboratory tes ts and field observations show
two major types of culvert flow: (1) flow with nlet control and (2) flow
with outlet control. For each type of control, different factors and formu
las are used to compute the hydraulic capacity of a culvert. Under inlet
control, the cross-sectional area of the culvert barrel, the inlet geometry
and the amount of headwater or ponding at the entrance are of primary impor
tance. Outlet control involves the additional consideration of the eleva
tion of the tailwater in the outlet channel and the slope, roughness and
length of the culvert barrel.
It is possible by involved hydraulic computations to determine the probable
type of flow under wni.cn a culvert will operate for a given set of condi
tions. The need for making these computations may be avoided, however, by
computing headwater depths from the charts in this circular for both inlet
control and outlet control and then using the higher value to indicate the
type of control and to determine the headwater depth. This method of de
termining the type of control is accurate except for a few cases where the
headwater is approximately the same for both types of control.
Both inlet control and outlet control types of flow are discussed briefly in
the following paragraphs and procedures for the use of the charts are given.
3-26
30221/2840922
3.4.3.4 Culverts Flowing With Inlet Control. Inlet control means that the
discharge capacity of a culvert is controlled at the culvert entrance by
the depth of headwater (HW) and the entrance geometry, including the barrel
shape and cross-sectional area, and the type of inlet edge. Sketches of
inlet-control flow for both unsubmerged and submerged projecting entrances
are shown in sections A and B of Figure 3.4.7. Section C shows a mitered
entrance flowing under a submerged condition witn inlet control.
In inlet control the roughness and length of the culvert barrel and outlet
conditions (including depth of tai Iwa t e r ) are not factors in determining
culvert capacity. An increase in barrel slope reduces headwater to a small
degree and any correction for slope can be neglected for conventional or
commonly used culverts flowing with inlet control.
In all culvert design, headwater or depth of ponding at the entrance to a
culvert is an important factor in culvert capacity. The headwater depth
(or headwater HW) is the vertical distance from the culvert invert at the
entrance to the energy line of the headwater pool (depth + velocity head).
Because of the low velocities in most entrance pools and the difficulty in
determining the velocity head for all flows, the water surface and the ener
gy line at the entrance are assumed to be coincident, thus the headwater
depths given by the inlet control charts in this circular can be higher than
will occur in some installations. For the purposes of measuring headwater,
the culvert invert at the entrance is the low point in the culvert opening
at the beginning of the net cross-section of the culvert barrel. (Refer to
para gr a ph 3. 4 • 3 • 1 ) •
Headwater-discharge relationships for the various types of circular and
pipe-arch culverts flowing with inlet control are based on laboratory re
search with models and verified in some instances by prototype tests. This
3-27
A
HW____ ...£ !!
research is reported in National Bureau of Standards Report No. 44441/ en
titled "Hydraulic Characteristics of Commonly Used Pipe Entrances", by John
L. French and "Hydraulics of Conventional Highway Culverts", by H. G.
BOssyZ/, Experimental data for box culverts with headwalls and wing
walls were obtained from an unpublished report of the U.S. Geological
Survey.
These research data were analyzed and nomographs for determining culvert
capacity for inlet control were developed by the Division of Hydraulic Re-
search, Bureau of Pub lic Roads. These nomographs, Charts 1 through 6,
give headwater-discharge relationships for most conventional culverts flow
ing wi th inlet control through a range of headwater depths and discharges.
Chart No. 7 is included to stress the importance of improving the inlets of
culverts flowing with inlet control.
3.4.3.5 Culverts Flowing With Outlet Control. Culverts flowing with outlet
control can flow with the culvert barrel full or part full for part of the
barrel length or for all of it, (see Figure 3.4.8). If the entire cross
section of the barrel ~s filled with water for the total length of the bar
rel, the culvert is said to be in full flow or flowing full, Sections A and
B. Two other common types of outlet-control flow are shown in Sections C
and D. The procedures given in this text provide methods for the accurate
determination of headwater depth for the flow condi tions shown in Sections
1/ Available from Division of Hydraulic Research, Bureau of Public Roads.
2/ Presented at the Tenth National Conference, Hydraulics Division, ASCE.,August 1961. Available on loan from Division of Hydraulic Research,Bureau of Public Roads.
30221/2 3-29840922
..
1 -HW
WATERSURFACE
A
_ ~ w.s.
8
1HW
IH
<, w.s.' ..... - ---
c
fH
-L.. w.s....... ------.
o
-----------~~--~~----....
OUTLET CONTROL
Figure 3.4.8
3-30
A, Band C. The method given for the part full flow condition, Section D,
gives a solution for headwater depth that decreases in accuracy as the
headwater decreases.
The head H (Section A) or energy required to pass a given quantity of water
through a culvert flowing in outlet control with the barrel flowing full
throughout its length is made up of three major. parts. These three parts
are usually expressed in feet of water and include a velocity head ~, an
entrance loss He' and a friction loss Hf• Tnis energy is obtained from
ponding of water at the entrance and expressed in equation from
(1)
30221/2840922
The velocity head Hv equals V2/2g, where V is the mean or average velocity
in the culvert barrel. (The mean velocity is the discharge Q, in cfs, di
vided by the cross-sectional area A, in square feet, of the barrel.).
The entrance loss He depends upon the geometry of the inlet edge. This
loss is expressed as a coeffcient k e times the barrel velocity head or
He = k e V2/2g. The entrance loss coefficients k e for various types of
entrances when the flow is in outlet control are given in Table 3.4.4.
The friction loss Hf is the energy required to overcome the roughness of
the culvert barrel. Hf can be expressed in several ways. Since most
engineers are familiar with Manning's n the following expression is used:
H =Rl. 33 2g
3-31
Where:
Where:
n a Manning's roughness coefficient
L = length of culvert barrel (ft)
V = mean velocity of flow in culvert barrel (ft/sec)
g = acceleration of gravity, 32.2 (ft/sec 2)
R = hydraulic radius or A/P (ft)
A = area of flow for full cross-section (sq ft)
P = wetted perimeter (ft)
30221/2840922
Substituting in equation 1 and simplifying, we get for full flow
29n2L v2H = (1 + k e + ------)
RI.33 2g
3-32
Table 3.4.4 Entrance Loss Coefficients
Coefficient ke to apply to velocity head V2/2g for determination of headloss at entrance to a structure, such as a culvert or conduit, operting fullor partly full with control at the outlet.
Entrance head loss He = ke V22g
Coeffi-Type of Structure and Design of Entrance cient ke
Pipe, ConcreteProjecting from fill, socket end (groove-end) •••••••••••••• 0.2Projecting from fill, sq cut end ••.•••••••••••••••••••••••• 0.5Headwall or headwall and wingwalls
Socket end of pipe (groove-end)........................ 0.2Square-edge 0.5Rounded (radius - 1/12D) •••••••••••••••••••••••••••••• 0.2
Mitered to conform to fill slope ••••••••••••••••••••••••••• 0.7*End-section conforming to fill slope •••.•••••••••••••••••• 0.5
Pipe, or Pipe-Arch, Corrugated MetalProjecting from fill (no headwall)Headwall or headwall and wingwalls
0.9
Square-edge' 0.5Mitered to conform to fill slope. ••••••••• ••• ••••. •••••.••• 0.7*End-section conforming to fill slope...................... 0.5
Box, Reinforced ConcreteHeadwall parallel to embankment (no wingwalls)
Square-edged on 3 edges 0.5Rounded on 3 edges to radius of 1/12 barrel dimension. 0.2
Wingwalls at 30° to 75° to barrelSquare-edged at crown................................. 0.4Crown edge rounded to radius of 1/12 barrel dimension. 0.2
Wingwalls at 10° to 25° to barrelSquare-edged at crown................................. 0.5
Wingwalls parallel (extension of sides)Square-ed ged a t crown O. 7
30221/2840922
*Note: "End-section conforming to fill slope", made of either metal orconcrete, are the sections commonly available from manufacturers.From limited hydraulic tests, they are equivalent in operation toa headwall in both inlet and outlet control. Some end sections,incorporating a clo~aper in their design have a superior hydraulic performance. These later sections can be designed usingthe information given in 3.4.3.8 Inlets and Culvert Capacity.
3-33
Figure 3".4.9 shows the terms of equation 2, the energy line, the hydraulic
grade line and the headwater depth, HW. The energy line represents the to
tal energy at any point along the culvert barrel. The hydraulic grade line,
sometimes called the pressure line, is defined by the elevations to which
water would rise in small vertical pipes attached to the culvert wall along
its length. The energy line and the pressure line are parallel over the
length of the barrel except in the immediate vicinity of the inlet where the
flow contracts and re-expands. The difference in elevation between these
two lines is the velocity head, V2/2g.
The expression for H 1S derived by equating the total energy upstream from
the culvert entrance to the energy just inside the culvert outlet with con-
sideration of all the major losses in energy. By referring to Figure 3.4.9
and using the culvert invert at the outlet as a datum, we get:
2g
Where: dl and d2 = depths of flow as shown in Fig. 3.4.9
= velocity hed in entrance poolVI2gLSO = length of culvert times barrel slope
Then:
And:
Vl2
dl + + LSO - d2 = Hv + He + Hf2g
vl2H = dl + + LSO - d2 = Hv + He + Hf
2g
From the development of this energy equation and Figure 3.4.9, head H 1S
the difference between the elevations of the hydraulic grade line at he
outlet and the energy line at the inlet. Since the velocity head in the
30221/2840922
entrance pool is usually small under ponded condi tions, the water surface
or headwater pool elevation can be assumed to equal the elevation of the
3-34
energy line. Thus headwater elevations and headwater depths, as computed
by the methods given in this text, for outlet control, can be higher than
might occur in some installations. Headwater depth is the vertical distance
from the culvert invert at the entrance to the wate surface, assuming the
water surface (hydraulic grade line) and the energy line to be coincident,
d l + Y.l2 in Figure 3.4.9.
2g
yl2
f 29 ~=".h-,'ll!..·s.r --.,....------/-----:--... -- f'~:;..;;_-=-_--:;;;::--=-==.:7--~~-'-;------=--:P H
HW dl =--', Hd2..!Ls.
~ ~2 DATUM
+LSo
Figure. 3.4.9
CULVERT HYDRAULICS DIAGRAM
Equation 2 can be solved for H readily by the use of the full-flow nomo
graphs, Charts 8 through 14. Each nomograph is drawn for a particular bar
rel shape and material and a single value of n as noted on the respective
charts. these nomographs can be used for other values of n by modifying
the culvert length for the use of the full-flow monographs as directed in
3.4.3.11 Outlet Control Nomographs.
In culvert design, the depth of headwater HW or the elevation of the ponded
water surface is usually desired. Finding the value of H from the nomo
graphs or by equation 2 is only part of the solution for this headwater
depth or elevation. In this case of Figure 3.4.8 Section A or Figure 3.4.9
where the outlet is totally submerged, the headwat~ pool elevation (assumed
3-35
30221/2840922
to be the same elevation as the energy line) is found by adding H to the
elevation of the tailwater. The headwater depth is the difference ~n eleva
tions of the pool surface and the culvert invert at the entrance.
When the tailwater is below the crown of the culvert, the submerged condi
tion discussed above no longer exists and the determination of headwater is
somewhat more difficult. In discussing outlet-control flow for this condi
tion, tailwater will be assumed to be so low that it has no effect on the
culvert flow. (The effect of tailwater will be discussed later.) The com
mon types of flow for the low tailwater condition are shown in Sections B, C
and D of Figure 3.4.8. Each of these flow conditions are dependent on the
amount of discharge and the shape of the culvert cross-section. Each condi
tion will be discussed separately.
Full flow at the outlet, Section B of Figure 3.4.8 will occur only with the
higher rates of discharge. Charts 15 through 20 are provided to aid in de
termining this full flow condition. The curves shown on these charts give
the depth of flow at the outlet control. This depth is called critical
depth dc' When the discharge is sufficient to give a critical depth equal
to the crown of the culvert barrel, full flow exists at the outlet as in
Section B of Figure 3.4.8. The hydraulic grade line will pass through the
crown of the culvert at the outlet for all discharges greater than the dis-
charge causing critical depth to reach the crown of the culvert. Head H can
be measured from the crown of the culvert in computing the water surface
elevation of the headwater pool.
When cri tical depth falls below the crown of the culvert at the outle t ,
the water surface drops as shown in either Sections C or D, depending again
on the discharge. To accurately determine headwater for these conditions,
computations for locating a backwater curve are usually required. These
backwater computations are tedious and time consuming an they should be
avoided if possible. Fortunately, headwater for the flow condition shown
in Section C can be solved by using the nomographs and the instructions
given in this text.
3-36
30221/2840922
For the condition shown in Section C, the culvert must flow full for part of
its length. The hydraul~c grade line for the portion of the length in full
flow will pass through a point where the water breaks with the top of the
culvert as represented by point A in Section C. Backwater computations show
that the hydraulic grade line if extended as a straight line will cut the
plane of the outle t cross section at a point above cri tical depth (water
surface). This depth is at a height approximately equal to one haif the
distance between critical depth and the crown of the culvert. The elevaton
of this point can be used as an equivalent hydraulic grade line and H, as
determined by equation 2 or the nomographs, can be added to this elevation
to find the water surface elevation of the headwater pool.
The full flow condition for part of the barrel length, Section C, will exist
when the headwater depth HW, as computed from the above headwater pool ele
vation, is equal to or greater than the quantity:
D + (l + k ) y2e _
2g
Where Y is the mean velocity for the net cross section of the barrel; Ke,the entrance loss coefficient; and D, the inside height of the culvert. If
the headwater is less than the above value, a free water surface, Figure 2D
will extend through the culvert barrel.
The part full flow condition of Section D must be solved by a backwwater
computation if accurate headwater depths are desired. Detai Is for making
this computation are not given in this text. Ins tead the solution used is
the same as that given for the flow condition of Section C, with the reserv
ation that headwater depths become less accurate as the discharge for a par
ticular culvert decreases. Generally, for design purposes, this method is
satisfactory for headwater depths above 0.75D, where D is the heignt of the
culvert barrel. Culvert capacity charts found in Hydraulic Enginering Cir
cular No. 10 give a more accurate and easy solution .for this free surface
flow condition.
3-37
Headwater depth HW can be expressed by a common equation for all outlet
control conditions, including all depths of tailwater. This is accomplished
by designating the vertical dimension from the culvert invert at the outlet
to the elevation from which II is measured as ho' The headwater dep t h HW
elevation is:
HW = H + h - LSo 0
All the terms in the equation are in feet. II is comptued by equation 2 or
found from the full-flow nomographs. L is the length of culvert in feet and
So the barrel slope in feet per feet. The distance ho is discussed in
the following paragraphs for the various conditions of outlet-control flow.
Headwater HW is the distance in feet from the invert of the culvert at the
inlet to the water surface of the headwater pool.
When the elevation of the water surfce in the outlet channel is equal to or
above the elevation of the top of the culvert opening at the outlet, Section
A, ho is equal to the tailwater depth. Tailwater depth 1W is the distance
in feet from the culvert invert at the outlet to the water surface in the
outlet channel. The relationship of HW to the other terms in equation 3 is
illustrated in Figure 3.4.10.
f-------=--------HW
JL -----------
Figure 3.4.10
CULVERT OUTLET SUBMERGED
3-38
If the tailwater elevation is below the top of the culvert opening at the
outlet, Sections B, C and D of Figure 3.4.8, ho is more difficult to de
termine. The discharge, size and shape of culvert, and the TW must be con
sidered. In these cases, h is the greater of two values (1) TW depth asadefined above or (2) (de + D) e- 2. The latter dimension is the distance
to the equivalent hydraulic grade line discussed previously. In this frac
tion dc is the critical depth, as read from Charts 15 through 20 and D is
the culvert height. The value of d can never exceed D, making the upperclimit of this fraction equal to D. Where TW is the greater of these two
values, critical depth is submerged sufficiently to make TW effective in
increasing the headwater. The sketch in Figure 3.4.11 shows the terms of
equation 3 for this low tailwater condition. Figure 3.4.11 is drawn similar
to Section C of Figure 3.4.8, but a change in discharge can change the water
surface profile to that of Section B or D.
LSoL--------
de +0--or2
Figure 3.4.11
CULVERT OUTLET LOW TAILWATER
3.4.3.6 Computing Depth of Tailwater. In culverts flowing with outlet con
trol, tailwater can be an important factor in computing both the headwater
depth and the hydraulic capacity of a culvert. Thus, in many culvert de
signs, it becomes necessary to determine tailwater depth in the outlet chan
nel.
3-39
30221/2840922
Much enginering judgment and experience is needed to evaluate possible tail
water conditions during floods. As has been mentioned previously, a field
inspection should be made to check on downstream controls and to determine
water stages. Often times tailwater is controlled by a downstream obstruc
tion or by water stages in another stream. Fortunately, most natural chan
nels are wide compared to the culvert and the depth of water in the natural
channel is considerably less than critical depth, thus the tailwater ~s ~n
effective and channel depth computations are not always warranted.
An approximation of the depth of flow in a natural stream (outlet channel)
can be made by using Manning's formula if the channel is reasonably uniform
in cross section, slope and roughness. Values of n for natural streams for
use in Manning's have been presented in Tables 3.4.1 and 3.4.2. If the
water surface in the outlet channel is established by downstream controls,
other means must be found to determine the tailwater elevation. Sometimes
this necessitates a study of the stage-discharge relationship of another
stream into which the stream in question flows or the utilization of data on
reservoir elevations if one of the dams is involved.
3.4.3.7 Velocity of Culvert Flow. A culvert, because of its hydraulic cha
racteristics, increases the velocity of flow over that in the natural chan
nel. High velocities are most damaging just downstream from the culvert
outlet and the erosion potential at this point is a feature to be considered
in culvert design.
Energy dissipators for channel flow have been investigated in the laboratory
and many have been constructed, especially in irrigation channels. Designs
for highway use have been developed and constructed at culvert outlets. All
energy dissipators add to the cost of a culvert, therefore, they should be
used only to prevent or to correct a serious erosion problem (see Reference
5).
3-40
The judgment of engineers working in the particular area 1S required to
determine the need for energy dissipators at culvert outlets. As an aid 1n
evaluating this need, culvert outlet velocities should be computed. These
computed velocities can be compared with outlet velocities of alternate
culvert designs, existing culverts in the area, or the natural stream
velocities. In many streams the maximum velocity t n the main channel is
considerably higher than the mean velocity for the whole channel cross
section. Culvert outlet velocities should be compared with maximum stream
velocities in determining the need for channel protection. A change in will
of culvert does not change outlet velocities appreciably 1n most cases.
Outlet velocities for culverts flowing with inlet control may be approxi
mated by computing the mean velocity for the culvert cross section using
Manning's formula:
v = 1.49 R2/3 So1/2
n
Since the depth of flow 1S not known, the use of tables or charts is recom
mended in solving this equation.ll . The outlet velocity as computed by
this method will usually be high because the normal depth, assumed in using
Manning's formula is seldom reached in the relatively short length of the
average cu I vert. Also, the shape of the outle t channel, including aprons
and wingwalls, have mucn to do with changing the velocity occuring at the
end of the culvert barrel. Tailwater 1S not considered effective 1n
reducing outlet velocities for most inlet control conditions.
In outlet control, the average outlet velocity will be the discharge divided
by the cros-sectional area of flow at the outlet. This flow area can be
either that corresponding to critical depth, tailwater depth (if below the
crown of the culvert) or the net cross section of the culvert barrel.
31 See References.
30221/2 3-41840922
30221/2840922
3.4.3.8 Inlets and Culvert Capacity. Inlet shape, edge geometry and skew
of the entrance affects culvert capacity. Both the shape and edge geometry
have been investigated by recent research but the effect of skew for various
flow conditions has not been examined. Results show that the inlet edge
geometry is particularly important to culvet performance in inlet-control
flow. A comparison of several types of commonly used inlets can be made by
referring to Charts 2 and 5. The type of inlet has some effect on capacity
in outlet control but generally the edge geometry is less important than in
inlet control.
As shown by the inlet control nomograph on Chart 5, the capacity of a thin
edge projecting metal pipe can be increased by incorporating the thin edge
in a headwall. The capacity of the same thin edged pipe can be further in
creased if the entrance is rounded, bevelled or tapered by the addition of
an attachment or the building of these shapes into a headwall. A sketch
on the nomograph, Chart 7 shows the dimensions of two possible bevels. Al
though nomographs have not been prepared for other barrel shapes, the capa
city of box culverts can be increased at little cost by incorporating a
bevel into the headwall. In computing headwater depths for outlet control,
when the above bevel is used, ke equals 0.25 for corrugated me tal barrels
and 0.2 for concrete barrels.
3-42
DRAINAGE STRUCTURE DESIGN DATA SHEET 1
Location: Township --------Section
Range
Meridian --------
Project Feature: (Project access road, material site access road, etc.)
Station:
Type of Water Course
User Fish Group (A & B Type Watercourse only)
A
I
B
II
C
III IV
Drainage Area: acres
years
Gradient
Q2: cfs
Frequency of Qdesign:
Watercourse Area for Q2:
Watercourse depth of flow for Q2:
Qdesign: cfs----------
ft/ft
ft
Classify channel substate:
Channel configuration: Braided
Other: (describe)
Meandering Straigh t
Culvert Type: Other
Size:
Slope:
V, Q2:
HW/D, Q2:
ft/ ft
ft/sec
%-----------
Length:
V, Qdesign:
HW/D Qdesign:
ft
ft/sec
%
30221/2840922
Attested to by:
Fisheries Biologist
A849/DATA-SH.l
3-43
D~sign Engineer
PROJECT: _
HVDRJLOGIC AKJ CHANNEL INFORMATIOO
DESIGNER: _
DATE:
SKETCHSTATION: _
QI ----~=----
TWI =----TW2 =---
EL.
.r _L-----:--__"'- 1--L ~~
'
so· tEL.__ L .-- I- ELo_7
ALLOWABLE OUTLET VEl.OCITY =
TW_
HEADWATER COMPUTATIONCULVERT
DESCRIPTION
(ENTRANCE TYPE
aINLET CONf.
.!:!.!et. HWD
OUTLET CONTROL
H dd .0
Ke c +HW-H ... "0 - LSo
TW ho Llu HW
1->",I.J-I-
u;:)00';:
>
COST COMMENTS
7{1-------I---4--+---1---4--4-4--1f---+---+---1--I--+--+-__I---+-------Ic
l ~ ...
SUMMARY a. RECOMMENDATIONS:
Drainage Structure Design Data Sheet 2
3-44
3.4.3.9 Procedure for Selectin of Culvert Size
Step 1: List design data. Drainage Structure Design Data Sheets 1 and 2
are provided for this.
a. Design discharge Q, 1n cfs., for required periods (i.e. Q2S
or QSO etc).
b. Approximate length L of culvert, 1n feet.
c. Slope of culvert. (If grade 1S given 1n percent, convert to
slope 1n ft. per ft.).
d. Allowable headwater depth, in feet, which is the vertical
distance from the culvert invert (flow line) at the entrance
to the water surface elevation permissible in the headwater
pool or approach channel upstream from the culvert.
e. Mean and maX1mum flood velocities 1n natural stream.
f. Type of culvert for first trial selection, including barrel
material, barrel cross-sectional shape and entrance type.
Step 2: Determine the first trial S1ze culvert.
Since the procedure given 1S one of trial and error, the intitial
trial size can be determined in several ways:
30221/2840922
a. By arbitrary selection.
3-4S
b. By using an approximating equation such as to = A from
which the trial culvert dimensions are determined.
c. By using inlet control nomographs (Charts 1-7) for the
HWculvert type selected. If this method ~s used, an D
Z~must be assumed, say D : 1.5, and the given Q, a trial
size ~s determined.
If any trial s~ze ~s too large in dimension of limited height of
embankment or availability of size, multiple culverts may be sued
by dividing the discharge equally between the number of barrels
used. Raising the embankment height or the use of pipe arch and
box culverts with width greater than height should be considered.
Final selection should be based on an economic analysis.
Step 3: Find headwater depth for trial size culvert.
a. Assuming INLET CONTROL
(1) Using the trial size from step 2, find the headwater
depth HW by use of the appropriate inlet control
nomograph (Charts 1-7). Tailwater TW conditions are to
be neglected in this determination. HW in this case ~s
found by multiplying ~obtained from the nomographs
by the height of culvert D.
30221/2840922
(2) If HW ~s greater of less than allowable, try another
trial size until HW is acceptable for inlet control
before computing HW for outlet control.
3-46
b. ASSUMING OUTLET CONTROL
(1) Approximate the depth of tailwater TW, in feet, above
the invert at the outlet for the design flood condition
in the outlet channel. (See general discussion on
tailwater, 3.4.3.6).
(2) For tailwater TW elevation equal to or greater than the
top of the culvert at the outlet set ho equal to TW
and find HW by the following equation (equation 3).
where
HW = vertical distance ~n feet from culvert invert (flow
line) at entrance to the pool surface.
R = head loss in feet as determined from the
appropriate nomograph (Charts 8-14).
h = vertical distance in feet from culvert invert at
outlet to the hydraulic grade line (In this case
ho equals TW, measured in feet above the culbert
invert).
So = slope of barrel in ft./ft.
L = culvert length in ft.
(3) For tailwater TW elevations less than the top of the
culvert at the outlet, find headwater RW by equation 3
as in b (2) above except that
h =o
2
or TW, whichever 1S the greater.
30221/2840922
3-47
30221/2840922
where
dc = critical depth in ft. (Charts 15 through 20 Note:
dc cannot exceed D
D = height of culvert opening in ft.
Note: Headwater depth determined in b (3) becomes increasingly
less accurate as the headwater computed by this method
2v-falls below the value D + (1 + Ke)2g- . (See
discussions under 3.4.3.5 Culvert Flowing Full with
Outlet Control.
c. Compare the headwaters found in Step 3a and Step 3b (Inlet
Control and Outlet Control). The higher headwater governs and
indicates the flow control existing under the given conditions
for the trial si~e selected.
d. If outlet control governs and the HW is higher than is
acceptable, select a larger trial size and find HW as
instructed under Step 3b. (Inlet control need not be checked,
since the smaller size was satisfactory for this control as
described under Step 3a).
Step 4: Try a culvert of another type or shape and determine s~ze and HW by
the above procedure.
Step 5: Compute outlet velocities for s~ze and types to be considered ~n
selection and determine need for channel protection.
a. If outlet control governs in Step 3c above, outlet velocity
equals to' where A=/Zo ~s the cross-sectional area of
3-48
30221/2840922
flow 1n the culvert barrel at the outlet. If dc or TW 1S
less than the height of the culvert barrel use Aocorresponding to dc or TW depth, whichever gives the greater
area of flow. Ao should not exceed the total cross
sectional area A of the culvert barrel.
b. If inlet control governs 1n step 3c, outlet velocity can be
assumed to equal mean velocity in open-channel flow in the
barrel as computed by Manning's equation for the rate of flow,
barrel size, roughness and slope of culvert selected.
Note: Charts and tables are helpful in computing outlet
velocities. (See References)
Step 6: Record final selection of culvert with size, type, required head
water, outlet velocity, and economic justification.
3-49
3.4.3.10 Inlet-Control Nomographs
Charts 1 through 7
Instructions for Use
1. To determine Headwater (HW), given Q, and size and type of culvert.
a. Connect with a straightedge the given culvert diameter or height
(D) and the discharge Q, or ~ for box culverts; mark
ZWintersection of straightedge on ~ scale marked (1).
H~b. If D scale marked (1) represents entrance type used, read Dn gz~
o scale (1). If another of the three entrance types listed on the
nomograph is used, extend the point of intersection in (a)
horizontally to scale (2) or (3) and read D. Compute HW by
ZHZWmultiplying D by D.
2. To determine discharge (Q) per barrel given HW, and s~ze and type of
culvert.
HWa. Compute o-for given conditions
b.HW
Locate n-0n scale for appropriate entrance type, If scale (2)
30221/2840922
HW. .(2) or (3) is used, extend o-po~nt hor~zontally to scale (1).
HWc. Connect point on n-scale (1) as found ~n (b) above and the size
of culvert on the left scale. Read Q or %on the discharge
scale.
HWd. If a-is read ~n (c) multiply by B (span of culvert) to find Q.
3-50
3. To determine culvert size, given Q, allowable HW and type of culvert.
a. !£ii.Using a trial size, compute
HWb. Locate n-0n scale for appropriate entrance type. If scale (2)
or (3) is used, extend ~int horizontally to scale (1).
c. Connect point on ~ale (1) as found in (b) above to given
discharge and read diameter,height or size of culvert required for
HWD value.
d. If D is not originally assumed, repeat procedure with a new D.
30221/2 3-51840922
FORWITH
CHART r12
600 ( I ) (2) (3)II500 EXAMPLE 8 9 10
10 400 5'12' eoa 0.75 ct. 7 80/8 • 15 ctt/fI. 7 8
679 300 ,/ll.t - MW 60- ' ••t 5 6
(t) 1.7' 3.5 58
200 (2) 1.90 3.8 4 5(3) 2.05 4.1 4
47 3
33
I- 1006 0
0 QIl. 80 2--......a:: ~ 2IIJ =.Q. 60 2S <II /1-Il. 50
/' ~ 1.5oI-
~ 40 / IIJ 1.5IIJ :x: 1.5IIJ
"'/Il. CD Il.
~ 4<, 30 p- O2- -.*",1- (/'I
§ :x: ,,7 ~l-
X 0 20/a::
0 IIJ 1.0CD ~ I-
0 ZIl.1.0 100 I- .9
3 /IIJ .."...~ :x:l- I-:x: /' "" .IRq_.O Q.
"" a:: 10 F'lar. --... IIJ .8 .9 9IIJ -: ct 0:x: :x:-: o 8 a::
<II IIJ8 ..J'-: Q .... .7 -4
-: Il. 6 ~
0 0-: 5.!:!.!. scs L E WINGWALL 4 .7 10 IIJ
~ I- 4 0 FLARE :x: .64a:: (I) 30· '0 1'-
3(2) 90· on4 15· .6 "6(Jl O· (1II,nllon, - .5
2ot l,di.l)
.5r. "•• Ical, (2) or (3) O',oj.e,"0'1'0".1'" fa leI', (I). ,1\,,,10111 ,'rolCaf'l' InClln.ct 1:1", rhrOUQn .4o anCi Q Icot••. Ot "W,tI, QSill".t'OU4.
.8 .4 4
.6
.5 .3035 35
HEADWATER DEPTH80X- CULVERTSI NLET CONTROL
3-52
1M 10,000CHART 2
I" 1,000 EXAMPLE (I) (3)
15. ',0000-41 I...... (3.S , ....
144 5,000Q-120 aft L
1324,000 y.- HW 5.,...3,000 (II 1.5 I.'
1204.
2,000(II t.1 1.4
loe(31 t.1 1.1 4.
'0 I_ ,... 3.
9& 1,0003.
80084
600 ,/'/·2. 2:-
500//
72 400 2.enl.&.I 300 9"V% ~~(,)
1.5 1.5
! en / en
&0 II. 200 /a::
z o l.&.I 1.5
! /....- l.&.I
e 54~
/ 2<
.... sa:: /~ 100l.&.I 48 !> ./' a:: 80...I ./" <::)
%
(,) ~2 ~ 60I-a. ~J \.0
II. en 50~
0 0HW ENTRANCE 0
a:: 40 o SCALE TYPE a:: 1.0
l.&.I 3&uJ
I- 30.... .9 .9
lIJIII Sq"art -.19' .lth C
2 33h,a4.all 3t .9
<0
a 20 (2' G,oo•• '''0 .,t" <
30 hea4••11lIJJ: .E! a
(3' G,oo...n4 .8
21 ptOl'Cli".
10
24 8.7
.7.7-
6 To u" Icol' (2' 0' (3) pto,IC!
21 5 hot llOnl ally to scol' (I). tI....
4uti It,ol9h! i"clt",4 Ii", tMou9h
o 0"4 Q Ical ... O' ''''t It ~. .63
II,,,.'tOU4. .6
18.6
2
1.0 .5.5 .5
12
HEAQWATER SCALES 2 t13
REVISED MAY 1964
HEADWATER DEPTH FORCONCRETE PIPE CULVERTS
WITH INLET CONTROL
3-53
CHART 3
151 I If3000 EXAMPLE
SiI,; re"...1"Q. 500 ctt (2)
13el I., 2000 (3)..t:\1*' HW
0 (f ...) ( I ) 40
121 a 71 (II Z.I 11.11.(2) Z.2 1.1 4.0 3.0
113 a12 (~) Z.~ t.Z3.0
"'0 i" f.,t3~loeael
...--- 2.091 a 83 -- 2.0
fo...---
91a 51400 .->1.~"" 2.0-- 1.500 Q 1.5
83a 53 -- )--- 1.5...- 200 :z:
Z ....To u...eol. (Zl "'(~I tJ)
.... _ • ""it/t' 11ft, ac:4- eni: I&. 100
tlltevtft .,,_ '0"''' I&.0 of .... 011" 'itc""9' 0..I ! 80 •• iftf.,••ct Icof. (I ) .
1.0 1.0
• tJ)
> - F,_ poi,,, 011 ••'"" (II :I0 eo a38 2- 60 ....j .., " ....0111111' It ac: .9 .9I&. .... .....".... 011 •••"., ICO" .... .90 " 50 (21 or (~l.
t-
- ac: z• 40 ,.... 53134 .8 ~
II) :z: :z:ac: 0 30 t-Il)
JC 49 a32 Q4-....
Z 0 .1 .7
• 20 .74- 45129 ac:II)
HW/O.....- ENTRANCE ~....
N 42127 SCALE TYPE • .8 Cu; 0 6
10 (I) Squo,. "9' ."" •....38124 8
n•••waU :z:(21 Groo.... _ ..,"
8 ...0...11 55 (3) (jto.....ncs 5
4OtO,ICltll4
30119 3
.4 .4 42
8 1S 0
1.0_1
23114
HEADWATER DEPTH FOROVAL CONCRETE PIPE CULVERTS
LONG AXIS H'ORIZONTALWITH INLET CONTROL
IUll(AU OJ' IOIJIC.IC ~I JAN. 1M3
3-54
\.014a23
CHART 4
'711 IS''000
4000 EXAMPLE (2)1711136 (3)3000 s"•. s.· I 10· 6
Q. 200 eft (I) 65
11lL12\ 2000 ? HW 5('''') 6 ..
12 lL 113 5 ..III 21 IS 0(I) 20 '00 368 lL 106 ..
1000 (3) 21 10 S 3_
63 1'8 800 it 0 ito ' ••t3
600 ./' - ...... 2--258 a 91
/" -500 ./" QI/) 400 ./" ... 2w 53 a 83 ~...,~ J: 1.5-J: ~ 1.5C,) 300 ./"!.
---w
48a16 -ZOO !! i.5! .--- II:
W --- I/) To w.. ac.l. (21 0' lSI ~
ea. 43lL 68 ./" ~ 4'... tttal9ftt "". 0i: ./" C,)
.",........ft • .,. veh,•• I/)... ./" Z .f "10 .'u, d'ieft.',• 2..-/ 10O II: 1.0 1.0• »> (; to ,,,,,,,,c, Ic.l. (I) .>~8.60 ,,_ ",to' Oft ,eel. II) W
0 - 80 l-~ W .",.C, hOIl"""'" to !
9 90 <:) 60 .O.... hOft Oft ., ."., Ie aM
a:: t2l 01(3)• 50 8 pw 34 a 53 J:!! C,) 40a:: I/)
JC32.49 a 30 .1 1
Z HW!O ENTRANCE II:w• 29a 45 SCAL.E TYPE l-ea.
20 ceI/)~- 6 .6_
I.I,j(I) SCI"." let,. w. ,ft Q
N27 I 42 h......u •
\I) I.W121 Grone .". w"" J:
10 ".Od.....24.38
8(S) Gtoove .".. 5 .5
'f"II''''''65..
19.30 4 43
2
HEADWATER DEPTH FOROVAL CONCRETE PIPE CULVERTS
LONG AXIS VERTICALWITH INLET CONTROL
3-55
CHART 5
<lOT'0,000 ( I )
'SI8,000 EXAMPLE
6,000 0.36 i.chel (3.0 I.et) 6.(2)
1~65,000 Q. I' eft (3)
\44 4,000 5. 6.
Ittw' ttW
132 3,000 T (I.." 6.2 ~..:_- -
(I) 1.1 5.4 4.-- -<,)
120 2,000 (21 2. I 1.3 5...... 4 .c (31 2.2 6.6
108 ...Ia. 3. 4.
...I'011'1 hit
C
96a: \,000 3.:l... 3-o 800:la:...
84 '" 600 2.
I500
400 /' --..,.I 2. '2
72 /'/(/'I
I 300 <3I.IJ j::: I (/'I /'
1.5o :::~ --l \0.
~ ....<r../(,)60 (/'I 1.5 1.5
~ ~ <r..;."y a:
,,/I.IJ
§ 54 ~to-w
to- W~
a: \:le:t
I.IJ 48 a: 0> e:t...l ::: Z::l
/~1.0o ::: I';
~42
./" 0,..c,
0/ w . 10 .
a:: a .9 .§I.IJ
36 HW ENTRANCEto- SCA .. EI.IJ 0 TYPE ....
to- .~~ 33
e:te:t :1) "tad_(UI ~ .8 .80
a30 121 -..it."c2 to c~nforrn
e:t
$UJ ato IIQIU :r
<.>
Q 27 10 (3) P'OI'~" I'IQ
a: .7 .7c 8Q;Z - 24 .7:: 6<II
5 To uti Ical, (2) or (31 CHOI'C:
2\ 4 hOllzon'aUy to leol, (I), thin 61&" ,'rait'" .ncllnld lin, fhrQuqft
.6
3 o .1nd Q ICOl.l, or r,.",.. 01 6
18illus,rat.d.
2
l~
_. -' .'3- ....5
1.0 5
12 HEADWATER DEPTH FORC. M. PIPE CULVERTSWITH INLET CONTROL
9URE Au OF Pvlll.IC ROAO' JAN 1963
3-56
CHART 6
.35
(I).-4 (2)-jr------4'--' l3l
r-s
r4
3
-F-t
2 I- 2
1.5
1.5 ~ 1.5
.AI ------a 1.0
1.0~ 1.0:. i- .t .,1MCIt .s.,ar:
I- .•~ ••lit ••2ar: I- .11M .1t-Z .7-
%:t-a- •• .11MQ
••ar:
iQ« .51M .5 .52:
I- ••.4
.4
.35 .35
1-1-1rnHEADWATER DEPTH FOR
C. M. PIPE-ARCH CULVERTSWIT H INLET CONTROL
1.0
••I." , II·
s.eee
J' ..·.,..10'·'· 4,000
la'·4·. "-S· 5,000 EX.....PLE
SI••: 31'. u·Z,OOO O. to .f.
• '1'-!d.I'-.·!U U' N_
I) '....,15 ...II'·S", 1'·5·a~ (II 1.10 1.0
I;' 1.000(II 1.1t 1.1
100 131 1.11 •• 2
.~, ••••• "-S"
100 wI) I. f ...,~ SOO~... S"Z" , S'·," 400en
1. 3001"0", S'-I"
200
1'-,· , 4'-1·~ar: "~ ./,
,/1M72",4."
C/) 100 ,/a- li.a: ~10 ,/
! ",/II. .5",40" +''70 - 10 "io~g
50 /'1M1M ,/C/) 5.",3.·
i: '" 40 ,/ar: ,/.. ~ ./2: 50 ,/z ~
~ 50"' 31" C/) ,/a- a io~1M ./' -? SCALE ENTR"'NCEN 43"' 21" TV'I;; ,/
/" III .......H./ 10a ./' III .. It...... _f...
I,) ,/ • te Me,.
Q/3.", 2a·
I. """'1"a: •cQ 5zc.. 4<It
T.... _I. Itl .. (SI "'1...2,""r s ....' .....11' ,••••,. (II, ,...........,11' I..UaM II...tlt.....
I)'" 0 •••,••, .. r........
Z5" ,I'· I III...,.,...
••.S..AOOfTIOMA1. !lUI NOT OIMDISlONm &filE
L.IITID I" 'A.AlCATQft'. CA1*.~
3-57
CHART 7
.6
.1
.6
.1
A •3.6 3.0
3.0
Q• 2.0:
Z.O ;;/I:1M...w 1.5:I
1,5 caz:~Q"
""0II:
""~.. 1.01.0 !
cw: .9
~--
• .8
•• t t • I.'••••n ...
0...1 o.4MJ 0.'" 00" •.... 0. III 0. 041 0. Itt •IIVILU.............u. JOO·
--l1."~'- --~----o
2000
1000
100
600500
400
300
'10I.15.
I."131
120
101
9.
8.
11InW:uz 60!S 54~
II:4'w
~;:)U... 410II:W~ 36w:Ic 332i~-21
24
II
II
15
ItHEADWATER DEPTH FOR
CIRCULAR PIPE CULVERTSWITH BEVELLED RING
INLET CONTROL
3-58
3.4.3.11 Outlet - Control Nomographs
Charts 8 through 14
Instruction for Use
Outlet control nomographs solve equation 2, paragraph 3.4.3.5, for head H
when the culvert barrel flows full for its entire length. They are also
used to determine head H for some part-full flow conditions with outlet
control. These nomographs do not give a complete solution for finding
headwater HW, since they only give H in equation 3, HW = H+h o - LSo•(See discussion for 3.4.3.5 Culverts Flowing with Outlet Control).
1. To determine head H for a given culvert and discharge Q.
a. Locate appropriate nomograph for type of culvert selected. Find
ke for entrance type in Table 3.4.4.
b. Begin nomograph solution by locating starting point on length
scale. To locate the proper starting point on the length scales
follow instructions below:
(1) If the n value of the nomograph corresponds to that of the
culvert being used, select the length curve for the proper
ke and locate the starting point at the given culvert
length. If a ke curve is not shown for the selected ke,see (2) below. If the n value for the culvert selected
differs from that of the nomograph, see (3) below.
(2) For the n of the nomograph and a ke intermediate between the
scales given, connect the given length on adjacent scales by a
straight line and select a point on this line spaced between
the two charts in proportion to the ke values.
30221/2 3-59840922
(3) For a di fferent roughness coefficient nl than that of the
chart n, use the length scales shown with an adjusted length
Ll• calculated by the formula
See instruction 2 for n values.
c. Using a straightedge, connect point on length scale to size of
culvert barrel and mark the point of cr os s i ng on the "turning
line." See instruction 3 below for size considerations for
rectangular box culvert.
d. pivot the straightedgeon this point on the turning line and connect
given discharge rate. Read head in feet on the head (H) scale.
For values beyond the limit of the chart scales, find H by solving
eq uation 2.
2. Values of n for commonly used culvert materials.
Concrete
30221/3840922
Pipe
0.012
Boxes
0.012
3-60
30221/2840922
Corrugated Metal
Small Medium large
Corrugations Corrugations Corrugations
(2 2/3" x 1/2") (311 xI") (6" X 2")
Unpaved 0.024 0.027 Varies*
25% paved 0.021 0.023 0.026
Fully paved 0.012 0.012 0.012
*Variation in n with diameter shown on charts. The various n values
have been incorporated into the nomographs and no adjustment for
culvert length is required as instructed in Ib (3).
3. To use the box culvert nomograph, chart 8, for full-flow for other than
square boxes.
a. Compute cross-sectional area of the rectanglar box.
b. Connect proper point (see instruction 1) on length scale to barrel
area ~/ and mark point on turning line.
c. pivot the straightedge on this point on the turning line and
connect given discharge rate. Read head in feet on the head (H)
scale.
~/ The area scale on the nomograph is calculated for barrel cross-sections
with span B twice the height D; its close correspondence with area of
squart boxes assures it may be used for all sections intermediate between
square and B = 2D or B = 1/2D. For other box proportions use equation 2
for more accurate results.
3-61
I ! ~ ~ i\ ,. o .. o .. .... .. ".. t
DIS
CH
AR
GE
tQ)
INC
FS
Ivr
II
II"
"1
1'1
'1'1
"1
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l""1
i'
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llil
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AR
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."".....
_""•
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_0
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'" So"-
+"t
~
~...,
~'t
.'-
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'~~
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:.\ "" \•
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EE
T
\\ \\
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\,..\
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<"0
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w'b
\
00
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\
o o z o ::0"1
"1...
.-t:
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DO
°G
lOo
X"
-"
0l\
leO
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....e
rr < 1"
1::0 -t (J
)
w I '"N
CHART 9
'0' Qu"a. eroWft 'tot Il.Ibm."e4, com,,,t....w by""'fMOI dnCtlM. 1ft ' ... d"I9ft ptoc.4ute
20
6
6
8
4
10
6
.5
- :i
··10
/g-+ =1:
SlOp. 50- ~OuTL£T CUl.v£IIT FLOWII<G FVI.L
·MW. tot. "0-\..50
"" -.-, 0
o ~
~
5ue.,£/lG£O
.,0, \.._110_
---~~ 00. "
2000
1000
800 120
600 106
500 96
400 64
JOO72
66
200 60U')
U. 54o
~U')
uJ::J:
0 '"- 100 ZuJ ~;
42I.:la: 8 -~ .;:)::J: J6
'" - 60U') a: J3uJQ 50 l-
..... JO40
:!<l0 21
3024
2021
18
10 15
8
6 ,2
5
4
aUlllAU 01 _I.IC ~.os ,.1< .963
HEAD FORCONCRETE -PIPE CULVERTS
FLOWING FULLn : 0.0 12
3-63
...
CHART 10
2000
'01' ClYlfe' era... "0' w."'.,...._COM,v'e H. by........ dHCltM4f ... ' .... ".'9" ","OC••..,.
---4
8
910
to.•
0.5
06
0.7
0.8
0.91.0
-%:-QC
"'"%:
. '0
7
~• •Q~ .,0
~• ·0.~
510'. 50SUIM(ItGlO OuTLET CULV( liT FLOWING FVLL
Jo4W. "'.1\0-\.$0
~3.
0"1""8'0'" Of'! .. ,. Icole 0"ot_.nd for IOft9 al.e l'lo'I,Oftfol
.,,"oUO"O" Th" tfto",ld b.
r~.".4 fot lon, :1111 ..."hcol
----------
1000
800
151.97
800138.87
500121.71
400 113.72
10••••300 98.83
91.58
200 (I) 83.53lU
(I) %: 78.4.II. (,)(,)
~Z
~sa. 43.
- -..i'!.l.9.0 -- _lU &0-38lU 100 !:!? --I:l Ill: --Ill:
80 53134C •
~;;%: Z(,) C(I)
&0 CI.Q (I) 45129-SO lU 42127N
U;40 38124
30
30 I \~
20
23.14
10 20
8
HEAD FOROVAL CONCRETE PIPE CULVERTS
LONG AXIS HORIZONTAL OR VERTICALFLOWING FULL
IVII£AU OF "VILle "0.605 .4".19413 n • 0.012
3-64
CHART II
2000
'0' 0",11" ero.., "" ........, •••, c:oift ...', 11'11 ty"",trloda ~"Cfl". IIfII 1M ca••,t" ~OC'dwe
SIO". 50-SU."EI'GlD OUTl.ET CU\.VE I'T FLOWING FUl.l.
HW. H+ 1\0-\,.5.
20
8
6
4
10
2
LO
.4
i "0
!HW
1000
800
600 120
500 108
400 96
300 84
20012
U
60III\I,. 54o~
100 III\0.1 48:z:
0 80 <.,)- ~\0.1
42<.:) 60 ~cz:
50 0~ 36:z: -o 40 cz:III 33Q Q.35 \0.1----~
30 \0.1 304 'l.1:I~ ..-f1Q
20 24
21
10 18
8
6 15
5
412
3
2
HEAD FORSTANDARD
C. M. PIPE CULVERTSFLOWING FULL
n·0.024
3-65
L
CHART 12
6
Fo, oull,t crow" ItOt ",tlm,rqlct, comout. HW 'by1'M'~d. dnCtlMd Ii1 1"4 4.I.q" 1)(0c.du,1
- .5
6I-u.I 1u.II&. 8~ 9
:r.: - 10.-
7
1
8
-9
10
Slap. so ....SUIIII("GlO oun.er CUI.V£llr f\'ow.NG FUll
w..-,. M~ 1\0-1-50
300
200
'"! ...:It :ItIE oJ:l..
10090
80
1012"X••"
60 6~"X 40"
~O J:o ~X36"a:c(
In 40 •S,~~
I&. Q";7Q~(.,) --a:: ~0":'(31"
~30 I&.
(5 0..... 43"X21"u.I u.I
Cl Ina: a:c( 20J: )(
o ZIn0 ~ 36"X 22"
In
u.IN
In
10 29"XIe"
9
825"XI6"
1
6
5
4
IlUll(AU Of ~u8llC llOAO!l JAN 1963
HEAD FORSTANDARD C. M. Pt-PE-ARCH CULVERTS
FLOWING FULLn =0.024
3-66
CHART 13
F.....'let cro_ ...t c.... ,.". w.., Ily""ft.~. _1_ '" tftO ~ proc_to
2
4
6
15
1
8
9
10
20
I
::I
Q4....
o+.'~",.p
o.",
q,g~o
~ f::'--;::OY ,0
...J...
5000
4000
3000
180
1682000
154
144I;f)....:: 132Q~
1000 ~ 120
I 114800 Q
108I;f)
700 II:.. .... 102Q I-600 ....
~ :I 96..0 !l00 Q 90
I.... .oJ<:)
400.. 84
a:: Z --..:I:: 78
Q 0 »>I;f) zQ 300
2
66
200 leo
10030
Di.",. ft
" 0.03217' 0.0320
10' 0.0311I" 0.0302
40
50
HEAD FORSTRUCTURAL PLATE
CORR. METAL PIPE CULVERTSFLOWiNG FULL
n· 0.0328 TO 0,0302
3-67
f'000
2000
CHART 14
.IT ~ :-1=:Slope 50-
SU8Mt:"G(O OUTLET CULYE"T FLOWI~G FULLHW_ H""o"L.So
'01 outl,t era .. " "ot ,ubm"9Id, compute HW bymeU'OCiI <t"CtlHd 1ft ,,,_ cS"14ft procldu,.
<16.6 I 10.1
-to (C'1-:O~; ,,0 G'-\
1000 ->. '<ZI-
1~.3 I 9.2LoJ
( 00 '"LoJ 2
I-
o'~1.1.
800 lW =lW '9" ~,\ I
1.1. 12.9 I 8.3
,0~ , ,00
J:
=I
0
600 J:~ :3lW
(Il o ::I:1.1. a:
.< /\~' \o !l00 ~ I 1.4 I 1. 2
•= lWI CL \,..\1'Z.V ,,-00 \ \.~ 4
0 400 a:I y/ \'lW 1.1. 9.5 I 6.4 .... 0. , \
<:J 0 sa: - .y c \ ' \-~ lW f). ., r-, .l" '\
J: 300 ~10' ,}' I r 't 1\00
o a:8.~ I
Ex .... "LE ~ \- \ 6(Il 5.8 ' .0 -'" Q. 280 C~
Io4t 6 I J:'T<loOO -\ \\z / ,
'r t.~ • \..f/l '!l00 j
8
200 .....1.0 I 5 IlW 9
~(Il 10
6 I I 46 Sir.6.1 .4.6 0,032 '... •. 1 I '.8 0.0321
z 11417.2 0.031 , 15::i 16.6110.1 0.0308
100
20
HEAD FORSTRUCTURAL PLATECORRUGATED METAL
50 PIPE ARCH CULVERTS18 IN. CORNER RADIUS
FLOW-ING FULLn=0.0327 TO 0.0306
3-68
CHART 15
.~
-----~
:..---, I......../""
.-.-V I ; -I ~ ....
CRITICAL DEPTH -I ./ _-l---!__ ! :I
i/ RECT~N6\JLAR StC7~ON
/! I I I I
I ..-t--l. ._+-_.-i i I '
4
....u. 3z-
u 2'"0
oo 10 20 40 50
r--.-'." '---~---1
,--- ------
: q! N C.F.S. ! I
! I I I 1 i i I1 1
I !
\ I i ; ;I I /
I Ii ,/ !' .
I : I ! V II I
I I
~'I I - -!~.!
: ; I
........ I..........._-I
I ! I! I I i 1
!I
I I I I! I II1 I
!
i I i i ~ iI
: I
I I I1 ! I
i ! I I
I I :I
i ! i
I : !
I ! i
I
iI
i ;i! !
I I
i II Ii
I
i I
II Ii i
i : iI
:i
) I I
)
16
15i ! I
i i
14 1
l- I Iu. ,Z 10
u"0 9
e
7
6
e
3002150-
I i I I ,: '; !150100
de C~NNOT EXCEED 0
4 --..""O-"""-~-.l. -.l. "'--I--'---_ -....__
50
-NOTE·
8UA[AU OF PUBLIC qoAOS ...... 1963
3-69
CHART 16
2
~ Ii-~"
......:~3,~EXCEED TOP OF PI PE iA ~ de CANNOT
~~2,O II.~
61,0'01••
I10 20 30 40 50 60
DISCHARGE - Q- CFS70 80 90 100
i II ~ ! I i I !
,I I II i
, i ---I Ii
~~ :, i i
~! I I,
~~l/~~ I !~r Ii I
~~V ~~I-+ I,~~
-.g, y- 7'1 i i ! Ii ,
:/~i8' i I I I I I/h I de CANNOT EXCEED ToP OF PIPE
id:Y~7' I II I I I I I i-6' I i : ! i I
~~,
i, , ! i ! I !
I "rI : , I i'OIA. I I ! I
6
ILIJLIJl.I.'u 4~,1:I-Q. 3LIJQ
...Jq:u 2I- 0
a:o
100 200 300 400 ~~0 600DISCHhRGE' Q -CFS
700 800 900
8
7
II.IJ
6~,
1:~ ....• Q.
I.IJo...Jq:
1000 :::I-
er'.J
14,..----.....--------..,-----.,..-....--....------,--,---....---.,....-....----,
400030002000DISCH ARGE· Q. CFS
+--+-"""7""'~ .--r-----"----l-~. -~---I--_-;i
'OCO
8 r--+---~-+--r-_t"7?"'b-'''::>_'"'--------+---
I
6 t---t--+-~>4'_-F--'-"l--.........--+--_+_-r--_+-..,.._-dc CANNOT EXCEE0 TOP OF P.:..;IP~E'-i'--lI I
I
I 2 r---r-----_+-+---+-.........--!--!------+----
r--------- --+-1-..,..---+..-------
BUREAU OF PI.;8LIC ROADS
JAN. i964 CRITICAL DE PTHCIRCULAR PIPE
3-70
CHART 17
18016014080 100 120
DISCHARGE- Q-CFS
604020
~~~ I
~P"
..".
.-'~.,..., ,
",V ! ,.A ,
# ./", i I.
~/" I
~I
~~ / I 1!
A ~v ,-+-
~~V de CANNOT EXCEED TOP OF P1PE !I
'---+--/-~~V I I I
i ;
.i//A~68"143" : II-
I ~'i "I :0.4"I IIIf! .....9' I ! !
38"129"iI !
" 14' I ! I_III !
: ! , I ! I
3.0
3.4
1.0
2.0
...L.IJL.IJ"I<,)
"CII
%
~ °0L.IJ
'0
,i
!!
400 500 600
OISCHARGE-Q - CFS
4
I ~~: ..........VII r 'l"--
5 1--l--+_.........-+_ol--+-+--+--+---:~~:;.~r-=~~::7""'~=t'-+_! ~--"-~~~: I; I
l--l----+-~_+-r__1___+___".6"""""""'--1r""_ ___i~-+--_+-+1,- - '--:---1' ----
'
I I ~~:::"''''--L/! ! I ,
I, ~V---:I./ ~ ,-- I I .I .#"~V-",V ' I I: i [ i .
.--,: _~~i I : dCICAN~(CE~D TrO~"'''1---
3 ~V:' ! 1---: I:: I
! j'j10'1'" 15;i97i ' --;-- I ~r-+--· /AV· I I I ! 1 I . ; I
2~ '2"x77I, ,. ,IOS"xq8' i ! i ! I I
91' 1 5 01 I ,I I --l'-"---~-··76"1148"60"138' i I;·
Bu REAU OF Pl.i3Li C ROAD S
JAN 1964CRITICAL DE PTH
OVAL CONCRETE PI PELONG AXlS HORrZONTAL
3-71
CHART 18
I I ~-- I i II
i~-rI i i I
i~! -b::::===
! I ! - '-:;;.- r-rr III --I ~~~- I iT I
~ ; i
.J~~ ::/:~..--L.
I i ::.,....--~-:'I-~~V "-i I
-+--i I II I iI
~~-97'.151' I +-f _CAM"'~_ ~'C:~ TO', 0, Pi77'.12" t !
~--68·.106· I53'. 9" I
-t.'-4S0.76·
I I 1 .38'.60" II I 1 1_- _+_~ __I I i i i
i J.-~
::::::: ::::-- i-~~~r::::~ ..... I
~~V"V ..... ! -i--'---:%V V 1
I
~1
I I I
~Y ""-,-
~ i I II
i I
~~~43·.68" I I 1 I iIde CANNOT EXCEED TOP OF PIPE.-Ae'i; ,....,. I I)
29'.45' !24'.38"
I H+-,4".23'
;
4
2
.... 0t:: 0u..Iu~,X....Q.LLlo..J<.to~~ 10o
8
6
4
2
20
100
40
200
60
300
SO 100 120
OISCHARGE-Q-CFS
400 500 600
OISCHARGE- 0- CFS
140
700
160
800
\80
900
200
iooc
BUREAU OF PUBLIC ROADS
JAN 1964
3-72
CRITICAL DEPTHOVAL CONCRETE PIPELONG AXIS VERTICAL
CHART 19
240220
50
200
.~--+--~
180
----4--------._---_-_de CANNOT EXCEED TOPOFPIPE
-,.-----,.--~
-----'------r--~~. --,-'-~---l
i . i i . ._..--------------------...~..
"'t'" "--'--- -.---- •• - - --------.- ------.
80 100 120 140 160DISCHARGE-a -CFS
20 30 40DISCHARGE-a- CFS
'/;~-...;.....--..;.---- ------ ---
. ,- -- ----....... _- -------..--~---+---~
---';"-.-+--- ---_. -
--- .....- -+0----, I
--=----+-----,-_.-.-- -- ---.-
604020
_.. _- ----------- --'-'-..-,---
t-.L..-l.--+-l-+-->--+--+-f-+-+-+-1r-+-+-+-1""7~I!f--h""':;:---+---r-,-~.,.
2.0
1.8
l- 1.6loWloWU.
I 1.4"'til"I
1:l-
1.2a-w0
..Jc( 1.0o....a::'~ 0.8
0.6
040
34
32
3.0
... 2.8ww 26u,
,;,,, 2 4
1: 22I-a. 20w0
18..Jc( 16oI- 14a::o 1.2
1.0
0.8
0.60
BUREAU OF PUBl.IC ROADS
JAN. 1964 CRITICAL DEPTHSTANDARD c. M. PI PE- ARCH
3-73
CHART 20
.......-;:;:" lA'"""",."..
,......~~ ~ ..... I
.JJ'~ ~V V !
~~ V l../, ,
/ ~ '/ ./V I
~V '/ ./fI" ~ I
/" ./ V V i I
V /,
~V
/ V /'v: ,/' I ,
V / ./ /,/
/ V V -/ I I i
i/V! / V I I ,,
/ V!/ / de CANNOT EXCEED TOP OF PI PE ! ! !//'./.....r I I I
,V/ / fr'!~o. S'-5" I I
I/~~g-rl~':9:
I I I....... -O"l}-I"
,....-~61_f·141- .!II
f
I I ,:
... 4LIJLIJ........"a•:z::...~ 3Q
..Jc(Q...a::Q 2
Io 100 200 300 400
OISCHARG:::· Q·CFS500
--r t---+.----'-+--4,
f .
t---+--+--jJ¥--#.....,.--+-+--t--t--~---I I de CA'INOT EXCEED TOP OF PIPE, : 1
r--~~-------~--t-"""7"!--7"If-7+-~'--- -- ---- --
f--+----1---+---!--------...-,...-----+-~··-----~I-+,
9
aII
-!
7
6
16'·7".10'-1'3 1---+---..,..:6JLi~JIf- 15'· 4', 9' 'J="~i--"""'-'--r---+-~-----....--+--i.--i.---'--i---+--l
12"10",8'· 4'11',5',7'· 3'
~+-,-g.:rE:9'-6"'6'- 5" !-+--+---l--+--+--t---t-----r-...-----'---r--+---+-......--t---+--i
2'-..u..'-I---l._1o--_--'----"__"""--.:...__~-'-.......---l_.:-.-.:...._J.,--l_~...J__J.,___:.___lo 200 400 600 800
...LIJLIJ....' ...
"CI,J:...Q.
LIJ
Q 5 I-........-...-------::'""~""""lr_~'-J------+----~ ---~--.o..-_-___i..J-<(,J
t:41-........_-_-h'-,~.,..,...~----- ......-+----.-....a::(,J
BUREAU 01: ;:>U8,.C ROADS
JAN. '964CRITICAL DE PTHSTRUCTURAL PLATE
C, M. PIPE-ARCHIS INCH CORN!R RAOIUS
3-74
3.4.3.12 Performance Curves. The principal disadvantage in using
nomographs for the selection of culvert sizes is that it requires the trial
and err or., method described in the text. Some engineers who limi t their
selection to a relatively small number of types of culverts would find it
advantageous to prepare performance curves such as shown in Figure 3.4.12.
These curves are applicable through a range of headwaters and discharges for
a length and type of culvert. Usually charts with length intervals of 25 to
50 feet are satisfactory for design purposes.
Figure 3.4.12 is plotted from the data shown in the following tabulations.
These data were obtained from the nomographs contained in the text.
(Computer programs are available from Public Roads for making these
computatios). The first tabulation is for the inlet-control curve on Figure
3.4.12, and the second tabulation is for the outlet-control curves.
Data for Inlet-Control Curve
HW
HW* ~ HWX 4
D (Read) D
.5 21 c.f.s. 2.0 ft.
.6 29 2.4
.7 37 2.8
.8 46 3.2
.9 56 3.61.0 65 4.01.1 74 4.41.3 90 5.21.5 102 6.01.7 112 6.82.0 126 8.02.5 145 10.03.0 165 12.0
* From Chart 5 Projecting Inlet (3)
30221/3840922
3-75
DATA FOR OUTLET-CONTROL CURVES
Q dc d c+D H HW for Various So
2
(Assume) Chart 16 (Compute) Chart 11 % .5% 1% 1.5% 2.0%
*20 cfs 1.3 ft. 2.6 ft. .2 ft. 2.8 ft. -40 1.9 3.0 .8 3.8 2.8 1.8 .8
60 2.3 3.2 1.9 5.1 4.1 3.1 2.1 1.1
80 2.7 3.4 3.3 6.7 5.7 4.7 3.7 2.7
100 3.1 3.6 5.2 8.8 7.8 6.8 5.8 4.8
120 3.3 3.6 7.5 11.1 10.1 9.1 8.1 7.1
140 3.5 3.8 10.2 14.0 13.0 12.0 11.0 10.0
160 3.7 3.8 13.6 17 .4 16.4 15.4 14.4 13.4
30221/2840922
2
* From Chart II - or by Equation 2.
The curves plotted apply only to the type and length of culvert shown.
Culverts placed on grades steeper than about 2.5 percent will operate on the
inlet control curve for the headwater-discharge range of this plot. If a
free outfall condition does not exist a correction for tailwater should be
made an instructed in Step 3b, 3.4.3.9 Procedure for Selection of Culvert
Size.
3-76
HYDRAULIC PERFORMANCE CURVESFOR
48-INCH C.M. PIPE CULVERTWITH
PROJECTING INLET
~.VIJI// If
s « ' I /'/3 O' il? 0 J I/ 0" ~ol
I/VIL~'/'1/VI
/1'I/;v I
I '/i,/ I1,
,I;Iii ! !
I l, ,,-
LIMITV '/,
.750:3' :.... ~ ke =0.9I"" / r I
/ n =.024 IJ LENGTH -:. 200 ft.
/ --;NLET CONTROLI -OUTLET CONTROL
I NO TAILWATER I,I 2i<) HW=O+(I+Ke}-L,
29
9
2
oo 20 40 60 80 100 120 140 160 180 200
DISCHARGE (Q) CFS
12
10
"
-~7J:-
Figure 3.4.l2
3-77
PROJECT: /42 £3 ._- DESIGNER: ..I..o.~
DATE: 2-/8-64-
HYDROLOGIC AND CHANNEL INFORMATION SKETCH
STATION : 32./ + 14-
EL.~
A:vt~L ~ -la, = /60 c.f.s ~ Q ti O TW, = .$.0. .l- ------
EL./ool
TWL.Q2 = TWz = So· .o//.
EL.;]tL :: -;;;0 ,
( a I : DESluH DISCHARGE. SAT QZ!I ) MEAN STREAM VELOCITY = B!~
°z = CHECIl DISCHARGE. SAT o~ OR 0'00 MAX. STREAM VELOCITY= /O'/SIC.
HEADWATER COM PuTA TlON<:t
CULvERTz ....J
INLET CONT. OUTLET CONTROL HW=H + ho -LSooJ 'l ... !:
DE S,.HIPTION Q SIZE ~ x .J,", COST CO",,"ENTS.. 0
.!::!..!. ~.. :;).J
IlHTRM'~E TYPE! HW :<e H de TW ho LSo HW s 0'"0 2 u >
1---'---' ._-Ic..,.,p (..', r) -- N_ ........ ,.....
~-(( /60 .$4" lSI. 71:1 e s '. "r-ry .... ~. - ..
:5 &.:./,.,..,./ ,w.,..
" 1..0 48 225 90 .S 85 3.7 3.8 38 /..0 //./ /11 (~~
- '" - rrr -S4"
.. ..3.6 .II .3 4./ /.0 7.B /1,( ~
",.I.,.,.y .,. til,'60 SJ / 5" 70 . .5 4. 7 7.8 ,5 •'s••.•.
(0 ,~ "'-- - -!
--- -- I--Co-:rtr-re C ..... / .. H .... it.y"
~. 4'd'f~ -#"'~/ / "- ;. .48 z 35" 94 S 47 3. 7 38 .3 3.8 /.0 7S' 94 /4; ic:. r.,.., S~ ..~--- -'~-- - -
t...h'...v 0.<
" /60 .:> ( leO 7.Z ,...29 36 4/ 3 .1../ /0 60 Jz. /47 ~....~~";;D_.......
--;:;",. c r" Ie--z;::-: r~). -_. - i -
~N""" ...:
<ireQ"e ~"d ·1.0...160
48t q
<78 ·z 10 3.7 3.8 3 ".8 /.0 '-B 78 /40.
",~I -t . .,;,r'-----.----- ----- - - ---
I"
-- - .. --~-
SUMMARY a RECOMMENDATIONS:
-'----- --_._.. -- - _..._----------- - J
3-78
PROJECT: E /4- -.2 (.5) DESIGNER: ~P.e
DATE: 2-20· 64
HYDROLOGIC AND CHANNEL INFORMATION SKETCH
STATION: 8+.,
EL.~
/
~f /AHW=JLJ
/
~Q, - 400 c../~ Qso TW1 = 6 S' -L_ ----.....-......-- TW .". ..s-O2
- TW2 =El./OI/ SO" "':'!:y;I.
EL..u1 T-
L;:~'
( ° I = Ot !>IGN DISCHARGE. SAY °2~ ) MEAN STREAM VELOCITY = S '(..s.c.°2 = CHEc.l( DISCHARGE: • SAY 0!l0 DR °100 MAX. STREAM VELOCITY= /J! '/.s.c
H(ADWA TER COMPUTATION~
CULI/ERT ! ........J ",'::
INLET CONI OUTLET CONTROL HW=:H ... ho -LSo...J ~DESCRIPTION 0 Silf ~ z
... u COST CO...... ENTS... 0..dC+D ... :;,...J
ttNIRAN(f IYPl) ~ HW t<~ H de TW ho LSo HW ~ 0'">0 2 0
c....... "" .. (c, .... )-
N-./ = 9./As.s",.,.4', S"d P,. •.., 400 /s j#;- Dc 78" r... J,.·.44;"" ac'~--- . ..-- --- ~--- ----~- r--- - ,--
Hvv N,.,,,..400 84' 118 83
r;.."" 90".--I ---1---- _._-1------ .- .- - .
.111;' rf ~... I."C.fc'c. x.«... ..;.:",,"'a 90..
/c:JS: 79 ·2 /9 sz ~3 6.s 6.S 6.0 Z4- 79 rry Z P'IPIJI ".. iG .. o.e~- .~ .. --1--.•_----1-----1·- ,-_.. _~
s .....c 1"y,...c 1'i:oo ~./I'Z jO';o<!:-S Z-oo 54 /US' 8.3
- 1--" - - .-- -1----- ---_.z.:s i lice. r c:; Void
" Z. G>O in- " .Jd fo 9 z: ;'54 4.0 4,S 6S 6,S 60 .59 '9 "0' ~c.. O.C:; .$••<::__,,.6
'--- . f-.- ... - -,.' f--- _._- '\.~ ., .. -- ..c,., C~P 14',(. e<- r c (..t.se (J~v,1 A
&".., a (I:-,r7) Zoo 60 " 54 67 zs . Z 4.0 4S D·S 6.S' 60 6.7 67/0/
C..,. b, ,,_• .4'''1:10:<- 0.<:
~-- ..- - --- - 1--.- -- _._.."4 'I it'" 1".,. bo' s''''J /~ c .. ' ~ c: rc v .. I .., ... • r,,1 Q,,,J <:~
SUMMARY a RECOMMENDA 110NS'
..
l -"- ----- .._------- - . . .-
3-79
PROJECT: r,s·z. DESIGNER: .I.. ",. H.
DATE: z· Jl' .•~HYDROLOGIC AND CHANNEL INFORMATION SKETCH
STATION : :I'~ "0
EL~
•..J=~".L ~ l-°1 /z D et··· Q,zs TWI = $.0, --L- ___
=Oz= TWz =
EL901 So· ~y. EL:J ,-TW~
L=~'
( 0 I • DtSIGN DISCH..RGE • S..Y Ou ) MEAN STREAM VELOCITY: ,~ '!SIIe.0 1 = CHECK DISCH....GE. S..Y 0 50 0fII 0
100 MAX. STREAM VELOCITY: /s Y.sec.
CULVERT HEADWATER COM PUTATION ~~~:::l
INLET CONT. OUTLET CONTROL HW=H + ho -LSo ..J 31 .... !:DESCRIPTION 0 SIZE iz ..JU COST CO....ENTS~o
g dC+D ...~;:IENTlIl ..NCE TYP!) HW Ke H dC TW hO LSO HW ~
,D > ,
2 u :eM'" (Ci...,) ~ "- N_ ",.~.. i,"""lwrwJ 1%0 :r." /.2$ s. '- ~ : "-"y Nil
,
II ~
~JN • ." ___
t, ,1..0 .0 .91 4.9 .7 .l.s 3.0 4..0 3.0 .... 0 leUJJI
4.9 c:._.~.~
C_P Arc" 1a .... ~ ~ .::4...... .-.,.~.,I'r""; ',"0 ~.H /'Z4 4." .7 '.4 2.4- 3.0 3.0 $.0 "'.0 4.6 , C.,/...... .,.
C.AC,..... lie" 4' ~ l/ZO..
1.:13 4.9 .4 Z.e 3./ 3-S ".0 s.s 1•. 0 ".9.50· 'tN. \N. ~' '\: ;;:
C.A~-"" 0<1.' 6u *. ~~ ~<fr. 1.-1 P,*v'. /20 "8" /.S/ 4.8 .2 2.9 %·7 2.9 .5.0 .3.0 / •. 0
"4.8
c_... h c,·..~~
\I
, Z'".
/. // S.O /7 3./ 3.8 3.0 3.8 '0." So~_~,.t:I S10qj $'-1- .%~
\0..~ i~
SUMMAID' a BECO-MM€NDATIONS:IN-PLACE COST, AYIILABllITY, LOCATION, COVER REQUIREMENTS, ETC., SHOULD BE tONSIDERED BY
THE DESIGNER IN SELECTING CUl HRT. CM PIPE 'RCH CULVERTS OR ';ONCRETE OYAl PIPES MIGHT BE A SOLUTION WHEU COYER IS LIMITED.
3-80
30221/2840922
3.4.4 Bridges
3.4.4.1 General. This paragraph will present the design criteria appli
cable to the locating of the bridge abutments and substructure, wnich
constrict the waterway, to insure hydraulic conditions for safe a structure
and the efficient passage of fish in watercourses that have been classified
Type A or B. The criteria for fish presented in Table 3.2.1 and a depth of
flow 50% greater than that specified in 3.2.2 Inadequate Water Depth shall
be required during the two year flood.
The criteria for design discharge determination shall be in accordance with
the applicable portions of 3.3 Drainage Structure Design Criteria. The
watercourse bed stability at the critical section should be investigated by
either of the methods indicated in 3.4.2.1 Permissible Velocity Method or
3.4.2.2 Tractive Force Method.
3.4.4.2 Hydraulics of Constrictions 1n Watercourses. When an area con
striction is introduced to an otherwise uniform, friction-controlled flow in
prismatic channel of mild slope a backwater profile is first developed
upstream from the constriction. Please refer to Figure 3.4.13.
3-81
Section(0)- B
«": .., Eddy zone'0..- '
T <-1-"(1) b ~ (3) Ccb (4)
1__---1-
......-:::;:- Live streom bO\lndary
",-
t ~ddY zone... I-
(u)
Note:horizontal scale distorted
Datum
(0)
~
Backwater profile
Normal profile ~i'lh
I'h;...J,..---
...."-
he=hl .o( Y.=Y3hon=htn r h4=h 3n
Channel bottom (zero slope /.
Datum-
(e)
n
Figure 3.4.13. Definition of flow through constriction. (a) Plan;
(b) elevation; (c) elevation, adapted to assunption of zero
friction loss.
3-82
_lzF_TYPE I
Type I opening, vertical embankment, vertical abutment
TYPE D
Type II opening, embankment and abutment slope.
~@\______J--- TYPE m ~--------
Type III opening, embankment and abutment slope/
Type IV opening, embankment slope and vertical abutment with wing
walls.
Figure 3.4.14 Constriction Types
3-83
The upstream end point of the backwater curve is assumed to be at section O.
Near the constriction at section 1 the central body of water begins to
accelerate. An adequate approximation for the location of Section 1 may be
taken at a point one opening width b from the center of the opening.
At the constriction, the flow as rapidly varied, characterized by marked
acceleration in directions both normal and parallel to the streamlines. The
longitudinal water surface drops rapidly in this region. Within the con
striction, the live stream contracts to a width somewhat less than the
nominal width of the opening, and the spaces between the live stream and the
constriction boundaries are separation zones occupied by eddying water. As
the water passes through the contraction, the contracted stream reaches a
minimum width at Section 2, which corresponds to the vena contracta in an
orifice flow. After the vena contracta, the live stream begins to expand
until it reaches downstream Section 4, where the uniform-flow regime is
reestablished in the full-width channel. Between Sections 3 and 4, the flow
is gradually varied. Over the whole reach from Sections 0 to 4 encompassed
by the backwater effect of the constriction, the total energy loss is the
same as that for uniform flow.
The equation for the discharge through the constricted Section 3 ~s
1 Eq. 1:
Q = CA3 [2g ( h - h +f
1/2
30221/3840922
A3 = area water prism at Section 3
VI = average water velocity at Section 1
hf = hydraulic friction loss between Sections 1 and 3
C = is an overall coefficient of discharge
3-84
Eq. 2:
The overall coefficient of discharge C is calculated by first determining
the Ct, the coefficient of discharge standard value whicn is a function of
the physical type of abutment configuration along the flow lines of the
constriction. The types are shown in Figure 3.4.14. The coefficient C' are
dependent upon two factors; m the precent of channel contraction and L/b the
ratio of the width of the abutment parallel to flow and the width of the
constricted opening.
The value of M may be calculated by:
K
m = [1 - Kl
+ KC
+ K ] 100%r c
where K refers to the conveyance capacity
Eq. 3:K = 1.486 r 2/ 3
nA
30221/2840922
and subscripts L, rand c refer to the Sections at 1 to the right of, left
of, and the constricted section.
The overall coefficient of discharge C is now determined by adjusting C' for
the effects of secondary variable by multiplying C' by the appropriate cor
rection factors k.
A listing of these corrections follows:
kF = a coefficient that adjusts C' for the influence of a nonstandard
value of F
k = a coefficient that adjusts C' for the influence of angularity of
flow
3-85
ke = a coefficient that adjusts C' for the influence of angle of wing
walls
ke = a coefficient that adjusts C' for the influence of eccentricity
of constriction
kj = a coefficient that adjusts C' for the influence of piers and
piles
kr = a coefficient that adjusts C' for the influence caused by round
ing entrance corner of abutment for vertical-faced constrictions
k t a coefficient that adjusts C' for the influence of submergence
of bridge members
kw = a coefficient that adjusts C' for the influence of length of
wing walls
kx a coefficient that adjusts C' for the influence of the ratio of
distances x/b (See Fig. 3.4.19c and Fig. 3.4.20c)
k y = a coefficient that adjusts for the influence of ratio of depth
of water width to opening,
y ya + b
2b
The C' values and the correction factors can be obtained from the Figures
3.4.15 to 3.4.23 at the end of this Section.
It is possible that certain combinations of the empirical coefficients
applied to C' may appear to yield a value of C greater than 1.0.
cases, however, a value of C = 1.0 should be used.
In such
30221/2840922
Referring to Figure 3.4.13 in designing bridge opening for the maXimum dis
charge we are concerned with backwater profile or the surcharge above the
normal profile and the depression in the normal profile at Section 3. The
interest in the former is to see whether overtopping of the banks occurs and
3-86
TABLE 3.4.5
Key to Tables for C' and k Values for Each Constriction Type
k k k~ k k k k k k kType C' F P e j r t w x y
Type I 3.4.15 3.4.15B 3.4.16 3.4.23 3.4.23 3.4.15 3.4.23 3.4.15A B D A C,D C B A,B&C
Type II 3.4.17 3.4.17 3.4.23 3.4.23 3.4.23 3.4.188S=1: 1 A C A C,D B B
Type II 3.4.18 3.4.18 3.4.23 3.4.23 3.4.23 3.4.18wI 8S=2: 1 A C A C,D B B
ex>--.J
Type III 3.4.19 3.4.19 3.4.23 3.4.23 3.4.23 3.4.1988=1:1 A B A C,D B C
Typed III 3.4.20 3.4.20 3.4.23 3.4.23 3.4.23 3.4.2088=2: 1 A B A C,D B C
Type IV 3.4.21 3.4.21 3.4.21 3.4.23 3.4.23 3.4.238S=1: 1 A B C A C,D B
Type IV 3.4.22 3.4.22 3.4.22 3.4.22 3.4.23 3.4.23 3.4.238S=2: 1 A C B 0 A C,D B
SS = Sides lope
the latter to determine water velocity at Section 3.
obtain a relationship for h.
By adjusting Eq. 1 we
Eq. 4
h F = b ( Q) 2j'kl K3 + L
the distance section 1 is upstream of the constriction, generally
where hF is the friction loss between Sections land 3 and may be calcu
lated by:
Eq. 5
where; b
equal to the breadth of the constriction
L = the length of the constriction
Kl & K3 = are the total conveyances of Sections 1 and 3 respectively
In Figure 3.4.13 the increase hl* in water surface from the normal stage to
the backwater stage at Section 1 is known as the backwater of the constric
tion. The distance h is the difference in water-surface elevation between
Sections land 3. The ratio hl*/ h is called the backwater ratio, which is
known to be a function of the channel roughness, percentage of channel con
traction, and constriction geometry. A laboratory investigation (Reference
7) was made on the backwater effect due to vertical-faced constrictions with
square-edged abutments. Data plotted in Figure 3.4.24 indicates the rela-
tionship among backwater ratio, Manning's n , and contraction ratio m, It
can be seen that the channel roughness is relatively unimportant as a factor
in determining the backwater ratio. In fact, the limit or change in the
backwater ratio due to roughness is practically reached at an n of about
0.050. The previously cited laboratory investigation also reveals that the
influence of cross-sectional shape on backwater ratio is included in the
contraction ratio.
30221/2840922
3-88
The backwater ratio in Figure 3.4.24 is for constriction of basic type, that
is, for a vertical-faced constriction with square abutments. The backwater
ratio for other types of constriction may be obtained by multiplying the
backwater ratio by an adjustment factor ka• This factor has been found to
be a function of the contraction ratio m and the ratio ct c .bas~c
Cbasic and C are, respectively, the discharge coefficients for thebasic type and for other types of constriction that can be determined by the
method described in the preceding text.
obtained directly from Figure 3.4.15 a and b.
The value of Cbas i c can be
Based on experimental data,
3.4.25.
the relationship among ka, m, and clc .bas~c ~s shown Figure
3.4.4.3 Procedure for Design of Bridge Waterway. The first step is to list
design data. Drainage Structure Design Data Sheet 1 is provided for this.
a. Design discharge Q i n cfs, for required periods (i.e. Q50 or QIOO
etc. )
b. Establish constriction type, (I, II III or IV) breadth of constriction,
length of constriction and the constriction centerline relative p r i.n-
cipal channel water prism. In watercourses with fish, Type A or B see
1.2 Scope, it is preferable that the abutments or piers fall outside of
the two year flood channel. This will avoid the need to undertake an
analysis for the two year flood.
During the field investigation the watercourse should be surveyed at Section
1 (a distance upstream of the proposed constriction equal to the breadth of
the constriction) and Section 3 (at the downstream end of the constriction),
refer to 3.4.2 Waterways. The field investigation should also determine
30221/2840922
Manning's n, the slope between Section 1 and 3, and the substrate classifi
cation for permissible velocities or tractive force calculations.
3-89
c. Determine a rating curve for the reach between Sections 1 and 3 using
the average of the areas and hydraulic radii for several depths includ
ing the design flood depth.
d. Calculate the conveyances K for Section 1 and the constricted channel
at Section 3 and the ratio Lib (embankment and constriction breadths).
e. Calculate m (channel cons t r ac t i.on ) from conveyances K (Eq. 2) with m
and Lib go to figure for constriction type (Figures 3.4.14 to 3.4.22)
to determine C' the coefficient of discharge (standard value).
f. Determine if the constriction type or location require any modification
to C' i v e , c' x k , kF etc. = C.
tion for modification factors.
See Table 3.4.5 for figure loca-
3u221/2840922
g. With nand m given enter Figure 3.4.24 to determine h1*1 h. (If the
constriction under investigation is not Type I a C' and kF are deter
mined for the m, Lib and the Froude number in Figure 3.4. IS' a and b.
The C' x kF C is used with C de termined f. In Figurebasic in3.4.25 to obtain ka· k a times h1*1 h will give the corrected
hl*1 h).
h. Witn the value hl*1 n estimate h (Trial starts 0.9 x (VI ~)2~g
A3and calculate hl*
1. Calculate trial A3 using depth of flow calculated in c less ( h - hl*)
which is Y3.
J. Using Eq , 5 and 4 and correcting C value in Eq , 4 for Froude number
kF calculate h, if value agrees with that assumed in h, the solution
is reached. If not repeat h , i and j with a new estimate of h.
3-90
30221/2840922
k , When solution is reached check V3 velocity per tractive force or per
missible velocity criteria, if satisfactory or close to satisfactory a
analysis at the 10 year flood may not be necessary.
1. For fish watercourses where the two year flood water prism is con
stricted, perform analysis a thru j to determine that velocity V3 does
not exceed requirements stipulated in Table 3.2.1.
3-91
COMPUTATION OF PEAK DISCHARGE AT CONTRACTIONS
--.-------,[Iz If---r-TYPE I
008030 "0 50 SO 0.Pltc'" of ~ c,",,,oct ..
A. Baa_ curve (or ~oefflci_nt o:C diacharC_
20
-"
... "I I I Ir- _ , "I... - l- I"'- lo- I
..... "'- I
t- - -~T-~--,
. 1-- -1- -
" r--I-- - 1-.....l-- l-- l0- t:-"",r-:-l.: I-tJ +t' I-'~~... I-- l-- 1"- q= -LCiiiI±"I-- ~ -:-, ' n"",
lo- - - -s_ co.... itt....
+0 f·o ; I ;-.::Il !ll ........1.J)zp'
F·O.S •• I I --r- .. 0 j'O , :
: ,;., ;
7 90 I
1.00
1i~!t 0.70ic!-U
1.I , , , , i....-i"'I .....-r I
i , I ......-f" ; I II ! : I ! ~ ,
I
I i 1 I I ! ~r-r I , II. , l-f+±.. .l.-l- , I I
I : : I
, I , .---J-o+- , ! I I I iI J...-j...- I , i I I I ; : , ;
I I I, ,I I I I I , I ,
o oJO 02CI 0.30 0."0 0.50 0.60F. Fr..... .......or •.,.9-A.llih
8. VariatiOD ol diacbarl(e coefficient wi.th Froude number
0.70 0.80
.20
=tc/'I' '!lO....
I I '---+-" I<r:..-1 .-'- I I
IS f- ._ L __ ~~ I
, : I :....1- : I I !'",=- ,
i I i I i~ I :
".i
I- '_f-o: ! I i I : :-Q , I I _I ,
I
I I.10 : ,I ; I !
r/ I II I I
I I , : :~ I I I I ,.os i I I I ,
~, , I
, I
I7f I , ,
1\,1
o 0.0& 0.04 0.Q6 0.01 0.10 0.12i' Aet" of cor"" ,0000clilll' 1o widt' of 0"*"''''
C. Variatioo at diac:ha.rae coefficient With entrance round1nc
0.14
Figure 3.4.15.--Type 1 opening t vertical embankment t vertical abutment.
3-92
DlSCHAIlGE·COEFFIClENT CURVES
oo..o
o...ci
,,
1
I~l-
l-f\ - ... i;
I' ~l;V~/ ~.
f'-
E.\ l-
I ! r-.1
! I I I,
I , ,I
!
~9,
'....•. .-T -
1 !o9: .
.J-
Ia
I- ,!!, ..
,. ,, 0a
-- :: ,, I
8I
,-+- d
, , ,-- , ,
I I
I , I ..
~, , :;
, ; , ; ,
"', , I ,
1, , ,
~ ri .v , ,~i, ~ I i\
~~~1
" I
, Ii- I <, "\! ,i-
,i- ;...;.- - ~ +. 1-- "'-'\
: N ,Si- t .~e
+-- I
I'-.J+--~,
I"
0
Figure 3.4.16.--kw and kep curves for vertical
ment of Type I opening see figure 3.4.23.
and abut-
...~..
o 5a ~
g
~¥:
embankment
,,
I
II0 .. , I..i : I
:~H, ..... 1 , :_+ I
,1 I I
i !I "I,
I I :1 I
I i I
I i\ ,
: :
~~I
\\1 I
\i
-h~ ~ \ II '\t ~/I I
I 1
I i r, Io
II
1
1, 1
,1
! I1
H I1 I
~L~,,
! I
-Il- ,
1i l
I"1 I "- i
I '\.\ ,,!I
1"\ 1\
!-:\
!! 3 -
3-93
COMPUTATION OF PEAK DISCHARG£ AT CONTRACTIONS
5, :
I , ~-- ...- If, I
I r-H-, I
I
:
90 '00so
i ! ! I~-L +tI : t
I ,
, (
;.t !
I . t-'I ;-1.. ....'i i
~ ~ ~ 80 roItt. ",rc••t· If eftGft"" COftt,octl ••
A. Baa. cut:ve (or coeCCiclent of discharge
20'a
1.00~iiifii:;;:r:r:'T'"""'~""'-'-"""irr--""""'~"""-:-""""'n-:-nITrrTrTTnTnTnlnrrl
:.t O'80I---l--..,...++.........--1---+_-:==r-r--==:::::::::-f::::::::.l~o::::l::::~rr=H-++~~~~'il..
~- 0.20 0'" ol>o>o_.
-... I I 0.1 I
~ i-..i.. r- ...... ~ -i-+-; It ; I i
~OTt -.. r-~ I I : - 0.'- I
;~~ -~r--lL....,........
-TO.01-r ,-f-.- : ! ! :
I :! I ~ -l. ~ -;--+-~
I .05 :..- --i t .. -.-I 0.03 I
,i j I [ ,
i I I ~ .... -+1 i . ----:-:-- ':--n-I , , I i I rt !I I I I I-. f I I ! ! I I I ! I I I : . I I I' ., I
1.00
l<.y O.9 0
0.80a 10 20 ~ ~ ~ 80 ro
m-Perc.nt of eM""" contractionB. Varlatlon of discharge coetttctera with Ya")b r at io
--zo-
eo 90 100
0.9C H-t---r++-H-+-++-':"'"1.......-+-::?"""''-t-'--:--''--'!-::;:.-''f-+--t-----f--'----I
o.so~-++++-+-!-+++-.;....:,.....l.--+O,.....=;-......-+-+..;....-f-
30 ~ so 60m. Pt!rctnt ot ,,,onntl controctioft
C. 'IIlriation ot discharge ccerftc ient wah antularity
Figure 3.4.17. --Type II opening, embankment slope 1 to 1, ve rt ieal
abutment. See figure 3.4.23.
3-94
DISCHARGE-COEFFICIENT CURVES
TYPE II
.....~- ... ,..1- I, , , ,
i \- ... 0_' -r-I- l'"o!'-.... I \ \ I I iI I I ... "- ;... I i ! I i :
I I I !-- ;... "- 't.: I.O~ I I I : I I Ii I
, ! """' .... ;-. N--o.:.. I I , ,i I i l' I ~""'" 0.50 ............. II
~I·Ston_.._ ......ltl... I , i :-.... -""'" I i ! ~ ..... I I !
I : , ~
~I I -
Ef~.0.20 • '1.00 I , I I i"'o!-- !""I.-.l.....[ I I
•-0· I I I Ii"".... , , r - .-o0li--....._-,... o.Z ,. 0.7 ! , I ,
~ I
I,.
r-L ~.O I ·0I I !+! H-<-
~ 's • I t i !-f-
~·tI I i I I I i
,I
, , I I I i I
~ 1.00
i"_I.-
0.'0
I PC I
;;;
'; 0.10
i!...oo'y 070
o 10 20 ~ ~ ~ ~ ro1ft. Pilre"t fJf eMMet COfttroctl..
A. Bu. curve for coefficient of discharie
eo 90 '00
'0080
~ 020 .... -.
30 40 30 ~ 70III' ,..,_ of _ ...." '1.
B. VariatiOl1 of d1acharie coefficient ith Ya'Yb ratio2i)
2010
- • .......1
I C""~ ---..:~ I i - i ! i I i I i I I I I I I I I i I I I I i --;-I
I :--.... ""':"4- I
I ; I ........ ' ; ~ , i ! I I i : ; , I ,.O~ I
I i I i -.... II I I , I : I I r I ~ .... I ! , ! , '1 0.03, : I ,, : I : , I I I
I I I i ,-
, I, ! , I I I i I i I I i I I, I I I, i ~....L.-...-
j I i I : I I I I ,I I I I I r f I ,
I , I! , I ,TI i I i ,
I , I i I I , i
kyO.sO
0.10o
1.00
eo7020 ~ 40 30 so".-Pete" '" eM_"" coettecU_
C. Variation of discharge coefficient .... ,th ancularity
.. .0-," 0- I , I ~ ! /"'f
~t t....- /.I ! I I I I I I , I I ! I A !AI I ! : 2(/ I I I ! .:.....-' -- -1 :7! ! , ,
I I , I i -:A I 1./1 , ,!
I ! I , : ! V I Y1 I I
I I I I I , I : I ~, A , I I
.... I - i I A I I I I I ! : I: I I I i I ! I I Y I
~~I t- i~-l- ;; -:-
I I vr I-- -t-, .LI ! 'A-'"- I ------!
.-~, I I
1-M [\ -'-I .L--- ,I I
! - ! ! I I -......- , I I ,
... ;. - , ! I , I I ,0 10
1.00
0.10
0.70
030
Figure 3.4.18.--Type II opening, embankment and abutment slope 2 to 1,
vertical abutment. See figure 3.4.23.
3-95
c.~ ~i.-...L.----------- TYPE m
~1"'---
I
I I II I I
!,
1 1 I i
i , I
I . l I
R
, 1
...--~.---,- , , ,
i ;~- t· ~~+H70 so 90 100
---! I i I--. --,.......
40 50 60",.Perc ... of eftc",", 'GfI~octi ...
A. aue curve for coefticient of diecharae
i.... I I"N. : .............. ! I
20
I i I I iI • I.... ,
i... ..... II , I I
I " I 1"'-,..... I I I I
... ! I I -....:. Ii I
,
10
I
so
f..
fIi-
".-ri~+-
i
2l) 30 40 50 60
~.PI~t of ~".. COfttrlctio.B. Variation of diacharge coefficient WLth angularity
, I~-
'-0'-
II 1
o 10
o.'0~~~~~~~~tdRt1;1L.-l""'1++' ·1·+·' I Vf iLL l-L.LLL I t., i-
k. F rL i! f 1H1 IR++- r r*flilH _~._oao8f J..1' iii I I+1- r 1\
1-H--I-+:~+:;:-t.t...?_i"9-.t f I [I l' ,(..~ ~ t,' r-t -I r t r r"', 'H-- b-\..~ .~ l. f-tr I I t-r' rT;! 1 r
0.- .-:- I 70
..-
r- f ~ -1t:·-IIi :
0.12 0.14
I iI I ,_! T--
0.100.04 o.~ o.~
t.II- of I '0 ....111 of ''''''''C. Variation of diecharge coelticient With .!..ratio
b
0.01
1.10 1~!li,
....~~ -f t l rtf 11 II i I I i I I Hf-T-+++-H'++-~
I-+- -
100 ~o
1.20
Figure 3.4.19.--Type III opening, embankment and abutment slope 1 to 1.
See figure 3.4.23.
3-96
DISCHARGE-COEFFICIENT CUR V ES
o30 40 50m.~c."t 01 channel CQftfroclion
A. Baa. curve Cor coefficient of discharge
2010
-,. ....- , , , I ll+r-::k=c -II! Iix-I'o.. ';". 1-1-l r~ t1 I I
I ! Ii
I~'l-, ~, I : i I I I ! I~" ,~..[ !"-. , I I :
,L'I ;~~-~- ~-:- - ,
~+--I- , ... ,~
, :-- ......... , , , I
", ".J. j .... ,...",,1 I~ .~ ,-... , --~- it- -- ..-+-I , I I
, .... -.... i-;"" , r-<.. ' l"-..... : ~ I t---..L.-
~H '" ....... ' ....... ., --. --- .0<1
I ........ ;-;....;.. -- ,....... ' ....... -....... --- i ------I i t
-H-t , ,'"""
......... -- - - osc"l , L' I ~~~- - - --L-o.4~ ...;.;' ~.;.....-::;::I , I ,eOftdltiOftI I .
i+--- ! --cl2J I i-S' .....d ttl ; I : ; r--' -,,. 0.2 '0 0.7 '-0· t r r : I ! ' I ; In,; ! f
0 I , , , 1 I,-lOO i' O ~- .. "---r-
"-; ,it- t. • I I I ! , , , ---1-.0 j'O I i i ; I
! I : i -I, ,"..~ I I ! i f I ! --, .-rTT r-tt I
, I I, ,0
60 70 80 90 10
1.00
o.so
I·0.90"!..j,:
c 10 80
;;;1;
1~ 0.7
~
7020 30 40 50 eo1ft. PwCllftt of d'IOI'tMt eontractl<ll
B. Variation or discharge coefficient wtth angula.rlty
10
<t. n--
1=60-';,1.'1;."" - .....-- I , ./, /' ,/,! I > i , , I I , , .... I ! /" V, ?rll
, ...- ; , .i., : .A-: I !...-r , ./,
, y, 1 , ! . ..:-~ , L/(i t- ----;--;---L......__.F... !
I, , , ! L
I , ; - I ; »« iiI
: I , ! ...- I, I ..r --:-:- - -1---- ----1-.; ~ ~ i i- ~ i Hiit
./ : \I ,.. , f ;
i
! ~- iI , , ' ! I ~, I f _.f ' i-r- i-H.....r I I
! i r-I... ..._t~ 1 ,I ,I I I , ;
80
1,00
0.90
0.80
0.700
0.30O.O~ 010 0.15 020 0.2~
1-- Ratle 01 1 to WId'. (ff 0ttt'Ifti""C.. Variation ot di.charge coeffici.nt with .!-ratio
b
~ "llI I I I , , , ! I
-F!-1.1 I i : I , , : ,i , i I ! :
I -" -+ ...L..i.l '- f-+ f-l-! t l. ~-~---~ . I I-\~ I !
, i! !.~ .±J:~ +- , Loa .;...l ! I !
to 1'0..~
I
II ,-.+-1._I
I ~o ~,' ............... i ! I i ,
-;.t- t-- --- I j-- fI....
.!--;- ! 1 !
....r- +t-+- I f I -:.- , ,II
115
1.'0
I.O~
1.00o
Figure 3.4.20.--Type III opening, embankment and abutment slope 2 to 1.
See figure 3.4.23.
3-97
_~..~~ r'-- _
1001IO~ ~ ~ ~ roI'll- Plre ...t 01~ COI'trOC'f'tcM
A. Baa. curve for coefficient of diacharae
2010
IF -, -I ...- j;;;:
....- ..L I- ..... i I II I ... ..... .,.. I I
.......... , :---. I : -~ I I I
l.~"'"I
" I , ......... I -+ ~-'---'- • ' I :
~F".....
! I Ii"..... r-..l- ~I i ~ I lao' -H-r-;- "i . ! ~..
tTl i-..J.. ~";;"'!--
, -;.... I ! i .... i I : o.ao±kI , I ,~ ... ~ I I I i !
,....." I r-- i , -·F I 0.iu.1 I51_.., e.....lt_
I .......... ,~
I - - --t·O.!I. ,.cr ! ~-
~ .'- ~+-t, ~1,,~'" ,
0.5 .. rr ...-- -I i .
;;;h' 0 '-30- I , I I I , I I i '"I i , , , , ----"""'1--..
1 ! , , ! i ! ,, .0.2 I. 0.1 j to· I i i I I I I I I I
I I I I I
•• 1.00i i : I I
,J
1.00
0.60o
.~ 0.10.'"~
..a;;.... o.to
!:.;0.110
:;;
It.. •.~
I II '2
- ._-. ---
w ~ ~ ~ 00",.Ptn:.-t of c..... cORtfoc::ti.,.
B. Variation of discharge coefficient .... uh angul.ar1.ty
I ,
i ! 4 . ..J-
10
I :
'-"""'i !
1'1; I
"
, y,, ./, ./ I I
./ I I
I I
I I
, 1 I,I I ! I
:\
I.I~"",,,,,,,,,,,,,,,,,""""'.,...-r----"""--""'....,.----r----.,
!40' 4!t ~cr ~~. 61!
9 ......qle 01 .i"" -01C. Variation of dbch.arge coefficient with win&~ .... all angle
See figure 3.4.23.
Figure 3.4.21. --Type IV
abutment with wing walls.
opening, embankment slope 1 to 1, vertical
3-98
DISCHARCiE·COEri'ICU;hT CURva
;.2Dd'~C--------
100~ ~ ~ ~ ~
....... ., c:...-~..A. 8&ae curve (or coefficient ot cit.ac.h&rp
zo,0
O~~...... 1
~. to...,........ 1 , i ,
......... ...... --..
, I -- I, I. ,
I i ,-- , a! I , ~ , -0. : ! : ,
,...... , ....... : I -.i. , - : -St_. .-...- , ," , : , ,t. 0.1 ,. 0.5 '-0· l"'- , , , -- -
~I
, , I
F·O.!lO •-so- I ~' I 'ala!, , !
·~.o I '0, -,..--
1,-tOO
I I ,, ,, I ! I I I I i , ,
1.0
··j 0,10
i
O.flO a
I10..
0
!
··~ 0.10
l.''"
1.00
O.SO
ala
.. '- I YI I , y L.-"I I
I 2 ,~ , I ,
I ! I -'-,
I: I I, I I I '~, I I
- I,I : I : , 1 ...,
J-: , 1I , I , , 1-, , , i v ! I I - ...----- -
r-l-r' I I I ! 1\ r-! y I I
~,t-
±-±~ .. : I I'-r I I , I
10 zo ~ ~ ~ c•• "'ruM fII~ ~tr"'"
B. Variaticm 01. d.1.Icharle coeltlcicnt witb ancular:l.ty
10 ee
0,81)
, I : ,i : : I :
i : .-.--! I --- I
, : ---, I i.-H"'T! ! I ,
..... : I
I ,: ,
I i , i I
1.10
~~ ~ ~ ~ ~ ~
,. 'ro,," """"'1.~C. Vu1&t1clll 01 d.1acharp coefficient with 1"roude rw.m.ber
k,. 1.00
I I , ! I
~, ! I ~! I , I I ••01 ......
-r-- : ;..........-:~~
I
--LlJ:L I , , J.-- I! , .....,
..... i......I ,
100XI'
1.10
c...... •, .l1li' __D. Varw&!"" 01 dUcharCe coetflcleac ...1<.11 ... lD(• ....u""Cia:
Figure 3.4.22.--Type IV opening, embankment slope 2 to 1, vertical
abutment with wing walls. See figure 3.4.23.
3-99
COMPUTATION OF PE<AK DISCHARGE AT CONTRACTIONS
L ~.P'"-.- .. --to, • 1,
losAwOf.... I>tt_ -.n... 131
II ,
I Il' i I I I :
-t- 'i, N I ! I
I :-..... , iI I i
.......... : I iI I , 1 I I
I I l' I I
+r- .1 : ,:-..... I
. I I ! i I I N- I I I, I I I I i
i I i :
1.00
0.80o O.O!! 0.10 0.15 0.20 0.25 0.30
~- arid" ."lIfft"OlnCe ratio
B. Variation of discharge coefficient with degree of submer-gence ot bndC.
L~••~! 1.0-
V~·..
,V
!
I
1.00
0.900 0.1 0.2 0.3 0.4•• Eceenttlclty rGflo
A. Vanation of discharge coefficient with eccentricity
PILES
• • •o • •
A'j'i;_____.....i~"'- _
W 30 ~ ~ ~ rom- PerCI"t of d'lo"nef COfttroctiofi
C. Variation of discharge coefficient Wlth area of brldge pile.
100
i '
80
---I I !
I '
l " -+---t-'H-i-~t--"-j !
l- ~ ~!... i
--r-- ,t f·
f-'\
I '
Ir
I I II I ,
-I-H-I100 'II
'n''-, I-t+~
100-.+--, 0" ~
0,~. A' ./// 1-;-.a »« /// s
2 ./" -"'i/' 0 ,.k· o 03 0
./ ,'r - 0.90J.: ./ ./ .-:.... 2/' /', • ...L-
a £,.- ,.- I , ,s-
f LU++,1-:'1- .- n""0.80
~PIERS
- = J'~=:z:z::a A,
~.0
I i I I I I i ,! f ! ! ! I I ! nti. I I I ! : I : :A"""!
, i I , I I I i i I ..--r-~'O
I I ..;......-,...-ri i , i ! i I
: i
100
0.9520 30 ~ ~ ~ ro ~ ~
"uPtrc_ 011 cfto''''11 contraC1IO'tD. Variation oflldischarge co.fficie~t with area. at bridge plera
100
Figure 3.4.23.--Types I-IV openings, ke, k t > and kj curves.
3-100
1.00
0.80
~l~~ 0.60..i• 0.40gm
0.20
-- -- m-80- 160-- ---I--- ~140- - --~- I
..-- I- - 20-I--r--
..-- - - -'" JOI
i----0.00
o 0.010 0.020 0.030 0.040 0.050 0.060 0.070MonninQls "nil
Figure 3.4.24. The effect of channel roughness on the backwater ratio
for basic-type constrictions.
1.21.1
C/Cbosic
~973
'"I": :::::-- 973--_973
\ <, "'-,-~m:80
v
'"~ I-- ~ ~x
\ ,. I :tt--'"r-\<, 952-948-
"",,-947 Iv52_I-v52
!\952 r-, II
\ 952<,
"'m:4~_N6 I ILegend _
~o m:80x m:60
~• m:40-v m:209 m: as_
.1. '1m: 2~ I indicatedV27 v
I0·51.0
0.6
0.7
1.0
0.8
0.9
Figure 3.4.25. The effect of constriction on the backwater ratio.
3-101
SUBJECT /1
IIAIlZAIIEWCO /2eo /(/4.Lvnc tid,., RIve r YSUS/TNA JO/NT VENTURE
COMPUTED »5IR CHECKED C C.
FilE NO./bS3-/03
DATE ~/2s:18'4
PAGE I-- OF .2 PAGES
-*/8/1
IIII•
J7 -;;; 0.0 3S .5 = c:J,OO/::{
ch?/7/7€/ CCJ~//o:s€c/t),eYr:2//e / s f"coJ;61es /cs..sr-/7a~ C /J //7 d/;?/n€r€,1'"
tt/Bler~O(/r'se ch SS/ h~d;;-S 77/2~ &rovj'?..IT'~fI /'SC.p/e
Oe-~/7n q /OOy,,- //00 dQoo = ~ ~20 ch CliO z: /200 Q-z =~50
o ; 3h2.CJQ-=-/20DQZZS-O
Susitna Hydroelectric Project
Culvert Design Data Sheet
Location: Township ~;t;?;)1
Secti on _.lw::3:........=O::...- _
Range gee _-: /} 0 ~o (2/\ If A /
Meri di an (:) A..../ U (V
Project Feature: (project access road, material site access road, etc.)
Station: /200 ~:sh.J-P7. o~j{;v€r Y J(.//2chor;
Type Water Course 0 B C
User Fish Group (8 &Conly)
Drainage Area: &050I ® III IV
0, ()012
cfs--------Q2: 2 ~Q cfs Qdesign:
Frequency of Qdesign: ~~ years
Watercourse Area for Q2: /08',0 . ft2 Gradi ent ft/ft
Watercourse depth of flow for Q2: 2, IS ft
Classify channel substate: ~5/c?/J/hc2/l;/CJm 0 Ul1fo/IC;;e5,;- :;;>
7rdt/fE/s h co,6,g,ks /~.55 /;4~/7 C'//7cAcs
============--- 01-
_ ;0%--------
________ ft/sec
Size:
Channel configuration: Braided Meandering Gaig~
Other (describe) ~~~~~~~=)7~t?------------Other g/ld9~ GUt'/); ce>'J,./c'/ p/G!'"
2 ¥
t..1d/h .:);-c/;~nntP13& 15 5 :1-{ : /
Length: 50 / ft.
734
Culvert Type:
Slope:
Attested to by:;??-~
Fisheries Biologist Design Engineer
lfAIZA.f&UC8 SUBJECT~~::cr"sS~20£) , FI.... roo/~53.-/tJ3 ~ __~tt: 11t:)#"'_1I( ,. Y DATe C'lzs/K4
SUSITNA JOINT VENTURE "'"' COMPUTeD 5"If CHeCKED C C PAGE .:3.- OF 7 PAGES
£)~~/,?~ / ~ ,b~S"~d' C)'7 /7r'~ 2ZJ C~A.f";"It::.f/an (.,c.n-l~ 5.5 -::: 15".'/ wIll, 38' .6~~w~lffh ~O~ o;/$h~~.$ ~r/~?G GV~// A;;JV"~ ~ C~/?/r;1/.coJ'?crl/E~~ ~/€;$vj?,Pcrr /8;'/rh/4Ck 5EI d.:7S'h oCJ///J'J~ on 5Lc?1~.3 atJr//n~ p:7j1tE /.
I
I
I
I
I I I
I
I 71
/. '" i'i '1/i~ Z$f-!.Qf. S"}) 10] ((17. Z$""'!!~$J)c7·~ 0. 0 '32 ~ . ;1 Li01'/7. ZS" f/,9t10)J
- 7t 27 & ..
L -::: :3 &. 7 S (S'~~ h~"",..~ 3. e,; /9 c..) ~ ;:: ~ 7S I
b ~ 3B L-~ ~ /. 0
m := 1/ - ~-) /~o .1. -:: [i - 7 /2 7~ ]/()O~ {I J<; / /()3 2Q~ •
-=- 30.3%
C / PI' //7~~~/;7nO/J h...-- S.5¥.S".'! frc-? h9vr~.5 J~~/9 ;:J'7d3~~.20
- 0.032
-
UID-fMlCO SlJSlTNA JOINT VENTURE
SUBJECT ~:r- C'135~~':2aO' U/05 u ,.u;:h~ ~ At::It!' yo Y
COMPUTED S;:? CHECKED C~
FILE NO. /~5J-/03
DATE tg/Zs/9# PAGE £ OF J... PAGES
s S := /:/ c ~ -:: {}.9Z$" '"
" ~I/s~ CJ.!J23 /0,.5.$ r/.S:/ 55::2:/ C -::::: 0. 92 /
,RtrJ/t"~W />,?oq;;he:;J ~ot" ~c::/a"'s ro c"(SI£~I/ TiJ~h :3,~ s
~ N~. -4 N./-(. ~9 /VA'.
-A~ N. 4. ~. ytf'S 0 ~~ 2J ~r /\( A
-It Ax ,y~s ri,•. 3.iI.19 c ~ /)/~./J( A. 3.~.20c. J
:= /() /(/.s)J:: ~.l.. /..ly (3 8 ~/()')( /. 5)/0"
=C/,03
~ I',..o~ h,. 3· ~ 23 /cr /1'7::: 3CJ.9 ,).j.:: 0.03
~ :: ..:3~9
,A1f /n/t?/;Po/;:;/€d' /'rOI'Y? 05.:;. f'. /.5?C d"c/ 3.l/. ZOe.
,t;;,,... L~ ::. I f'" Y -.:.':3- 7 S- 0 .. I 0 rb .. 7ii" -=39
55:./.'/ '·$it S.5&2:1
;'X /./7~ /.03 ~x 1./0
C C <:1./ A/I x' ~2:J (99!3}(;' ID)Ie
-;;~CJ~4 >.1.0 t/s~t-:tJ
c=~o
MJAm~EIAS:C,OSUSITNA JOINT VENTURE
SUBJECT S!r€:Ji"YJ c;.t:;ss/n? /2t%f FILE No.!.~S"3-/03 -t//S JvnCnt:>¥'} ;f)1/~r Y DATE &/2.s-/f14- A
COMPUTED' S ,/f) CHECKED C C PAGE 5 OF 2.. PAGES
S/nc~ LO~$~/C'ht;#7 /5 /J~/ 7f.P~ Td6?~~rn?/;?~ C'" :2.nd~ /rd i'Yl h~ 3,<1; / S 4 el8
h r: .I'Y1 ~ :3 o. 9 I % =/. C)
A C"'~ 4 93<;-
hd(.)eI~ /1/0.-:: q .. _....;.3_C--:-:z-:-(J-=-~==.4:; r;i -(('3 9Jtl.~(;o))/o) 112.? (/0;'
»o- 3 ¥
43 ~ = 0.:77S
C C~ / - 0.93<;- (0.:;;75)b.:J SIc:. -::: ~r-
~ 0.9/5"
~o
c:J.915-
=/.09
~ x: 0.77
h~iY) h? '3. L-/. 24 wt'~A /') z; a0'32 f 1Y7::. 30. 99'f
hIM h =0'~3
h* )h~ h CQ"r~c~d = 44 (A.;; =: (J. L/9!d, 77)
:: Cl. 377
<..
TrI .2 / L1 l] ~ . 3 (}i~):2 5 '3
- ,9 ( S,S<;(ff!)!2 ('32, 2
_ 0. &53
<....
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REFERENCES
1. "Hydraulic Tables", Corps of Engineers, U.S. Army. For sale bySuperintendent of Documents, Government Printing Office, Washington,D.C.
2. "Hydraulic and Excavation Tables", U.S. Bureau of Reclamation. Forsale by Superintendent of Documents, Government Printing Office,Washington, D.C.
3. "Handbook of Hydraulics", by H.W. King, McGraw-dill Book Company, NewYork City.
4. "Design Charts for Open-Channel Flow", U.S. Department of Commerce,Bureau of Public Roads. For sale by Superintendent of Documents,Government Printing Office, Washington, D.C.
30221/ REF840922
5.
6.
7.
"Open-Channel Hydraulics", by Ven Te Chow, McGraw-rlill Book Company,New York City.
U.S. Geological Survey, Circular No. 284, 1953 Computation of PeakDischarge at Contractions C.E. Kindwater, R.W. Carter, H.J. Tracy.
Backwater Effects of Open Channel Constrictions, Transactions, ASCE,Vol. 120, pp . 993-1006, 1955.
4-1
APPENDIX A
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