EM 1110-2-1602 Hydraulic Design of Reservoir Outlet Works

CECW-EH-D

Engineer Manual

1110-2-1602

Department of the ArmyU.S. Army Corps of Engineers

Washington, DC 20314-1000

EM 1110-2-1602

15 October 1980

Engineering and Design

HYDRAULIC DESIGN OF RESERVOIROUTLET WORKS

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unlimited.

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The text of this manual and all illustrative materials therein,which were prepared by government personnel, are public property andtherefore not subject to copyr$ght.

All uses in this manual of information from non-governmentalsources are in the form of findings or opinions and credit has beengiven in the text at the point of use through superscript numberscorresponding to the list of references and/or bibliography. Anyonewishing to-make further use of any of-the non-governmental.info~-tion referenced, by itself and apart from the context in which hereinpresented, should seek any necessary permissions direct from suchsources.

Since all use in this manual of materials from non-governmentalsources has been permissible in nature, and is fully credited, reprintor republication in whole or in part would appear properly subjectonly to the crediting of this manual, as follows: *** Engineer Manual

No. 1110-2-1602,Engineering and Design, Hydraulic Design of ReservoirOutlet Works, 15 October 1980, Department of the Army, Corps ofEngineers, U.S.A. *H*.

DAEN-CWE-HD

Engineer ManualNo. 1110-2-1602

DEPARTMENT OF THE ARMYOffice of the Chief of Engineers

Washington, D.C. 20314

EM 1110-2-1602

15 October 1980

Engineering and DesignHYDRAULIC DESIGN OF RESERVOIR

OUTLET WORKS

1. -“ This manual presents guidance for the hydraulic designanalysis of reservoir outlet works facilities. The theory, procedures,and data presented are generally applicable to the design of similarfacilities used for other purposes.

2. Applicability. This manual applies to all field operating activitieshaving responsibility for the design of Civil Works projects.

General.3. Studies pertinent to the project functions and their effectson the hydraulic design of outlet works are briefly discussed in thismanual. Also where appropriate, special design guidance is given forculverts, storm drains, and other miscellaneous small structures. In thismanual, theory is presented only where required to clarify presentation orwhere the state of the art is limited in textbooks.

FOR THE CHIEF OF ENGINEERS:

‘~RREST T. GAY 111/Colonel, Corps of EngineersExecutive Director, Engineer Staff

This Manual Supersedes EM 1110-2-1602, 1 August 1963.

DEPARTMENT OF THE ARMY EM 1110-2-1602Office of the Chief of Engineers

Washington, D. C. 20314DAEN-CWE-HD

Engineer ManualNo. I11o-2-I6o2 15 October 1980

Engineering and DesignHYDRAULIC DESIGN OF RESERVOIR O~EI’ WORKS

Table of Contents

Subject

CUTER 1.

Section I.

Section II.

cHAPTm 2.

Section I.

Section II.

Section III.

Section IV.

INTRODUCTION

GeneralPurpose--------------------------------Applicability--------------------------References-----------------------------Bibliography---------------------------Symbols--------------------------------Other Guidmce and Design Aids---------WES Capabilities and Senices ----------Design Memorandum Presentations--------Classification of Conduits-------------Project Functions and Related StudiesGeneral--------------------------------

HYDRAULIC THEORY

IntroductionGeneral--------------------------------Basic Considerations-------------------Conduits Flowing Partially N1General--------------------------------Discharge Controls for PartiallyFull Flow------—----— --------------

Flow Profiles--------------------------Conduits Flowing FullGeneral--------------------------------Exit Portal fiessure Grade-LineLocation-----------------------------

GradientsGeneral--------------------------------Hy&aulic Grade Line and ~erg

Grade Line---------------------------Mean Pressure Computation-------------–

i

Parawaph

1-11-21-31-41-51-61-7~-81-9

1-1o

2-12-2

2-3

2-42-5

2-6

2-7

2-8

2-92-1o

a

1-11-11-11-21-21-21-31-31-3

1-4

2-12-1

2-2

2-22-3

2-3

2-4

2-4

2-52-6

EM 1110-2-16021.98(

Section V. Ener~ Losses

Section VI.

cHAmm 3.

Section I.

Section II.

Section III.

Section IV.

General----------— --------------------Suface Resistance (Friction)----------Form Resistance---------—-------------CavitationGeneral --------------------------------Theory---------------------------------Design Practice------------------------Preventive Measures--------------------Boundary Layer-------------------------Air Demand-----------------------------Air Flow-------------------------------

SLUICES FOR CONCRETE GRAVITY DAMS

Basic ConsiderationsLocation-------------------------------Size, Shape, ad Number----------------Elevation and Alignment----------------Sluice IntakesGeneral---------------------------—---Trash Protection----------—-----------Entrance Curves----——--— ------------Intake Energy Losses---------------—--Gate Passage, Gates, and ValvesGeneral--------------------------------Gate Types-----------------------------Control Valves--—----— ---------------Metering Devices-----------------------Gate Passageway Requirements-----------Gate Slots-----------------------------Gate Recess----------------------------Gate Seats-----------------------------Steel Liners---------------------------Air Vents------------------------------Sluice Outlet DesignGeneral Considerations-----------------Exit Portal Constructions--------------Sluice “Eyebrow” Deflectors------------

Para~aph

2-112-122-13

2-142-152-162-172-182-192-20

3-13-23-3

3-b3-53-63-7

3-83-93-1o3-113-123-133-143-153-163-17

3-183-193-20

-

2-72-72-15

2-192-202-212-212-222-232-24

3-13-13-1

3-23-23-33-4

3-53-53-73-83-93-93-1o3-1o3-1o3-1o

3-113-123-12

ii

EM 1110-2-1602

CHAPT~ 4.

Section I.

Section II.

Section III.

Section IV.

Section V.

CHAPTER 5.

Section I.

OUTLET FACILITIES FOR EMB~KMENT DAMS

Basic ConsiderationsApproach Channel----------------—-----Conduits and Tunnels forEmb@ent Dams----------------------

Intake and Gate FacilitiesInt&e Structures----------------------Intake Tower Versus CentraJ.ControlShaft-—-----------------------------

Submerged Intakes----------------------Combined Intake and Gate Structure-----Underground Control Structures---------Downstream Control Structures----------Gate Passageway Requirements-------—--LOW-F1OW Releases------------------—--Entrance ShapesGeneral--------------------------------Selection of Entrance Shape forDesign-------------------------------

Line= Sidewall or Pier Flare-—--—---Control GatesGeneral----------------------—--------Gate Lip Geometry----------------------Vertical-Lift Gate Discharge

Computations---------—--------------Commercial Gates-----------------------Hydraulic Load for Vertical-Lift

Gates--------------------------------Vibration of Cable-SuspendedGates-----TransitionsGeneral--------------------------------Entrance =d Int*e Transitions--------In-Line Transitions--------------------Exit ~snsition ------------------------

ENERGY DISSIPATION AND IX)WNSTREAMCHANNEL PROTECTION

Energ DissipatorsGeneral--------------------------------Hydraulic-Jump Type Stilling Basins----Low-Head Structures--------------------

iii

Paragraph

4-1

4-2

4-3

4-44-54-64-74-84-94-1o

4-11

b-124-13

L-144-15

4-164-17

4-184-19

4-204-214-224-23

5-15-25-3

1980

s

4-1

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4-34-44-44-54-54-54-6

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:::

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4-124-124-124-14

5-15-15-8

EM II1o-2-I6o21980

Subject

Section II.

CHA~ER 6.

APPENDIX A.

WPENDIX B.

APPENDIX C.

APPENDIX D.

APPENDIX E.

APPENDIX F.

Outlet ChannelGeneral---------------------------------Ripra~--------------------------------Side-Slope Erosion---------------------

SELECTIVE WITHDRAWAL STRUCTURES

~es----------------------------------Design---------------------------------F1OW Regulation------------------------Model Investigations-------------------

BIBLIOGRAPHY

NOTATION

PLATES

COMPUTATION OF DISCHARGE RATING CURVESFOR OUTLET WORKS (IllustrativeExample)

COMPUTATION FOR DESIGN OF TRANSITIONSECTION (IllustrativeExample)

COMPUTATION FOR DESIGN OF OUTLET WORKSSTILLING BASIN (IllustrativeExamples)

Para~aph Page

5-4 5-95-7 5-1o5-6 5-1o

6-1 6-16-26-3 ::;6-4 6-4

iv

EM 1110-2-160215 Ott 80

CHAPTER 1

INTRODUCTION

Section I. General

1-1. m“ This manual presents guidance for the hydraulic designanalyses of reservoir outlet works facilities. Although primarilyprepared for the design of reservoir outlet works, the theory, procedures,and data presented are generally applicable to the design of similarfacilities used for other purposes. Studies pertinent to the projectfunctions and their effects on the hydraulic design of outlet works arebriefly discussed. Where appropriate, special design guidance is givenfor culverts, storm drains, and other miscellaneous small structures.Procedures are generally presented without details of theory since thesedetails can be found in many hydraulic textbooks. However, some basictheory is presented as required to clarify presentation and where thestate of the art is limited in textbooks. Both laboratory and prototypeexperimental test results have been correlated with current theory in thedesign guidance where possible.

1-2. Applicability. This manual applies to all OCE elements and allfield operating activities having responsibilities for the design of civilworks projects.

1-3. References.

a. National Environmental Policy Act (NEPA), PL 9-190, Section102(2)(c), 1 Jan 1970, 83 Stat 853. 6

b. TM 5-820-4, Drainage for Areas Other than Airfields.

c. ER 1110-1-8100, Laboratory Investigations and Materials Testing.

d. ER 1110-2-50, Low Level Discharge Facilities for Drawdown ofImpoundments.

e. ER 1110-2-1402, Hydrologic Investigation Requirements for WaterQuality Control.

f. ER 1110-2-2901, Construction Cofferdams.

g. ER 111o-2-815o, Investigations to Develop Design Criteria forCivil Works Construction Activities.

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EM 1110-2-16021980

EM 1110-2-1601,(Chan:;s 1-2).

i. EM 111o-2-16o3,

j. EM 1110-2-2400,Works.

k. EM 1110-2-2901,

1. EM 1110-2-2902,

m. EM 111o-2-36oo,

l-3h

Hydraulic Design of Flood Control Channels

Hydraulic Design of Spillways (Change 1).

Structural Design of Spillways and Outlet

Design of

Conduits,

Reservoir

n. Hydraulic Design Criteria

Miscellaneous Structures,

Culverts & Pipes (Changes

Regulation (Changes 1-3).

(HDC) sheets and charts.

Tunnels.

1-2).

Availablefrom: Technical Information Center, U. S. Army Engineer Waterways Ex-periment Station (wES), P. O. Box 63I.,Vicksburg, MS 39180:

Conversationally Oriented Real-Time ~ogram Generating System(CORP;j computer programs. Available from: WESLIB, U. S. - Engi-neer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 3918o,and from several CE computer systems.

Where the above-listed references and this manual do not agree, theprovisions of this manual shall govern.

1-4. Bibliography. Bibliographic items are indicated throughout themanual by numbers (item 1, 2,.etc.) that correspond to similarly num-.~ered items in Appendix A. They are available for loan by request tothe Technical Information Center Library, U. S. Army Engineer WaterwaysExperiment Station, P. O. Box 631, Vicksburg, MS 3918o.

1-5. Symbols. A list of symbols is included as Appendix B, and as faas practical, agrees with the American Standard Letter Symbols forHydraulics (item 3).

1-6. Other Guidance and Design Aids. Extensive use has been made ofHydraulic Design Criteria (HDC),n prepared by WES and OCE. Similarly,data md information from Engineer Regulations md special reports havebeen freely used. References to Hydraulic Design Criteria are by HDCchart number. Since HDC charts are continuouslybeing revised, the user

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1-6 m 1110-2-160215 Ott 80

should verify that the information used is the most up-to-date guidance.Applicable HDC charts and other illustrations are included in Appendix Cto aid the designer. References to specific project designs md modelstudies are gener~ly used to illustrate the structme type, and thedimensions are not necessarily the recommended dimensions for every newproject. The WES Automatic Data Processing Center (ADPC) ComputerProgram Library (WESLIB) provides time-sharing computer services to CEDivisions and Districts. One such service is the ConversationallyQriented ~eal-Time ~ogram-Generating ~stem (CORPS) that especiallyprovides the noncomputer-oriented or noncomputer-expert engineer a setof proven engineering applications programs, which he can access onseveral different computer systems with little or no training. (Seeitem 54 for instructions.on use of the system and a partial list ofavailable programs. Updated lists of programs can be obtained throughthe CORPS system.) References to available programs that are applicableto the design of reservoir outlet works are noted in this manual by theCORPS program numbers.

1-7. ~S Capabilities and Services. WES has capabilities and furnishesservices in the fields of hydratiic modeling, analysis, design, andprototype testing. Recently, expertise has been developed in the areasof water quality studies, mathematical modeling, ad computer pro-gramming. Procedures necessary to arrange for WES participationinhydraulic studies of dl types are covered in ER 1110-1-8100.C WES alsohas the responsibility for coordinatingthe Corps of Wgineers hydraulicprotot~e test program. Assistance during planning and making the testsis included in this progra. (See ~ 111o-2-815o.g)

1-8. Design Memorandum Presentations. General and feature designmemoranda shodd contain sufficient informationto assure that thereviewer is able to reach an independent conclusion as to the designadequacy. For convenience, the hy~aulic information, factors, studiesand logic used to establish such basic outlet works features as type,location, alignment, elevation, size, and discharge should be.summarizedat the beginning of the hydraulic design section. Basic assumptions,equations, coefficients, alternative designs, consequences of flowexceeding the design flow, etc., should be complete and given inappropriate places in the hydraulic presentation. Operating character-istics and restrictions over the full range of potential dischargeshould be presented for all release facilities provided.

1-9. Classification of Conduits. Two broad classifications of reser-voir outlet works facilities are discussed in this manual: concretegravity dam and embankment dam facilities. Outlet works through concrete

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m 1110-2-1602 1-91980

gravity d= will be called sluices while those through embankment damswill be called conduits and/or tunnels.

a. Concrete Gravity Dams. Generally, sluices that traversethrough the masonry of concrete gravity dams have rectangular crosssections ad are short in comparison with conduits through embankmentdams of comparable height. Use of a number of small sluices, at one ormore elevations> provides flexibility in flow re~ation and in qu~ityof water released downstream. Sluices are controlled by gates at theupstream face and/or by gates or valves operated from a gallery in theinterior of the dam. Sluices are usually designed so that the outflowdisch=ges onto the spillway face and/or directly into the stillingbasin. When sluices traverse through nonoverflow sections, a separateenergy dissipator must be provided. Arch dams, multiple arch dams, andhollow concrete d= are less common; and although the outlet worksdesign may require special features, the same hydraulic principles areapplicable.

b. tibankment D-. Conduits and/or tunnels for embankment damsmay have circular, rectangular, horseshoe, or oblong cross sections mdtheir length is primarily determined by the base width of the embarkment.Due to the greater length, it is usually more economical to constructa single large conduit than a number of small conduits. Conduits shouldbe tunneled through the abutment as far from the embankment as practi-cable, or placed in an open cut through rock in the hbutment or on thevalley floor. Gates and/or valves in an intake tower in the reservoir,in a central control shaft in the abutment or embankment, or at theoutlet portal are used to control the flow. Generally, placement ofthe control device at the outlet portal should be avoided when theconduit passes through the embankment due to the inherent dangers of apossible rupture of a conduit subject to<ull reservoir head. Diversionduring construction or reservoir evacuation requirements, especiallyon large stresms, may govern the size and elevation of the conduit(s).Foundation conditions at the site may also govern the design. (SeeEM lllo-2-2901k and EM 1110-2-2902.1)

Section II. Project ~ctions and Related Studies

1-10. General. Project functions and their overall social, environ-mental, and economic effects greatly influence the hydraulic desi~ ofoutlet works. Optimization of the outlet works hydraulic design andoperation requires an awareness by the designer of the reliability,accwacy, sensitivity, ad possible variances of the data used. Theever-increasing importmce of environmental considerations requires thatthe designer maintain close liaison with many disciplines to be sure

1-4

1-1o

environmental and other objectives =e satisfied in theproject functions and related design considerations arecussed in the following paragraphs.

a. Functions.

EM 1I1o-2-I.6o215 Ott.80 .------

design. Generalbriefly dis-

(1) Flood Control. Flood control outlets are designed forrelatively large capacities where close regulation of flow is lessimportant than are other requirements. Although control of the outflowby gates is usually provided, the conduits may be ungated, in whichcase the reservoir is low or empty except in time of flood. When largedischarges must he released under high heads, the design of gates,water passages, and energ dissipator should be carefully developed.Multilevel release provisions are often necessary for water qualitypurposes.

(2) Navigation. Reservoirs that store water for subsequentrelease to downstream navigation usually discharge at lower capacitythan flood control reservoirs, but the need for close regulation of theflow is more important. The navigation season often coincides with theseason of low rainfall, and close regulation aids in the conservationof water. Outlet works that control discharges for navigation purposesare required to operate continuously over long periods of time. Thedesigner should consider the greater operation and maintenance problemsinvolved in continuous operation.

(3) Irrigation. The gates or valves for controlling irrigationflows are often basic~ly different from those used for flood controldue to the necessity for close regulation and conservation of water inarid regions. Irrigation discharge facilities are normally much smallerin size than flood regulation outlets. The irrigation outlet sometimesdischarges into a canal or conduit rather than to the original riverbed.These c=als or conduits are usually at a higher level than the bed ofthe stream.

(4) Water Supply. Municipal water supply intakes are sometimesprovided in dams built primarily for other purposes. Such problems asfuture water supply requirements and peak demands for a municipality orindustry should be determined in cooperation with engineers representinglocal interests. Reliability of service and quality of water are ofprime importance in water supply problems. Multiple intakes and controlmechaisms me often installed to assure reliability, to enable thewater to be drawn from any selected reservoir level to obtain water of adesired temperature, and/or to draw from a stratum relatively free fromsilt or algae or other undesirable contents. Ease of maintenance md

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m 1I1o-2-I6o2 l-10a(4)

15 oct 80

repair without interruption of service is of primary importance. Anemergency closure gate for priority use by the resident engineer isrequired for water supply conduits through the dm.

(5) Power. Power penstocks are not within the scope of thismanual. However, if reservoir outlets =e to be located in the vicinityof the power plants and switchyards, conduit outlets and stilling basinsshould be designed so as not to cause any undesirable eddies, spray, orwave action that might jeopardize turbine operation. Power tunnels orpenstocks may be used for flood control and/or diversion of the streamduring construction of the dam and in such cases the discharge capacitymay be determined by the principles outlined in this teti.

(6) Low-Flow Requirements. Continuous low-flow releases arerequired at some dams to satisfy environmental objectives, water supply,downstream water rights, etc. To meet these requirements multilevelintakes, skimmer weirs, or other provisions must be incorporated sepa-rately or in combination with other functions of the outlet worksfacility. Special provisions for these purposes have been incorporatedin concrete gravity dm nonoverflow sections. Embankment dams with mid-tunnel control shafts also require special considerations for low-flowreleases.

(7) Diversion. Flood control outlets may be used for total orpartial diversion of the stream from its natural channel during construc-tion of the dam. Such use is especially adaptable for earth dams (seeEM lllo-2-2golk and ER 1110-2-2901f).

(8) Drawdown. Requirements for low-level discharge facilitiesfor drawdown of impoundments are given in ~ 1110-2-50.d Such facilitiesmay also provide flexibility in future project operation for unantici-pated needs, such as major repairs of the structure, environmental con-trols, or changes in reservoir regulation.

(9) Multiple Furpose. Any number of purposes may be combinedin one project. The designer should study carefully the possible eco-nomics of combining outlets into a single structure

b. Related Studies.

(1) ~vironmental. The general philosophypreservation, mitigation, and/or enhancement of thehave been set forth (item 96). Many scientific andplines are involved in the environmental aspects of

I.-6

for multiple use.

and guidance fornatural environmentengineering disci-hydraulic structures.

l-lob(l) m II1o-2-16o2

15 Ott 80

Some studies influencing the outlet works design are briefly discussedbelow. Pertinent data from these studies should be presented in thedesign memorandum. The designer should have a working knowledge ofthese data and their limitations.

(a) Fish and Wildlife. Outlet works design and operation canmaintain, enhance, or damage domstream fish and wildlife. Flow re-leases not compatible with naturally seasonable stream quantity andquality can drastically change aquatic life. These changes may bebeneficial or may be damaging, such as adverse temperatures or chemicalcomposition, or nitrogen supersaturation (item 86). Information fromfish ad wildlife specialists on the desired stream regimen should beobtained and considered in the design. Downstream wildlife requirementsmay fix minimum low-flow discharges. The water quality presentationshould include summary data on requirements and reference to sourcestudies.

(b) Recreation. Recreation needs including fishing, camping,and swimming facilities, scenic outlooks, etc., should be considered inthe design of energy dissipators and exit channels. ~ese requirementsare usually formulated by the planning discipline in cooperationwithlocal interests. To accomplish the desired objectives, close coopera-tion between the hydraulic and planning engineers is required. Specialconsideration should be given to facilities for the handicapped, suchas wheelchair ramps to fishing sites below stilling basins. Safetyfences for the protection of facilities and the public are important.Appreciable damage to stilling basins has resulted from rocks thrown inby the public. The hydraulic engineer should recognize the need forsuch things as: (1) nonskid walks ad steps with handrails designedto protect the elderly and young children; (2) periodic lowering ofreservoir levels and flushing of stagnant pools downstream for vectorcontrol (mosquitoes, flies, etc.); (3) elimination Of construction sc~sresulting from borrow pits, blasting, lad clearing, etc; and (4) main-tenance of relatively constant pool levels for reservoir recreationactivities.

(c) Water Quality. An awareness of maintaining red/or enhanc-ing the environment within the past decade has brought into existence arelatively new and expanded art of reservoir hydrodynamics. Untilrecently, the study of reservoir hydrodynamics has been limited to afew prototpye vertical temperature gradients md recognition of theseasonal inversions accompanying the fall surface water cooling. How-ever, environmental considerations of today have necessitated the devel-opment of preproject capability for prediction of the expected seasonalreservoir stratification and circulation to permit construction and

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m 1110-2-1602 l-lob(l)(c)

15 Ott 80

operation of outlet works designed to meet storage and outflow regimesneeded for the reservoir and downstream environment. Reservoir hydro-dynamic studies may be done by other than the hydraulic designer (suchas the hydrologic engineers) and they would specify the withdrawalrequirements (quantity, elevation, etc.). The hydraulic engineer thendesigns the outlet works to meet these requirements. However, thehydraulic designer furnishes some of the information for the hydrologicstudies.

(2) Foundations. In concrete dams, foundation conditions havelittle if any effect upon the hydraulic design of sluices. However, thehydraulic design of outlet works for embankment dams can be appreciablyaffected by foundation conditions. The conduit shape and control towerlocation are usually fixed primarily by foundation, structural, andconstruction considerations in addition to hydraulic requirements.Energy dissipator and outlet channel designs for either sluices orembmkment dam outlets =e sometimes influenced by local foundation con-ditions. Foundation information of interest to the hydraulic designerincludes: (a) composition and depth of overburden, (b) quality ofunderlying rock, and (c) qu~ity of exposed rock. In addition, side--slope stability is of considerable importance in the design of riprapprotection. Outflow stage chage rates are required for bank stabilitydesign. Sufficient foundation data red/or reference to its sourceshould be included or referred to in the hydraulic presentation tosubstantiate the energy dissipator and exit channel design.

(3) mvironmental Impact Statements. Section 102(2)(c) of theNational Environmental Policy Act (NEPA)a requires detail documentationin the project design memoranda on the impact of the planned project onthe environment. The hydradic engineer may be required to cooperatein the preparation of impact statements. An analysis of 234 Corps ofEngineers environmental impact statements on various projects is givenin IWR Report No. 72-3 (item 122). This report ca be used as a guideas to the t~e of material needed and format to be used in developingthe statements. Basic to the environment~ statements are studies madeto define the preproject and project functions and their effects on theenvironment. In most cases the effect of each project function must beset forth in detail. A recent publication by Ortoano (item 87) summa-rizes the concepts involved and presents examples relative to waterresources impact assessments. Presentation of the hydraulic design indesign memoranda must identify environmental requirements and demonstratehow these are satisfied by the hydraulic facility.

(4) Project Life. Two factors in the life of a project of con-cern to the hydraulic engineer in the design of outlet works are

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l-10b(4) m 1110-2-160215 Ott go

(a) do-strem channel aggravation and degradation, and (b) structuraldeterioration.

(a) Channel Aggravation and Degradation. In many rivers de-termination of the dominant factors causing bed shaping action likedegradation and aggravation is difficult. Changes in the hydrographiccharacteristics caused by a dam can result in undesirable changes inthe elevation of the riverbed. Degradation, or lowering of the riverbed,immediately downstream of a da may threaten the integrity of thestructure. Removal of all or part of the sediment by the reservoir mayinduce active erosional attack downstream. Similarly, although thetotal annual sediment transport capacity of the river will drop signifi-cantly, the sediment supply by downstream tributaries will be unalteredand there may be a tendency for the riverbed to rise. This channelaggravation can increase the flood hazards from downstream tributariesmd may cause reduction in outlet works allowable releases. Resultingtailwater level changes can also adversely affect the stilling basinperformance.

(b) Concrete Deterioration. Excessive invert erosion of outletstructures has occurred where sands, gravel, and construction debrishave passed through conduits used for diversion during extended periodsof low reservoir stages. Construction of a submerged sill upstream ofthe intake to trap the debris should be considered where this conditionis likely to occur. Special materials or liners may be helpful in pre-venting invert erosion in etiremely cold climates where deteriorationof the conduit interior from freezing-and-thawing cycles is possible.

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2-1 EM 1110-2-16021980

CHAFTER 2

HYDRAULIC THEORY

Section I. Introduction

2-1. General. This section presents hydraulic design theory, availableexperimental data and coefficients, and discussions of certain specialproblems related to reservoir outlet works design. Generally, the pre-sentations assume that the design engineer is fully acquainted with thehydradic theories involved in uniform md gradually varied flow, steadyand unsteady flows, energy and momentum principles, and other aspectssuch as energy losses, cavitation, etc., related to hydraulic design asnormally covered in hydratiic handbooks and tetis such as those by Kingand Brater (item 56) ad Rouse (items 99 and 101). This manual ispresented as guidance in the application of tetibook material and asadditional information not readily available in general reference mate-rial. The theory of flow in conduits from a reservoir is essentiallythe same for concrete ~d embankment d-. The application of thetheory of flow through conduits is based largely upon empirical coeffi-cients so that the designer must deal with maximum and minimum values aswell as averages, depending upon the design objectives. To be conserva-tive, the designer should use maximum loss factors in computing dis-charge capacity, and minimum loss factors in computing velocities forthe design of ener~ dissipators. As more model and prototype data be-come available, the range between maximm and minimum coefficients usedin design may be narrowed. An illustrative example, in which the hy-draulic design procedures and guidance discussed in this manual areapplied to the computation of a discharge rating for a typical reservoiroutlet works, is shown in Appendix D.

2-2. Basic Considerations. The hydraulic analysis of the flow througha flood control conduit or sluice usually involves consideration of twoconditions of flow. When the upper pool is at low stages, for exampleduring diversion, open-channel flow may occur in the conduit. As thereservoir level is raised, the depth of flow in the conduit increasesuntil the conduit flows fall. In the design of outlet works, the nwberand size of the conduits and the elevations of their grade line are de-termined with consideration of overall costs. The conduits are usuallydesigned to provide the required discharge capacity at a specifiedreservoir operating level, although adequate capacity during diversionmay govern in some cases. Conduits should normally slope downstream toensure drainage. The elevation of good foundation materials may governthe invert elevation of conduits for an embankment dam. If it is plannedto use the conduits for diversion, a study of the discharge to be

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Ott 80 ‘1.10-2-16021980

2-2

diverted at the time of closure of the river channel may limit the maxi-mum elevation of the conduit. If the conduits are adjacent to the powerpenstocks, the level of which is governed by the turbine setting, itmay be feasible and convenient to place all conduits on the same level.After limiting conditions are determined and preliminary dimensions andgrades established by approximate computations, a more exact analysismay be made of the flow through the conduits. It is often more expedi-ent to estimate the size, number, and elevation of the conduits andthen check the estimated dimensions by an exact analysis rather than tocompute the dimensions directly.

Section II. Conduits Flowing Psrtially N1

2-3. General. Analysis of partially full conduit flow is governed bythe same principles that apply to flow in open channels. The longitu-dinal profile of the free-water smface is determined by discharge,geometry, boundary roughness, and slope of the channel. Reference ismade to plate C-1 for illustration of the principal ty-pesof open-channel water-surface profiles. A study of the various profiles willindicate, for any particular conduit, where the discharge control islikely to be located and the type of water-surface profile that will beassociated with the control.

2-4. Discharge Controls for Partially N1 Flow.

a. Inlet Control. The control section is located near the conduitentrance and the discharge is dependent only on the inlet geometry andheadwater depth. Inlet control will exist as long as water cm flowthrough the conduit at a greater rate than water can enter the conduit.The conduit capacity is not affected by hydraulic parameters beyond theentrance, such as slope, length, or boundary roughness. Conduits opera-ting under inlet control will always flow partially full for some dis-tance downstream from the inlet.

b. Outlet Control. The control section is located at or near theconduit outlet; consequently, the discharge is dependent on all the hy-draulic p~ameters upstream from the outlet, such as shape, size, slope,length, smface resistance, headwater depth, ad inlet geometry. Tail-water elevation exceeding critical depth elevation at the outlet exitmay influence the discharge. Conduits operating under outlet controlcan flow either full or p~tially full.

c. Critical Depth Control. Critical flow appliesface flow and occurs when the total ener~ head (sum ofand flow depth) for a given discharge is at a minimum.

only to free sur-velocity headConversely, the

2-2

2-4c EM 1110-2-1602

15 oct 80

discharge through a conduit with a given total ener~ head will be maxi-mum at critical flow. The depth of flow at this condition is definedas critical depth and the slope required to produce the flow is definedas critical slope. Capacity of a conduit with an unsubmerged outletwill be established at the point where critical flow occurs. A conduitoperating with critical.depth occurring near the entrance (inlet con-trol) will have maximum possible free-surface discharge. The energyhead at the inlet control section is approximately equal to the headat the inlet minus entrance losses. When critical flow occurs down-stream from the conduit entrance, friction and other losses must beadded to the critical energy head to establish the headwater-dischargerelation. Critical depth for circular and rectangular cross sectionscan be computed with CORPSO H6141 or H6140 or from charts given inHDC 224-9n and 610-8,n respectively. Reference is made to TM 5-820-4band to King’s Handbook (item 56) for similar charts for other shapes.

d. Gate Control. It is generally necessary to compute surfaceprofiles downstream from the gate for different combinations of gateopenings and reservoir heads to determine the minimum gate openings atwhich the conduit tends to flow full. The transition from partly fullto full flow in the conduit may create an instability that results inslug flow pulsations (“burping”) at the outlet exit portal which cancreate daaging wave action in the downstream channel (item 2). Gener-ally, this instability occurs near fully open gate openings and theoutlet works are not operated in this discharge r=ge for any extendedperiod of time. However, it is particularly critical in projects thathave a long length of conduit below the gate, and the conduit frictioncauses the instability to occw at smaller gate openings that are inthe planned operating range of the outlet works. The conduit must beexamined for slug flow where the ratio of downstream conduit length toconduit dismeter or height exceeds T5 (i.e., L/D ~ 75). A larger con-duit or steepened invert slope may be required to avoid this condition.Additional details ad an example analysis are given in Appendix D.

2-5. Flow Profiles. EM IIIO-2-1601h presents the theory involved incomputing flow profiles for prismatic channels. Its application to theproblem with a sample computation is given in Appendix D.

Section III. Conduits Flowing N1

2-6. General. The objective of the analysis of conduits flowing fullis to establish the relation between discharge and total head and todetermine pressures in critical locations. The solution is implicit andinvolves the simultaneous solution of the Darcy-Weisbach equation, thecontinuity equation, and the Moody diagram to determine the unknown

2-3

m 1110-2-1602 2-6

1.5Ott gQ

quantities. A detailed explanation of the computational procedure ispresented in Appendix D. The total head H , which is defined as thedifference in elevation of the upstream pool and the elevation of thehydradic (pressure) grade line at the exit portal, is consumed in over-coming frictional (hf) and form (hg) losses and in producing the exitportal discharge velocity head (hv). These component heads may beequated to the total head as follows:

H =hf+hl+hv (2-1)

Plate C-2 is a definition sketch showing the relation between thesevarious components in an outlet works system.

2-7. Exit Portal Pressure Grade-Line Location. The elevation of thehydraulic (pressure) grade line at the exit portal for unsubmerged flow(into the atmosphere) is not as obvious as it may appear. Laboratorytests made at the State University of Iowa (item 103) have indicatedthat the elevation of the intersection of the pressure grade line withthe plane of the exit portal is a function of the Froude number of theconduit flow. Plate C-3 shows the results of these ud other tests forcircular and other conduit shapes. The values of yp/D are ~sodependent upon the condition of support of the issuing jet. The“Suggested Design Curve” on this plate is based upon an~yses of modelad prototype data. Plate C-3 indicates that a good approximation forthe initial location is two-thirds the vertical dimension above theexit portal invert. Model and prototype tests have indicated the hy-draulic (pressure) grade line at the exit portal can be depressed tonear the conduit invert for certain geometries and flow conditions (seeChapter 5, p=a 5-2d(2)). If the exit portal is deeply submerged,the hydraulic grade line at the outlet will be at the local tailwaterelevation. However, at lower degrees of submergence the outflow willtend to depress the local.water surface below the surrounding tailwaterelevation. This depression and the accompanying hydraulic jump actionfor two-dimensional flow can be analyzed as described by Rouse or Chow(items 101 or 17, respectively). However, submerged conduit outflowinto a wider channel is not subject to simple analysis. If submergedflow conditions are critical relative to conduit capacity, local pres-sures at the outlet, or stilling basin performance, a hydraulic modelinvestigation will be needed.

Section IV. Gradients

2-8. General. The basic principle used to analyze steady incompressible

2-4

..—

2-8 EM 1110-2-160215 Ott 80

flow in a conduit is the law of conservation of energ as expressed bythe Bernodli equation. Generalized so that it applies to the entireflow cross section, the expression for the ener~ at any point in thecross section in foot-pounds per pound of water is given by:

(2-2)

where

H=

z=

P=

y.

v=

g=

a=

For mmyerror.

total head in

difference indatum plane

feet of water above the datum plane

elevation of the point and the elevation of a

pressure at the point, lb/ft2

specific weight of water, lb/ft3

flow velocity, fps

2acceleration due to gravity, ft/sec

dimensionless kinetic-ener~ correction factor

practical problems a may be taken as unity without series . ,

2-9. Hydraulic Grade Line and tier= Grade Line. The hydraulic gradeline, also referred to as the mean pressure gradient, is p/y abovethe center line of the conduit, and if Z is the elevation of the cen-ter of the conduit, then Z + p/y is the elevation of a point on the.hydratiicgrade line. The locus of values of Z + p/y along the con-duit defines the hydraulic grade line or mean pressure gradient. Thelocation of the hydraulic grade line at any station along the conduitis lower than the ener~ grade line by the mean velocity head at thatstation as reflected by equation 2-2. See plate C-2 for a definitionsketch of the energy grade line, hydraulic grade line, etc. The hy-draulic grade line is useful in determining internal conduit pressuresand in determining cavitation potentialities. Information on localpressure conditons at intakes, gate slots, and bends is given in theappropriate pwagraphs of this manual.sign, pressure gradient determinationslimiting conditions.

2-5

For purposes of structural de-are usually required for severti

~ 1110-2-1602 2-1o

15 Ott 80

2-10. Mea Pressure Computation. The mean pressure at any stationalong a conduit is determined using the conservation of ener~ principleas expressed by the Bernoulli equation. The principle states that theenergy at one station of the conduit (point 1) is equal to the energyat any downstream location (point A) plus any intervening losses. Ex-pressed in equation form and in the units of equation 2-2,

lr2

TT2

Plzl +

‘l_z +PA &+H‘+a12g A ~+aA2g “Y

If the upstream station is taken in the reservoirtrance where the velocity head is negligible, andttien as the pool elevation, equation 2-3 reduces

(2-3)bl-A

near the conduit en-Z1 + (pI/Y) is

to

— .72

‘= pool elevation ‘AY ‘~-HLIA-zA

(2-4)

applicable to the general case of determining the meanstation along the conduit, with proper consideration

Equation 2-4 ispressure of anybeing given to head losses due to friction and form changes between theentrance md station in question. For a uniform section, the pressureat any station (point A) upstream of the exit portal (point 2) can bedetermined by the following equation:

‘A—=Z2+y -ZA-+HLY P 2-A

(2-5)

where

pA/y =

*L2 A ‘

z2+y -zA=P

pressure head in feet of water at any station

total hydratiic loss in feet between the exit portaland the station

difference in feet between the mem pressure grade-line elevation at the exit portal and the pointelevation at the station in question.

2-6

/ .

2-11

Section V. Energy Losses

EM 1110-2-360215 oct 80

2-11. General. Ener~ losses within conduits fall into two generalclassifications: (a) surface resistance (friction) causedby shear be-tween the confining boundaries and the fluid and (b) form resistanceresulting from boundary alignment changes. Computationalproceduresfor both types are given in the following paragraphs.

2-12. Surface Resistance (Friction).

a. General. Three basic equations have generally been used in theUnited States for computing ener~ losses in pressurized systems. TheManning equation has been used extensively for both free surface andpressure flow. The Hazen-Williams formula has been used for flow ofwater at constant temperature in cast iron pipes. The Darcy-Weisbachformtia is adopted in this manual and is preferred because through useof the Moody diagram (plate C-4), the Reynolds number and the effectiveroughness properly account for the differing friction losses in boththe transitional and fully turbtient flow zones.

b. Darcy-Weisbach Formula. The Dacy-Weisbach formula is expressedas

.fLv2‘f D 2g

(2-6)

where hf is the head loss, or drop in hydraulic grade line, in theconduit length L , having an inside diameter D , and an average flowvelocity V . me head 10SS (hf) has the dimension length and iS ex-pressed in terms of foot-pounds per pound of water, or feet of water.The resistance coefficient f is a dimensionless parameter. Moody(item 73) has constructed one of the most convenient charts for deter-mining resistance coefficients in commercial pipes and it is the basisfor pipe-flow computations in this manual.

c. Effects of Viscosity. Nikuradse (item 82) demonstratedby ex-periments that the resistance coefficient f varies with Reynolds num-ber JR. (Reynolds number is defined in plate C-4.) Von Karman and~andtl (items 142 and 94, respectively) developed a smooth pipe equa-tion based on the Nikuradse tests as follows:

1

z=2 loglo 0.8 (2-7)

2-7

w 1110-2-1602 2-12C

15 Ott 80

This equation is shown as the “smooth pipe” on curve in plate C-4. Pro-tot~e tests have shown that a hydraulically smooth condition can existin both concrete and steel conduits over a wide rmge of Reynolds num-bers. Reference is made to plate C-4 for data from tests of concreteconduits and to HDC 224-1/in for steel conduits.

d. Effect of Relative Roughness. The rough pipe tests ofNikuradse have served as a valuable basis for determining the effect ofrelative roughness (D/k). The s~bol k represents the absolute rough-ness of the pipe wall, which for random roughness is taken as 2a whereu is considered to be the root-mean-square of the height of the rough-ness elements. D represents the pipe diameter. The Von Karman-Frandtl(item 142) equation for a rough pipe and fully established turbulentflow is:

1 D—= 2 loglo ~ + 1.74G

(2-8)

Thus, for this type of flow, the resistance coefficient is a functiononly of relative roughness and is independent of Reynolds number.Therefore, representation of the equation appears as a series of hori-zontal lines on the upper right-hand portion of plate C-4. Values of fbased on protot~e concrete conduit measurements are plotted in thisplate. These values of k were obtained mathematically from hydraulicmeasurements and are essentially effective roughness values rather thanphysical values. Very few published roughness coefficients (items 16and 30) are physical values and all should be considered as effectiveor hydraulic rather than absolute roughness values. Rouse (item 101)has proposed an equation that defines the lower limit of the rough flowzone as follows:

The equation is shown as a dotted line in plate C-4.

(2-9)

e. Transition Region. The area on the Moody diagram between thesmooth pipe curve and the rough flow limit may be considered as a tran-sition region. Colebrook and White (item 18) published an equationbased on their experiments to span the transition region. Theequation is:

2-8

2-12e EM 1110-2-1602

15 Ott 80

1 (L+%)_= -2 loglo 3.7D

G(2-lo)

The relation is shown as dashed lines in plate C-4.

, f. Noncircular Cross Sections. The Darcy f is expressed interms of the conduit diameter and therefore is theoretically only appli-cable to conduits having circular cross sections. The concept ofequitialentor hydraulic diameter has been devised to make it applicableto noncircular sections. This concept assumes that the resistancelosses in a noncircular conduit are the same as those in a circular con-duit having an equivalent hydraulic radius and boundary roughness.

D= 4R=~ (2-11)

where

R=

D=

A=

P=

hydraulic radius of the noncircular conduit

dimeter of a circular conduit having the sae hydraulic radius

conduit area

wetted perimeter

A WS study (item 19) has shown that the equivalent diameter concept isapplicable to all conduit shapes normally used in the Corps’ outletworks structures. Plate C-5 gives the relation between A , P , and Rfor various common conduit shapes. Geometric elements of rectangular,circular, oblong, and vertical-side horseshoe-shaped conduits showingfull or partly full can be computed with.CORPSO H2041, H6002, H2042,and H2040, respectively. See paragraph 4-2c for a discussion of whenconduit shapes other than a circular section should be considered. Flow

characteristic curves computed by the USBR (item 50) for their standard,curved-side, horseshoe-shaped conduit are presented in plate c-6. Thisshape is the same as that presented at the bottom of plate C-5.

m Guidance for Roughness. The Colebrook-White equation(eq 2~~O)D~~1recommendedfor computing the resistance coefficient fsince it is applicable to either smooth, transition, or rough flow

2-9

-. .;

~ 1110-2-1602 2-12g15 Ott 80

conditions. Computations of discharge and head loss at given totalheads for rectangular, circular, or oblong, and vertical-side horseshoe-shaped conduits flowing full can be computed with CORPSO H20~h, H20~5,and H2043, respectively. The solution is implicit; and without the aidof a computer, it is more convenient to graphically obtain values of ffrom a Moody-type diagram as illustrated in plate C-4. However, to usethe Moody diagram requires knowledge of the effective roughnessparameter. Recommended k-values for various conduit materials areshown below:

(1) Concrete. The following values of k are recommended foruse in the design of concrete sluices, tunnels, and conduits.

(a) Capacity. Conservatively higher values of roughness shouldbe used in designing for conduit capacity. The k values listed beloware based on the data presented in paragraph (c) below and are recom-mended for capacity design computations.

ConduitSize k

me ft ft

Asbestos cement pipe Under 2.0 0.0003Concrete pipe, precast Under 5.0 0.0010Concrete conduits (circular) 0.0020Concrete conduits (rectangular) 0.0030

(b) Velocity. The smooth pipe curve in plate C-4 should beused for computing conduit flow velocity for the design of outlet worksenergy dissipators. It should also be used for all estimates for criti-cally low pressures in transitions, bends, etc., as well as for theeffects of boundary offsets projecting into or away from the flow.

(c) Miscellaneous. Available test data on concrete pipes andconduits have been analyzed to correlate the effective roughness kwith construction practices in forming concrete conduits md in treatmentof interior surfaces (HDC 224-in). The following tabulation gives infor-mation pertinent to the data plotted in plate C-4. The type of construc-tion and the resulting effective roughness can be used as guides inspecific design problems. However, the k values listed are notnecessarily applicable to other conduits of different sizes.

2-1o

2-12g(l)(c) EM II1o-2-I6o2

Plate C-4Symbol

●

Tc

AAv

oAv‘8

e-1-

Project

Asbestoscement

Asbestoscement

NeyrpicDenver #10hat illsRiver

Presserhatilla Dam

Deer FlatVictoria

Denver #3Denver #13Spavinaw

DenisenOntarioChelanAdam Beck

Fort PeckMelvernBeltzville

OaheEnid

Size k

-ft ft

c

c

ccc

cc

cc

ccc

Precast Pipe

1.2 0.00016

1.7 0.00008

2.82 0.000304.5 0.000183.83 0.00031

2.54 0.001522.5 0.00024

3.0 0.000433.5 0.00056

2.5 0.000115.0 0.000165.0 0.00013

Steel Form Conduits

c 20 0.000120 18 0.00001c 14 0.00061c 45 0.00018

c 24.i’ 0.00014H 11.5 0.00089c 7 0.00009

Wood Form Conduits

c 18.3 0.00004c 11 0.00160

(Continued)

15 Ott 80

Construction

Steel mandrel

Steel mandrel

19.7-ft steel form12-ft steel form8-ft steel form

Oiled steel form4-ft sheet steelon wood forms

6-ft steel form4-ft oiled steelforms

12-ft steel form12-N steel form12-ft steel form

on

Hand-rubbed

Invert screeded andtroweled

Joints ground

* C = circular, O = oblong, R = rectangular, and H = horseshoe.

2-11

EM 1110-2-160215 Ott 80

2-12g(l)(c)

Plate C-4 Size kSymbol Project Shape* ft ft Construction

Wood Form Conduits (Continued)

o Pine Flat 52 R 5x9 0.00103@ Pine Flat 56 R 5x9 O 00397 Longitudinal planking

Miscellaneous

o Quabbin H 11 x 13 ().()()015lJnkno~

* C = circular, O = oblong, R = rectangular, and H = horseshoe.

(2) Steel.

(a) Capacity. The k values listed in the tabulation beloware recommended for use in sizing cast iron and steel pipes and conduitsto assure discharge capacity. The values for large steel conduits withtreated interior surfaces should also be useful in the design of surgetanks under load acceptance. The recommended values result from analysisof 500 resistance computations based on the data presented inHDC 224-1/in and in Table H of item 13. The data are limited to continu-ous interior iron and steel pipe. The recommended desi~ values sreapproximately twice the average experimental values for the interiortreatment indicated. The large increase in k values for large sizetar- and asphalt-treated conduits results from heavy, brushed-on coatings.

Diametere

Under 1.0lto5Over 5Under 6over 6AllAll

Treatment

Tar-dippedTa-coatedT=-brushedAsphaltAsphalt-brushedVinyl or enmel paintGalvanized, zinc-coated or uncoated

kft

0.00010.00030.00200.00100.01000.0001

0.0006

2-12

.../

2-12g(2)(b) ~ 1110-2-160215 Ott 80

(b) Velocity. The smooth pipe curve in plate C-4 is recom-mended for all design problems concerned with momentum and dynamicforces (stilling basins, trashracks, water hammer, surge tanks for loadrejection, critic~ low pressures at bends, branches, offsets, etc.).

(c) Miscellmeous. The following tabulation summarizes thedata plotted in HDC 224-1/in and can be used as a guide in selecting kvalues for specific design problems. However, the k values listed donot necessarily apply to conduits having different diameters.

Diameter kReject ft ft Remarks

NeyrpicNeyrpicMilanMilmMilanSan GabrielSan GabrielHooverFort RandallFort RandallFort RadallGarrison

2.602.610.330.490.82

10.254.250.8322.0022.0022.0024.oo

0.0000100.0001350.0000390.0000260.0000710.0000040.0001520.0001330.0009360.0003820.0000080.000005

Spun bitumastic coatingUncoatedZinc-coatedZinc-coatedZinc-coatedEnameledEnaeledGalvanized pipeTar-coatedTar-coatedVinyl-paintedVinyl-painted

(d) Aging Effects. Interior treatment of pipes and conduits isof importance to their service life. Chemical, organic, and inorganicdeposits in steel pipes and conduits can greatly affect resistancelosses and conduit capacity over a period of time. Data by Moore(item 7b) indicate that over a 30-yr period, incrustation of bacteria upto 1 in. thick formed in uncoated 8-in. water pipe. Similar conditionsprevailed in 10-in. pipe where the bond between the pipe and the inte-rior coal tar enamel was poor (item 38). Computed effective k valuesfor these pipes were 0.03 and 0.02 ft, respectively. Data compiled byFrarike(item 38) indicate that organic and inorganic incrustations anddeposits in steel conduits up to 6 ft in dimeter increased resistancelosses by as much as 100 to 300 percent with effective k values in-creasing twenty to one-hundred fold. The data indicate that the inte-riors of some of the conduits were originally treated with a coat ofbitumen. The changes occurred in periods of 5 to 17 yr.

(3) Corrugated Metal. The mechanics of flow in corrugated metal

2-13

EM 1110-2-1602 2-12g(3)

15 Ott 80

and structural plate pipe are appreciably different from those occurringin steel and concrete pipe (items bh and 117). Both the height ofthe corrugations (k) and their angle to the flow are important factorscontrolling the resistance coefficients (f) values. HDC 224-1/2 and224-1/3n show the effects of pipe diameter, corrugation height and spac-ing, and flow Reynolds number for pipes with corrugations 90 deg to the -flow. More recently Sil’bermanand Dahlin (item 112) have analyzedavailable data in terms of pipe diameter, helix angle, and resistancecoefficient and published a design chart based on these parameters.This chart is included as Plate C-7. The correlation shown indicatesthat pipe size ad helix mgle are of primary importance in resistancelosses. The use of plate C-7 for the hydratiic design of corrugatedpipe systems is recommended. Corrugated metal is not recommended forhigh pressure-high velocity systems (heads >30 ft, and velocities >10fps). For this reason the published f values can be used for bothcapacity and dynamic design. Invert paving reduces resistance coeffi-cients for corrugated metal pipe about 25 percent for 25 percent pavedand about 45 percent for 50 percent paved.

(4) Unlined Rock Tunnels.

(a) General. Unlined rock tunnels have been used for floodflow diversion and hydropower tunnels where the rock is of sound quality.Generally, it is more economical to leave these tunnels unlined unlesshigh-velocity flows are involved, considerable rock remedial treatmentis required, or lining in fractured rock may be required. Existing re-sistance coefficient data have beennstudied by Huval (item 52) and sum-m~ized in HDC 224-1/5 and 224-1/6. Field measurements of frictionlosses in the Corps’ Snettisham diversion tunnel have been reported byWES (item 75). Accurate k values cannot be determined prior to initialtunnel blasting. Consequently, a rmge of probable k values based uponblasting technique and local rock characteristics must be investigatedto determine tunnel size. Information of this type can sometimes beobtained by studying blasting techniques used and results obtained in theconstruction of tunnels in rock having similar characteristics. Adjust-ment to the tunnel size could be made after tunneling begins.

(b) Shape. Unlined rock tunnels are usually horseshoe-shaped.Structural stability normally requires a rounded roof. Economicalblasting and rock removal operations usually require a flat or nearlyflat invert.

(c) Limiting Velocities. Generally, velocities in unlined tun-nels should not exceed 10 fps except during diversion flow when veloci-ties up to about 15 fps may be acceptable. For a tunnel with downstream

2-14

2-12g(4)(c) EM 1110-2-160215 Ott 80

turbines, penstocks, or valves, it has been recommended that velocitiesbe limited to 5 fps or less to prevent damage from migration of tunnelmuck fines and rock falls.

(d) Rock Traps. Rock traps must be provided where damage todownstream turbines, stilling basins, etc., can result from rock fallmaterial moving with the flow. Access to these traps is required forinspection ad occasional cleaning out. The development of satisfactoryrock trap design and size is presented in items 23 and 66. A rock trapdesigned to trap debris without interrupting the tunnel flow is de-scribed in item 47.

2-13. Form Resistance.

a. General. Energ losses caused by entrances, bends, gates,valves, piers, etc., are conventionally called “minor losses” althoughin many situations they are more important than the losses due to conduitfriction discussed in the preceding section (item 118). A convenientway of expressing the minor losses in flow is

where

‘1 =

K=

v=

g=

$hk=K—

2g

head loss, ft

dimensionless coefficient usually determined

designated reference velocity, fps


(2-12)

experimentally

The reference velocity in the following ener~ loss equations correspondsto a local reference section of the conduit at or near the point wherethe loss occurs. In a conduit with varying cross-sectional area (andinversely varying average velocity) along its length, the individuallocal loss coefficients (K’s) cm be adjusted to a single, generalreference section for combining into a single total loss coefficient.To do this, each local coefficient (K) should be multiplied by a factor

A~/< , where AG is the cross-sectional area at the general reference

section and ~ is the mea at the local reference section.

b. Sudden Expansion. In almost all cases the loss coefficient

2-15

EM 1110-2-1602 2-13b15 Ott 80

K is determined by experiment. However, one exception is the head lossfor a sudden expansion (items 101 and 118).stream section as section one and the largersection two, equation 2-12 may be written as

Desi@ating the smaller up-downstream conduit as

2 ~2

()

2‘1 1

hl=l-~‘1

2z=K~ (2-13)

in which

2

()

‘1K= l-~ (2-14)

2

where ~ and A2 are the respective upstresm ad downstream conduitcross-sectional areas, and the reference velocity is the upstream veloc-ity V~ . Note that the head loss varies as the square of the velocity.This is essentially true for all minor losses in turbulent flow.Furthermore, if the sudden expansion is from a submerged exit portalinto a reservoir, Al/A2 = O and the loss coefficient K becomes unityand the head loss hl is equal to the velocity head. A plot showing Kas a function of the area ratios is shown in plate c-8.

c. Sudden Contraction. Plate c-8 also illustrates the loss coeffi-cient K as a function of a ratio of the downstream to upstream cross-sectional areas. The head loss h~ due to a sudden contraction is sub-ject to the same analysis asof contraction of the jet isdownstream conduit velocitytion 2-14 may be written as

the sudden expmsion, provided the amountknown (items 101 and 118). Using the

‘2as the reference velocity, equa-

in which

(2-15)

()2

K=:-lc

2-16

(2-16)

,.

2-13c EM 1110-2-160215 Ott 80

where Cc is the contraction coefficient (i.e., the area of the jet atthe vena contracta section divided by the conduit area at the venacontract). Thus, as illustrated by plate c-8, the head loss at the en-trance to a conduit from a reservoir is usually taken as 0.5 V2/2g , ifthe entrance is square-edged.

d. Transitions. Plate C-9 smarizes the available data forgradual expansions and gradual contractions in circular sections(conical transitions). Gradud expansions, which are referred to asconical diffusers (items 101 and 118) have been tested by Gibson(item 41), Huang (item 51), and Peters (item 92). These tests show theloss coefficient to be a function of the flare angle of the truncatedcone. In the case of the gradual contraction, Schoder md Dawson(item 10~) give the head loss in the upstream contracting section of aventuri meter as 0.03 to 0.06 (V2/2g),where V is the throat velocity.More recent data by Levin (item 59) gives loss coefficient values forflare angles up to 90 deg. Levin’s data appear on the bottom ofplate C-9. The loss coefficients shown in plate C-9 are applicable inequation 2-13 for both expansions and contractions where the referencevelocity is in the sm~ler conduit. Approximate loss coefficients forrectangular-to-rectangular and rectangular-to-circulartransitions havebeen published by Miller (item 72).

e. Bends.

(1) General. The mechanics of flow in bends is discussed byYarnell (item 146), Hoffman (item 49), Anderson (item 4), and Zmkerand Brock (item 147). Anderson includes detail summaries of theliteratme with may design graphs. More up-to-date but less detailedsummaries are presented by Zanker and Brock.

6(2) Losses. The bend loss, excluding friction loss, for a

conduit is a function of the bend radius, conduit size ad ‘Shape,anddeflection angle of the bend. It has been found that the smoothness ofthe boundary surface affects the bend loss, but the usual surface ofa flood control conduit permits it to be classeddetermination of bend losses. Hoffman (item 49)(item 144) have established that bend losses aeReynolds number for values in excess of 200,000.need not be considered for computing bend lossescontrol conduits, but it may be of import=ce inbends. Dimensionless loss coefficientsbased ondetermined e~erimentallyand rectan~ar (items 64

as smooth pipe for theand Wasielewskiindependent of theThe Reynolds numberfor the design of floodsmall-scale models ofequation 2-12 have been

for bends in circda (items 49, 144, and 146)and 116) conduits.

2-17

~ 1110-2-1602 2-13e(2)(a)

15 Ott 80

(a) Circtiar Conduits. Loss coefficients for circular con-duits having circular or single miter bends with deflection angles up to90 deg are given in plate C-10. Bend loss coefficients for multiplemiter bends in circular conduits with deflection angles from 5 to 90 degare given in plate C-n (item 4).

(b) Rectangul~ Conduits. Loss coefficients for rectangularconduits having circular and single miter bends have been published bySprenger (item 116) and Madison and Parker (item 6h). Plate C-12 showsthe effects of Reynolds nmber and bend radii on rectangular conduitshaving 90 deg bends and height-width ratios of 0.5 and 2.0. Plate C-13gives relative loss coefficients for rectangular conduits having circu-lar bends Varying from10 to 18o deg (item 64). The bend loss coeffi-cient from plate C-12 shodd be multiplied by the appropriate relativeloss coefficient given in plate C-13. Plate C-14 shows the effects ofReynolds nmber (D) on 10SS coefficients for various triple bendcombinationswith ~ in the vicinity of 105 (item 116).

f. Branches ad Junctions.

(1) General. Branches (wyes, tees, etc.) are not normallyfound in outlet works but are encountered in the design of penstocks andwater supply systems. Junctions (manholes) are frequently encounteredin sewer (storm and domestic) design and junction boxes are occasionallyused with gates as control structures for low-head outlet works. HDC228-5n presents design information on pressure change coefficients forjunction boxes with in-line circular conduits and illustrates a proce-dme to compute the head loss for these structures.

(2) Experimental Data. Early interest in dividing and com-bining flow was generally limited to commercial pipe fittings (Vogel(item 141, 1928); Petermann (item 91, 1929)). In 1938 the USBR(item 135) published the results of expertients on junction losses. Thiswas probably the first effort to minimize head losses and optimize pres-swe conditions in large diameter branching conduits through experi-mental design. The more recent works of Marchetti and Nosed: (item 65),Syamala Rao (item 119), Ruus (item 105), ad Williamson and Rhone (item145) indicate the reviv~ of interest in branches and junctions of largeconduits. Miller (item 72) presents a summary of experimental data ondividing and combining flows in branches through 1970. Correlation ofdimensionless loss coefficients from the literature is difficult becauseof the wide variations in geometry tested. Since structures of thistype are not frequently used in reservoir outlet works, only the litera-ture is cited to assist the designer.

2-18

2-13g EM 11.10-2-I.60215 Ott 80

g. Equivalent Length. Form losses may be expressed in terms ofthe equivalent length of pipe L that has the sme head loss for thesame discharge. Equating the he~d loss due to form losses and theDarcy-Weisbach equation,

(2-17)

in which K may refer to one form loss or the sum of several losses.Solving for Le

(2-18)

For example, assume the tota3 form loss coefficient in a 4-ft-diam con-duit equals 20 (i.e., K = 20) and f = 0.02 for the main line; thento the actual length of conduit may be added 20 x 4/o.02 = 4000 ft ,md this additional or equivalent len@h causes the same resistance asthe form losses, within a moderate range of Reynolds numbers.

Section VI. Cavitation

2-14. General. (Items 8, 57, 97md 127.) Cavitation is the succes-sive formation and collapse of vapor pockets in low-pressure areas asso-ciated with high-velocity flow. Cavitation frequently causes severed-ge to concrete or steel surfaces and it may occur at sluice en-trances, downstream from gate slots, on edges of baf’fleblocks, at sharpbends in pipes, on tips of needle v~ves, etc. The roughening or forma-tion of pockets in surfaces resulting from cavitation is commonly called“pitting.” Surface erosion resulting from debris (rocks, gravel, etc.)is sometimes mist~en for cavitation, and cavitation damage may be diffi-cult to determine from examination of the surface within the daagedaxea. Debris erosion may sometimes be identified by grooves in thedirection of flow. While cavitation is normally associated with high-velocity systems, it ca occur in low-velocity systems with certainlocal boundary geometry and flow conditions. The classical case is thatof the venturi meter (item 99) in a low-head system (plate C-15). Cavi-tation is usually associated with closed systems such as in-line gatesand valves, but it can occur locally in free-surface systems. Pressuresin the cavitation range have been measured on a model of a navigationdam with a submergible tainter gate where the flow passages under thesubmerged gate had venturi-like characteristics. Similar flow conditionsbut with very high head losses can exist with lock culvert valves and

2-19

>..

. .

EM 1110-2-1602 2-14

15 Ott 80

with conduit gates operating under submerged conditions (plate C-15).In effect, cavitation can occur following any constriction when theback pressure in the system allows the jet flow piezometric head toapproach the vapor pressure of water.

2-15. Theory.

a. General. Cavitation results from the sudden reduction of localpressure at any point to the vapor pressure of water. Such reductionsin pressure ~e caused in water passages by abrupt changes in theboundary which causes a tendency of separation of the flow from theboundary, by constrictions which produce high velocities and low pres-sures, and by siphons in which pressures are reduced by reason of ele-vation. Vapor cavities form as bubbles in the low-pressure areas andcollapse when a higher pressure area is reached a short distance down-stream. The collapse (“implosion”) is very rapid and sets up high--pressureshock waves or possibly small, high-velocity local “jets” inthe water that cause damage to the nearby boundary. The basic equationassociated with cavitation studies is

(P. - Pv)

where

0=

P. =

V. =

Pv =

Y =

general

u =

dimensionless

-(2-19) ~

o—2g

cavitation parameter

9absolute pressure, lb/ft’

average velocity of the flow

vapor pressure of the fluid at a particular temperate, lb/ft2

unit weight of the fluid

Abrupt boundary changes also cause large local fluctuations in pressuresand velocities. Computation of these fluctuations is essentially impos-sible md cavitation potential can only be investigated under carefullycontrolled tests. In such tests a value of u. is determined forincipient cavitation by visual or specially in~trumented observations.The value of oi applies only for the partictiar geometry tested. As

2-20

2-15a

long as O’S for other flow conditions exceedexpected to occur. The reader is referred to

EM 1110-2-160215 Ott 80

‘i Y cavitation is notthe book by Knapp, Daily

and Hammitt (item 57) for additional discussion on the theory ofcavitation.

b. Effects of Temperature. The vapor pressure of water (PV orPv/Y) v~ies somewhat with the temperature of the water. The vaporpressure of fresh water at 40°F is about 0.29 ft of water and at 70°Fis 0.83 ft of water. The variation in vapor pressure is not large com-pared with the variation in atmospheric pressure due to elevation abovesea level. For example, atmospheric pressure at sea level is 34 ft ofwater, whereas at Denver, Colorado (elevation 5332), atmospheric Pres-sure is 28 ft of water (see HDC 000-2n). Thus, if the water temperatureis 600F, cavitation occurs at negative pressures of 33.L and 27.4 mof water at sea level and Denver, respectively.

2-16. Design Practice. Application of the theory of cavitation to.practical design problems is difficult. Available desi~ information onthe magnitude of instantaneous pressure fluctuations is meager. Ingeneral, such fluctuations increase in magnitude with increasing totalhead. For this reason two minimum average pressure values are recom-mended for general design where the total head is less than 100 ft.These values are based on experience md should be conservative. Whereboundary changes are gentle and streamlined, such as in entrances andtransitions, minimum average local pressures as low as -20 ft of watercan be expected to be cavitation-free. Where boundary changes are abruptor the local flow is highly turbulent, such as at gate slots, offsets,and baffle piers of stand=d design, minimum average pressures shouldnot be lower than -10 ft of water for safe design. In these highlyturbulent cases, local instantaneous pressure fluctuations of ~10 ftof water or more can be expected. For higher heads, an average pressureexceeding O ft of water is often necessary as instantaneous pressurefluctuations can materially exceed atmospheric pressure.

2-17. Preventive Measures. Once pitting has started in an outlet con-duit, the effect of cavitation may be accelerated by the existence ofa depression or hole in the surface which intensifies the local turbu-lence and the negative presswes in the area just downstream from thedepression. Thus, early repair of pitted surfaces is important andshould be done preferably with a more resist~t material. Stainlesssteel welding has been used to repair cavitation damage to steel surfacessuch as gate frsmes and turbine blades. Successful repairs have beenmade to concrete surfaces with epoxy concrete or mort=. The cause ofcavitation should be determined md corrected or avoided if due to aparticular operating condition. The preventive measures to be taken in

.2-21

~ 1110-2-1602 2-17

15 Ott 80

the design of outlet works conduits depend on puticular conditionsas follows:

a. Improvement of the shape of water passages to minimize the pos-sibility of cavitation. Examples are the streamlining of conduit en-trances, increasing the amount of offset and decreasing the rate oftaper downstream of gate slots, and using larger bend radii.

b. Increasing the pressure by raising the hydraulic grade line atdisturbance areas, which may be accomplished by flattening any down-ward curve, restricting the exit’end of the conduit, or increasing thecross-sectional area in such localities as gate passages to decreasethe velocity and increase the pressure.

c. Introducing air at low-pressure areas to partly alleviate nega-tive pressure conditions and to provide,air bubbles in the flow thatwill reduce the formation of cavitation pockets and cushion the effectsof their collapse. In the design of high-head outlet conduits, it isoften desirable to combine any two or all three of the above preventivemeasues. It is especially desirable to maintain a substantial backpressure in the vicinity of entraces, roof openings, bulkhead slots,and gate slots whenever the velocity is sufficiently high to producecavitation. For long conduits, the pressure gradient will ordinarilyproduce the required back pressure, but for short conduits, gate passagesfrequently must be enlarged or exit constrictions provided to producethe back pressure. When conduits are to be operated at p=t-gate open-ing, special care should be taken to provide streamlined shapes at theaforementioned locations and downstream therefrom because back pressurewill not be provided when the conduits flow partly full. The floor andwalls of a conduit just downstream from a high-head gate are particularlytinerable when operated at small openings for m extended period oftime (items 93 and 136). It is especially important that during con-struction, small protrusions resulting from incorrect monolith alignment,

.concrete spills, unground welded joints, etc., not be permitted.

2-18. Boundary Layer. (Items 101 and 106.) Conduit systems are gen-erally designed on the assumption that the boundary layer generated inthe flow by the she= between the fluid and the boundary is fully devel-oped and exists the entire length of the uniform conduit section. Testsat WES (item 129) and other places show, in fact, that conduit len@hsof about 40 diameters are required for the boundary layer to becomefully developed. A recent study reported by Wang (item 143) showed thatfor rough pipes, the wall shear stress becme fully developed in about15 diameters and the velocity profile was almost fully develop d in 50

%diameters for a Reynolds number range of 1.2 x 106 to 3.7 x 10 . In

2-22

2-18 EM 1110-2-160215 Ott 80

sluices and conduits of very small length-diameter ratios, the exitportal flow can contain a central core having a velocity head approxi-mating the full reservoir head. Ener~ dissipators for very short con-duits should be designed using the total reservoir head.

2-19. Air Demand. Under certain conditions of operation, the pressurein a conduit may fall considerablybelow atmospheric pressure. Sub-atmospheric pressures, approaching the vapor pressure of water, may beaccompanied by large fluctuations that can cause dangerous vibration or

destructive cavitation> particularly in the gate section, and are there-fore undesirable from the operating standpoint as well as for structuralreasons. Large reductions in these pressure fluctuations ca be ef-fected by providing air vents through which air will flow into the con-duit where less than atmospheric pressure exists. The vents usuallyopen through the conduit roof immediately downstream from the servicegate. (See para 3-17 for details.) Air requirements are most criti-cal in this area and reach a maximum value when the service gate isoperated at about three-q-u~ters open under the highest head. It isparticularly important that the air vent opening extend across the fullwidth of the conduit, that the high-velocity air actually spreads acrossthe full width, and that the water flow does not impinge into theopen-ing. An illustrative example showing the methods used for determiningthe size of air vent required and for compu~ing the pressure drop insuch ~ air vent is presented in HDC 050-2. The air discharge whichmust be supplied by air vents is dependent upon the rate of air entrainedby high-velocity flow and upon the rate of air discharged above the air-water mixture at the conduit exit. Both factors are variable and areinfluenced by the hydraulic and structural features of the conduit andthe method of conduit operation. plate c-16 indicates the types offlow that cause air demand and the relative amounts. When conduit dis-charge is not influenced by tailwater conditions and a hydraulic j-does not form in the conduit, the jet issuing from a small gate openingforms a fine spray or mist that fills the conduit and is dragged alongthe conduit by the underlying high-velocity flow, finally producing ablast of air ~d spray from the exit portal. At large gate openings, apartial hydradic jwp is formed in the conduit and the jet will entrainair as previously cited; but the air inflow from the vent at the top ofthe conduit will be entrained by the turbulence of the jump and drawnby the jump action into the conduit flow downstream. Both conditions ofwater flow in the conduit result in reduced pressures at the back of theservice gate and at the vent exit, thus causing air inflow through thevent. Air demand, in most instances, is not subject to a rigid analysis.Quantitative estimates of air requirements for design purposes have beenbased principally on empirical application of appropriate experimentaland prototype data. A paper by A. A. Kdinske and J. M. Robertson

2-23

“‘\

.//-.—

EM 1110-2-1602 2-1915 Ott 80 .

(item 55) correlated experimental data obtained on the rate of airentrainment by the hydraulic jump as a function of Froude number.Data on the prototype has also been obtained. A summary of existingdata is presented in plate C-17. Data presented by Sharma (item 111)indicate that the air demand for free flow and spray conditions may beabout 3 ad 6 times, respectively, that for the hydraulic jump condition.

2-20. Air Flow. Air vent flow encountered in the hydraulic design ofoutlet works is generally treated as an incompressible fluid and conse-quently conveyance systems are designed using conventional hydraulictheory and procedures. In extremely high-velocity systems (>200 fps)the air should be treated as a compressible fluid and the system designedaccordingly. Scott (item 109) has prepared many flow charts fordesi~ing air conveyance systems.

2-24

3-1 EM 1110-2-160215 Ott 80

SLUICES FOR

Section I.

CHAPTER 3

CONCRETE GRAVITY DAMS

Basic Considerations

3-1. Location. Sluices for concrete dams are generally located alongthe center line of spillway monoliths (plate c-18). When more than onesluice per monolith is required they are spaced appropriately in eachmonolith (plate C-19). A sluice should never be located close to orstraddling a monolith joint. Since it is also general practice to placecrest piers on the center line of spillway monoliths, the sluice airvent intakes can be placed in the crest pier, eliminating any danger ofsubmergence during spillway flow. Air vents should not be cross-connected below the highest possible pressure grade line. In some casesit may be desirable to locate the sluices in the nonoverflow section ofthe dm. Such a location requires either (a) a sepwate energ dissi-pator or (b) a careful design for discharging into the spillway ener~dissipator.

3-2. Size, Shape, and Number. The sluices for concrete gravity damsusually have a relatively small cross-sectional area. One of the prin-cipal reasons for making the sluices small in cross section is adversestructural.effects of large openings in a concrete gravity section. Inaddition, the use of a large number of small sluices, each controlled byindividual gates, provides a finer degree of regulation than could beobtained from a smaller number of sluices of larger cross-sectional area.The flood control sluices installed in Corps of Engineers’ dams arepredominantly rectangular in cross section. The size of sluices usuallyvaries from 4 ft O in. by 6 ft O in. to 5 ft 8 in. by 10 ft O in., de-pending on discharge requirements. Larger sizes may be indicated incertain cases. All sluices should be large enough for inspection,main-tenance, and repair purposes.

3-3. Elevation and Alignment.

a. General. The reservoir operational requirements normally playan important part in determining the elevation of the flood controlsluices. The inlets of the sluices must be set low enoughdto drain thereservoir to the required limits of drawdown (ER 1110-2-50 ). In a damfor flood control only, the reservoir is normally dry and the sluice in-let elevations are set at, or slightly above, the streambed with due con-sideration of the sluice outlet elevation relative to stilling basin de-sign. In a multipurpose dam with fixed reservoir storage allocationsad in which high reservoir stages may be maintained for long periods of

3-1

.,

EM 1110-2-160215 Ott 80 -

3-3a

time, it may be desirable to have both high- and low-level sluices(plate c-18). Low-level sluices are sometimes desirable for the passageof sediment through a reservoir and for aiding in water quality controlif a special intake tower is not provided. If the sluice intake ispermanently or frequently submerged, the servicing and inspection neces-sary for maintenance are more costly than for a high-level sluice. Ahigh-level sluice usually requires that the outlet portal be sloped todirect the flow along the face of an ogee spillway section or into astilling basin. The invert may slope on a straight line from the int~eto the outlet portal, or curve downward at some point downstream fromthe inttie. Setting the outlet portal at a lower elevation than theint~e reduces the pressure at critical locations such as the intake,gate slots’,and bends. An area reduction is usually provided in thevicinity of the outlet portal of sluices to assure positive pressuresin these sluices when operated under full gate openings, or the sluiceis enlarged downstream of the gate to ensure open-channel flow at fullgate openings”. Area reductions may be used to spread the emerging jet.

-b. Bends. Flow around conduit bends results in acceleration offlow along the inside of the bend accompanied by a local pressure reduc-tion and the potential for cavitation (partictiarlyfor short-radiusbends). Cavitation is not likely to occur in bends where long-radiuscurves are used. Pressue drop coefficients to evaluate cavitationpotential for 90-deg bends are given in plate C-20. The minimum pres-sure occurs at 22.5 deg and h5 deg from the beginning of curvature forcircular and rectangular conduits, respectively. Since the computedminimum pressure is an average pressure, the guidance given in para-graph 2-16 should be adhered to.

Section II. Sluice Int*es

3-4. General. Sluice intakes are integral parts of concrete spillways,and are usually rectan@ar in shape and flared in four directions. Thecurved entrance is followed by the sluice passage, normally having aheight-width ratio of about 1.5:1 to 2:1. In some cases considerableeconomy in stop log costs can be effected by projecting the intakecurves upstream beyond the face of the dam. This permits a reductionin the required size of the stop log or bulkhead gate. Bulkhead slotsmust extend vertically above the maximum reservoir pool or be providedwith slot covers. Open roof slots for closure bulkheads at Kinzua Dampermitted flow through the slot and resulted in extensive cavitationdamage downstream (item 20). Plate C-21 shows t~ical designs forflush ad protruding sluice int-es.

3-5. Trash Protection. The intake may be equipped with struts or

3-2

3-5 ~ 1110-2-160215 Ott 80

trashracks, depending upon the need for protection against clogging anddebris damage to gates and turbines.

a. Trash Struts. A simple trash strut usually of reinforced con-crete with clear horizont~ and vertical openings not more than two-thirds the gate or other constricted section width and height, respec-tively, should be adequate for highly submerged flood control outletconduits. The purpose of such struts is to catch trees and other largedebris which may reach the entrance but would ‘notpass through the gatepassage, thereby possibly preventing closure of the gates. Trash strutsshould be located to effect local net-area velocities not greater than15 fps. A flow net or model test should be used to determine localvelocities through this area (items 99, 101, and 135). The strutsshould be circular cylinders or have rounded noses and square tails,depending upon the structural design requirements ad economy. Teardropdesigns are not required if the local velocity guidance is maintained.Trash strut losses are usually included in the over~l intake loss.If necessary to consider separately, use of equation 2-12 is recommendedwith a loss coefficient K value of 0.02. V in this equation is theflow velocity in the uniform conduit section just inside the intake.Trash struts should be provided with a working platform located aboveconservation pool elevation to facilitate removal of debris. Additionalinformation on the design of trash struts is given in EM 111o-2-24oo.J

b. Trashracks. Trashracks are provided where debris protectionfor dowstream devices such as valves or turbines is required (item 22).Such racks are designed to retain debris of such size and type of mate-rial that could result in damage to these devices. Because of dangerof overstressing from clogging, trashracks should be located in lowervelocity seas than trash struts and must be provided with raking orcleaning facilities. They should be designed for safe operation with50 percent clogging. Such devices can be fabricated from circular barsand pipe. Trashracks shotid not be located in velocities exceeding3 to 4 fps. Where additional strength is required, elongated sectionswith rounded noses and tails can be used. Trashrack head losses dependon the flow velocity and area construction (items 22, 39, 100, 108, and135). me design of vibration-free trashracks is necessary to preventfailure from material fatigue. It is especially important where reverseflow ca occur (items 21, 37, 53, 63, and 110).

3-6. Entrance Curves.

a. General. The c~ved converging section, which begins at theupstrea face of the dam or intake structure =d terminates in tangencyto parallel walls, is commonly referred to as the entrance section.

3-3

.,.-

EM 1110-2-1602ij Ott 80 -

The curves thattrance curves.

3-6a

determine the rate of convergence are designated as en-It is the function of the entrance section to guide the

flow with minimum disturbance until it is contracted to the dimensionsof the gate passage or to the upstream transition of m ungated intake.If the entrance curve is too sharp or too short, negative pressureareas may develop in the entrance section where the jet is inadequatelysupported or improperly guided. On the other hand, a long and gradualentrance curve may require an unnecessary amount of expensive forming.The objective is to design an entrance of minimum length in which posi-tive pressures can be maintained at dl flows.

b. Circular Inlets. A bell-mouthed entrance, which conforms toor encroaches very slightly into the free jet profile of a circularorifice, eliminates occurrence of negative pressure in localized areasat the entrance to a circular conduit (see p 414 of item 101). Anelliptical entrance curve for a circular conduit will satisfy the re-quired streamlining and jet contact requirements if the curve is ex-pressed by the following equation:

X2 , Y2 ,= (3-1)(0.5D)2 (0.15D)2

where X and Y are coordinates measured parallel to and perpendicularto the conduit center line, respectively, md D is the diameter infeet.

c. Noncircular Inlets. The”sluices of a concrete dam are commonlyrectantiar in cross section. WES (item 128) has tested entrance curvesof various shapes. A laboratory-tested elliptical curve is shown infigure a, plate C-22, with the pressure drop coefficients. This simpleellipse is normally satisfactory. For designs of high-head dams mdwhen the conduit has insufficient length to produce substantial backpressure, the comp~und elliptical curve (fig. b, plate C-22) should beused. HDC 211-1/2 shows the effect of upstream face slope of the damon the entrance curve pressures.

3-7. Intake ~er~ Losses. Intake head losses are considered to in-clude all the enerw losses between the reservoir and the sluice proper.The head loss incl~des the form losses generated by the entrance curves,bulkhead or stop log slots, gate passage and gate slot, air vents, -dthe transition between the intake and the sluice proper. They also in-clude the friction losses occurring in the intake structure. Intmelosses are experimentally determined (model and prototype) by assuming

3-4

3-7 m 1110-2-160215 Ott 80

that the fully developed turbtient friction gradient exists between theconduit exit portal and the intake as shown in plate C-2. On the basisof limited model and prototype intake loss data for sluices, an intakeloss coefficient value of 0.16 is recommended for capacity design and avalue of 0.10 when high velocity is critical. When gate slot lossesare not included in the intake lossbe considered.

, a value of 0.01 for each gate mayIf trashracks are provided this value shodd be in-

creased in accordance with data referenced “inparagraph 3-5b.

Section III. Gate Passage, Gates, and Valves

3-8. General. The gate passage may be defined as the passageway inwhich the gate leaves operate. The hydraulic design problems of thegate passage are often closely associated with the structural andmechanical problems in the design of the gate, gate frames, and gatehoist. One of the most important problems in design of gates andappurtenant features is to eliminate cavitation. A basic condition iswhether the gate will be required to operate partially open or willonly be operated fully open. When high-head gates are operated underpartial opening, they may be subject to severe cavitation and vibrationand have a high air demand. When valves =e used for regulation they=e commonly.placed at or near the downstream end of the outlet conduits.This location permits the valves to dischage freely into the atmosphereand eliminates most of the cavitation potential. In some cases, however,the spray so produced may be troublesome to power plmts ad switch-ymds . Gate passages of circular cross section are designed when nec-essary to accommodate circular gates or valves, such as knife or ring-follower gates or butterfly, fixed cone, or needle valves. Rectangulargate passages are used for ordinary slide, tainter, and tractor orwheel-type gates.

63-9. Gate ~es.

a. Vertical Lift. Vertical-lift gates for outlet works are de-fined according to their method of movement. Due to the friction be-tween the gate and the vertical guides, slide gates are generallyoperated by hydraulic cylinders. Tractor and fixed-wheel gates are usedwhere closure of large openings is required. Tractor gates move on anendless chain of rollers on each side of the gate. Fixed-wheel gateshave a series of wheels down each side of the ‘gatewhich be= on verti- --cd guides in the gate slots. Vertical-lift gates are operated eitherby cables or a rigid stem connection to the hoist mechanism. Cable-suspended gates operate in open wet wells which fill to the reservoirpool elevation when the gate is closed; therefore, the hoist mechanism “is located at an elevation above the maximum pool level. This type of

3-5

>,

EM 1110-2-1602 3-9a

15 Ott 80

operation is not usually used for gates which operate partly open forlong periods of time because of possible vibration. See paragraphs4-18 and 4-19 for design problems concerning cable-suspended gates.Hydratiicdly operated gates are preferred for high heads and for longperiods of operation at parti~ openings. These gates have rigidriser stems that recess into bonnets or etiend to a higher floor levelwhere the hydraulic hoist mechanism is located. The hydraulicallyoperated slide gate is used preponderantly in designs for service gateinstallations in sluices of concrete dams. me rectangular slide gategenerally has a height greater than the width to minimize both theflexure on the horizontal members and the unit loads on the verticalguides, and to reduce the possibility of binding in the slot. Thecross-sectional shape of the gate passage in the sluice is usually thesame as the shape of the gate. The upstream face of vertical-lifttype gates must be flat rather than “bellied,” as some gates were inthe past, and the 45-deg lip should terminate in a l-in. verticaletiension (see plate C-23). Rating curve computations =e discussedin paragraph 4-16 md in Appendix D.

b. Tainter Gates. Tainter gates have been used in the PacificNorthwest as service gates in sluices operating under extremely highheads (>250 fi). The characteristics of the tainter gate are favorableto its use for accurate reservoir regulation in both concrete andembankment dams. Advantages of the tainter gate over the vertical-lifttype gate include: gate slots are not required in the walls of thegate passage, which is favorable in partly open gate operation; a rela-tively small hoist capacity is required because the direction of theresultant water load is through the trunnions; and the friction betweenthe gate seals and the gate passage walls is low. A disadvantage ofthe tainter gate is that the entire gate cannot be easily lifted outof the well for maintenance. Tainter gates are placed in an enlargedsection of the sluice and some have eccentric trunnions to facilitatemovement and sealing under a very high head. The enlarged gate sectionmay include an invert step-down as well as side and roof offsets toprovide for complete sealing and for aeration of the jet which most fre-quently discharges as openychannel flow downstream at full gate opening.Under this condition, back pressure in the intake section is essentiallynonexistent and the boundary layer is not fully developed. A modelstudy is usually required to resolve pressure and vibration problemsin pressure flow conduit designs. Discharge coefficients of a partiallyopened tainter gate in a rectangular conduit ~e shown in plate c-24.In general, the discharge coefficient can be considered the same as thecontraction coefficient based on a study of the jet profile (~C 320-3n).

3-6

3-1o

3-10. Centrol Valves.

a. Valve Hydraulics. ~ife gate, needle-type, fixed-cone, andvaious commercial valves have been used for flow control. Dischargerating curves for a valve discharging freely into air or into an en-larged, well-vented conduit can be developed from the equation

Q= CA= (3-2)

where

Q=

c =

A=

H=

g =

discharge in cfs

discharge coefficient

2nominal conduit or valve flow area in ft

energy head immediately upstresm and generally measured fromthe center line of the conduit in feet of water

2acceleration due to gravity in ft/sec

Disch~ge coefficients for freely discharging valves of many t~eshave been determined empirically and will be presented in subsequentdiscussions on specific valve types. Head loss across in-line valvesin pressure conduits can be computed by equation 2-12 using the dimen-sionless valve-loss coefficient K determined experimentally for theparticul= valve and valve opening.

b. Butterfly Valves. Butterfly valves have been used extensivelyfor cutoff valves but are not recommended for flow regulation. Thereis evidence that the butterfly valves in the 11-ft-diam flood controlconduits at Summersville Dam may have contributed to the failure ofthe 9-ft-diam fixed-cone valves immediately downstream (item 80).

c. Needle-Type Valves. The needle valve opens and closes by thehorizontal movement of a needle; the valve is closed when the needleis advanced to its efireme downstre~ position. The water flows in anannular passageway first diverging and then converging past the needle.Discharge from nee~e valves can be computed using equation 3-2, whereA and H are the area md ener~ head, respectively, at the inlet end,and C is a discharge coefficient. Kohler and Bdl (in Davis andSorensen, item 24) show the full open coefficient to be about 0.60 when

3-7

m u1o-2-16o2 3-1OC15 Ott 80

the ratio of outlet diameter to inlet diameter is 0.95. Thomas (item120) gives discharge coefficients for partly open 86-in. needle valves.me hollow-jet valve is a modification of the needle and the needlemoves upstream to close the outer casing of the valve. Model testsof the hollow-jet valve for Anderson Ranch Dam showed ftily open dis-charge coefficients of approximately 0.70. Thomas also presents dis-charge coefficients for partly open valves in item 120. Nag presentsa good summary of the characteristics,the uses, and the limitationsof free discharge regulating valves in item 78.

d. Fixed-Cone V~ves. The fixed-cone valve is similar in princi-ple to the hollow-jet valve except that the cone pointing upstream onthe downstream end is stationary ad a sleeve of the outer casing movesdownstream to close the valve. The shape of the issuing jet is ahollow cone. The discharge coefficient curves for fixed-cone valvesare shown in plate C-25. The coefficients for the six-vine valve arebased on tests by TVA (item 29). A comparable coefficient curve for afour-vane valve reproduced from HDC 332-in is also shown in this plate.Model-prototype confirmation of the hydraulic characteristics of thesev~ves has been studied by Lancaster (item 58). The shell of a six-vane valve has been found to be less likely to vibrate than that of afour-vane valve. In a nmber of cases, flow-induced vibration offixed-cone valves has resulted in serious and costly damage (items 71and 80). Hoods cm be designed for these valves to control the sprayof the jet (items 31 and 81).

e. Comtnercid Valves. Many types of commercially available valvesare available for small conduits and water-supply systems. Some ofthose most commonly used are the knife gate and other gate valves. Headloss coefficients for lenticular- ~d crescent-shaped opening, in-linegate valves are given in HDC 330-1. Kntie gate valves are recommendedfor free discharge installations.

3-11. Metering Devices. mere accurate monitoring of outflow is re-quired the inclusion of a metering device in the system should be con-sidered. Mmy schemes can be considered, varying from venturi udelbow meters to acoustic and electronic systems. The installation ofsuch devices eliminates the need for extensive calibration of gates andvalves under varying operating conditions and generally results in flowmeasurements with errors from about ~5 percent to 21 percent. It is nec-essary that all flow measuring devices of these types be installedaccording to standard specifications for proper, cavitation-free oPera-tion. If the provision of metering equipment is contemplated, WESshould be consulted relative to available t~es and to their installa-tion and operation requirements and limitations.

3-8

3-12

3-12. Gate Passageway Requirements. Normally, whenflows require regulation the following are provided:

EM 1110-2-160215 Ott 80

reservoir outlet

a. Two or more gate passages such that if one passage is inopera-tive, a reasonable flow re@ation as pertains to project purposes isobtained.

b. Rnergency gate provision (tandem or transferable) for eachservice gate passage so that if a service gate is inoperative in anyposition, closure of the gate passage can be made with the emergencygate for any pool level.

c. Bulkhead provisions for each gate passage for inspection andmaintenance of the service and emergency gates. As a minimum, thebulkheads must be capable of being installed at the lowest pool eleva-tion that has a reasonable frequency and length of occurrence sufficientfor inspection ad repair purposes. All judgment factors involved inthe above should be fully discussed in the design memorandumpresentation.

3-13. Gate Slots. The guide slots of rectangular gates produce a dis-continuity in sidewalls which may cause cavitation, unless speciallydesigned. It has been common practice to use metal-liner plates down-stream from the gate slots to protect the concrete from the erosiveaction of cavitation. The recommended guide lines for metal liners aregiven in paragraph 3-16. The gate slot in the roof of the gate chambermd air vent slots present similar design problems. Design details forslide gate roof, side, and air vent slot details are shown inplate C-23. Pressure coefficients (item 123) for detailed examinationof this gate slot design for high heads (>250 ft) ae given in figure a,plate c-26. To obtain dimensional local gate slot pressure data, thepressure coefficients given in this plate are multiplied by the flowvelocity head in the gate passage and algebraically added to the back-pressure gradient elevation at the gate slot. Tests by Ball (item 6)show that doubling the downstream taper length from 12 to 24 units re-duces the severest pressure drop coefficients (C) from -0.16 to -0.12for comparable slot geometry. Therefore, it is recommended that forheads >250 ft the taper downstream of the gate slot be modified to1:24. For conservative estimates of minimum pressures at gate slotswhere streamlining is not provided, the pressure coefficients in fig-ure b, plate c-26, shouldbe used. In detailed design studi~s it may bedesirable to check the gate slot design for potential incipient cavita-tion. This can be done by solving equation 2-19 for the absolute con-duit pressure PO necessary for cavitation and comparing it with thecomputed minimum pressure at the slots. Plate C-27 gives incipient

3-9

m 1110-2-1602 3-13

15 Ott 80

cavitation coefficients ai for various slot geometries. These valueswere obtained using relatively large scale (1:3) plastic models to re-duce possible errors from scale effects. A Ui value of 0.4 is recom-mended to check cavitation potential. For conservative design, thecomputed minimum pressure should be appreciably higher (15 ft or more)than the incipient cavitation pressure. The head losses for gate slotsare generally included in the composite intake loss discussed in para-graph 3-7. When gate slot losses are not included in the int~e loss,a loss coefficient K value of 0.01 is recommended for each pair ofgate slots for use in equation 2-12.

3-14. Gate Recess. Hydraulically operated control gates recess intobonnets and cable-suspended gates into wet wells. The necess~ dimen-sional clearances for gate operation ~e usually based on mechanicaland structural requirements rather than hydraulic. The primary hy-draulic consideration is the relative upstream and downstream clearaceat the roof recess when the gate passage is operated at part gate open-ing. The upstream clearance at the roof should be appreciably largertha the downstream clearance to assure maintenance of a hydrostatichead in the well or bomet for gate stability. If the downstreamclearance exceeds the upstream cle=ance the gate well can be suckeddry =d the gate may float or catapult or oscillate under certainoperating conditions (see p=a 4-18b).

3-15. Gate Seats. In general, the gate seat is flush with the floorof the gate passage.

3-16. Steel Liners. Steel liners in concrete conduits have been usedwhere experience indicates cavitation is likely to occur such as down-stream from control gates and valves where a high-velocity jet occurs.For heads above 150 ft, a metal liner should etiend 5 ft downstreamfrom the gate. For heads below 150 ft, no liner should be required.If a liner is necessary, it should not terminate at a monolith jointor in a transition.

3-17. Air Vents. The following guidance is recommended for air ventdesign:

a. Control valves and gates that are located a considerable dis-tance upstream ffom the exit (i.e., do not dischmge into the atmosphere)require air vents. An air vent is required for each service gate. Airvents are not required for emergency gates when those gates are lo-cated immediately upstream of air-vented service gates. Extreme cautionmust be observed if the emergency gate is used for regulation. Airdemand will create very low pressures in the service gate recess. The

3-1o

3-17a EM 1110-2-160215 Ott 80

attendant conditions must be carefully analyzed to prevent damage and/ordanger to personnel.

b. The size of air vents can be determined as per HDC 050-2nwhich assumes that the maximw air demand occurs at a gate opening of80 percent fully open and the maximum air velocity in the vent does notexceed 150 fps. It is further suggested that air vents be designed sothat the head loss through the vent not exceed 0.5 to 1.0 ft of water(i.e., air vent outlet pressure head of -0.5 to -1.0 ft of water).Although air vents are usually designed assuming incompressible flow,high-velocity local flow should be checked to determine if flow isincompressible (item 109).

c. Air vent passages should use generous bend radii and gradualtransitions to avoid losses and, particularly, excessive noise.

d. Air vent intakes should be so located that they are inacces-sible to the public and they shodd be protected by grills. The intakeentrance average velocity should not exceed 30 fps.

e. Interconnected air vents (one main vertical stem manifolded tovent more than one gate) should be avoided; but if they are necessary,the connections should be above the maximum possible elevation of thepressure grade line at the air vent exit opening to prevent crossflowof water.

.....Of. The air vent exit portal should be designed to assure spread of

air across the full width of the conduit. The air vent should terminateinto a plenum located in the conduit roof and immediately downstream ofthe gate. The plenm should extend across the full width of the conduitand should be vaned so that the air flow is evenly distributed. PlateC-23 illustrates a typical air vent exit into the gate chamber.

Section IV. Sluice Outlet Design

3-18. General Considerations. Generally, sluices should not be designedfor combined spillway and sluice operation. However, in cases wherelarge sluice capacity is required for diversion flows or normal reser-voir regulation, combined operation may be considered and evaluated interms of economic, hydrologic, and hydratiic benefits to be obtained.Potential benefits include (a) reduction in spillway length with savingsin spillway and stilling basin construction costs, (b) reduction in maxi-mum head on the spillway, and (c) more advantageous use of reservoirsurcharge to reduce peak outflows. Simultaneous spillway and full sluiceoperation should be limited to conditions of thick (at least 10 ft)

3-11

m 1110-2-1602 3-1835 oct 80

spillway nappe flow over the outlet to minimize the possibility of nega-tive pressures at the sluice exit portal (item 15). With thinnernappes, the sluice flow should be limited to 40 to.’i’Opercent gateopenings to obtain maximum air intake to relieve low pressures at theexit portal and on the spillway face immediately below (item 140). Ex-perience with combined operation has been limited to structures not ex-ceeding 150 ft high. Caution should be used in designing for greaterheights where very high velocities and thinner spillway nappes wouldOccw . In general, sluices should be closed when spillway operationbegins. In projects not model-studied for combined flow operation,combined flow should only be permitted when the free flow capacity ofthe spillway is expected to be exceeded and the structure is endangered.The sluices should be opened and operated preferably only with a thickspillway nappe flowing over the sluice outlets. One sluice inoperativeshould not jeop~dize the integrity of the dm. Operation @d reservoirregulation manuals must reflect these restrictions.

3-19. Exit Portal Constructions. A sluice in a concrete dam is seldomlong enough to develop the desired back pressure from friction lossesnecessary to prevent cavitation damage and it may be desirable to usean exit constriction. A 10 to 15 percent area constriction at theexit portal can be provided by gradually depressing the conduit rooffrom some point upstream to the exit portal or by a deflector formed inthe exit portal invert (plates c-28 and C-29). Roof constrictionsshould be used when the sluice is curved vertically downward to ter-minate the conduit invert tangent to the sloping spillway face or tothe spillway toe curve (plate c-28). This t~e of design does not aidin horizontal spreading of the sluice jet; but if jet spreading isrequired to improve stilling basin performance, it can be accomplishedby flaing the sidewalls in combination-with”a roof constriction‘-(plate C-30), or by use of sidewall flare with a tetrtiedral deflector(plate C-29). Both designs require efiension of the sidewall flaresin the spillway face downstrem of the exit portal. Tetrahedral de-flectors are also used when the sluice forms an abrupt junction withthe spillway face nd the sluice flow spreads in a free fdl into thetailwater (plate C-29). When the sluice is appreciably above thespillway toe curve and spreading of the sluice jet is not a problem,gradual depression of the sluice exit portal roof and curving thesluice vertically downward to a smooth junction with the sloping spill-way face (plate C-30) is preferable to deflector blocks and the jetplunging into the stilling basin.

3-20. Sluice “Eyebrow” Deflectors. Extensive cavitation damage hasoccurred at exit portals during s~illway flows with and without simul-taneous sluice operation. This damage usually originates at low

3-12

3-20 EM 1110-2-160215 Ott 80

pressure areas where the outlet portal.roof intersects the spillway faceand progresses downward along the intersection of the sluice ‘sidewallsand the spillway face. USBR studies (item 140) of the Folsom Damspillway showed that when the junction between the sluice invert andthe spillway face is abrupt, the spillway jet can impinge upon thesluice invert with part of the flow entering and intermittently fillingthe sluice. This restricts effective venting by the sluice gate airvent with subsequent subatmospheric pressure at the sluice outlet roof.The USBR tests also showed that impinging of the spillway flow on thesluice exit portal invert res~ted in flow separation from and undesir-able low pressure on the spillway face downstrem. The use of “eyebrow”deflectors on the spillway face (plate C-31) effectively lified thespillway jet away from the sluice invert and permitted adequate ventingof the exit portal by the sluice gate air vent. However, undesirablelow pressures at full sluice gate opening were still evident immediatelydownstream on the spillway face. Deflectors of this type have beenmodel-tested by the Corps of Engineers for Detroit, Red Rock, and otherprojects.

. .. ..

3-13

..,,

4-1 EM 1110-2-160215 Ott 80

CHAPTER 4

OUTLET FACILITIES FOR EMBANKMENT DAMS

Section I. Basic Considerations

4-1. Approach Chmnel. The purpose of the approach channel is to con-vey the water from the reservoir to the conduit intake structure. Insome cases, the channel may function for diversion of the river duringconstruction. The outlet.channel design, bless extremely long, is-usually dictated by the outlet works size and alignment. The alignmentof the approach charnel should take advatage of the area topography todecrease the channel excavation. Excessive curvature in the outletchannel near multiple gate intake structures should be avoided to helpprevent unequal distribution of flow through the gate passages.

4-2. Conduits and Tunnels for fibankment Dams.

a. Aliment. The alignment and grade of conduits and tunnels aregoverned by diversion, evacuation, and operating requirements; tailwaterelevation; topography; foundation conditions; and location of the damand spillway. It is desirable to design conduits or tunnels that areas straight in alignment as practical, since a bend increases the hy-draulic losses and creates unbalanced flow downstream from the bend.If it is necessary to change the direction of flow, the change shouldbe accomplished with a long, easy, circular curve. ~.e curved sectionshould be located as far upstream from the exit portal as feasible inorder to improve the flow conditions in the stilling basin. A modelstudy should be made for questionable cases. Flow around bends causesdynamic and static reactions against the conduit or tunnel wall whichshould be considered in design, particularly for free-standing steelconduits within tunnels. Conduits and tunnels should have adequateslope for drainage; and when appreciable foundation settlement causedby embankment loading is anticipated, the vertical alignment shouldcontain sufficient camber to compensate for the settlement.

Conduit Elevation. As with sluices for concrete gravity dams(see ~~a 3-3a), the reservoir appurtenance requirements pl~ an impor-tant part in determining the elevation of the flood control conduit.me inlets must be set low enough to drain the reservoir as required(ER 1110-2-50d) with due consideration of the conduit elevation rela-tive to stilling basin design. A conduit at a low level may have betterfoundation conditions and higher discharge capacity for diversion andother low pool level operation; however, a longer conduit may be re-quired ud poor stilling basin action may result from high tailwater

4-1

y5 ;::oj;-1602 4-2b

levels. Higher level conduits may have shorter length and the bestpotential for good stilling basin action and good flow conditionsthrough the conduit for all discharges; but foundation conditions mayrequire its location to be farther from the river channel, and alarger conduit may be needed for diversion or design capacity.

c“ % Flood control conduits for embankment dams are usuallyeither cut-and-cover or tunnel construction. Although some cross-sectional shapes are superior to others from a hydraulic standpoint,structural md construction considerations usually establish the typeof cross section. A circular cross section is the most efficient sec-tion for a tunnel flowing full. Horseshoe-shaped and rectangular sec-tions provide large flow areas at low depths, which m~e them desirablefor diversion purposes. The discharge capacity decreases sharply whenthe depth of flow in a rectangular conduit increases from nearly fullto completely full flow, since the wetted perimeter is suddenly in-creased. The oblong shape has depressed pressure gradients at the exitportal compared with other shapes, when the outlet chute walls actsomewhat like a draft tube (see para 5-2d(2)). Hydraulic characteris-tics of several shapes are shown in plate C-5..—

d. Spacing. Where more than one conduit or tunnel is required,the spacing affects the stilling basin and intake design. Multiplecut-and-cover conduits should be spaced as close together as structuralrequirements permit in order to allow use of a singlekstillingbasinand a minimum width intake structure. EM 1110-2-2901 discusses thespacing of multiple tunnels from the standpoint of geological andstructural requirements. If the tunnels are designed with individualstilling basins, the spacing at the outlet portal must be sufficientto provide the necessary width of stilling basin for each outlet.

Section II. Intake and Gate

4-3. Intake Structures. The types of intakeinclude gated tower, multilevel, uncontrolled

Facilities

structures commonly usedtwo-way riser, and/or a

combination of these. Intakes &d control gates for embankment dmsare discussed as integral structures, but if designed as separatestructures, the principles of the hydraulic design are essentiallythe sac. me hydraulic design of the intake structure should addressthe problems of (a) head loss, (b) boundary pressures, and (c) vorticesin the approach.

a. Loss Coefficients. Loss coefficients for conduit intake struc-tures with all gates operating range from 0.06 to 1.32 times the conduitvelocity head. Available data from various geometries ad gate

4-2

4-3a ~ 1110-2-16021980

operating schedules are summarized in plates C-32, C-33, and C-34. Itis recommended that for discharge calculations, conservativevalues beselected from these plates in accordance with the planned intakegeometry. Many of the coefficients given include allowance for trashstruts or fender losses.

b. Boundary Pressures. Pressure gradients for intake structuresshould be developed to show local average pressure chages resultingfrom flow velocity changes. These gradients are helpful in evaluatingpressure conditions in”intakes, gate passages, and transitions. Theyshould be examined in terms of the conduit back pressure for the entireoperating range. This can be done by applying the energy equation(eq 2-3) to local changes in areas. Average pressures do not reflectpressure fluctuations due to turbulence, and cavitation potential shouldbe evaluated according to the criteria ”tiscussedin paragraph 2-16.

c. Vortices. Vortices at intake structures can affect int*eefficiency and create a safety hazard to the public. Although vorticesare usually associated with high discharges and shallow intakes, theyhave been observed at intakes submerged as much as 60 to 100 ft (items “43, 95, 125, 1313 and 138). Antivortex devices have been installed atint~es located at shallow depths. The intensity of the circulationphenomena set up around an intake is a function of the submergence ofthe intake, the discharge, and the intake and approach channel geometry.Gordon (item 43) has developed design guidance for preventing undesir-,able vortices (intensity such that they draw air and surface debrisinto the structure) at power plant intakes (plate C-35). Data forobserved prototype vortices at Enid (item 131) and Denison (item 125)Dams have been included in this plate. It is recommended that Gordon’scurve for unsymmetrical flow be used for design purposes. Reddy andPickford (item 95) have analyzed vortex &ta pertinent to pump sumps andpublished a design chart for evaluating vortex potentiality for thesestructures. They concluded that when vortex prevention devices are usedthe critical submergence (ratio of water depth above top of inlet toinlet diameter - both dimensions at the entrance to the inlet bell mouth)should equal or exceed the inlet flow Froude number (otherwise,it shouldequal.or exceed Froude number plus one) to provide vortex-free operation.Model studies are suggested in questionable instances.

d. Trashracks and Struts. If protection against clogging or debrisdaage to gates or turbines is needed, see the design guidance given inparagraph 3-5.

4-4. Int~e Tower Versus Central Control Shaft. Both the intake towerand the centr~ control shaft have their respective advantages. The

4-3

~ ~::o----16o2 4-4

intake tower may be expected to have higher back pressure at the gatesection caused by the friction loss of the long downstream conduit.This is an advantage in the elimination of possible cavitation. As theintake tower has gates near the upstrem end of the conduit or tunnel,the danger of leakage into or out of the embankment or abutment, withresultant piping of the material, is minimized. When the gates areplaced near the upstream end of a conduit, there is the important ad-vantage of being able to unwater the entire length of conduit for in-spections. A central control shaft, which is usually located in anabutment near the axis of the dam, has the advantage of being protectedfrom freezing and thawing and from forces due to ice action. In a cen-tral control the intermediate pier or piers are subject to high veloci-ties and me designed to eliminate possible cavitation. The centralcontrol shaft has an advantage of not requiring a bridge for access asis the case of an intake tower. However, the conduit upstream of acentral control shaft must be designed to withstad the reservoir head,and a trasition is required both upstream and downstream of the gatepassages. Foundation conditions and economic comparisons may dictatethe choice between the intake tower and the central control shaft.Reservoir operating schedules may require the release of dischargesunder various heads and gate openings resulting in the pulsating flowcondition (“burping”) discussed in paragraph 2-4d. In some cases thisundesirable condition can be eliminated by use of a central controlshaft to shorten the conduit length downstream from the control gate.Further discussion of gate structure locations is given inEM 111O-2-24OO.J

4-5. Submerged Int*es. The submerged int~e is a comparatively simpleand economical structure most often equipped with trash struts and bulk-head slots, having a streamlined entrsnce to the conduit or tunnel whichis submerged at a low reservoir level. The submerged intake is satis-factory for reservoirs that function solely for flood control. However,when the intake will be permanently submerged by a conservation pool,difficulty arises in unwavering the conduit or tunnel upstream of theservice gates. When bul~ead slots are located downstream from the in-take face, provisions must be provided for closing the roof slot to pre-vent a high-velocity jet from entering through the slots and causingcavitation damages to the roof immediately downstream (item 20). Useof divers for bulkhead installation is to be avoided.

4-6. Combined Intake and Gate Structure. This is a coxmnontype of in-take tower that usually requires a bridge for access, and gate wellsare.provided to accommodategency gate is upstream fromtion and maintenance of the

the service and emergency gates. The emer-the service gate and is utilized for inspec-service gate passage. The gate wells are

4-4

4-6 EM 1110-2-160215 Ott 80

generally wet for low head, wet-dry combination for intermediate head,ad dry for high head structures. Determination of the well type isfrom structural and mechanical.design considerations. A float well isnormally provided for installation of a reservoir stage recorder.Bubbler gages are also used for this purpose and require less space.It is desirable to have two or three separate levels for the float wellint~es, and they should be away from any drawdown effects when re-leasing large flows.

L-7, Underground Control Structures. An alternative to the conventionaltower-t~e structure is an underground control structure buried beneaththe embankment or in the abutment with a downstrea access gallery.The access gallery should be placed adjacent to and at the same eleva-tion as the water passages, essentially forming a multiple-box structure.Horizontal air vents will require check valves to prevent flow of waterthrough them. The underground gate structures may be more economicalthan the conventional tower-dry well structure for high operating heads(~150 ft). Another economical advantage of this type of structure isthe elimination of the service bridge which is required for a towerstructure. Other conditions under which an underground structure shouldbe considered include projects where water quality releases do not re-quire multiple intakes over a wide range of reservoir levels and wherereservoir operation results in periodic drawdown of pool level to thetop of the int&e bulkhead structure. Structural considerations arediscussed in item 83. ~is type of structure has been used by othersand by the Corps at the Fall Creek Dam in the Portland District md theNew Hogan Dm in the Sacramento District.

4-8. Downstream Control Structures. Flow control facilities locatedat the downstream end of a conduit, when closed, subject the entire con-duit to the full reservoir head and the possibility of high pressureleaks, piping along the conduit, and subsequent failure of the embank-ment. Therefore special design precautions are necessary when the con-trol structure is located at the downstream end of the outlet conduit.The conduit between the impervious cutoff and the control structure maybe a freestanding steel conduit housed in a concrete-lined tunnel ofsufficient size to permit access for maintenance. This type of construc-tion is frequently used for penstocks through embankments. Outlet facil-ities with downstream control must also have an emergency gate upstreamof the steel conduit and stop log provisions at the conduit entrance.Provisions must be made for continued releases as required during shut-downs of primary release facilities.

4-9. Gate Passageway Requirements. The requirements discussed forsluice gates in paragraph 3-12 also apply to control gates for conduits

4-5

EM u1o-2-16o2 4-9

1980

through embankment dams. Normally a service gate, an emergency gate,and slots for bulkheads or stop logs should be provided for each gatepassage to the conduit or tunnel. The total flow cross-sectional areaof gate passages should exceed the downstream conduit area by 10 to 15percent. ~ical gate installations for both tainter and vertical-lifigates are shown in plate c-36.

4-10. Low-Flow Releases. The operation of large gates at small openings(<0.5 ft) is not recommended because of the increased potential for cav-itation downstream from the gate slot. In cases where low-flow releasesare required, consideration should be given to low-flow bypass culverts,center pier cdverts , multilevel wet well facilities (see Chapter 6),or a low-flow (“pig~-back”) gate incorporated in the service gate.

Section III. Entrance Shapes

4-11. %neral. The general design of entrance shapes, discussed inparagraph 3-6, is equally applicable to conduits for embankments andconcrete dams although the structmal setting and some details aredifferent. Entrances in concrete dams are ordinarily constructed asbell mouths for circular conduits and with entrance curves at the top,bottom, and sides for rectangular conduits. In embankment dams, theconduit inverts are normally set at approximately the same elevation asthe floor of the approach channel. Consequently, there is little curva-ture of the invert approachso that a bottom curve is not required.In the case of embankment dm intakes with two or more gate passages,there usually is insufficient lateral space for full bell-mouthed en-trance curves on the sides, so that only the roof is bell-mouthed andthe piers and sides are extended upstream to support the trash struts.The sides and piers are c=efully transitioned from rounded noses to thegate passage. In the case of a single r~tangular gate passage”,the topand sides can be flared or treated as above.

4-12. Selection of Entrance Shape for Design. A comprehensive seriesof tests on flared entrances has been conducted at WES (item 76). In-take roof curves for conduits with fully suppressed intake inverts andlimited lateral space for side flares should be designed as indicatedin plate C-37. The short elliptical shape (fig. a, plate C-37) issatisfactory when the back pressure on the intake is great enough toprevent low local pressures. The long elliptical shape shotid be usedwhen back pressure is not adequate to eliminate low local pressures(fig. b, plate C-37). The effects of upstre~ face geometry aregiven in HDC 221-2n and item 20. Int*es with sufficient lateral spacefor sidew~l stretiining should have curves as shown in plate C-22 anddiscussed in paragraph 3-6c.

4-6

4-13 EM 1770-2-160215 Ott 80

4-13. Linear Sidewall or Pier Flare. WES studies show that entranceroof pressure conditions for two-dimensional curves can be improved bytapering the divider piers. Plate c-38 shows the improvement of pres-sure conditions from using line= sidewall ad/or pier flare. ~necomputational procedure is illustrated in HDC 221-3 and 221-3/l. Two-dimensional roof curve pressure coefficients can be converted to three-dimensional coefficients for side flare by:

where

c =

A=

2

()

‘2C3 = C2 q

pressure drop coefficient

flow area in square feet at the point of interest

(h-l)

Subscripts 2 and 3 indicate two- and three-dimensional values, respec-tively. Unless model-tested, it is recommended that application ofequation ~-l be limited to the cases where the horizontal flare doesnot exceed 1 horizontally to about 12 longitudinally.

Section IV. Control Gates

4-14. General. The types of gates and valves md their operatingcharacteristics discussed in paragraphs 3-8 to 3-17, are equally appli-cable to conduits for emb-ent dams. Generally, a service gate, anemergency gate, and slots for bulkheads or stop logs =e provided foreach gate passage to the conduit or tunnel (plate c-36). Cable-suspended tractor or hydraulically operated tractor or slide gates arenormally used in conduits for embankment dams. The problems of deter-mining the hydraulic forces acting on tractor gates, with emphasis oncable suspension, will be discussed in this section. Although downpullforces on a partially opened gate constitute a hoist design problem inboth hydraulically operated and cable-suspended gates, the vibrationproblem is more critical in the design of cable-suspended gates. Forthis reason cable-suspended tractor gates are not recommended for flowregulation or for heads in

4-15. Gate Lip Geometry.the 45-deg gate lip designunder all flow conditions.

excess of 150 ft.

Laboratory and field tests have shown thatshown in plate C-23 performs satisfactorilyThe 45-deg lip should terminate in a l-in.

4-7

,...

~ 1110-2-1602 4-15

15 oct 80

vertical etiension to ensure that the jet springs free from the upstremedge of the lip. The upstrem face should be flat rather than “bellied”in order to have uniform flow conditions across the width of theconduit.

4-16. Vertical-Lift Gate Discharge Computations. Plate C-39 presents asuggested design discharge coefficient curve for use with equation 3-2for developing rating curves for vertical-lift gates with 45-deg bottoms(plate C-23) md assuming free-surface flow downstream of the gate.Stage-discharge relations for selected gate openings and ~r free-surface flow downstream can be computed with CORPS H3201. Single gatepassage structures of nominal length and reservoir head generally havedownstream free-surface flow for gate openings up to 80 percent of thegate passage height. In multiple gate passage structures, this 80 per-cent value may be greatly reduced with two or more gates partially open.In any event, computation of the flow profile between the gate and con-duit exit portal is necessary to ascertain the gate opening at which flowcontrol shifts from the gate to the exit portal due to conduit frictionfor a given pool elevation, thus possibly causing flow pulsations(“bmping” ) as discussed in para~aph 2-4d. Generally, the downstreamconduit slope is mild and the flow profile will be the M3 type (seeplate C-l). Therefore, an initial depth in the downstrem conduitproper must be estimated and the profile computation proceeds in thedownstream direction. For a single passage structure, or for a mtitiplepassage structure with balanced operation, it is recommended that thisdepth be estimated from the jet vena contracta and assume an ener~ lossbetween the gate and the conduit proper (transition loss) of 0.1 timesthe jet velocity head. For unbalanced gate operation, it is recommendedto assume this ener~ loss at 0.2 times the average jet velocity head.

4-17. Commercial Gates. There are many commercially available slidegates, tainter gates, knife-gate valves, flap gates, etc., that arereadily adaptable to low headnand small disch=ge flood control anddrainage projects. HDC 340-1 presents head loss coefficients for flapgates used extensively in flood protection ad drainage projects.Pickett et al. (item 93) have compiled considerable data on dischargeand head loss coefficients for various types of gates and valves.

L-18. Hydraulic Load for Vertical.-LiftGates.

a. General. The hydradic load on the gate leaf should be deter-mined both for gate closed and part gate operation. Hydraulic loadsare computed in the usual manner with the gate closed and the reservoirat maxim level. The vertical hydraulic loads on the gate duringpartly open operation can be separated into upthrust on the bottom =d

4-8

4-18a EM 1110-2-1602

15 Ott 80

downthrust on the top as indicated in HDC 320-2.n The upthrust for ~5-deg gate bot~oms determined from model and prototype tests is shown inHDC 320-2/1. Both slide gates and tractor gates are included. Theunit upthrust load is in terms of the effective head on the gate. Asimilar typenof graph for downthrust on the top of the gate is shown inHDC 320-2/2. The data on downthrust are applicable only to gates withsimilar upstream and downstream clearances between the gate and the roofslot boundaries. HDC 320-2/3 pre~ents a smple computation illustratingthe use of HDC 320-2/1 and 320-2/2 in the solution of a hydraulic andgravity force problem. AdditionQ hydraulic load data have been reportedby Simmons, Naudascher et al., and Smith (items 113, 79, ad 115, respec-tively). The occurrence of free-surface or ftil conduit flow downstreamfrom the gate, the trmsition from either to the other, and the gatespeed may have considerable effect on the hydraulic load.

b. Gate Catapdting. An intake gate is sometimes used for rapidlywatering-up the penstock and turbine scroll case, or the space betweenthe sefiice and emergency gates, by simply opening the int~e gate a few ‘inches. As the space between the int~e gate and downstream gate be-‘comesftil, the water may rise through an opening between the downstreamside of the intake gate and the gate slot. If this back-of-gate openingarea is smaller than the gate opening area, it may restrict the verticalflow of water into the gate slot. Under these conditions sufficient hy-dratiic forces on the gate have occurred at several projects that wouldabruptly raise or “catapult” the gate tens or even hundreds of feet upthe slot (items 40 and 98).

4-19. Vibration of Cable-SuspendedGates. Thompson (item 121) treatsthe theory of vibration with the determination of whether any disturbingfrequencies are inherent in the hydraulic system of a design that may -approach the natural frequency of elements of the system (gates, valves,splitter piers, stilling basin walls, etc.). As the magnitudes and fre-quencies of the exciting hydraulic forces can only be approximated inmost cases, it is necessary to effect conservative designs. Fortunatelymost of the exciting hydraulic forces have high frequencies and thenatural frequencies of the various elements of the structure =e verylow. The case of an elastically suspended conduit gate is used toillustrate application of the theory.

a. Resonance. When the forcing frequency is exactly equal to thenatural frequency a condition of resonance exists. The displacement~plitude for the vibrating system increases without bound ad is gov-erned onlystructural

by the amount of damping inrupture. The amplitude can

4-9

the system. This may result inalso increase rapidly if there is

EM 1110-2-1602 4-19a15 Ott 80

only a small difference between the forcing and natural frequencies.The undamped magnification factor

x 1—=xo ff 2

1-()~

(4-2)

where ff/fn is the ratio of the forcing frequency to natural frequency,represents the factor by which the zero frequency deflection x of thespring-mass system under the action of a steady force must be m~tipliedto determine the aplitude x . It is desirable to produce a desi~with a low magnification factor.

b. Forcing Frequencies. Two possible sources of distmbing fre-quencies are the vortex trail shed from the bottom edge of a partiallyopen gate and the pressure waves that travel upstream to the reservoirand are reflected back to the gate. The frequency of the vortex trailshed from a flat plate oriented with face perpendicular to flow directionca be defined by the dimensionless Strotial number, St’

as follows:

(4-3)

where

Lp = plate width

f= = vortex trail shedding frequencyL

V = velocity of the fluid

The Strouhal nwber for a flat plate isfrequency of a vortex trail shed from a

approximately 1/7. The forcinggate may be estimated as:

(4-4)

L-1o

1+-19b

where

He =

g =

Y =

EM 1110-2-160215 Ott.80

ener~ head at the bottom of the gate

acceleration due to gravity

projection of the gate into the conduit or half of the platewidth L

P

Unpublished observations of hydraulic models of gates have indicatedthat the vortex trail will spring from the upstream edge of a flat-bottomgate causing pressure pulsations on the bottom of the gate. The vortextrail springs from the downstream edge of a standard 45-deg gate lip,eliminating bottom pulsations. A more recent research study at Iowa(item 60) on flat-bottom gates indicates that the 45-deg sloping gatebottom used by the Corps should be free of “vibrationinduced by vorticesshed from the gate lip. The frequency of a reflected positive pressurewave may be determined from the equation:

‘f ‘k(4-5)

where

c = velocity of the pressure wave

L= length of the conduit upstream from the gate

The pressure wave velocity is dependent upon the dimensions and elasticcharacteristics of the pipe or of the ~ining and surrounding rock of atunnel. Data are given in HDC 060-1/2 by Parmakian (item 90) for vari-ous combinations of these variables.

c. Natural Frequency. The natural frequency of free verticaloscillation of a cable-suspended gate can be expressed by the equation:

(4-6)

4-11

m 1110-2-1602

15 OCt so

4-19C

where

E=

2=

0=

d.

modulus of elasticity of

len@h of the supporting

unit stress in the cable

Sample Computation. HDC

the cable

cable

060-I/4 and 060-1/5n present samplecomputations illustrating the above theory.

Section V. Transitions

4-20. Genera. Transitions are required to effect changes in conduitsize (expansions and contractions) and shape (rectangularto circular,circular to rectan~=, etc.). They may be abrupt with high head lossor streamlined with small head loss depending upon the purpose. At MicaD~ abrupt expansions have been designed as in-line ener~ dissipators(item 104). Singh (item 114) has recently presented a procedure for de-signing a streamlined circular-to-rectan~ar transition resulting inessentially a straight-line variation in area effecting improved hy-draulic performance. Transitions fall into three general categories:(1) entrance, (2) in-line, and (3) exit. In flood control conduits,trmsitions are used to connect a usually rectangular gate passage tocircular- horseshoe- r oblong-shaped conduits. They are also used atconduit exits to help spread the flow prior to entering the energy dis-sipator. In sluices they are frequently used to effect exit portalconstrictions, to increase sluice back pressure, ad to spread the jeton the spillway face.

4-21. Entrance and Intake Transitions. Entrance transition design forboth circular and noncircular inlets has been discussed in paragraph 3-6.~ical entrance transitions are shown in plates C-21, C-32, and C-33.From the data presented in these plates, it cancoefficients for well-designed simple entrancesthe conduit velocity head. In complex intakes,eluded in the combined intake loss. Comparableare given in plates C-22, C-37, ~d c-38.

4-22. In-Line Trmsitions.

a. Location. Water usually flows through

be assumed that losswill not exceed one-tenththe entrance loss is in-entrance pressure data

several different passage-ways in its route from the reservoir to the river below the dam. Transi-tions have the function of providing a smooth change from one cross sec-tion to another in such a maner than hydradic losses and cavitation

4-12

4-22a EM 1110-2-160215 Ott 80)

potential are minimized. Transitions are generally required at one ormore of the following locations: (1) between the intake gate passagemd the upstream end of a circular conduit, (2) upstream and downstremfrom a central control gate passage, and (3) at the outlet end of theconduit. If gate passages are the sme height as the downstream conduit,double curvature of the transition fillets will be avoided.

b. Smoothness in Direction of Flow. A well-designed transition .should provide a gradual change in area boundary shape. The trasitionbounduies should follow easy curves, with intervening tangents ifrequired, and the curves should be well defined to facilitate construc-tion. The maximum change in flow direction occurs along the path ofconvergence of the outside corners of the transition. The junction ofthe corners of the transition with the desired section downstream shouldbe carefully checked to determine whether the desired curvature is ob-tained to prevent the occurrence of separation or negative pressuresalong corner boundary lines. Construction joints should not be locatedat or nea the end of the transition. Since a negative direction changeof boundary (away from the flow direction) reduces pressure, any mis-alignment of construction forms or subsequent small movement of monolithson either side of a joint may further accentuate the drop in pressuremd cause cavitation. (See item 7.)

C“ ~ The required length Ofthe transition as Comparedwiththe conduit diameter depends upon the lateral, vertical, and diagonalboundary changes. The number ad arrangement of gate passages alsoaffect the len@h of the transition. As the number of gate passagesincreases, the lemgth of the transition generally increases. As a gen--eral rule, to eliminate the possibility of cavitation damage withinmd just downstream of the transition and to minimize head loss, theratio of a contraction transition length to maximum radial offset fromthe outside boundary of the gate passage to the corresponding locationon the conduit boundary shotid be about V/@ (V and D being theaverage of the maximm average velocities and equivalent diaeters atthe beginning and end of the transition). However, for certain combina-tions of gates and tunnel sizes, this ~ideline may result in toosevere contraction for low heads, in which case the length should be in-creased to reduce the angular rate of change along the transition. Thus,maximum angle of contraction or expansion relative to the conduit centerline shotid be limited to about 7 deg. A sample computation for thedesign of transitions is presented in Appendix E. The procedure isapplicable to all in-line transitions.

d. fiessure Gradients. A study should be made of the local average

4-13

d“ ,

m 1110-2-1602 4-22d15 Ott 80

pressure throughout the transition. Average pressures can be computedusing the Bernoulli equation (eq 2-3) and the average pressure shouldbe equal to or greater than atmospheric pressure. Fressure data intransitions may be found in items 68 and 132 for entrance and midtunneltransitions, respectively.

b-23. Exit Transition. Normally the shape (circular, horseshoe,oblong, etc.) of = outlet conduit or tunnel for embankment d- ismaintained to the exit portal and the transition into the energy dissi-pator is made in an open channel downstream from the portal. When theembankment slope is relatively flat, the tunnel or conduit can beshortened by moving the transition upstream into the embankment andabruptly raising the roof to ensure free-surface flow in the transition.Design details of a typical outlet works exit transition are presentedin Chapter 5.

4-14

CWTER 5

ENERGY DISSIPATION ti DOWNS~

EM lliO-2-1602Change 115 Mar 97

C-EL PROTECTION

Section I. Energy Dissipators

5-1. General. The outlet flow, whether it be from the world’s largest dam.or from a small storm drain, usually requires some type of energy-dissipating stmcture to prevent downstream channel degradation. Thedesign may vary from an elaborate multiple basin arrangement to a simpleheadwall design, depending upon the size and number of conduits involved,the erosion resistance of the exit channel bed material, and the duration,intensity, and frequency of outlet flows. The structure(s) may consist of(a) abrupt expansions in high-pressure conduits (item 104), -(b)hYdraulic

jumps in low-pressure conduits (item 130), (c) flip buckets, valves, anddeflectors which spray high-velocity jets into the air before plunging intoa downstream pool, and (d) conventional hydraulic-jump type stilling basins.The latter vary from sluice jets spreading on spillway faces and toe curves,to impact dissipators (item 46), to horizontal aprons with baffle piers and ~end sills (item 69). In many cases of low-pressure flow (storm drains,etc.), adequate dissipation of energy can be obtained by the use of riprapaprons~ preformed scour holes (items 10 and 33), and other economicaldevices (item 34). This chapter treats in detail the design of the transi-tion, hydraulic jump, and the rectangular cross-section stilling basin fora single conduit.

5-2. Hydraulic-Jump Type Stilling Basins.

a. General. The typical energy dissipator for an outlet works struc-ture reqtires a stilling basin to produce a hydraulic jump. The stillingbasin is joined to the outlet portal with a transition chute which hasflared vertical sidewalls and a downward parabolic invert. Appendix Fpresents the procedure as set forth i% this chapter for the design of out-let works stilling basin to include an illustration of a “low-level outletwith respect to tailwater” where an eddy problem may occur within thestilling basin for low and intermediate discharges.

b. Low-Level Outlets @th Respect to Tailwater. The invert of theoutlet portal of a conduit is “low” tith respect to tailwater if for anyoperating discharge the

‘2curve intersects the tailwater for that dis-

charge in the transition chute between.the conduit and the stilling basinproper at a section where the slope of the chute invert is flatter than IVon 6H (see plate C-40 for definition sketch, and items 85, 88, and 89). Atseveral Corps installations such stilling basins performed adequatelythroughout the higher ranges of discharges; but at low and intermediate

5-1

~ 1110-2-i602Change 1Is y~r s;

flows, an eddy formed in the basin and downstream flow was confined to anarrow section along one of che sidewalls. Rocks and debris were trappedin the eddy and were moved upstream to the point at which they met theefflux from the conduit; here they were agitated and some were bounced vio-lently against the apron as they were picked up by the issuing jet and moveddownstream where they again were trapped in the eddy. This action resultedin impact and abrasion damage to the concrete apron, baffles, and sidewalls.Thus, the idealized example problems given in Appendix F illustrate the pro-

* cedure to determine whether eddy problems may or may not occur. If eddyproblems are likely to occur, the trajectory should be designed with aninverted V as shown in para 5-2d(3). This divides low flows down both sidesof the stilling basin and prevents an eddy from forming until the tailwaterbecomes excessively high. A model study should be made if the above guid-ance cannot be followed or if the flow from the outlet portal is not “ideal”with a horizontal transverse water surface and a uniform, s~etric velocitydistribution. (See also para 2-7 relative to submerged outlets.)

c. Basic Considerations. Stilling basins are generally designed foroptimum energy dissipation of controlled flows equal to the capacity of theoutlet channel. Suc~ flows usually occur for lorigperiods of time and arethe most critical to the lffe of the structure. Appreciably less-thanoptimum performance can be accepted for higher flows of short duration aslong es the jump is confined to the stilling basin. The design of stillingbasins usually includes the following considerations: (1) the design dis-charge for the basin will exceed that for outlet works capacity and isrecomputed assuming smooth pipe flow in the flood control conduit (see Moodydiagram in plate C-4), design pool elevation, and negligible energy lossesin the flow between the conduit exit portal and the stilling basin (see alsopara 2-18 relative to short conduits); (2) the minimum anticipated tailwaterfor the design discharge is used in establishing the basin floor elevation;(3) 0.85 to full d downstream depth is recommended for design dependingon the lateral distribution of flow as it enters the stilling basin, dura-tion end frequency of high flows, foundation conditions, and submergenceneeded to minimize cavitation; (4) the riprap immediately downstream fromthe stilling basin is designed using the average velocity of the flow depthover the end sill; and (5) whether the conduit will operate in conjunctionwith spillway flows. In many instances, closure of the outlet works duringspillway operation will effect appreciable economy in the outlet worksstilling basin design.

d. TransitIon Chute.

(1) Sidewall Flare. The angle ($)the projected conduit axis and the stillingequation:

5-2

of the flared section betweenbasin sidewall is defined by the

5-2d(l)

$ = tan

(i

-1 1E

(5-1)

where AL is termed the flare ratio and represents the distance along theaxis in the direction of flow for unit divergence. The sidewall flareshould terminate at or upstream from the beginning of the stilling basinapron. If the flare ratio (AL) is too large, the length of chute betweenthe outlet portal and the stilling basin becomes excessive. If the flare

ratio is too small, the flow will not spread uniformly over the flared sec-tion and lateral nonuniform energy dissipation will occur in the stillingbasin. In extreme cases two side rollers will form. Tests performed atthe State University of Iowa (item 102) showed that the flare of a jet fol-lowed a curved path and was dependent upon the Froude number of the jet atthe exit portal. Model studies with circular conduits indicate that astraight wall with a minimum flare ratio (AL) of twice the Froude number butnot less than six produces a satisfactory design, i.e.,

where

D.

~.

2Vfi.2~.— or = 6 , whichever is greater@

conduit diameter, ft

flow velocity at the exit portal, fps

(5-2)

This should also be satisfactory for rectangular conduit outlets. Thetransition chute sidewalls should be connected to the exit portal with aradius not less than five tfies the outlet diameter or height (SD) and theinvert continued on conduit slope for the length of the corner fillets (seeplate C-41). The length of the fillets for a circular conduit outlet tran-sition should be approximately 1.5 times the conduit diameter or height(1.5D)..

(2) Sidewall Restrictions and Abrupt Offsets. The possibility ofa depressed pressure gradient throughout a conduit and subsequent more thannormal discharge has been noted in laboratory and field tests. In modeltests on an oblong-shaped conduit, side venttig of che free-surface jet wasapparently restricted by the sidewall design, and the energy gradient at theexit portal was depressed nearly to the conduit Invert. The conduit shapewas vertically oblong; the vertical sidewalls had a mitered flare (1 on

5-3

5-2d(2)m 1110-2-1602Change 115 Wr 87

5.63) from the horizontal diameter; corner fillets were not provided at theintersection of the invert and sidewalls; and the transition invert curvewas parabolic. Offsetting the walls laterally (1.5 ft on each side of theconduit) raised the pressure gradient and reduced the discharge; however,there was less satisfactory spreading of the jet into the stilling basin.Moreover, abrupt offsets result in flow riding up the sidewalls. Sucheffects on other conduit shapes have not been determined and this type ofsidewall design shouldexist at one discharge(See Tuttle Creek data

(3) Parabolicfrom the outlet portal

be avoided unless model-tested. These effects canand disappear at either a higher or lower flow rate.in plate C-3 and item 134.)

Drop. The profile of the transition chute invertinvert to the stilling basin floor is in the form of

a parabolic tune based on the trajectory of a jet. The invert curve mustnot be steeper than the trajectory that would be followed by the high-velocity jet under the action of gravity, or the flow will tend to separatefrom the transition floor with resultant negative pressures. The floorprofile should be based on the theoretical equation for a free trajectory:

where.

X and y =“

g=

g“

v= =

Y= -x tan 0 -

*’

horizontal and vertical coordinates measured from thebeginning of the tune, ft

angle with the horizontal of the approach invert at thebeginning of the verti%al curve, deg


average velocity for smooth pipe flow at the beginningof the cume, fps

(5-3)

As a conse~ative measure to prevent separation of flow from the floor, thevelocity (Va) in equation 5-3 has been increased 25 percent over the

average flow velocity computed for smooth pipe flows. The trajectory shouldbe joined to the stilling-bash floor with-

* to the entering depth, i.e., R-d . ~

subject to low-flow eddies as discu~sed in

5-4

a tune that has a radius equaloutlet works stilling basinpara 5-2b should be designed

5-2d(3) Ey lllo-~_~602

Change 1~~ War 87

with an inverted V beginning at the exit portal and sloping upward on a lVon 7.9H slope for a distance equal to the length of the fillet

‘f : ‘heheight of the inverted V above the invert of the exit portal at a distance

‘ffrom the outlet will be 0.19D as shown in Plate C-41A (where D = equiv-

alent di&eter of the conduit). Plate C-41A shows an elevation view andsection of an outlet works stillin~ basin with an inverted V. The equationof theby the

where

new parabolic trajectory al~ng the center line of the basin fdrmedaddition of the inverted V can be computed by the equation:

Y’ = -cmx~ (5-3a)

Y’ and x are the vertical and horizontal coordinates measured fromthe beginning of the curve in feet. The center-line trajectory shouldintersect the floor of the stilling basin at the same distance downstreamfrom the outlet as the ordinary trajectory. Thus, C for the center-linetrajectory can be determined by using y’ equal to t~e elevation at thebeginning of the cu~e (outlet portal elevation + 0.19D) minus the elevationof the stilling basin apron, and x equal to the distance from the begin-ning of the tune to its intersection with the stflling basin apron (sameas ordinary trajectory).

e. Elevation of Stilling Basin Floor. The stilling basin is designedas an energy dissipating device for the flow from the outlet works conduits.Its purpose is to reducechannel velocities. Thejump. The formula for a

where

dl and d2 =

F=

.

sequent

the high-velocity outlet flow to permissible exitenergy dissipation phenomenon is the hydraulichydraulic jump in a level, rectangular section is:

+=+(JQ- ,)(5-4)

depths

Froude number of the flow entering the jump, i.e.,

= ‘1

F ml

5-5

(5-5)

~ 1110-2-1602Change 115 &r 87

5-2e

where‘1

and‘1

are the average flow velocity and depth, respectively,

of the entering flow. It is of value for the designer to examine the typeof jump to be expected with the Froude number involved. Chow (item 17)presents a discussion on the types of jump to be expected with variousmagnitudes of Froude numbers. The stilling basin design flow (generally,maximum discharge through the outlet channel) is used in determining theelevation of the basin floor. A floor elevation may be assumed in the caseof a drop from the conduit outlet and the corresponding depth and velocityof flow entering the basin computed using Bernoulli’s equation and neglect-ing energy loss between the conduit outlet portal and the stilling basin.This depth and velocity are used to compute the Froude number ( E). Thedepth of tailwater required to form a jump is computed as d, . Therequired depth (d2) is then compared with the available depth (obtained

from a tailwater rating cume) and the floor elevation assumption adjustedaccordingly. Laboratory investigations have demonstrated that in the rangeof Froude numbers ( lF) from 4 to 10, a satisfactory hydraulic jump can bemade to form in a stilling basin with end sill and baffle blocks by a tail-water that produces 0.85 of the theoretical

‘2 “The adequacy of the

tailwater cume to fit d2 values for flows less than the design discharge

should also be checked. If downstream degradation is likely to occur afterconstruction, estimates should be made of the possible lowering of thetailwater curve and the lowest expected tailwater tune should be used indesigning the stflling basin. If the natural tailwater depth is greater \than the computed

‘2depth (see para 5-2b), the length of the jump and

position of the jump toe on the cu~ed i~ert should be determined usingKDC sheets and charts 124-1 and 124-1/1. If the basin floor is to be levelwith the conduit invert, equations 5-2 and 5-4 may be combined in a tinnerto relate the stilling basin width and depth for convenience in an economicstudy.

f. Basin Width. The effect of increasing the stilling basin width isto reduce the required depth of basin. Basically, the problem is an eco-nomic one in which various combinations of width and depth of basin arecompared to obtain the least cost combination. (Also see para 5-2d(l)above.)

g- Basin Length. Basically, the length of a stilling basin is pre-dicated on the length of the hydraulic jump for which it is designed. Forbasins with Froude numbers (IF) axceedlng 3 and less than 12, a length of3d2 is recommended. Longer basins should be considered when Froude numbers

(~) -teed 12 due to the magnitude of residual energy leaving the basin.When the outlet channel is located in rock (item 17), a basin length of2.5d2 may be adequate. A basin length of 3.5d2 to 4.0d2 shotid be

5-6

5-2g

considered for highly erodible outlet channels. Stflling basins withoutbaffle piers and end sills should have paved apron lengths of 4d2 to5d2 .

h. Baffle Piers. Baffle piers on the apron should have a height of

‘1or l/6d2 , whichever is less. They should be located 1.5d2 down-

stream from the toe of the transition chute for entering velocities s60 fpswith Froude numbers of 3.5 to 6.0. For higher velocities they should bemoved farther downstream. A second row of baffle piers is ve~ effectivein reducing scour downstream from the stilling basin. If the basin apronelevation is placed such that existing tailwater produces 85 to 90 percentof d a second row of baffle piers is recommended. The second row shouldbe ap~r~ximateiy 0.5d2 dotistream from the first row. The width and

spacing of piers should be equal to or slightly less than their height(dl) . A distance of at least half of a pier width should be allowed

between the end piers and the basin walls (see plate C-41). Velocitiesagainst the face of the baffles can be estimated from HDC 112-2/l.n

i. End Sills. Sloping end sills (1V on,lH) are preferable to verticalend sf.llsbecause their self-cleaning characteristics reduce damage fromtrapped rocks and debris. However, they impart a vertical component to thebottom exit velocity increasing the intensity of the bottom backrollerimmediately downstream. End sill height of half of the baffle height isrec~nded (see plate C=41). Riprap at the downstream end of the stillingbasin should be lower than the top of the end sill. This will help preventbackrollers from pulling rock into the basin which can cause concreteabrasion damage.

Jo Training Walls. Vertical parallel training walls are recommended.Walls with as little as 4V-OU-lH batter can create downstream eddies. Thetop of the stilling basin walls should be at the maximum tailwater elevationthat may occur during operation of the outlet work in order to prevent sideflow onto the hydraulic junrp. Any higher tailwater resulting from spillwayflows during outlet works operation must be considered, although such com-bined operation is not recounnended. The ~it transition flare should notbe carried through the stilling basin. Freestanding training and dividingwalls are designed to tithstand static loads due to turbulence in thehydraulic jump. The static load is usually assumed to be that resultingfrom maximum tailwater on one side of the freestanding wall and no wateragainst the opposite wall. A stilllng basin with a high entering Froudenumber flow ( F >10), foreshortened by virtue of baffle blocks and high endsill, has very violent turbulence. This dynamic loading created by the jumpcannot be easily computed and where such loading is critical, model testing

5-7

w. 1110-2-1602Change 1i5 >kr S7

is recommended. Results of a study of pressure fluctuations in modelstilling basin sidewalls is reported in item 35 and prototype tests resultsin item 48.

k. Wing Walls. Wing walls are usually not required if the exit chan-nel invert is made at least 0.3d2 wider than the stilling basin and wrap-

around side slopes are provided (plate C-42). Quadrant wing walls at the

end of stilling basins are effective in protecting the exit channel invertagainst scour. However, they permit more attack on the channel side slopesthan freestanding basin walls with wraparound offset slopes.

1. Multiple-Basins. Where more than one conduit discharges into acommon outlet channel (items 124 and 126), the dividing wall or wallsbetween basins should be sufficiently high to prevent side flow into a basinover the dividing wall when the adjacent conduit is not operated. Effi-ciency of the operating basin can be appreciably reduced by this flow.Whenever ”possible, operating schedules should provide for equal dischargefrom all conduits or symmetrical operation of conduits. The stilling basindesign should be based on the tailwater ~th all conduits discharging theirdesigm flows. However, the design should be checked for design flow opera-tion of a single conduit to be sure that the reduced tailwater is sufficientto hold the jump in the basin. Under this condition of operation a tail-water depth equal to 0.85d2 may be acceptable. The stilling basin designshould ensure satisfactory energy dissipation for all anticipated conditionsof operation. .In such cases the designer must exercise considerable judg-ment and a model study may be desirable. Dynamic loading of the dividing-wall(s) may be significant.

m. Dewatering S- s. Dewatering sumps are required in the floor ofall outlet works stilling basins to facilitate dewatering for inspection andmaintenance. It is recommended that the sump be located close to the train-ing wall in the low-velocity area between the baffle piers and the end silland that the stilling basin floor have a slight slope toward the sump. Whenpractical, drainpipes should be provided to alleviate standing water and toreduce pumping costs during inspections.

5-3. Low-Head Structures. Many types of energy dissipators have beendeveloped for low-head outlet structures such as outfall storm sewers,drainage culverts, farm ponds, low dams, etc. (items 137 and 139).

a. Impact Energy Dissipator. The impact energy dissipator (items 46and 139) is an effective stilling device even with deficient tailwater.Dissipation is accomplish.edby the impact of the incoming jet on a fixed,vertically hung baffle and by eddies formed by changes in direction of thejet after it strikes the baffle. Best hydraulic action occurs when the

5-8

5-3a

tailwater approaches, but (ioesnot exceed, a level halfway up cne height ofthe baffle. The impact basin is recounnendedfor outflow velocities between2 and 50 fps. me dimensionsnof this energy dissipator in terms of itswidth are given in HDC 722-2.

b. Stilling Wells. (Items 46 and 133.) Energy dissipation from asloping conduit can be accomplished by apansion in an enlarged verticalstilling well, by the impact of the fluid on the base and walls of thestilling well opposite the incoming flow! and by the change in momentumresulting from redirection of the flow. The top of the well is usually setflush tith the outlet channel. Its action is essentially independent oftailwater and ~S tests indicate that it performs satisfactorily for

2.5discharge-pipe diameter ratios (Q/D ) up to 10 with a stilling well-inflowpipe diameter ratio of 5. Q is the conduit flow in cubic feet per secondand D is the con:uit diameter in feet. Pertinent design information isgiven in HDC 722-1.

c. Impact-Jump Basin. (Items 9 and 46.) The impact-jump basin wasdeveloped by the U. S. Department of Agriculture for small dams and achievesenergy dissipation through impact on baffle piers and end sill in additionto that accomplished in an incomplete hydraulic jump. It involves a veryshort apron with chute blocks, baffle piers, and end sill. Basin widthsgreater than three times the conduit diameter have proven unsatisfactory

for~,D 2.5

greater than 9.5. Tailwater depth equal to at least 0.85d,

is required for acceptable performance. EDC 722-3n presents design dimen~sions in terms of the entering flows having velocities less than 60 fps”andFroude numbers between 2.5 and 3.5.

d. Flared Outlet Transitions. Economical energy dissipation and scourcontrol can be accomplished by a paved horizontal apron at a culvert outlet

for discharge-conduit df.ameterratios (Q/D2“5) up to 5. Appreciable addi-tional energy dissipation is obtained by setting the apron at an elevationup to 0.5 conduit diameters below the exit portal invert and adding an endsill of appropriate height. The necessary dimensionless design informationis presented in item 34. .

e. Riprap Energy Dissipators. Riprap energy dissipators for stormdrain outlets have been developed by WES (items 10 and 33) for both hori-zontal aprons and preformed scour holes. This type of energy dissipator isadaptable to regions where riprap in the required sizes, gradation, andquantity is readily and economically available. The necessary informationfor sizing these structuresrequired D50 riprap stone

.

can be computed using HDC 722-4 and 722-5.n Thesize can be estimated using KDC 722-7.n The

5-9

m 1110-2-1602Change 115 Yar 87

5-3e

major dimensions of unprotected scour holes and the riprap Size and hori-zontal blanket dimensions can be computed with CORPS H7220.U

Section II. Outlet Channel

5-4. General. The function of the outlet channel is to connect the outletworks to the downstream river channel. The flow leaving an outlet worksenergy dissi-patoris generally highly turbulent~ and contains inversevelocity gradients and large surface waves. Provisions are recommended foran enlarged channel immediately followlng the hydraulic structure in whichthe flow can expand and dissipate excess energy. Generally, a riprapped-lined trapezoidal channel provides this function. Model tests (items L5and 77) have demonstrated the advantages in providing for or preforming a“scour hole” in which the flow can expand and dissipate its exce”ssenergyin turbulence rather than in direct attack on the channel bottom and sides.A relatively smell amount of expansion, preferably both vertically andhorizontally, will greatly reduce the severity of attack on the channelboundaries. ~is makes it possible to “stabilize the channel”with rock ofan economical size and provide”additional factors of safety against riprapfailure end costly maintenance (plate C-43). The provision of recreationfacilitie$ should be a consideration in the outlet channel design; forexample, preformed scour holes provide areas of good fishing. Tailwater atthe stillhg basin should also be a consideration; and Zf feasible, thechannel shodd be designed so that the tailweter cume will, es nearly aspractical, approximate the

‘2cu=e for the full range of flows.

Response tl.meof tailwater to increase with increases in the outflow dis-charge may also be a factor. Avoid using a “perched” outlet channelspilling into a lower river channel in erodible material.

5-5. - Dete--tion of the ’50size of riprap for the channel

sides to a distance of 10d2 downstream from the upstream end of a stillingbasin should be made in accordance with the guidance given in HDC 712-inusing the average flow velocity leaving the stilling basin. Beyond this

point, channel riprap design based on EM 1110-2-1601h should be used. Ariprap transition between the two riprap design sections is recommended.As riprap creates locally high boundary turbulence, a transition zone pre-ceding the nsturd channel surface should be provided. This zone shouldhave a length of three times the flow depth with a gradual downstre~reduction h the D stone size. Design of exit channel riprap shouldprovide protection ~~atist waves as well as velocity; therefore, reductionin stone sizes at upper levels is not recommended. All riprap gradation

should be in accordance with ~ 1110-2-1601.h Additional information isgiven in item 84.

5-1o

5-6. SiIe-SloDe Ercsion. As nccerlin paragraph 5-2k, a quaaranc wali cneccing the training wall at the end of stilling basin to the channel b:ilasbeen found effective in protecting the floor of the exit channel ag:scour. However, this wall permits more severe attack on the side slope:the outlet channel than does a training wall terminated at the end sillextended straight downstream as a freestanding wall. Therefore, exceptnoneroding beds and banks, the training walls should terminate at the ersill and the toe of the side slopes should be offset at least 0.15d2 a

ing the bottom of the outlet channel 0.3d2 wider than the stilling bas

(plate C-42). Furthermore, the original streambed load should be consicin the outlet channel design. The bed load is cut off by the dam, resulin possibly more erosion downstream. Consideration should be given to aing the outlet channel wider and lower in an area with erodible soil, a:with a preformed scour hole.

\

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6-1 EM 1110-2-1602

15 Ott 80

CHAFTER 6

SELECTIVE WITHDRAWAL STRUCTURES

6-1. Types. Selective withdrawal structures fall into three generaltypes: (a) inclined intake on a sloping embankment; (b) freestandingintake tower, usually incorporated into the flood control outlet facili-ties of embankment dams; and (c) face-of-dam intake, constructed as anintegral part of the vertical upstream face of a concrete dam. meappropriate t~e of int~e structure for a given project depends on anumber of considerations including reservoir size, degree of stratifica-tion, discharge rates, water quality objectives, need for flow blendingbetween withdrawal levels, and project purposes. Types (b) and (c)predominate at Corps projects. A description of the design ad opera-tion of each type is presented by Austin et d. in item 5 (seeplate C-44). The most common type of selective withdrawal structureis (b), the freestanding intake. Three general types of freestmdingintties predominate. The first consists of a flood control passage andweirs or ports in a single collection well. This type is generallyappropriate for shallow reservoirs with minimum stratificationwheresingle weir or port operation is anticipated and blending between in-tties is not required. The second is the dual wet well structure whichconsists of a flood control passage and two collection wells. Thistype is generally appropriate for reservoirs expected to exhibit strongstratification where anticipated operations for water quality objectivesindicate that the capability for blending between intakes is desirable.“Inboth the single and dual collection well systems the selective with-drawal capacity is generally less than the flood control capacity. Thethird is one through which all discharges, except spillway, can be re-leased. For all types of selective withdrawal structures, the with-drawal device usually consists of one or more ports or weirs, or acombination of the two. The weir(s) can have a fixed elevation orvariable elevation.

6-2. Design.

a. State of the Art. Each individual reservoir exhibits uniquewater quality and hydrodynamic characteristics and therefore it is diffi-cult to provide general information pertinent to the desi~ and opera-tion of outlet structures for water quality control of reservoir re-leases. Water quality control structures can be used in a variety ofsituations including single purpose and multipurpose projects. Thedesign of a water quality control structure requires an understanding ofthe mechanics of stratified flow, water quality and hydrologic considera-tions, and hydraulic design requirements. A general description of the

6-1

EM 1110-2-1602 6-2a15 Ott 80

zone of withdrawal from a stratified body of water for single and simul-taneous multilevel releases has been described in item 12. Requirementsfor water quality and hydrologic investigations neces;ary to designwater quality structures are given in ER 1110-2-1402. Several exmplesof physical and mathematical model studies that have been conducted todesign water quality structures from a water quality and hydrologicstandpoint are given in items 26, 27, 28, 36, 61, 62, and 67. meprinciples of design given in this manual apply to the hydraulic designof water quality structures. Mmy needed design principles have yetto be established and in many cases, economic considerations dictatethe design. This section summarizes a nwber of designs and designproblems that have been investigated with physical models.

b. Design Information. Water quality outlet structures naturallydivide into three parts: (1) inlets and collection well(s), (2) controlgate passage(s), =d (3) exit passage(s). Presently availaile pertinentdesign information is smarized in the following paragraphs.

(1) Inlet Ports. The capacity of ports and collection wells isbased on water quality and hydrologic considerations. Additionally, theport size md geometry affect selective withdrawal characteristics.Inlet ports to water quality collection wells are designed to operatefully open or closed. Total flow is regulated by a downstream controlgate. Ports should be operated under submerged flow conditions. Freeflow conditions should be avoided. Ports are generally placed directlyfacing the upstrem direction. Placing inlet ports vertically aboveeach other can result in interference of operating equipment. Portvelocities primarily affect trashrack design, flow stability, and collec-tion well turbulence. Velocities of 4 to 6 fps or lower are recommendedfor normal operation, but designs with velocities up to 20 fps may bepossible with hydraulic model studies (item 68) of conditions wherefine control of selective withdrawal is not a governing consideration.Inlet ports operating under appreciable submergence with relatively lowvelocity can be expected to be cavitation-free. However, their entr=cesshould be bell-mouthed for efficient inflow conditions. The entracecurves terminate possibly with a short tangent section at the insidevertical walls of the collection well where the gate is located. Inletports should be provided with trashracks to prevent debris from enteringthe collection well. Since inlet port gates are not normally subject tocavitation pressures, they do not require venting. Upstream bulkheadslots or other provisions for maintenance and repairs are required.These slots may also be used for trashracks.

(2) Inlet Weirs. An inlet port that is not totally submerged

6-2

,,,’ ,

6-2b(2) EM 1110-2-160215 Ott 80

can be operated as an inlet weir provided sufficient flow constrictionis maintained by a downstream control gate so that submerged weir flowrestits. Without sufficient flow constriction, flow control may shiftbetween the inlet weir and the control gate, causing a flow instability.Inlet weirs should always have trashracks to prevent debris floating onthe water surface from entering the structure. If the release of sur-face water is desired most of the time, a structure may be designed tobe operated specifically as an inlet weir. The crest of such a weir isusually thin and vertical, thus allowing movable bulkheads or a selectorgate (variable position, mechanically actuated gate) to serve as amovable weir so that upper pool releases can be made for varying poolelevations. The weir flow should be submerged with flow control main-tained downstream. Entrance velocities should be within the range of4 to 6 fps and are normally governed by selective withdrawal considera-tions. The depth of flow over the weir and the weir length are sized toprovide the required discharge and release water quality objective.

(3) Collection Wells. Collection well geometry and size are de-pendent upon the number, size, m d spacing of inlets and vary appreciablyfrom project to project. The primary purpose of a collection well is toprovide a tower facility for the inlets ad their gates. The collectionwell also serves as a junction box where the flow direction changes fromhorizontal to vertical to horizontal. Sometimes the flow directionchanges can result in appreciable surging and head loss. Equipment inthe collection well should be securely anchored. Damage to ladders inthe collection well at Nolin Dam has occurred with 2- to 5-ft surgesoccurring with a 3-ft head differential from the pool elevation to thewater-surface elevation in the wet well. Head losses that normally occurin the intake are the int~e loss, velocity head through the inlet,friction in the well, entrance loss to service gate passage, and thevelocity head of the vertical velocity in the well when the service gatepassage is at an angle to the collection well. Blending of flows forwater quality proposes should be done by blending flows from separatewet wells in a dual wet well system. Each wet well should have individ-ual flow control, and inlet(s) at only one elevation should be open ineach wet well. Experience has shown that erratic blending due to flowinstability between inlets in sepwated wet wells may occur where thewet wells are connected and only a single service gate and gate passageare provided for flow regulation.

(4) Outflow Passages. Water quality outflow passages areusually very short and operate with free-surface flow except sometimesfor the maximm design flow. In concrete gravity d-s they may be lo-cated in the nonoverflow section and discharge through the sidewall ofthe stilling basin (plate C-45). They may also be located on the

6-3

m 1110-2-1602 6-2b(4)

15 Ott 80

upstream face of the dam and discharge onto the spillway. Water qualityfacilities for embankment dams are most frequently incorporated in theintake towers of the flood control outlet works and discharge into theflood control conduit. In multiple flow passage flood control intakes,the water quality releases can be made through the intake dividing pier(plate c-k6), through bypass pipes around the service gate (plate C-47),or through the emergency gate well (plates C-47 ad c-48). In the lattercase, the flood control service gate is used to regulate the waterquality flow release discharge.

(5) Submerged Weirs. Submerged weirs upstream of outlet works(plate C-49) can be used to prevent withdrawal of bottom waters fromreservoirs by flood control conduits and penstocks (items 11 and 32).The principles involved have been studied and reported by WES (item 12).Local topography, flow requirements, and adjacent structures have appre-ciable effect upon the performance of these weirs. Therefore, a modelstudy to determine the selective withdrawal characteristics is recom-mended where sn upstream submerged weir is included in the project design.

6-3. Flow Rem ation. Flow regulation is accomplished by means of acontrol gate(s) located in a uniform conduit section(s) downstream fromthe collection well(s). me gate passage section can be connected tothe bottom of the collection well by a bell mouth or by a long radiuselbow. In either case$ press~es in this transition should be careffilystudied in accordance with guidance in paragraph 2-16. Since the gatenormally operates under little or no back pressure, it is essential thatthe issuing jet be adequately vented. Discharging the gate jet into aenlarged section with venting all around should’be considered. Ventingshould be provided in accordance with the guidelines presented inparagraph 3-17.

6-L. Model Investigations.6

a. Concrete Gravity Dams. A water quality outlet design for a con-crete gravity dam is shown in plate C-45. Qualitative model tests ofthis design were made at WES (item 1). The location of the water qualitytower adjacent to the left abutment of the spillway resulted in undesir-able flow contraction around the tower with spillway flows in excess of25,000 cfs. Preliminary tests of the water quality inlet orifices indi-cated that their elevation and size were not capable of meeting the re-quired withdrawal characteristics. Model tests were dso conducted onthe multiple penstock intake structure at the proposed Dickey Dam(plate C-50). These tests were conducted towithdrawal characteristics of this structurewill consist of two earthen embankments with

6-4

determine the selective(item 26). The Dickey Dmthe multiple penstock

.-. .

6-4a EM 1110-2-160215 oct 80

intake structure located in the concrete gravity section. The intakestructure will have individual collection wells connected to each offive 27-ft-diam penstocks. The level of withdrawal of flow into thecollection wells will be controlled by the location of the top of themovable selector gates. The selector gates will function as a variablecrest elevation submerged weir.

b. Embankment Dams. Five model-tested earth dam water qualitycontrol structure designs are shown in plates c-46, c-47, c-48, c-51,and c-52. The Beltzville design (plate c-46) releases the water qualityflows into the flood control conduit through an outlet with its exitportal in the nose of the dividing pier of the flood control intaketower. At New Hope Dam, renamed B. ~erett Jordm Dam, (item 70), theemergency gate well serves as the water quality collection well(plate c-48). The flood control regulating gate serves as the waterquality regulator. When the emergency flood control gate is closed,water quality releases pass from the collection well into the floodcontrol gate passage and under the regulating gate. Model tests showedthe need to limit service gate openings to a maximum of 34 percent offully open for water quality releases to prevent serious negative pres-swes in the throat section between the collection well and the floodcontrol gate passage. The Taylorsville design (plate C-47, and item 25)has dual collection wells similar to the New Hope (B. Everett Jordan)design. During selective withdrawal operation, the emergency gates willbe closed and flow will be discharged through the multilevel intakesinto the wet wells and through an opening or throat located in the roofof the gate passages between the emergency md service gates. Theservice gates will be used to regulate the selective withtiawd releases.Additionally, an 18-in.-diam pipe bypass around each service gate willbe provided to regulate the release of low flows with the service gatesclosed. Similar to the model tests of the New Hope (B. Everett Jordan)structure, tests of the Taylorsville structure dso showed the need tolimit service gate openings for water quality releases. For the Taylors-ville structure, service gate openings greater than 55 percent of fullyopen resulted in negative pressures in the throat section. The DeGraydesign (plate C-51) consists of a single four-sided intake tower equippedwith multilevel openings and a cylindrical gate (item 14). This struc-ture provided selective withdrawal capability for both flood controland hydropower releases. The tower has two bulkheads and a trashrack ina single set of gate slots in each of its four sides. Placement of thetrashrack pael determines the withdrawal elevation. The cylindricalgate in the intake tower is not operated as a flow control device. Flowpasses vertically from the intake tower through a 21-ft-radius elbowinto a 1205-ft-long, 29-ft-diam conduit. The conduit is bifurcated toprovide for flood control ad power generation releases. The flood

6-5

\

m 1110-2-1602 6-bb15 oct 80

control releases are regulated at the end of the bifurcated conduit sothat releases for both flood control and power generation can’be drawnconcurrently through the intake tower. Model tests were conducted onthe water quality outlet structure at Beech Fork Dam (plate C-52)primarily to evaluate the effects of local terrain on the water qualityperformance of the outlet works (item 42). The structure has dualcollection wells, each with 30-in.-diam conduits and control valves thatrelease water quality flows into the flood control conduits immediatelydownstream of the flood control service gates.

6-6

EM 1110-2-160215 Ott 80

APPENDIX A

BIBLIOGRAPHY

1. Ables, J. H., Jr., and Boyd, M. C. 1970 (Jun). “Spillway andOutlet Works, Rowlesburg Dam, Cheat River, West Virginia; HydraulicModel Investigation,” Technical Report H-70-7, U. S. Army EngineerWaterways E~eriment Station, CE, Vicksburg, Miss.

2. Ables, J. H., Jr., and Pickering, G. A. 1973 (Feb). “Outlet Works,Warm Springs Dam, Dry Creek, Russian River Basin, Sonoma County,California; Hydraulic Model Investigation,”Technic~ ReportH-73-3, U. S. AW ~gineer Waterways Experiment Station, CE,Vicksburg, Miss.

3. American Society of Mechanical Engineers. 1958. “AmericanStandard Letter Symbols for Hydraulics,” ASA Y1o-1958, New York,

4. Anderson, A. G. 19~7 (Aug). “Fluid Flow Diversion; A Summary andBibliography of Literature,” Project Report No. 1, St. AnthonyFalls Hydraulic Laboratory, University of Minnesota, Minneapolis,Minn.

5. Austin, G. H., Gray, D. A., and Swain, D. G. 1969 (Nov). “Mdti-level Outlet Works at Four Existing Reservoirs,” Journal, Hy-dratiics Division, American Society of Civil Engineers, VOI 95,No. HY6, Proc Paper 6877, pp 1793-1808.

6. Ball, J. W. 1959 (Ott). “Hydraulic Characteristics of Gate Slots,”Journal, Hydraulics Division, American Society of Civil Wgineers,VO1 85, No. HY1O, Pp 81-114.

7. . 1963 (Sep). “Construction Finishes and High-VelocityFlow,“ Journal, Construction Division, American Society of CivilEngineers, Vol 89, No. c02, Paler 3643, pp 91-11o.

8. . 1970 (Aug). “Cavitation Design Criteria,” Control ofF1OW in Closed Conduits, Proceedings of the Institute, held atColorado State University, Ft. Collins, Colo., 9-14 Aug 1970,PP 379-416.

9. Blaisdell, F. W. 1959 (Apr). “The S~ Stilling Basin,” Agricul-tural Handbook No. 156, Agricultural Rese~ch Service andSt. Anthony Falls Laboratory, Minneapolis, Minn.

EM 111o-2-I.6o215 Ott 80

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

Bohan3 J. P. 1970 (Jan). “Erosion and Riprap Requirements atCulvert Storm-Drain Outlets; Hydraulic Laboratory Investigation,”Research Report H-70-2, U. S. Army Engineer Waterways ExperimentStation, CE, Vicksburg, Miss.

. 1970 (Feb). “Water Temperature Control Weir forMeramec Park Dam, Meramec River, Missouri; Hydraulic Model Investi-gation,” Technical Report H-70-1, U. S. Army Engineer WaterwaysExperiment Station, CE, Vicksburg, Miss.

Bohan, J. P., and Grace, J. L., Jr. 1973 (Mar). “Selective With-drawal from Man-Made Lakes; Hydraulic Laboratory Investigation,”Technical Report H-73-4, U. S. Army Engineer Waterways ExperimentStation, CE, Vicksburg, Miss.

Bradley, J. N., and ~ompson, L. R. 1951 (Mar). “Friction Factorsfor Large Conduits Flowing Full,” Engineering Monograph No. 7(Revised 1965), U. S. Bureau of Reclamation, Denver, CO1O.

Bucci, D. R. 1965 (Jul). “Outlet Works, DeGray Dam, Caddo River,Arkansas; Hydraulic Model Investigation,” Technical Report No.2-684, U. S. Army Engineer Waterways Experiment Station, CE,Vicksburg, Miss.

4

Bucci, D. R., and Mmphy, T. E. 1965 (Mar). “Spillway and Sluices,Red Rock Dam, Des Moines River, Iowa; Hydraulic Model Investiga-tion,” Technical Report No. 2-673, U. S. Army Engineer WaterwaysExperiment Station, CE, Vicksburg, Miss.

Campbell, F. B., md Pickett, E. B. 1966 (Nov). “tiototype Per-formance and Model-Prototype Relationship,” Miscellaneous PaperNo. 2-857, U. S. Army Engineer Waterways Experiment Station, CE,Vicksburg, Miss.

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

Colebrook, C. F. 1939. “Turbulent Flow in Pipes with ParticularReference to the Transition Region Between Smooth and Rough PipeLaws,” Journal, Institution of Civil Engineer, London, Vol 11,pp 133-156.

Cox, R. G. 1973 (J=). “Resistance Losses in Noncircular FloodControl Conduits and Sluices,” Miscellaneous Paper H-73-1, U. S.Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

A2

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20.

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EM 1110-2-160215 Ott 80

Cox, R. G., md Chu, Y.-H. 1969 (Sep). “Characteristic PressureDistribution in Outlet Works Intakes,” Miscellaneous Paper H-69-8,U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg,Miss.

Crandall, S. H., Vigander, S., and March, P. A. 1975 (Nov). “De-structive Vibration of Trashracks Due to Fluid-Structure Inter-action,” Journal of Engineering for Industry, American Society ofMechanical ~gineers, Paper No. 75-DET-63, p 1359.

Creager, W. P., and Justin, J. D. 1950. Hydroelectric Handbook,2d cd., Wiley, New York.

Dann, H. E., Hartwig, W. P., md Hunter, J. R. 1964 (Ott). “Un-lined Tunnels of the Snowy Mountains Hydro-Electric Authority,Australia,”

Davis, C. V., and Sorensen, K. E. 1969. Handbook of AppliedHydraulics, 3d cd., McGraw-Hill, New York.

Dortch, M. S. 1975 (Aug). “Outlet Works for Thylorsville Lake,Salt River, Kentucky,” Technical Report H-75-12, U. S. Army Engi-neer Waterways Experiment Station, CE, Vicksburg, Miss.

Dortch, M. S., et al. 1976 (Dee). “Dickey-Lincoln School LakesHydrothermal Model Study; Hydraulic Laboratory Investigation,”Technical Report H-76-22, U. S. Army Engineer Waterways ExperimentStation, CE, Vicksburg, Miss..

Dr~ond, G. R., and Robey, D. L. 1972 (Apr). “Heat Budget Analy-sis and Development of Design Criteria for Selective WithdrawalOutlets, Taylorsville L~e, Kentucky,” Speci~ Report No. 2, U.Army Engineer Division, Ohio River, Cincinnati, Ohio.

. 1972 (Nov). “Heat Budget Analysis and DevelopmentDesign Criteria for Selective Withdrawal Outlets, Stonew~lJackson Lake, West Virginia,” Special Report No. 4, U. S. -Engineer Division, Ohio River, Cincinnati, Ohio.

Elder, R. A., and Dougherty, G. C. 1950 (Nov). “HydratiicCharacteristics of Howell-Bunger Valves and Their AssociatedStructures,” Tennessee Valley Authority, Norris, Term.

s.

of

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Fagerburg, T. L. 1977 (May).Conduit, Melvern Dam, Kansas,”

“Pressure Tests in Flood-ControlMiscellaneous Paper H-77-5, U. S.

Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

Fletcher, B. P. 1969 (15 J=). “Howell-BungerValves, Summers-ville Dam,” Memorandum Report, U. S. Army Engineer Waterways Ex-periment Station, CE, Vicksburg, Miss.

. 1971 (Ott). “Spillway for Clarence Cannon Reservoir,Salt River, Missouri; Hydratiic Model Investigation,”TechnicalReport H-71-7, U. S. Army Engineer Waterways Experiment Station,CE, Vicksburg, Miss.

Fletcher, B. P., and Grace, J. L., Jr. 1972 (May). “PracticalGuidance for Estimating and Controlling Erosion at Culvert Outlets,”Miscellaneous Paper H-72-5, U. S. Army Engineer Waterways Experi-ment Station, CE, Vicksburg, Miss.

. 1972 (Jun). “~aluation of Flared Outlet Transitions;Hydraulic Model Investigation,” Research Report H-72-1, U. S. ArmyEngineer Waterways Experiment Station, CE, Vicksburg, Miss.

Fletcher, B. P., et al. “Dynamic Loading on Stilling Basin Side-wdls” (in preparation), U. S. Army Engineer Waterways ExperimentStation, CE, Vicksburg, Miss.

Fontane, D.-G., et al. 1977 (Apr). “Marysville Lake Hydrothem.alStudy; 900-MW Project; Hydraulic and Mathematical Investigation,”Technical Report H-77-5, Report 1, U. S. Army Engineer WaterwaysExperiment Station, CE, Vicksburg, Miss.

Fortey, J. W. , and Tiry, R. F. 1972 (May).tions of Trashrack Bars,” Civil Engineerin~pp 44-45.

“Flow-InducedVi’bra-Vol 42, No. 5,

Franke, P. G. 1969 (Feb). “Some Roughness Values of Water Pipe-lines,” L’Energia Electrica, VO1 46, NO. 2, pp 78-80.

Freeman, J. R., ed. 1929. Hydraulic Laboratory Practice, Ameri-can Society of Mechanical Engineers, New York.

George, J. F., and Pickering, G. A. 1977 (Apr). “Powerhouse In-take Gate Catapult Study, Big Bend Dam, South Dakota, and Stockton,Harry S. Trman, and Clarence Cannon Dams, Missouri; Hydraulic

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Model Investigation,” Technical Report H-77-8, U. S. Army EngineerWaterways Experiment Station, CE, Vicksburg, Miss.

Gibson, A. H. 1914. “The Conversion of Kinetic to PotentialEnergy in the Flow of Water Through Passages Having DivergentBoundaries,” Engineering, vol 93, p 205.

Gloriod, T. L., and Bohan, J. P. 1973 (Sep). “Selective With-drawal from Beech Fork L~e, Beech Fork River, West Virginia;Hydraulic Model Investigation,” Technical Report H-73-14, U. S.Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

Gordon, J. L. 1970 (Apr). “Vortices at Intakes,” Water Power,pp 138-139.

Grace, J. L., Jr. 1966 (Feb). “Resistance Coefficients forStructural Plate Corrugated Pipe; Hydraulic Model Inves$i,gation,”Technical Report No. 2-715, U. S. Army ~gineer Waterways E~”eri-ment Station, CE, Vicksburg, Miss.

. 1972 (Jan). “Outlet Works for Branched Oak andCottonwood Springs Dams, Oak Creek, Nebraska, and CottonwoodSprings Creek, South Dakota; Hydraulic Model Investigation,”Technical Report H-72-1, U. S. _ Engineer Waterways ExperimentStation, CE, Vicksburg, Miss.

Grace, J. L., Jr., and Pickering, G. A. 1971 (Apr). “Evaluationof Three Ener~ Dissipators for Storm-Drain Outlets; HydraulicLaboratory Investigation,” Rese~ch Report H-71-1, U. S. Ar~Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

Griffiths, P. T. A., and Brett, T. M. 1974 (Dee). “A ScouringRock Trap in Lemonthyme Power Tunnel,” Fifth Australasian Confer-ence on Hydraulics and Fluid Mechanics.

Hart, E. D., and Tool, A. R. 1976 (oct). “Sluice Fressures, GateVibrations, and Stilling Basin Wall Pressures, Libby Dam, KootenaiRiver, Montana,” Technical Report H-76-17, U. S. - EngineerWaterways Experiment Station, CE, Vicksburg, Miss.

Hoffman, A. 1929. “Losses in 90-Degree Pipe Bends of ConstantCircular Cross Section,” Transactions, Hydraulic Institute of theMunich Technical University, Bulletin 3; Translation published byAmerican Society of Mechanical Engineers, New York, 1935.

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Hu, W. W. 1973 (Nov). “Hydraulic Elements for the USBR StandardHorseshoe Tunnel,” Journal, Transportation Engineering, AmericanSociety of Civil Engineers, Vol 99, No. TE4, pp 973-984.

Huang, T. T. 1964. ~erg Losses in Pipe Expansions, M.S. Thesis,University of Iowa, Iowa City, Iowa.

Huval, C. J. 1969 (Jul). “Hydraulic Design of Unlined Rock Tun-nels,” Journal, Hydraulics Division, American Society of CivilEngineers, Vol 95, No. HY4, ~oc Paper 6679, pp 1235-1246.

Johnson, P. L. 1971 (Sep). “Hydraulic Model Studies of theReservoir Inlet-Outlet Structure for Horse Mesa Pump-Storage Unit,Salt River Project, Arizona,” Report REC-ERC-71-34, Bureau ofReclamation, Denver, Colo.

Jones, H. W. 1977 (Jun). “Manual for a ~onversationally ~riented~eal-Time ~ogram-Generating ~stem (CORPS),” Unnumbered Report,U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg,Miss.

Kalinske, A. A., and Robertson, J. M. 1943. “Entrainment of Airin Flowing Water-Closed Conduit Flow,” Transactions, AmericanSociety of Civil Engineers, Vol 108, pp 1435-1447.. ‘

King, H. W., and Brater, E. F. 1963. Handbook of Hytiaulics forthe Solution of Hydrostatic and Fluid-Flow Problems, 5th cd.,McGraw-Hill, New York.

Knapp, R. T., Daily, J. W., and Hammitt, F. G. 1970. Cavitation,McGraw-Hill, New York.

Lancaster, D. M., and Dexter, R. B. 1959 (Nov). “HydraulicCharacteristics of Hollow-Jet Valves,” Journal, Hydraulics Divi-sion, American Society of Civil Engineers, Vol 85, No. HYll, p 53.

Levin, L. 1973 (Jan). “Study of Peculiar Head Losses in ConicalConvergence,” Translation No. 73-3, U. S. - Engineer WaterwaysExperiment Station, CE, Vicksburg, Miss.

Lecher, F. A. 1969 (Feb). “Some Aspects of Flow-Induced Vibra-tions of Hydratiic Control Gates,” Contract Report H-69-1, U. S.Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

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65.

66.

67.

68.

69.

Loftis, B., and Fontane,Quality Study; HydraulicPaper H-76-6, U. S. ArmyCE, Vicksburg, Miss.

Loftis, B., Saunders, P.

D. C. 1976 (Apr). “FQIsLaboratory Investigateion,”

w 1110-2-160215 Ott 80

L&e Water-Miscellaneous

Engineer Waterways Experiment Station,

E., and Grace, J. L., Jr. 1976 (Feb).“B. Nerett Jordan Lake Water-Quality Study,” Technical ReportH-76-3, U. S. Army Engineer Waterways Experiment Station, CE,Vicksburg, Miss.

Louis, D. S., and Allen, A. E. 1971 (Jan). “Trash Rack Studies -Seneca Wped-Storage Plant,” Meeting Preprint 1284, NationalWater Resources Engineering Meeting, American Society of CivilEngineers, Phoenix, Ariz., 11-15 Jan 1971.

Madison, R. D., and Parker, J. R. 1936. “Pressure Losses inRectan@ar Elbows,” Transactions, American Society of MechanicalEngineers, VO~ 58, pp 167-176.

Marchetti, M., and Noseda’,G. 196o (Apr). “Head Losses inS~etrical Penstock Bifurcations with a Constant Diameter,”L’Energia Electrica, Vol XXXII, No. 4; also published as Transla-tion No. 63-2, Aug 1963, U. S. &II.WEngineer Waterways ExperimentStation, CE, Vicksburg, Miss.

Mattimoe, J. J., Tinney, E. R., and Wolcott, W. W. 1965 (oct).“Rock Trap Experience in Unlined Tunnels,” Journal, Power Division,American Society of Civil Engineers, Vol 90, No. P03, Paper 4067,pp 29-45.

Maynord, S. T., Loftis, B., and Fontane, D. G. 1978 (Jan).“Temperature Analysis and Selective-Withdrawal Design Study,Tallahala Creek Lake, Mississippi; Mathematical Model Investiga-tion,” Technical Report H-78-1, U. S. Am Engineer WaterwaysExperiment Station, CE, Vicksburg, Miss.

Melsheimer, E. S. 1969 (Dee). “Outlet WorksPohopoco Creek, Pennsylvania; Hydraulic ModelTechnical Report H-69-18, U. S. Army EngineerStation, CE, Vicksburg, Miss.

“forBeltzville Dam,Investigation,“Waterways Experiment

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15 Ott 80

70.

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73.

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78.

79.

Melsheimer, E. S., md Oswdt, N. R. 1969 (oct). “Outlet Worksfor New Hope Reservoir, Cape Fear River Basin, North Carolina;Hydraulic Model Investigation,” Technical Report H-69-14, U. S.Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

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Miller, D. S. 1971. “Internal Flow; A Guide to Losses in Pipesand Duct Systems,” British Hydromechanics Research Association,Englmd.

Moody, L. F. 1944. “Friction Factors for Pipe Flow,” Transac-tions, American Society of Mechanical Engineers, Vol 66, pP 671-684.

Moore, M. O. 1968 (oct). “Incrustation in Water Pipelines,”Journal, Pipeline Division, American Society of Civil Engineers,Vol 94, No. Pm, Paper 6161, pp 37-47.

Munsey, T. E., and Neilson, F. M. 1971 (Apr). “Prototype Observa-tions of Snettisham Project Diversion Tunnel, Long Lake, Alaska,”Miscellaneous Paper H-71-7, U. S. @ Engineer Waterways Experi-ment Station, CE, Vicksburg, Miss.

Murphy, T. E. 1959 (Jun). “Entrances to Conduits of RectangularCross Section; Investigation of Entrances Flared in Three Direc-tions md in One Direction,” Technical Memorandum No. 2-428,Report 2, U. S. Army Engineer Waterways Experiment Station, CE,Vicksburg, Miss.

. 1971 (Mar). “Control of Scow at Hydraulic Struc-tures,“ Miscellaneous Paper H-71-5, U. S. Army Engineer WaterwaysExperiment Station, CE, Vicksburg, Miss.

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Naudascher, E. , Kobus, H. E., and Rae, Ragam Pondu R. 1964 (May).“Hydrodyn-ics Analysis for High-Head Leaf Gates,” Journal.,Hydraulics Division, American Society of Civil Engineers, Vol 99,No. HY3, Proc Paper 3904, pp 155-192.

A-8

EM 1110-2-160215 Ott 80

80. Neilson, F. M. 1971 (Sep). “Howell-Bunger Valve Vibration,S~ersville Dam, Prototype Tests,” Technical Report H-71-6, U. S.Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

81. Neilson, F. M., and Carstens, M. R. 1967 (Jul). “Hydraulic ModelStudies of Pahlaui Dam Sluiceways,” Industrial Research ProjectA-962, Georgia Institute of Technology, Atlanta, Ga.

82. Nikuradse, J. 1932. “Gesetzmassigkeiten der Turbulenten Stromungin Glatten Rohren” (in German), VDI Forschungshefi 356.

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85. . 1974. “Stilling Basins for Reservoir Outlet Works,”ETL 1110-2-193, 30 Aug 1974, U. S. Army Engineer Waterways Experi-ment Station, CE, Vicksburg, Miss.

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93.

94.

95.

96.

97.

98.

99.

100.

101.

102.

Peters, H. 1934 (Mar). “Conversion of Ener~ in Cross-SectionalDivergencies Under Different Conditions of Inflow” (translation),Technical Memorandu No. 737, National Advisory Codttee forAeronautics, Washington, D. C.

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~ouse, H., Bhoota, B. V., and Hsu, En-Yun. 1951. “Design ofChannel Expulsions,”Engineers, Vol 116.

Transactions, American Society of Civil

A-10

EM 1110-2-160215 Ott 80

103. Rueda-Briceno, D. 1954 (Feb). “Pressure Conditions at the Out-let of a Pipe,” M.S. Thesis, University of Iowa, Iowa City, Iowa.

104. Russell, S. O., and Bell, J. W. “Sudden Enlargement EnergyDissipators for Mica Dam Outlets,” Western Canada HydraulicLaboratories, Ltd., Port Coquitlam, B. C., Canada.

105. Ruus, E. 1970 (Mar). “Head Losses in ~es and Mmifolds,”JournQ, Hydraulics Division, American Society of Civil Engineers,Vol 96, No. HY3, proc Paper 7130, pp 593-608.

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A-n

.,

m 1110-2-160215 Ott 80

115.

116.

117.

118.

119.

120.

121.

122.

123.

124.

125.

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Straub, L. G., and Morris, H. M. 1950. “Hydraulic Tests onCorrugated Metal Culvert Pipes,” Technical Paper NO. 5, Series B,St. Anthony Falls Hydraulic Laboratory, University of Minnesota,Minn.

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Syamala Rae, B.,

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U. S. Army Engineer Waterways Experiment Station, CE. 1947 (Jun).“Model Studies of Conduits and Stilling Basin, Bull Shoals Dam,White River, Arkansas,” Technical Memorandum No. 2-234, Vicksburg,Miss.

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A-12

/,

Tests in

126.

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128.

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132.

133.

134.

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136.

Flood-ControlMiscellaneous

EM 1110-2-160215 Ott 80

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Yarnell, D. L. 1937 (Ott). “Flow of Water Through 6-Inch PipeBends,” Technics.1Bulletin No. 577, U. S. Department of Agriculture,Washington, D. C.

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A-14

APPENDIX B

NOTATION

- Term Units

a

A

B

c

c

c=

* Ck

* cm

cP

cows

d

‘1

Length of miter bend segment

Cross-sectional area (subscripts denotelocations)

Width (in breadth)

Distance in fillet detail

Circular shapeDischarge coefficientPressure drop coefficient (subscripts denotedimension of flow)

Celerity (velocity) of pressure wave

Resistance coefficient in Chezy’s equationRelative loss coefficientHalf width of conduitCritical-slope surface profile (subscripts

denote relation to depth)

Contraction coefficient

Conveyance factor (1.486 AR2/3,

Coefficient for modified center-line trajectoryfor stilling basins subject to low-floweddies

Pressure drop parameter

~onversationally ~riented ~eal-Time~rogrmGenerating ~ystem

DiameterDepth of flow

Depth of flow entering hydraulic

(Continued)

B-1

ft

ftz

ft

ft

—--—

ft/sec

ftl’2/sec--

ft--

--

ftLg/6/~ec *

—

*

—

—

ftft

ft

(Sheet 1 of 8)

E?f1110-2-1602C1hange !i5 Yar 8?

NOTATION

= Term Units

‘2

dy/dx

D

‘h

’50

e

E

EGL

f

‘f

fn

IF

a

Depth of flow leaving hydraultc jump

Differential of y with respect to x

Diameter or height of conduit (subscriptsdenote locations)

Dimension of conduit in plane of entrancetune

Valve diameterDepth of gate slot

Equivalent hydraulic diameter (4 x hydraulicradius)

Median diameter of riprap stone (by weight)

Uf of transition wall conveyance

Modulus of elasticityGate passage invert elevation

Energy grade line

Resistance coefficient (factor) in Darcy-Weisbach formula

Forcing frequency

Natural frequency

Froude number

Gravitational acceleration

Gate opening

Bend loss

Entrance (intake) loss

(Continued)

B-2

ft

ft/ft

ft

ft

ftft

ft

ft

ft

lb/ft2ft msl

--

--

Hz

Hz

--

ft/sec2

ft “

ft

(Sheet 2 of 8)

EM 1110-2-160215 oct 80

NOTATION

- Term Units

‘fHead loss due to surface resistance (friction)

hg Head loss due to form

ho Pressure head in ‘disturbed flow

hv Velocity headVapor pressure

H Total ener~ headHorseshoe shapeHeight of conduit or wallPiezometric headHorizontalHorizontal channel smface profile (subscriptsdenote relation to depth)

‘d

%

He

Hi

‘L

Hv

k

K

L

Pressure drop

Pressure drop

Ener~ head

Minimum piezometric head

Total head loss (subscripts denote locations)

Velocity head

Roughness height

Loss coefficient (subscripts denote type)

Length of cable

Length of conduitDistance along conduit

(Continued)

ft

ft

ft

ftft

ft--

ftft-.--

ft

ft

ft

ft

N

ft

ft

--

ft

ftft

(%eet 3 of 8)

B-3

NOTATION

m Term Units

Le

‘f

LP

‘t

‘T

LN

M

n

o

P

Pv

P

Pc

PI

PT

Length of basic

Equivalent conduit length

Length of fillet

Plate width

Length of targent

Length of transition

Natural logarithm (base e)

Mild-slope surface profile (subscripts denoterelation to depth)

MomentumModel data

Resistance coefficient in Manning’s formula

Oblong shape

Pressure (subscripts denote locations)

Vapor pressure

Wetted perimeterOffset distancePrototype dataNumber of gate passages

Point of curvature

Point of intersection of tagents

Point of tmgency

(Continued)

ft

ft

ft

ft

ft

ft

-.

--

ft3--

~1/6

lb/ft2

lb/ft2

ftft

--

--

(Sheet 4 of 8)

B-4

m 1110-2-1602

15 Ott 80

NOTATION

- Term Units

Pcc Point of compound curvature

PGL Piezometric grade line

PRC Point of reverse curvature

Q Discharge

Qa Air demand

%Water discharge

r Curve radius (subscripts denote locations)

r Arc radiusa

‘fFillet radius

R Hydraulic radiusRectangular shapeCurve radius (subscripts denote locations)Radial offset distance

IR Reynolds number, IR = ~/v

s Average loss of head per unit of length(energy gradient slope)

Steep-slope surface profile (subscripts denoterelation to depth)

SubmergenceConduit invert slope

‘f

‘t

Friction slope

Strouhal n’mber

--

--

--

ft3/sec

ft3/sec

ft3;sec

ft

ft

ft

ft--

ftft

--

ft/ft

--

ftft/ft

ft/ft

--

(Continued)

(Sheet 5 of 8)

B-5

m 1110-2-1602

15 Ott 80

NOTATION

- Term Units

s Critical slope for normal depthcn

t Gate leaf thickness

‘h Local transition half height

tw Local transition half width

T TemperatureWidth of water

v Average (mean)locations)

Vertical

v Average (mean)sm

w Conduit widthGate slot width

surface

velocity (subscripts deno’te

velocity for smooth pipe flow

‘bWidth of basin

Ws Local width of basin on sloping apron

’50 Medim weight of riprap stone

x Vibration amplitudeHorizontal or longitudinal coordinate or

distance

xo

x

Y

Zero frequency deflection

Horizont~ or longitudinal coordinate ordistance (subscripts denote locations)

Vertical or transverse coordinate or distanceDepth of flow (subscripts denote locations)

(Centinued)

ft/ft

ft

ft

ft

‘Fft

ft/sec

--

ft/sec

ftft

ft

ft

lb

ftft

ft

ft

ftft

(Sheet 6 of 8)

B-6

NOTATION

- Term Units

Y=

Y.

* -Y’

Y

z

a

6

Y

AA

AB

AL

Critical depth ft

Normal depth ft

Height of pressure grade line at exit portal ft

Average piezometric

Vertical coordinate

pressure ft

ft *

Vertical or transverse coordinate or distance ftProjection of gate into conduit ft

Elevation above datum plane (subscripts denote itlocations)

Section factorft5/2

Kinetic energy correction factor (subscripts —

denote locations)

Angular distance to location ofGate lip angle ‘i

degdeg

Specific (unit) weight

Change in area*

Increment of width

Flare ratio of stilling basin sidewallLength of reach between two sections

Pressure difference

Depth ratio (y/yo)

lb/ft3

ftz

ft

ft/:tft

ft

ft/ft

(Conttiued)

B-7

(Sheet 7 of 8)

NOTATION

= Term Units

@ Conduit invert slope degBoundary contraction or expansion angle degAngular displacement or deflection deg

e Slope bf tangent extension from pier degP

v Kinematic viscosity ftzlsec

T 3.14159 ...... --

u Root-mean-square of random roughness height ft ,Unit stress in cableInterracial surface tension

u Cavitation number or index

Ui Incipient cavitation number

4 Flare angle of stilling basin

~ Center line

‘F Fahrenheit temperature

> Greater than

< Less than

sidewall

lb/ft’lb/ft

—

—

deg

-

deg

—

--

(Sheet 8 of 8)

B-8

EM 1110-2-1602

15 Ott 80

APPENDIX C

PLATES

Paragraphs in WithPlate Is MentionedPlate No.

c-l

c-2

c-3

2-3,4-16Open-Channel Flow Classifications

Pressure Flow Definition Sketch

Exit Portal Pressure

2-6,2-9,3-7

2-7,5-2d(2),TableD-~,F-3e(l)

c-4 2-12a,c,d,e,g,g(l)(b),g(l)(c),g(2)(~)>5-2c,Table D-4

Resistance Coefficients, ConcreteConduits

2-12f,4-2cc-5 Hydraulic Elements, ConduitSections

c-6 Flow Characteristics, HorseshoeConduits

2-12f

2-12g(3)C-7 Resistance Coefficient, CorrugatedMetal Pipe

c-8 Head Loss Coefficients, AbruptTransitions

2-13b,c

c-9 Loss Coefficients, ConicalTransitions

2-13d

Bend Loss Coefficients, CircularConduits

2-13e(2)(a)c-lo

2-13e(2)(a)C-n Loss Coefficients, Circular Con-duits, Multiple Miter Bends

Loss Coefficients, Rectangular Con-duits, 90° Circtiar Bends

2-13e(2)(b)C-12

2-13e(2)(b)C-13 Relative Loss Coefficients, Rectan-gular Conduits, Circular Bends

C-14 2-13e(2)(b)Loss Coefficients, Rectangular Con-duits, Triple Bend

2-14

2-19

C-15

c-16

Examples of Cavitation ~draulics

Air Demand, Primary and SecondaryMaxima

C-17 Air Demand 2-19

c-1

m 1110-2-160215 Ott 80

Plate No.

c-18

C-19

C-20

C-21

c-22

C-23

c-24

c-25

c-26

c-27

c-28

c-29

C-30

C-31

C-32

c-33

c-34

c-35

Title

Sluice Location, Monolith CenterLine

Typical Off-Monolith Center LineSluice Location

Conduits, Circular Bends, MinimmPressure

Sluice Intakes

Pressure Drop Coefficients, SluiceEntrances

Vertical-Lift Gate, Gate SlotDetails

Discharge Coefficients, ConduitTainter Gates, Free Flow

Discharge Coefficients, Fixed-ConeValves

Pressure Coefficients, Gate Slot

Incipient Cavitation Coefficientsfor Slots

Sluice Exit Portal, RoofConstrictions

Exit Portal Deflector, AlleghenyDam Model

Sluice Exit Portal, Sidewall flarewith Roof Constriction, RedRock D= Model

Sluice Eyebrow Deflector, FolsomDam Model

Intake Loss Coefficients, All GatesFully Open

Intake Loss Coefficients, All orFewer Gates Open

Concrete Conduits, Intake Losses,Drop Inlets

Vortex Formation

Para~aphs in WhichPlate Is Mentioned

3-1,3-3a

3-1

3-3b

3-4,4-21

3-6c,4-12,4-21

3-9a,3-13,3-l?f,4-15,4-16

3-9b

3-10d

3-13

3-13

3-19

3-19

3-19

3-20

b-3a,4-21,D-8,TableD-4

4-3a,4-21

4-3a

4-3C

c-2

EY 1110-2-1602Change 115 ?Iar87

Paragraphs in Ifiichplate Is Mentioned

4-9,4-14

4-12,4-21

Plate ??0.

C-36

c-37

Title

Types of Conduit Gates

Pressure Drop Coefficients,Entrance with Roof Curve Only

4-13,4-21C-38 Conduit Entrances with Roof Curveand Side Flare

4-16c-39 Discharge Coefficients, Vertical-Lift Gate

C-40 Definition Sketch, Low-LevelOutlets

5-2b

Stilling Basin Layout, SingleOutlet

5-2d(l),5-2h,5-”2iC-41

Stilling Basin Trajectory Modifi-cation to Reduce Low Flow Eddies

5-2d(3)* C-41A*

5-2k,5-6

5-4

6-1

6-2b(4),6-4a

C-42

c-43

c-44

C-45

Outlet Channel

Preformed Scour Hole

Water Quality Intake Types

Water Quality Outlet, ConcreteGravity Dam, Rowlesburg Dam

C-46 Water Quality Outlet, Earth Dam,Beltzville

6-2b(4),6-4b

Intake Structure, ”MultilevelDetafl, Taylor-ille Dam

c-47 6-2b(4),6-4b

6-2b(4),6-4bC-48 Intake Structure, MultilevelDetail, New Hope Dam

6-2b(5)

6-4a

c-49

c-so

Temperature Control Weirs

Multiple Penstock Intake Struc-ture, Dickey Dam

c-51 Cylindrical Gate Intake Tower,DeGray Dam

6-4b

C-52 Water Quality Intake, Earth Dam,Beech Fork

6-4b

c-3

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OATA SOURCE

STATE UNIVERSITY OF lOWA

OCNISON MOOELOCNISON PROTOTYPE

GARRISON MOOELYOUGHIOGHENY MOOELENIO PROTOTYPEFORT RANOALL MOOELfORT RANOALL PROTOTYPEOAHE PROTOTYPEBELTZVILLE

TUTTLE CREEK PROTOTYPEKLVERN P~TOTYPE

SOTTOM SUPPORT

NONE

LEVEL

LEVELPARABOUCi ON 20PARASOLICLEVZLLEVELPARABOLICPARASOLK

PARA~LICPARAB&lC

CONOUIT SHAPE

CIRCULARCIRCULAR

CIRCULAR

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HORSESHOEHORSESHOE

EXIT PORTAL PRESSURE

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AREASECTION (A)

WETTEDPERIMETER

(P)

HYDRAULICRADIUS

(R)

TnRECTANGULAR SHAPE

z

i

BH

@

CIRCULAR SHAPE

.vD2

4

2(B+H)

VERTICAL-SIDE HORSESHOESHAPE

r?BH+~ B+2H+nr

2(H+nr)

BH

2(B+H)

4

2

BH+~

B+2H+nr

BH+T$

2(H+nr)

SLOPING-SIDE HORSESHOESHAPE 7r rz,< H(B+AB)+~

Lo

7r f!zH(B+AB)+~ B+2(H*+(AB)*)~+7rr

HB+2(H2t(AB)2)%+mr

+B4 LAB

aL CURVED-SIDE HORSESHOESHAPE (USBR)-t2r ~y 3.3172r2 6.5338r 0.5077 r

HYDRAULIC ELEMENTS

CONDUIT SECTIONS

FROMHDC224-2

PLATE c-5

EM 1110-2-160215-Ott 80

Sen/n2 ONLY

I.OO10 20 30 40 50 60 70

0.9

0.8

0.7

0.6

~o.5

0.4

0.3

0.2

0.1

000.5 1.0 1.5 2.0 2.5 3

*,*, .L, &,&,$,+

a. FLOW CHARACTERISTICS OF USBR

STANDARD HORSESHOE TUNNEL SECTION

b. GEOMETRY OF CROSS SECTION OF

USBR STANDARD HORSESHOE TUNNEL

LEGEND

A AREA OF FLOW CROSS SECTION H/2 CROWN RADIUS

y.H

CK

P

Rs~~TYz@

HYDRAULIC DEPTH OF SECTION -A/T n MANNING ROUGHNESSCENTRAL HEIGHT OF TUNNEL AND FACTORSMAXIMUM WIOTH OF TUNNEL

CONVEYANCE FACTOR OF MANNING FORMULA= I.* AR%WETTED PERIMETER

HYDRAULIC RADIUS-A/PCRITICAL SLOPE FOR NORMAL OEPTH

WIDTH OF WATER SURFACE

CENTRAL FLOW DEPTH

SECTION FACTOR-A-ANGLE OF HORIZONTAL DIAMETER WITH

FLOW CHARACTERISTICSWATER SURFACE ON OPPOSITE SIOE HORSESHOE CONDUITS

FROM HOC 224-10

EM 1110-2-160215 Ott 80

0.20 .

0.15

90-*= 0.122 D-0”4

0.10\ 90

0.00 \.% 90 \ 90

-\

O.=\

\

0.05“-

\ !. \c 01

o= -. *

0.04b 80”

966-.

062 070\ \ ,

-70” HELIX ANGLEb\

0.03 \\

0.0210.5 0.6 0.8 1 2 3 4 56 8

PIPE DIAMETER D, FT

RESISTANCE COEFFICIENT

CORRUGATED METAL PIPE

(FromSAFHL, item112)

PMTE c-r

m 1110-2-1602

Ott 80

K

1.0

0.8

0.6

0.4

0.2

0.00.0 0.2 0.4 0.6 0.8 1.0

EXPANSIONS

1 A2v,

*1

A: (EXPANSIONS) ,= (cONTRAc TIONs)

2 Al

CONTRACTIONS

6

v, I—Al

IV2

A2

2v’

h~=K~

WHERE

he = HEAD LOSS, FT

K = LOSS COEFFICIENT

V = REFERENCE CONDUIT VELOCITY, FPS

A = CROSS-SECTION AREA, FT2

g = AccELERATION OF GRAVITY, FT/SEC2

CC = CONTRACTION COEFFICIENT

(FROM WEISBACH) HEAD LOSS COEFFICIENTS

ABRUPT TRANSITIONS

m 1110-2-1602

15 Ott 8(

K

K

0.8

A%/-

T----- J +___ - _ _

/ - GIBSON D=/o,G5F-&---/

!

f’1 2.0

0.e I

0,4

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0.2

/

~&‘

o0 20 40

e,oEG w60 I 00

a, EXPANSIONS

/ X’ I /.2 ~0.2

LEV!N—

m

.“––0 20

40 6.,02. m80 100

b. CONTRACTIONS

+ FROM PLATE C-8

BASIC EQUATION FOR O=9W.

hfK =—

v2/2g

WHERE:kl=HEAD LOSS, FTs =ACCELERATION OF GRAVITY, FT~C2

V, =AVfRAGE VELOCITY IN THE SMALLERLOSS COEFFICIENTS

CONOUIT. FPS CONICAL TRANSITIONS

FROM HDC 228-4

PLATE C-9

m 1110-2-1602.5 Ott 80

0.20

0.15

0.!0

I

0.051

I~1

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0.8

6. OE. LEc TtONANGLEINRAbIANs

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0

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// /’

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Norc:FIGURESONGRAPH INOICATf r/o RATIO

20. 40“ So” so’ 120”

DEFLECTION ANGLE e

., C!RCULAR BENDS

12

-T .=2=104y { / /

/10

R=6x 10’

/ T

+ ~

‘R =2.5x705

0.8

i

/

10 20 30 40 50 60 70 ao

0,

0.

0,

elN DEGREES

b. SINGLE MITER ❑ ENDS

SA31C EQUATION

WHERE K - BENO LOSS COE~F,ClEN7hi- neAO LOSs ouc TO 8END BEND LOSS COEFFICIENTS

CIRCULAR CONDUITS

FROM HOC 228- 1 AND 228- 2/1

m~ 1110-2-160215 Ott 80

mF. 30.%8

,-*

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9.1-

m

@

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PLATE C-n

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I‘2 O.OH I

— =—(MITER BENDJ

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-. --.-- ----- - --- --”

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8 105 2

REYNOLDS NUMBER, TR

4 6 8

BASIC EQUATION

v’hb=KZ

G

‘2 ‘mORclH

r,w w

WHERE:t

H = W/2 H=2W— -----

hb = BEND HEAD LOSS, FT

K = BEND LOSS COEFFICIENT LOSS COEFFICIENTSV = FLOW VELOCITY, FPS

9 = AcCELERATION OF GRAVITY, FTISEC2 RECTANGULAR CONDUITS

90 °Cl RCULAR BENOS

‘FromASME, item 64, andWES Tram.,item116)

EM 1110-2-160215 Ott 30

u

2.0

1.5

1.0

0.8

0.6

0.4

0.3

0.2

0.110 20 30 40 60 80 100 150 180

BEND DEFLECTION ANGLE @, DEGREES.

BASIC EQUATION

hb=CK ;2

WHERE

hb = EEND HEAD LOSS, FT

I= ‘ RELATIVE LOSS COEFFICIENT

K n 900 BEND LOSS COEFFICIENT (pLATE 12j

V = CONDUIT VELOCITY, FPS

g . ACCELERATION OF GRAVITY, FTISEC2

Gr2•1

H

r,w

H=We

~_ 1.5Hr, 0.5H

REYNOLDS NUMBER ASOUT ~,000 RELATIVE LOSS COEFFICIENTSRECTANGULAR CONDUITS

(FromASME, item64)CIRCULAR BENDS

PLATE C-13

EM 1110-2-160215’oct 80

3.5

30

2.5

2.0

u

15

1.0

0.s

o2X

o

\ PL ANE OF 8EN0

)

o

NOTE: m = REYNOLDS NUMBER

Dh = EQUIVALENT HYORAULIC OIAMETER

V = KINEMATIC VISCOSITY, fT2/SEC

,. 5 lo~

~=v’v

BASIC EQUATION

hb. KV2/29

5

WHERE:hb=HEAD LOSS, FT

LOSS COEFFICIENTSv= CONDUIT VELOCITY, FPSK= LOSS COEFFICIENT

RECTANGULAR CONDUITSg= ACCELERATION OF GRAVITY, FT/SEC2 TRIPLE BEND

EM 1.11o-2-1602

15 Ott 80

~ HEAD LOSS =O.15AP .5.0’8

} ~ ;.;-~E.G. L.. —

o

-’6’W:I=I,,-40 ~ I ]1 VArUK rKl=SJUK= ‘-2a. - 1 I I I

a. VENTURI METER

11 ~-- -*-+mm0 Ii ; PR’ESSU’RE

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I I I I I

’48VAPOR PRESSURE = -33.4 ‘

+~ -

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G_o =02D’ I

GO VENA cONTRACTA (Cc = 0.67, HDC 320-3)

V =82 FPS

b. IN-LINE GATE

PHYSICAL CONDITIONS:

ATMOSPHERIC PRESSURE = 33.8 FTAT 50” F AT SEA LEVEL (HDC 000-2)

VAPOR PRESSURE = 0.17 PSIA = 0.4 FTAT 50” F (HDC 001-2)

EXAMPLES OFCAVITATION HYDRAULICS

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2,00

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~~w=0.0066 {F-1)’4ao4 I

2 3 45 678910 20 30 ho

NOTE :F = V/~ (FROUOE NUMBER)

v = WATER VELOCITY AT VENACONTRACTA , F- :

B = WATER DEPTH AT VCNACONTRACTA, FT

q= AIR DEMAND, CFS

G= WATER DISCHARGE, CFS

LEGEND~ PINE FLAT- H = 370 FT

O----4 PINE FLAT-H= 304 FT*-4 PINE FLAT ‘H = 254 FT~ Of NISON - H = 6.4 FTx~ HULA H- H=24 VT

~ NOR FORK -H=154FT

TYGART ‘H = 92 FT

; S12LTZVILLE H= 114 FT(3-TEST AvG1*

H = HEAD, POOL TO CONDUIT CENTER LINE

FIGURE5 ON GRAPH SHOW GATEOPENING IN FEET.

● PR08 ABLY FREE FLOWCONDITION

(F-1)

AT

TEMP“F

So

AIR PROPERTIES

SEA LEVEL ATMOSPHERIC PRESSURE

KINEMATIC SPECIFICVISCOSITY OENSI TY WEIGHT

~T2/5~c SLUG/FT3 LB/FT3

1.69 x 10-4 2.26 x 10-3 7.35 x 10-2

60 1.36 x 10-4 2.m x 10-3 7.63 x 10-2

40 1.46 x 10-4 2.47 x 10-3 7.94 x 10-2

AIR DEMAND

FROM HDC 050-1

PLATE c-1

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L-..-----.-------—..\----------.;-----ii

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m 1110-2-160215 Ott 80

C*

8

7

6

5

4

3

2

I

o0 2 4 6

R/C

EQUATIONS

“2 “2—=H, +~ , U=cp

‘+29 29 V2

~

NOTE:

6 10 1

@ = 22,5* FOR CIRCULAR CONDUITS

AND 45° FOR RECTANGULAR

CONDUITS.

H . PIC20METRIC HEAD FROM PRESSUREGRADIENT CXTENSION, FT

V . AvERAGE VELOCITY, FPS

9 “ACCELERATION 0!= GRAVITY. FT/SEC2

HI = MINIMUM PIEZOMETRIC HEAD. FT

v, * vELOCITY AT LOCATION OF H,, FPs

CP - PRESSUR~ OROP PARAMETERC =CONDUIT HALF WIDTH

F ROM HCD 228-3

CONDUITS

CIRCULAR BENDS

MINIMUM PRESSURE

EM 1110-2-160215 Ott 80

*. I

SECTION A-A

HALF SECTION INTAKE

w/3

w/2

SECTION B-B

.A

OPERA TINGGALLERY

n

\- ~ —SLUICE~ - y — . -i —.— -—T.j :::”

<6/

INSPECTJON GALLERY~:. . ..’+ .

V:,:*: ..4 .,?.. .

LONGITUDINAL SECTION

a. FLUSH INTAKE

K7 TAINTER GATE

‘1

.*.. . 4.’:4

:f.

i

---

LOW-LEVEL SLUICE HIGH-LEVEL SLUICE

b. PROTRUDING INTAKES

SLUICE INTAKES

PMTE C-21

EM 111o-2-16o215 Ott 80

“ 0.2

●.

:~ 04cL

:u 06

EK0

: 08>

2uaa 10

120,0 0.2 04 0.6 0.6 1.0 1.2 1,4 1.6 1.8

&D

P c. x —. r ORIGIN

‘‘Iy

3=033

TPT.

a. SIMPLE CURVES

0,0

“ 02*.z

04

0.6

Oe

o

20.0 0.2 0.4 0,6 0,6 I.0 I .2 1.4 !6 16 20

P.c. oR,Gl:A—p‘~YI

x’ Y’~+—.(032 0)2 1 +=0.32

T PT.

NOTE: $=067CONOUIT HEIGHTCONDUIT WIDTH = ‘ ’765 b. COMPOUND CURVES

~ , OIMENS1ON OF cONDUIT INOIRECTIOh CONCERNED, FT

L ❑ OISTANCE ALONG CONDUIT, FT PRESSURE DROP COEFFICIENTS

FROM HOC 211-1,1/1SLUICE ENTRANCES

Mm c-22

EM 1110-2-160215 Ott 89-

—

BOTTOM—-- --— .-

mw~w;l(p-INCREASE TO 2W FOR

HEADS >250 FT

DETAIL OF ROOF SLOT

R

DETAIL OF SIDEWALL SLOT

NOTE: GATE LEAF, FRAME, AND LINERMAY BE OF CAST OR WELDEDCONSTRUCTION.

VERTICAL-LIFT GATE

GATE SLOT DETAILS

EM 1110-2-160215-Ott 80

0.65 Om 0,75 0

OISCHARGE COEFFICIENT> C

BASIC EQUATIONLEGEND

Q= CGOB~— vON MISES

FWHERE

Q =DIsCHARGE, CFS—-— GARRISON (THEORETICAL,

c =DIsCHARGE COEFFICIENTFROM VON MIS ES)

~=GATE OPENING, FT

0 =WIOTM OF GATE OPENING, FTH =ENERGY GRAD. EL. MIW~

(INVERT EL. +cGoI, FT

DISCHARGE COEFF

“

.~= GARRISON MOOEL (H MEASURED TO LIP)

Cl ENTS

CONDUIT TAINTER GATES

FREE FLOW

5

FROM HDC 320-3

EM 1110-2-160215 Ott 8

09

0.8 ISUGGESTEDDESIGNCURVE / /

(SIX- vANE VALVES] J /

/

O.e

/ ~/

[

❑

v LEGEND●.~~ 0.5

V WATAUGA PROTOTYPE VALVE NO 2, 0=8 O“O FONTANA PROTOTYPE

k

D=7.0, —❑ NARROWS MODEL 0=7.0,

u0u

;

<

mE

‘SUGGESTED DESIGN CURVE

0.2

0.1

0Ov

0.0 01 02 0.3 04 0.5 06

BASIC EQUATION

Q=CAfi

SLEEVE TRAVEL

OIAMETER

WNERE.

CGOISCHARGE COEFFICIENTA= AREA OF CONDUIT M.4MEOIATELY uPSTREAM

FROM VALVE, FTZ

He= ENERCY HEAO MEASUREO TO CENTERLINE OFDISCHARGE COEFFICIENTS

CONDUIT IMMEDIATELYUPSTREAM FROM VALVE, FT FIXED-CONE VALVES

FROM HDC 332-1, 1/1

EM 1110,2-16025 Ott 80

a20 n

1 I I 1

r

REFERENCEPRESURE-—

~*~sso~

o 0.10 n●’z \ * -~u~ DEFINITION SKETCH

kg

IAlK o22 0,00 \ua 5

0

. NOIE X/W= RATIOOF OISTANC~FROM~WNSTREAM EOGEOF SLOT TOWJOTH OF SLOT

w00

-0.10 t- la 0.0 I .0 2.0 3.0

xw

k w . &

0.557Wl;12taper; imrease to 1:24 for

(MA Y BESOUAREI heads> 250fi.1‘

fo, 091 w

a. PRESSURE DETAILS

-0,10

v*.zwG$

~

u -0.20a~m: MINIMUM PRESSURE DOWNSTREAM FROM SLOT&

-0.300.0 0.5 I ,0 1.5 2.0 2,5

EQUATION

Hd=CHV

yo

b. MINIMUM PRESSURE

WHERE:

Hd = pRESSURE DIFFERENCE FROM

REFERENCE PRESSURE, FT

C = PRESSURE COEFFICIENT PRESSURE COEFFICIENTSHv = CONDUIT VELOCITY HEAD AT

REFERENCE PRESSURE STATION, FT GATE SLOT‘ROM HOC 212-1/1, 1{2

LATE C-26

EM 1110-2-160215 Oct,sc

*

● SLOTS A, B, C, ANDDmlco

bb

Vo* —

R —-! ,

+

-“+ ,

SLOTS E, F, G, AND H

1

hPc

+

11--

PLAN

*UF 1DIMENSIONS RELATIVE TO W u;

SLOT TYPE R P L

t t:4

A 0.425 0.200 2.50 0.36

0.425 0.42S .SLOTS A, B, C, AND D 0.725 0.625 .

1.025 0.825 . .

,& ! : ::: ‘!w :’L H . . 1.675 10.00 0.27

SLOTS E, F, G, AND HNOTE: CONDUIT HEIGHT = 0.708W

DOWNSTREAM PI_AN OF GATE SLOTS

a. GATE SLOTS

0.556 W

FLOW -

“4

*

w * L9I B 0.18 1

BASIC EQUATION:b. AIR VENT AND ORAIN INLET PROFILE

hO-ha. -; IF U> ~i, cAvITATION WILL NOT OCCUR

V20

WHERE, ‘gVO . CONDu IT vEI_Oc ITy, Fps

he = PRESSURE HEAD IN UNDISTURBED FLOW, FT

h, = VAPOR PRESSURE OF WATER, FT INCIPIENT CAVITATION~ = CAVITATION INDEX COEFFICIENT CO E FFO I C I EN TS F R SLOTSg = ACCELERATION OF GRAvITY, FT/SEC2

mm c-27

EM 1110-2-1602i ~Ct 80

Pu~ c-28

PLAN

,V ;.. -,

P’ .4

N“II

oE’

n0

., . . .

Q

0.5;7 D.

1-------

1.;1 D4

Q SECTION DOWNSTREAM ELEVATION

EXIT PORTAL DEFLECTORALLEGHENY DAM MODEL

..

BA

SIN

EL

EV

AT

ION

SLU

ICE

EX

ITP

OR

TA

L

SID

EW

ALL

FLA

RE

WIT

HR

OO

FC

ON

ST

RIC

TIO

N

RE

DR

OC

KD

AM

MO

DE

L

EM 111o-2-16O215 Ott 80

Y =0.00

ELEVATION

\ \

)9

c

0.,7D+ 0.556 Q

b ‘ :

B B

--

VIEWA- A

SPILLWAY FACE

L

w 0“’+’”

0:”0. 0:’ T

VIEW B - B

0.89 D

po.J7D

B

““. ”:.”O .”. :.”.df: . . .b .. . . .. .. . “0...’ ::. :?: ‘

VIEWC - C

SLUICE EYEBROW DEFLECTOR

FOLSOM DAM MODEL

PLATE C-31

m 1110-2-1602

15 Ott 80

~ UPSTREM ELEVATION

K-.O.O7M; 0.16P K-0,C6M

(WES: PINE FLAT) (OROVILLE)

k●m

~K- O.12M; 0.16MK- O.19P 0.25P

(DENISON; FT. RANDALL)

=~

K- O.13M

(NEW HOPE)

m~

K- O.12M; O.ll P

(TUTTLE CREEK)ROM HDC 221.1, 1/1

PM PM

K-0,06M K= O,1OM

(OAHE) (OROVILLE)

PrnFILE _

--

~ ~K- O.33M K-1.21M; 0.57P

(TIONESTA) (BELT2vILLE)

8ASIC ERUATION:

WHERE:

~ . HEAO LOSS, FT

K = LOSS COEFFICIENTV .VELOCITYINCONOUIT

PROPER, FPS9 =ACCELERATIONOF

GRAVITY, FTISEC2

NOTE:

M . MOOEL OATAP =PROTOTYPE OATA

SEE ALSO PLATE C-32.

INTAKE LOSS COEFFICIENTSALL GATES FULLY OPEN

PLATE C-32

EM 1110-2-160215 Ott Bc

PRoFILE

c —

PLAN

K (TwO GATESI = 0.16 MK IONE GATE) = 3.10 M

~1~ = O.w

(FT. RANDALQ

&P~FILE

PLW

K (THREE GATES) = O.OS MK (GATES 1 & 3) = 0.29 MK (GATE 2) = 3.~ M

~1~ = 0.S27

(wAPPAPELLO)

kPROFILE

PLAN—

K (FOUR GATES) = 0.20 MK (THREE GATESI = 0.2s MK (TwO GATES) = 2.o7 M

~/~ = 0.3? 7

(SARDIS)

PROFILE

L

PLAJ4

K ITWO GATESI = 0,22 MK IONE GATE) = 1.S0 M

~{~ = 0.s0s

(EAST BRANCH)

LPROFILE

:-PLAN—

K ITHREE GATES) = 0.33 MK IGATE 2) = 5.6SM

~J4 =0,423

(TIONESTA)

NOTE:

PROFILE

PLAN

K ITV40 GATES) = 0.57 PK (ONE GATEI = 2,62 P

~[+ = 0.539

(BELT2VILLE)

&‘.. .

.-.. ~-. .

-.. . ~----

PROFILE

PLAN

K [THREE GATESI ~ 0.20 MK IGATES 1 & 3) = 0.40 M

~/+ = 0.631

[ARKABUTLA)

a-c EQuATION:

~=K:

wHEREhq = HEAO LOSS, FT

K-= L053 cOEFFICIENTv = vELOCITY IN CONDUIT

PROPER, FPS9 . ACCELERATION OF

GRAVITV. FT/SEC2

NOTATIONS INC NCATE GATES OPEN.

M = MODEL OATAP = PROTOTYPE OATA

sEE ALSO PLATE C-32.

~(~ = RATIO OF ONE GATE PAS3AGEFLOW AREA TO THE CONOUIT AREA.

TO CONVE RT L= COEFFIC1 ENTS INTO TERMS

OF GATE PASSAGE VELOCITY HEAO. MULTIPLYK BY THE SOUARE OF THE RATIO OF THEOPERATIVE GATE PASSAGE(SI FLOW AR EA TOTHE CONOUIT AREA.

INTAKE LOSS COEFFICIENTS

ALL OR FEWER GATES OPEN

:ROM HOC 221.1,1. 1‘2

PMTE c-33

...

PIP

ET

RA

SH

RA

CK

UP

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EM 1110-2-1602

15 Ott 80

llQ

OROVILLE

100

90

NONVORTEX REGION

80

/ (VORTEX)

70/

i-IL

.

~ 60wu

zoz 50

Vo RTEX REGION

w { i ‘2mJ /’W /

40

/t ,l_

I/

[ “:1 -/~~-

30 NOTE: S = SUBMERGENCE. FT -

/ ENID v =vELOCITY IN

/ (VORTEX) CONDUIT, FPS

s

/

L

D =CONDUIT HEIGHT

20 -OR DIAMETER. FT -

/

/’

10/ >

00 40 80 120 160 200 240 280

OROVILLEDEN ISON

ENID-----

D

VD;

LEGEND

MODELPROTOTYPEPROTOTYPE

GORDON (Symmetrical App RoACH)GORDON (UNSYMMETRICAL APPROACH)

VORTEX FORMATION

Pum C-3

m 1119-2-160215-Ott 80

PIER NOSE

D.....:f

. .. .

,4::!.A’

i. . ..:&ti:“.;. ‘ ‘4. . .’. ~::

‘4”. .:

EM FRGEN CY

GATE SLOT-

T“&. .

4:SERVICE GATE WELL

.“<.-

\F TAINTER GATE

TAINTER GATE

GARRISON DAM

EMERGENCY GATE SLOT

BULKHEAD 5LOT\ \.

T v“

r

1

TRASHRACK SLOT.4”!

d

/SERVICE GATE SLOT

VERTICAL-LIFT GATE

FORT RANDALL DAM

TYPES OF

CONDUIT GATES

mm c-36

m lllQ-2-$60215 Ott 80

CONDUIT

0.4

0.6

0.8

tEaUATION

WHERE

Hd= PRESSURE DROP FROM POOL, FT

C ,PRE5SURE DROP COEFFICIENT

. .0.0 0.2 0.4 9A 0.8 1.0 1.2 1.4 1.6 1.8 2.0

x

7

a. “SHORT” CURVE

0.4

NOTE: O. HEIGHT OF RECTANGULARCONOUIT SECTION, FT

OA% <10 P CORNER

X= DISTANCE ALONG CONDUIT, FT

1.0. -

N

‘c

0.0 0.2 0.4 0.6 0.s 1.0 1.2 1.4 1.6 1.8 2.0~

b. “LONG’;CURVE

P.c.

t

;

:

:

It “SHORT” PT

+J&

.—. — &--—-—-—-.2

x

DEFINITIONSKETCH

HEIGHT-WIOTHRATIO= 1.785

PRESSURE DROP COEFFICIENTSFROM HOC 221-2, 2/1 ENTRANCE WITH ROOF CURVE ONLY

PMTE c-37

~ 11 Lo~2-160215 Ott 80

9“ r~.%1 ; I I I L= OISTANCE ALONG CONDUIT, FT I

1+’

NOTE: O- DIMENSION OF RECTANGULAR

zGATE SECTION IN OIRECTION

:CONCERNEO, FT ‘i

L~ I ty

k 0.8 “ t,ov& i \- -0K i, \o 1.0 %:

w

> i.g \

<j I 1THREE - D/MENS/ONAL

COMPUTED II I I I I7

0: 1.2 1 - EQUATION

‘--- ------.

“2.x

---- ‘d=c%

TjO-D/MEjS,0N4L- ~y “, -

WHERE:

1.4 Hd= PRESSURE DROP FROM POOL, FT

C =PRESSURE OROP COEFFICIENT

P.T. —=vELOCITY HEAO IN RECTANGULAR29 ~ATEsEc~,~N,FT

1.6 I I

0.0 0.2 0.4 0.6 0.8 1.0 1.2 I .4 1.6 1.0 2.0

FROM HDC 221-3

PLAN

ELEVATION

CONDUIT ENTRANCES WITHROOF CURVE AND SIDE FLARE

LATE c-38

EM 1110-2-1602

100

90

80

70

60

50

40

3C

2C

m●

\1

Q A

\/’},\

It}

SUGGESTED DESIGN CURVE

+

GATE LIP GEOMETRY

— LEGEND

D FORT RANDALL MODELo WES MODEL TEST CWI 803& DORENA PROTOTYPE

VA ADJUS’TEDEAKAGE I

0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

DISCHARGE COEFFICIENT, C

BASIC EQUATION

Q = CGOB~

WHERE:

Q = DISCHARGE, CFS

C = OISCHARGE COEFFICIENT

GO = GATE OPENING, FT

B = GATE WIDTH, FT

H . HEAD, FT: EN=RGV GRADE LINE DISCHARGE COEFFICIENTSTO ~ OF GATE OPENING VERTICAL-LIFT GATE

FROM HDC 3~-1

PMTE c-3’

EM 1110-2-1602.5 Ott 80

“NolLvA3i383LvA71vl ‘

(M07 SI ~37~no uo

---t

H91H S1 M31 VM71V1) Noll>v Nlsy8

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I

i

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I

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EM 1110-2-1602

za_lL I

PMTE c-43

EM 1110-2-160215 Ott 80

SHUTTER GANTRY CRANE INTAKE GATEGANTRY HOIST

TRASH RACKS

TEMPERATURECONTROL SHUTTERS

PENSTOCK

INCLINED INTAKE

, BULKHEAD SLOT

WATER QuALITY

WATERQUALITYlNTAKES

E000 FLOW

EMERGENCY GATE ~ ‘SERVICE GATE

FREESTANDING INTAKE

I I*- “ /

WATER QUALITYINTAKE TYPES

‘MTE C-44

EM 1110-2-160215 Ott.80

LOWER ACCESS ROAO ~

PLAN

4 1700

2~ 1600

~- 1500

L

; 14Wu

~ 13000+00 5+00 10+00 15+00

STATIONS ALONG AXIS OF DAM

ELEVATION LO”OKING DOWNSTREAM

FACE OF TRAINING WALL

SECTIONAL PLAN OF CONTROL TOWER AND SLUICE

WATER QUALITY OUTLETCONCRETE GRAVITY DAM

RONLESBURGDAM

PMTE c-45

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3....-I ,...+. . .. .:,.,.

&A- 4-A

,.,!. ... ... . . ,..,,, .. . .. ,.

~

,’. <

‘i.,’

. . ...

“.& /

. . . . . . .

GATE SEAL ATWATFR PASSAG

NOT TO SCA~

[SECTIONAL PLAN B-B

u..-SECTION A-A

SCL~A IN FEFT

/

CYLINDRICAL GATEINTAKE TOWER

DE GRAY DAM

EM 111o-2-16o2IS oct 80

MAX WATER SURFACE.— —

—-

MAX FLOOD CONTROLPOOL

.—. —

UPSTREAM ELEVATION

LEFT SELECTIVEWITHDRAWAL WELL

RIGHT SELECTIVEWITHDRAWAL WELL

WATER QUALITY INTAKE

EARTH DAM

BEECH FORK

D-1 EM 1110-2-160215 Ott 80

APPENDIX D

COMPUTATION OF DISCHARGE RATING CURVES FOR OUTLET WORKS(IllustrativeExample)

D-1. Introduction. The following simplified example is presented toillustrate some of the procedures and guidance given in Chapter 2 andparagraph 4-16 for developing rating curves for outlet works. The pro-cedures are applicable with or without the aid of a programmed computer.A number of comments applying to any conduit discharge computations are “included.

D-2. Multiple Conduits. For an outlet works composed of several con-duits operating in parallel, the total flow must be proportioned amongthe conduits before the head-discharge relation can be determined. Thedivision of flow depends upon the nature of the conduit layout; that is,when all the conduits are identicd in size, length, shape, and invertelevation and have uniform flow conditions at entrances and exits, theflow will be distributed equally. When the outlet works contain con-duits of several sizes which have the same entrance control, the distri-bution of flow in the conduits is determined by assuming pool elevationsand calcdating individual conduit discharges. When the conduits arevariable in size or the invert elevations are not identical.and thedisch=ge control does not occur at the entrance, trial distributions ofass~ed total discharges must be made; and pool elevations, correspond-ing to the trial discharges, must be determined for each conduit. Thecorrect flow distribution will be determined when the computed poolelevations are identical for all of the conduits.

D-3. Example Structure. The outlet works selected for this samplecomputation have two 11- by 22-fi gate passages, a transition section, a22-ft circular conduit, and a parabolic drop into the stilling basin.A section along the center line of the conduit is shown in plate D-1.Rating curves should be computed for both k = 0.002 ft (capacity) andsmooth pipe (velocity) conditions for full flow and k = 0.007 ft and0.002 ft , respectively, for partly full flow. This example is limitedto the capacity curve computations.

D-4. Computer Programs. A number of computer programs applicable todeveloping rating curves have been developed and these ae available onthe computer-aided design system CORPS. The applicable CORPS progrsmrime(s) will be noted throughout this example problem. It is recommendedthat the designer periodically check the list of available progrms inCORPS to determine if additional programs have been added to the system.

D-1

m 1110-2-160215 Ott 80

He should also check with the WES ~gineer Computer Progrmsee if programs are available outside of the CORPS system.

D-h

Library to

D-5. Discharge Controls. The computation of flow through a conduitusually involves consideration of several conditions of flow. ~ringdiversion when the upper pool is at low stages or at lower partial gateopenings at any stage, open-charnel flow may occur in the conduit. Asthe reservoir level is raised or the gate opening is increased, thedepth of flow in the conduit increases until the conduit flows full.Determinations are needed of whether there is inlet control, outlet con-trol, critical depth control, or gate control and when the controlshifts from one type to another. Definition of the discharge curvesrequires open-channel, pressure flow, and gate discharge computations.The open-channel flow computations probably will require flow profilesto evaluate ener~ losses and establish the limits of the open-channelflow ranges for both diversion and gated flow conditions.

S6 . Hydraulic Characteristic Curves. Prior to determining conditionsof open-channel flow and type of control and computing the rating curves,the following hydratiic characteristic curves should be prepared:

a. Tailwater stage-discharge curves for several conditions of anymticipated downstream channel degradation or aggravation (see paral-10b(4)(a)).

b. Conduit cross-sectional areas of flow in square feet plotted asabscissas against flow dept:s in feet plotted as ordinates. (CORPSH6002, H2040, H2041, H2042, or King’s Handbook (item D-4) Table 7-4.)

c. Conduit hydraulic radii of flow section in feet as abscissasagainst flow depths in feet as ordinates. (CORPS H6002, H2040, H2041,H2042,0 or King’s Handbook (item D-h) Tables 7-1 or 7-5.)

d. Conduit discharges in cubic feet per second as abscissas againstthe corresponding critical depths in feet as ordinates. (CORPS H6140,H6141,0 or King’s Handbook (item D-4) Tables 8-4, 8-5, 8-9, or 8-1o.)

e. Conduit discharges in cubic feet per second as abscissasagainst the corresponding normal depths in feet as ordinates. (CORPSH6113 to H6118.0)

If manual computations are used, the conduit chmacteristic curvesshould be plotted to a sufficiently large scale so that areas may beread to the nearest square foot and hydraulic radius to the nearest0.01 ft. Approximate characteristic curves for the 22-ft circular

D-2

.

D-6

conduit are shownwhen open-channel

EM 1110-2-160215 Ott 80

in plate D-1. The discharge curves indicate thatflow occurs in the conduits, normal depth is greater

than critical depth for each discharge, and a practical maximum depthis about 18 ft. Therefore, critical depth discharge control will occwat the outlet (sta 10+70). If the tailwater causes the flow to be atgreater than critical depth at the outlet, there will then be less dis-charge for a given pool elevation. Backwater computations are requiredto determine the water-surface elevation at the intake. Also, they maybe required at selected discharges extending over the full range ofopen-channel flow to determine whether and how much the tailwater in-fluences open-channel discharge in the conduits.

D-7. Discharge Curves. The computed discharge curves (capacity) forthe 22-ft circular conduit are shown in plate D-2. Computations of thevarious parts of the curves for the different flow conditions are ex-plained in the following paragraphs. The transitions from partly fullto’full or pressure flow md vice versa cannot be computed with presenttheory and must be estimated by judgment. The shaded areas on the curverepresent these regions in which head-discharge relations may be un-stable, subject to a rising or falling pool. On a rising pool (withgates fully open) it was assumed that open-channel flow conditionsexisted until the flow depth in the intake was equal to approximately90 percent of the conduit diameter, afier which flow conditions shiftedrapidly to less efficient, full conduit flow at a lower discharge. Ona falling pool it was assumed that pressure flow existed until the poolelevation hopped a few feet below the shift elevation for a rising pool,in this case to the intake crown level. Actual prototype behavior of aconduit with similar geometry would be helpful but such information isgenerally lacking. Model studies may be helpful in some cases whereoperation in the unstable range is necessary.

D-8. Open-Channel Discharge. Flow control will occur at sta 10+70 fordl open-channel discharges (without gate control). In this case, thehead-discharge relation for open-channel flow is determined from thecurve of discharge at critical depth (see para D-6d above and plate D-l),backwater curve computations to sta 2+00, and intake losses upstream ofsta 2+00. Typical computations are s~rized in table D-1 and plottedas curve A in plate D-2. Backwater cwve computations are describedin paragraphs D-n and D-12.

D-9. Pressure Flow. Discharge for a conduit flowing full is deter-mined by equations and computations for conduit losses and dischargesgiven in table D-2 and plotted as curve B in plate D-2.

D-3

m 111o-2-I.6o215 Ott 80 -

Table D-1

Suary of Example Computations for Head-Discharge CurveOpen-Channel Flow, Critical Depth Control at Outlet

(Capacity Flow)

D = 22 ft; S = 0.00115; k = 0.007 ft; L = 870 ft; V = 1.21 x 10-5

ft2/sec at 60°F; Ke = 0.38?-;K = 1.00

See plate D-1 foryn (critical d~pth), y. (normal depth), R (hydraulicradius) and Area b u

See table D-3 for example manual computations of water-surfaceor use CORPS H6208.

For a given Q:

Pool elevation = conduit invert elevation (1229) + y + (Ke +all se~ents at sta 2+00.

profile,

$Kv) ~ ,

Sta 10+70 0.99 yn Sta 2+00

Qcfs

250500

1,0002,0003,0003,900

Yc

ft

2.984.246.048.6510.6912.26

Y.

ft

3.675.217.4911.1014.4518.05

Sta -ft

2+50*l-ttttt

t-t

t+

Y*ft

3.675.117.2610.4112.9615.01

A6.007.459.1411.2912.8914.11

?/2gft -

0.560.861.301.982.583.09

1.38 v2/2gf’t

0.771.191.792.733.564.26

PoolEl

ft msl

1,233.41,235.31,238.01,242.1l,2b5.51,248.3

Conduit flows full at 3940 cfs

* Values obtained with CORPS H6208.0t Coefficient for open-channel flow intake loss upstream from sta 2+00assumed to be 50% larger than pressure flow coefficient of 0.25 fromplate C-32.

tt 0.99% would occur upstream from sta 2+00 if conduit section wasextended upstream.

D-4

‘/

TableD-2

ExampleHead-DischargeComputationsforConduitFlowingMl

PressureFlow(Capacity)

k=

0.00

20ft

(for

capacity)

D=

22ft

A=380ft2

T=

60°F

v=1.21.10-5fi2/se~

L=870ft

D –=

11,000

m.%

kKf=f;

Foragivendischarge:

Poolelevation=Exitportalinvertelevation(1228.0)+yp+H

.,2

whereH=K~ 2g

andK=Ke+Kf+K

v

Qv

@/2

gPool

y/D+f

‘P

cfs

HElevation

m/107

-Am

~a

——

—.

—.

—f+

‘f

Ke*~

Kv

Kft

ftmsl

5,00

013

.15

2.7

0,5

1.00

22.0

2.37

0.01

1810

,000

26.3

10.7

1.()

0.47

0.25

1.00

1.72

4.6

~,25

4.6

0.82

18.0

4.74

0.01

180.

4715

,000

39.5

24.2

1.5

0.72

0.25

1.00

15.8

1.72

7.12

18.h

1,26

4.4

52.6

0.01

180.

470.

2520

,000

1.00

1.72

41.6

43.0

2.0

0.67

14.7

9.48

1,28

5.4

0.01

1825

,000

65.8

67.2

2.5

0.47

0.63

0.25

1.00

13.9

11.9

1.72

74.0

1,31

6.7

0.01

180.

4730

,000

78.9

96.7

3.0

0.25

0.61

1.00

13.4

1.72

14.2

115.

61,

357.

50.

0118

0.47

0.25

1.00

1.72

116.

31,

407.

7

tFroudenumber.

Gs

tt

PressuregradientatexitportalfromplateC-3(extrapolatedfor~

=0.5).

OL

$Dcrcy-Weisbachresistancecoefficientfromplatec-4.

(Incomputingconduitdischargeandflowvelocity

01

ft~

forener~

dissipator,usesmoothpipecurve.)

cog

++

Intakelosscoefficientfordoubleintake(similartoFortRadall

prototype)fromplateC-32.

ON

EM 1110-2-160215 Ott 80

D-10

D-10. Gate-Controlled Discharge. The head-discharge relation forpartial gate openings with free-surface flow downstream (see para 4-16and CORPS H3201°) is modified to include intake losses upstream of thegates. Typical computations are given in table D-3 and plotted ascurve C in plate D-2. If pressure flow occurs downstream from thegates, the head-discharge relation can be computed as in paragraph D-9above with an added loss coefficient for the partly open gates. Thisloss coefficient can be determined from the gate flow contraction coef-ficient (plate c-39), an abrupt ewansion loss coefficient (plate c-8),and a conversion to the appropriate reference section (as noted inpara 2-13(a)). Local pressures just downstream from the gate shouldthen be checked by subtracting the contracted jet velocity head fromthe pressure grade line just upstream from the gate. If the localpressure is subatmospheric, air will be drawn through the vents.(See para 3-17 in main teti.) ~is will reduce the effective headthrough the gate and produce aerated flow in the conduit downstrem fromthe gate, both factors severely complicating calculation of a head-discharge relation in this flow condition. Slug flow also may occur inthis range of unstable flow (see para D-13 below).

D-n . Profile Analysis. The open-channel flow computations generallyinvolve flow profile calculations. A qualitative profile analysis shouldprecede computations in order to predict the general shape of the possi-ble flow profiles that may occur in a conduit system. See paagraph 2-3,plate C-1, and Chow (item D-2, Chapter 9) for more information andprocedures. ~pical

a. M2 upstreamcontrol.

b. m, M2, cl,stilling basin apron

c. H3, M3, C3,

profiles in an outlet works conduit might include:

and S2 downstream from a point of critical depth

or S1 upstream from conduit outlet, depending onslope and tailwater elevation.

or S3 downstream from a partly open gate.

Rapidly varied profiles may occur in the intake and transition, at theoutlet, at any hydraulic jump, at changes in cross section and align-ment, and past obstacles. Except for a few relatively simple boundaryconfigurations, these conditions are very difficult to compute accuratelyand will require experimental evaluation. In this exaple M2 curvesoccur upstrem of the outlet for low flows and M3 curves occur down-stream

D-12.can be

of the gate at partial openings.

Flow Profiles Through Conduits.done with CORPS H6208 and H6209°

D-6

Most of any needed computationsfor straight, uniform-section

—

m 1110-2-160215 Ott 80

Q=

B=p.g.~.

cc =

GO =

H=

Q=

Pool

Ke =

Vp =

Table D-3

Head-DischarEeComputationsfor PartlyOpen GatesOpen-ChannelFlow Downstream

B Cc Go P ~2g(H-E-CcGo)

gate passagewidth = 11 ftnumber of gate passages= 2

gravitationalacceleration= 32.2 ft/sec2gate passageinvertelevation= 1229 ft mslcontractioncoefficient(plateC-39)

gate opening,ft

ener~ gradeline elevationat gate,ft msl

22 CCGO J64.4 (H-1229-CCGO)

V2El=H+K~

e 2g

Intakeloss coefficient= 0.I.6 (plateC-32)(short,streamlinedentranceupstreamfrom gate assumedsimilarto sluiceintake,or abouthalf of full loss for this type of tunnel intake).

averagevelocityin gate passageupstrem from gate= Q/(2xllx22)= Q/484 fps

Gate Contr EGL Disch v Ke </2gPool El

& ftH+Ke v2/2gOpening Coeff El

Go, ft & H, msl

5.50 0.’734 1,250.001,260.001,280.001,300.oo1,320.001,340.oo~,360.oo1,380.00

11.oo 0.752 1,250.001,260.001,280.001,300.001,320.001,340.oo1,360.001,380.00

~6.50 0.T93 1,250.001,260.oo1,280.oo1,300.oo1,320.001,340.oo~,360.oo1,380.00

Qcfs

2,9353, ~ol4,88b5,8356,6497,3748,o348,6b4

5,a56,9699,555

11,57813,29614,81616,19h17,464

6,5039,782

lb,22917,58520,39722,86525,09127,136

6.077.65

10.1012.0613.7415.2416.60.17.86

10.7714.bo19.7423.9227.4730.6133.4636.08

13. kh20.2129.40

36.3342.14h7.2k51.8456. o?

0.090.150.250.360.470.580.680.79

o.2g0.510.971.421.882.332.783.23

0.451.012.153.284.415.546.687.81

1,250.091.260.151;280.25~,300.361,320.491,340.581,360.681,380.79

1,250.291,260.511,280.971,301.421,321.881,342.331,362.781,383.23

1,250.451,261.011,282.15~,303.281,324.411,3115.541,366.681,387.81

D-7

/

D-12

conduits flowing partly full. Although the Manning n coefficient hasbeen etiensively used for free-surface flow, use of the Darcy f orChezy C relates losses to the Reynolds number of the flow as well asto a physical estimate of the equivalent boundary surface rou@ness k .The relations between the coe ficients C , f

E, and n can be expressed

as C/1.k86 = 10.8/fl/2 = R1/ /n , where R is the hydraulic radius ofthe flow boundary. The basic theory is given in Chapter 2 of the maintext. Application of the theory to free-surface flow is covered inparagraphs 7 and 8 of EM lllo-2-1601.h A sample computation using kand C in a nonprismatic channel is given in plate 9 of EM lllo-2-1601.hEquivalent roughness heights k of 0.007 ft for capacity and 0.002 ftfor velocities are recouended for concrete conduits in accordance withthe guidance given in EM 1110-2-1601.h Although it is sometimes assumedthat free-surface flow is hydraulically rough flow in large concreteconduits, the example given in table D-4 for a surface profile upstreamfrom the outlet is applicable to smooth surface and transition zoneflows. An enlarged portion of the open-channel flow resistance coeffi-cients diagram from HDC 631n (similar to Moody diagram in plate c-h) is

given in plate D-3 for computational convenience.

D-13. Slug Flow. Slug flow occurs when the discharge and ener~ levelare almost sufficient to cause the conduit to flow full. It will occurin any conduit that is operated at a given pool level with dischargesthat will produce either full or partly full flow conditions. It ismost often encountered in long, small diameter conduits. In this flowtransition zone, between partly full and full flow, large air bubbles(the slugs) are trapped by the flow and are separatedby sectionsof full flow in the conduit. Although these slugs can move in an up-stream direction in conduits with steep slopes, or low velocities (seeplate D-4 and item D-3), they most commonly move downstream in an outletconduit. Neither the air bubbles nor t~ water sections will cause ayimpact on the conduit proper; but they may impact on appurtenances atthe ends of a conduit. Should the slugs move upstrem they can causeadverse gate vibrations and possible air vent damages, or if the conduitdoes not have gates, trashrack vibration problems. In the more commoncase with the slugs moving downstrem, tineimpact is wave action throughthe energy dissipator and the downstream channel. Because these impactsme usually very adverse, the designer should try to obtain a designsuch that the range of troublesome discharges is sufficientlynarrow topermit it to be quickly passed through without changing the downstremwater levels ad/or velocities too rapidly, or a design such that slugflow conditions will occur only under unusual and infrequent operatingconditions of short duration.

D-14. Slug Flow Limits. The following procedure can be used to

D-8

D-14 m 1110-2-160215 Ott 80---

determine the lower and upper discharge limits for a given pool levelwithin which slug flow can be expected to occur. Reasonably good corre-lation was obtained between the calculated limits and those obtainedfrom the Warm Springs Outlet Works model study (item D-l). The lowerdischarge limit of slug flow for any pool level is approximately equalto the minimum, p=t-gate discharge which will cause the conduit to flowfull. The conduit is determined to flow ftil if a water-surface profilecomputation initiated at the vena contracta immediately downstream of thegate indicates that the depth will increase to about 80 to 85 percentof the conduit height before exiting the downstream portal. Entrainedair is assumed to bulk the flow 15 to 20 percent ad thereby effect fullconduit flow with the above-computed depths of nonaerated water. Theupper discharge limit for a given pool level is approximately equal tothe discharge for which the downstream momentw at the vena contractawith partly full flow is equal to the upstream momentum that would occurat the gates with the sme discharge if the complete conduit were flow-ing full. The sketch in plate D-4 defines these two conditions forcomputation of this discharge. For a given pool level, assume a gateopening Go and compute the free flow discharge Q and the momentmat the vena contracta (condition 1):

where

A=

?=

v=

cross-sectionalarea of flow

distance from hytiaulic grade line (free surface for open-channel condition) to centroid of flow area

average velocity through A

(D-1)

Then, assuming the conduit to flow full at the same Q , compute theelevation of the piezometric grade line (PGL) at the gate (stinting fromthe dowstream portal) and the momentum of the full-conduit flow at thegate (condition 2):

QV2

‘2= A2~2 + ~ (D-2)

Adjust the assumption of Go as necessary to give a value of Q thatwill result in equal values of M and M2 . Then m*e similar computa-tions for other pool leveis in the range of interest. Increasing theconduit slope will raise both limits and will narrow the band of

D-9

m 1110-2-160215 Ott 80

TableD-4. ExampleComputationof Flow Profileat 3000 cfs using k and Chezy C

‘2-Vi * . Trial

V2+V1

2

InvertEl

ft msl

1228.00

W.s.El.

ft mal

1238.69

hv=g EGLEl

ft ft mlStationft

10+70

:

10.69 4.17

3.75

3.61

3.21

3.31

3.46

3.31

3.18

3.14

2.98

2.83

2.70

2.71

2.73

2.66

2.63

2.71

2.68

2.66

2.64

2.62

1242.86

1242.90

1242.93

1243.14

1243.09

1.243.04

1.243.21

1243.39

1.243.40

1.243.62

x43.84

1.244.08

1.244.OT

1244.04

w44.23

abh.25

u44 .18

1.244.32

u44.46

1.244.4T

1244.50

-.

0.053

0.018

0.059

0.044

0.022

0.022

0.021

0.026

0.026

0.027

0.025

0.023

0.018

0.014

0.019

0.005

0.005

0.005

0.008

0.013

10+65 1228.01 1239.15 11.14 193.15 15.53

196.6715.25lo+5r) 1228.02 1239.32 11.30

10+00 1228.08 1239.93

1239.78

1239.58

11.85

11.To

11.50

208.75 14.37

205.46 14.60

201.06 14.92

205.46 14.609+00

8+00

1228.20

1228.31

1239.90 11.70

12bo.21

1240.26

11.90

11.95

209.84 14.3o

210.94 14.22

1228.43

1228.54

1228.66

1240.63 216.4113.867+00

6+00

5+00

12.20

12.47

12.72

12.70

12.65

1241.01 222.31 13.50

1241.38

1241.36

1241.31

227.?5 13.17

227.32 13.20

226.23 13.26

4+00 1228.77 1241.57

1241.62

1241.47

12.80

12.85

12.70

229.49 13.07

230.57 13.&l

227.32 13.20

3+00

2+00

1228.89

1229.00

1241.64 12.75 228.40 13.14

1241.80

1241.83

1241.88

12.80

12.83

12.88

229.49 13.07

230.14 13.04

231.22 12.97

note:Q = 3000 cfsk = 0.007 ft (capacity)s = 0.00115a = 1.000D = 22.00 ftv = 0,0000121ft2/secat 60° F.

* If not ~0.10, reducedistancebetween stations.** If in fully rough flow, C = 32.6 loglo (12.lR/k).

D-10

Check Y from

?EGL CORPS

R .=?sf=— Sf avg L hf

El H6208

ft R/k C** C2R ft mal ft.— —— ——

5.40 771.37 2.92 x lo7 129.54 0.002959 1242.86 10.69

0.002769 5 0.01 K42.875,54 791 2.8b x 107 129.9 0.00258 11.14

0.00252 5 0.01 1.242.88

5.59 798.6 2.82 x 107 130.0 0.00246 11.27

0.00228 50 0.114 12b2.995.76 822.86 2.’74 x 107 130.45 0.00211 0.00233 0.116 1243.00

5.71 816.24 2.76 x 107 130.34 0.00220 0.00239 0.12 1243.oo

5.66 808.57 2.79 x lo7 130.19 0.00232 II. 62

0.00226 100 0.226 1243.235.71 816.24 2.76 x 10T 130.34 0.00220 11.97

0.00214 100 0.21 1243.44

5.77 824.48 2.73 x 107 130.48 0.00208 0.00202 0.20 1243.43

5.79 826.51 2.72 x 107 130.52 0.00205 12.20

0.001985 100 0.198 1243.635.86 836.43 2.68 x 107 130.69 0.00192 12.38

0.oo186 100 0.186 1243.82

5.93 846.75 2.65 x lo7 130.86 0.00179 12.53

0.00174 100 0.174 1243.995.99 855.95 2.61 x 107 131.01 0.00169 0.00174 100 0.174 1243.99

5.99 855.71 2.61 X.107 131.01 0.00169 0.00175 0.175 1.244.00

5.97 853.41 2.62 x 107 130.97 0.00172 12.66

0.00169 100 0.169 124h.176.01 858.81 2.60 x 107 131.06 0.00166 0.00168 0.168 1244.17

6.02 860.59 2.59 x 107 131.09 0.00164 0.00171 0.171 1244.17

5.99 855.22 2.6I. x 107 131.00 0.00170 12.77

0.00169 100 0.169 1244.34

6.00 857.02 2.61x lo7 131.031 0.oo168 12.87

0.00167 100 0.167 U44.516.01 858.8I 2.6o x 107 131.06 0.00166 0.00166 0.166 1244.51

6.o2 859.88 2.60x lo7 131.08 0.00164 0.00165 0.165 1244.50

6.03 861.64 2.58 x lo7 131.11 0.00162 12.96

D-n

m 1110-2-160215 Ott 80

D-14

discharge within which slug flow will OCCW, while reducing the slopewill produce the opposite effect. Changing the conduit size will primar-ily affect the lower limit. Increasing the size will raise the lowerlimit while decreasing the size will lower the lower limit. In mostcases a change in both slope and size will be necessary to maintain dis-charge capacity and effect the desired change in band width or shift ofthe limits of slug flow. As the normal change combinations have oppo-site effects, each case will be unique and generalized guidance cannotbe given.

D-15. References.

D-1. Ables, J. H., Jr., and Pickering, G. A. 1973 (Feb). “OutletWorks, Warm Springs Dam, Dry Creek, Russian River Basin, Sonoma County,California; Hydraulic Model Investigation,” Technical Report H-73-3,U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

D-2. Chow, V. T. 1959. Open-Channel Hydraulics, McGraw-Hill,New York.

D-3. Falvey, H. T. “Air-Water Flow in Hydraulic Structures” (inpreparation), Engineering Monograph 41, U. S. Bureau of Reclamation,Denver, Colo.

D-k. King, H. W. , and Brater, E. F. 1963. Handbook of Hydraulicsfor the Solution of Hydrostatic =d Fluid-Flow Problems~ 5th cd., McGraw-Hill, New York.

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APPENDIX E

COMPUTATION FOR DESIGN OF TRANSITION SECTION(Illustrative Example)

E-1. Introduction. The following example is presented to illustratethe principles of transition design discussed in paragraph 4-22. Thetransition considered is located between a two-gate intake gate sectionand a circular conduit, and the design involves only horizontal con-vergence. However, the procedure discussed is applicable to transitionshaving both horizontal and vertical convergence.

E-2. Desi~ Conditions. The example int*e gate section consists oftwo 9- by 20-ft parallel rectmgular conduits separated by a 6-ft-thickpier. The downstream conduit is 2C ft in diameter resulting in an areareduction of 12.8 percent. Maximum discharge will be 50,000 cfs. Allcurves should be selected to effect gradual changes in the direction offlow. The necessary outer wall convergence is formed by reverse curvesof equal radii. The pier taper is also curved. The minimum thicknessof the tapered pier section has been limited to 2 ft for structuralreasons. Tangent extensions from the end of the pier are assued toenclose a nonflow area, which’is believed to be realistic. The end ofthe pier is blunt to ensure a stable point of separation of the flowfrom the pier. The fillet design conforms to circular quadrants ofvarying radii to accomplish the required geometric change from rectangu-lar to circdar and to provide a gradual mea reduction. The generaltransition layout is shown in plate E-1.

E-3. Design Computations. Transition designs are generally based onsimple curves and tangents which result in relatively easy but laboriousdesign computations. Therefore, detailed computations =e omitted fromthis illustration but the general procedure and equations are includedas a guide.

E-4. Convergence Computations.

a. Area Reduction. The percent area reduction is computed by thefollowing equation:

AA (percent) .loo~fl~)=,oo(, -*)=12.8% (E-,)

E-1

m 1110-2-160215 Ott 80

E-4a

where

‘d= downstream circular conduit area

Au = upstream total gate section area

b. Transition Len@h. The required transition length (LT) isbased on flow conditions and a limiting angle of contraction by themore conservative of the computations:

Lm = (R,,- Ra) /~\—L u u \~gD/

= (15.62- 10)[4

149 )1=32.4 ft32.2 (20.70

(E-2a)

where

Ru-Rd=

V,D=

maximm radial offset from the outside boundary upstreamto the corresponding location in the conduit boundarydownstream

average of the velocities and equivalent area diametersat the upstrea and downstream end of the transition(139and-159

(Ru- Rd)‘T = tan 8 =

fps; 21.41 and

(15.62- 10)0.1228 =

20 ft)

45.8 ft (use 46 ft) (E-2b)

where 13 is the maximum allowable angle of contraction of the boundaryrelative to the conduit axis (use e ~ 70).

c. Wall Curves. The sidewall transition curves are composed ofreverse circular arcs of equalequation:

%RC2 ,‘w==

radii and therefore are defined by the

_ _ (23)2 + ~= 265 fte _—2 2(1) 2

(E-3)

E-2

E-4c EM u1o-2-16o215 Ott 80

where

‘w =

%RC =

wall curve radius

conduit center-line distance PC to PRC or PRC to end oftransition (=~/2)

one-half of convergence of one wall from PC to end oftransition

d. Pier Curves. The pier curves are also composed of circulararcs of equal radii and are based on equation E-3 (with e = 1.5 ft inexample). Additiond computations are required to locate the piercurve PT where the minimum pier thickness is 2 ft. In these computa-tions the curve (rp) is considered to st,=t at the conduit center lineat the end of the transition and efiend upstream to (~T) to the pointwhere the example value of e is 1 ft.

e. ~gent Extension. The slope of the tangent etiension (tan 9n)and its intersection with the conduitarea computations md may be computed

center line are required for the’using the following equations:

.,

tm ep =

%=t;ep=

where

‘P =

%T =

e =

‘T =

‘FT‘P-e

(E-4)

(rP-e) e

%T(E-5)

radius of pier curve

conduit center-line distance from pier ~ to end of transition

0.5 minimum pier thickness

conduit center-line distance from pier FT to the intersectionof the tangent extension and the conduit center line

E-5. Area Curves. The development of a transition area curve requiresarea computations at cross sections normal to the transition center line.These sections me usually selected close together at the beginning andend of the transition to accurately define the curve in the region where

E-3

m 1110-2-160215 oct 80

the slope of the curve is approaching zero. The shapepends upon the horizont~ and vertical convergence ofand the taper of the pier as well as upon the radii of

E-5

of the curve de-the outer wallsthe quadrant

fillets. fien the ho~izontal and vertical convergence me-fixed(plate E-l), an area curve for the converging rectangul~ sections(plate E-2) is helpful in designing the fillets which result in thefinal transition =ea curve. Sever~ trial fillet designs are usuallyrequired in the development of a satisfactory curve.

a. Areas of Converging Rectangul= Sections. The computation ofthe areas of the converging rectangular sections requires determinationof the distances of the walls, pier surface, and tangent extensionfrom the conduit center line at the selected sections. The curve andtangent extension equations previously discussed can be used for thesecomputations. The total flow width at each section is multiplied bythe transition height to obtain the cross-sectional area. With verti-c~ convergence the appropriate height at each section is used. Theresulting areas are plotted as shown in plate E-2.

b. Fillet Quadrant Desi~. The design of the quadrant filletsnecessitates the determination of fillet radii that will adjust theconverging rectan~ar sections to provide a smooth, gradually changingarea curve as well as result in gradual changes in the direction offlow ~ong the fillets. Weliminary computations based on uniformvariation of the fillet radius from zero at the beginning of the transi-tion to the conduit radius at the end of the transition are helpfulin developing fin~ radii for the fillets. A satisfactory area curvewas obtained by use of nonuniformly varying fillet radii defined bycircular arcs near the upstream and downstream ends of the transitionand uniformly vaying radii in the middle section, as shown by thefillet radius plot in plate E-2. Tangent distances of 2 and 5 ft,selected for the upstream and downstream arcs, respectively, resultedin a slope of 0.25641on 1 for the uniformly varying radius curve.The fillet radius (r+) for each section was then computed using thefollowing equation: ‘

Upstream arc

(r2 - ~ 1’2

‘f=ra- a )

Downstrea arc

r<:- [r= ~:- (LN .)2]”2

(E-6)

(E-7)

E-4

E-511

Uniformly varying fillet radii

m 1110-2-160215 Ott 80

‘f= slope (x - tangent length of upstream arc) (E-8)

where

‘f= fillet radius

r = arc radiusa

x= center-line distance from beginning of transition

c. Fillet Area. The full fillet =ea to be subtracted from therectangul= cross-sectional area is computed by the equation

‘f= 0.8584r: (E-9)

where

‘f= fillet area

‘f= fillet radius

The final transition area curve is shown in plate E-2. This curve has azero slope at both ends of the transition. The slight irre@arity inthe curve near the downstream end results from use of the tangent ex-tensions in the area computations rather th= theoretically extendingthe pier curve to the end of the transition.

E-6. Fillet at 1+5-DegPoint. The change in direction of flow along the45-deg points of the fillets should be smooth and gradual. The pathof the flow is three-dimensional and cannot be readily illustrated.However, examination of the locus of the 45-deg point in the horizontal(X) plme and the vertical (Y) plane is helpful in judging the smoothnessand rate of change in direction. Such a plot referenced to the conduitcenter line is shown in plate E-2 and indicates a smooth ad gradualchange in the direction of flow. Computation of the coordinates (X andY) of the 45-deg points (Point C on Section C-C, plate E-2) is accom-plished using the following relations:

c = rf versine 45° (E-10)

x= o.5tw- c (E-n)

E-5

EM 1110-2-1602

15 Ott 80

and

E-6

Y = o.5th- c (E-12)

where

c = horizontal or vertical distance from corner of local rectangu-lar section

‘f= local fillet radius

tw ‘ local transition half width

‘h= local transition half height

E-7. Transition Pressures. General pressure conditions throughout thetransition can be computed by examination of the fiange in velocity headfrom section to section. However, local pressure conditions can only beinvestigated by means of a model study. Model experience indicates thatundesirable pressure conditions may exist immediately downstream fromthe transition unless the transition is c=efully designed. These con-ditions result from the relative outward flare of the bound=y as itchanges from converging to straight.

E-8. Layout Data Information. Plates E-1 to E-3 illustrate transitiondrawings and data pertinent to review of transition designs and to fieldconstruction. Plate E-1 illustrates the general transition layout andfillet intersections with the sides and floor of the transition. Plate&2 shows graphically the variations in the fillet radii, the transitionarea, and the locus of the fillet 45-deg point. Superimposed upstream,middle, and downstream transition sectio- are ~so shown in this plateto illustrate the geometric changes from section to section and toidentify data tabulated in plate E-3.

E-6

\

EM lua-2- 160215 Ott 80

FLOW_ &

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‘/ PRC

L ~ INTERSECTION OF FILLETWITH FLOOR AND ROOF

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-+ INTERSECTIN OF--- FILLETS WITH SIDES

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SECTION A -A cJELEVATION

1 1 I I 1 1 1 I Io

I5 10 Is 20 2s 30 35 40 46

DISTANCE ALONG ~ OF TRANSITION , FT

SEE PLATE E-2 FOR SECTION C-C.

EXAMPLE TRANSITION LAYOUT

P~TE E-1

EM 1110-2-160215 Ott 80

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COORDINATES OF 4S-DEGREE POINT (C)

I t I 1 I I 1 1 I

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ORfGIN OFCOORDINATES SECTION I (DISTANCE = 0’)

I SECTION 11 (DISTANCE= 23’)

SECTION 21 (DISTANCE= 46’)I

I

SECTION C-C[SEE PLATE E-1 )

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F-1EM 1110-2-1602

Change 115 Mar 87

APPENDIX F

COMPUTATION FOR DESIGN OF OUTLET WORKS STILLING BASIN(Illustrative Examples)

F-1. Introduction. The following detailed examples are presented toillustrate the procedures for the design of outlet works stilling basindiscussed in Chapter 5. Two examples with different tailwater and exitchannel elevations are used to illustrate a normal design and a design fora low-level outlet with respect to tailwater were eddy problems within the

* stilling basin are likely to occur. (Note: These calculations may also beperformed using the computer program H2261, Stilling Basin Design for Con-duit Outlet Works, found in the USAE computer program library, CORPS.) *

F-2. Design Conditions. The following information is used for designexample:

Case

Case

F-3.

Conduit diameter D=14ft

Conduit slope s = 0.01 ft/ft (0= 0“ 34.5’ = 0.573”)Design discharge Q = 12,320cfs (for smoothpipe and design pool)Elevation outlet portal invert = 100 ft mel

1:

Exit channel invert elevation = 90 ft mslTailwater rating cume shown in plate F-1

2:

Exit channel invert elevation = 98 ft mslTailwater rating curve shown in plate F-1

Design Computations.

a. Transition Sidewall Flare.

2rDConduit area A = ~ = 3.14(14)2 - 154 ftz “

4

Q- 12,320cfs; Vm

v=80.0

~= ~32.2(14)

= 80.0 fps

= 3.77

F-1

.

E?!1110-2-1602 F-3a

*

From equation 5-2, paragraph 5-2d

b.cular to

c*

AL=21F = 2(3.77) = 7.54 Since AL>6, use AL = 7.54

Radius to Connect Outlet to Sidewall. The shape change from cir-rectangu3.arcross section till be made with free surface flow.

R,= 5D = 5(14) = 70 ft

6Lt = tangent length = R tan ~ = 70 tan

(

~ Arc tan ~

)

= 4.61’●

Length of Fillets.

Lf = ~05D = 1.5(14) = 2] ft

Therefore invert must continue on slope of conduit (0.01 ft/ft) for adistance of 21 ft.

d. Parabolic Invert Drop. Using equation 5-3 paragraph 5-2d(3).

*L

Y- -x tan 8 -

1.25 Vm = 100 fps

therefore

tan 0.573° -32.2x2

Y=-x

~ *or

y = -().OIX- 0.00161x2

e. Case 1 Design.

(1) Stilling Basin Geometry. From plate F-1, the tailwater eleva-tion at design discharge (12,320 cfs) is 100.2 ft msl. Assume various basinapron elevations and compute basin width (Wb), entering flow depth (dl),entering flow velocity (Vl), Froude number of entering flow ( lFl), requireddownstream depth to force jump (d2), 0.85d2 and actual depth from apron

floor to tailwater water surface (d). Assume energy losses bemee~ outletportal and basin apron are negligible, i.e.,

F-2

F-3eLl)

V2 ‘:~+yp ‘Z+dl

- (Outlet el - Apron el)

where = height of pressure grade line at ‘wit portal (plate C-3)‘P

= 0.57D = 0.57(14) = 8.0 ft

and

Also2(x+Lf-Lt)

Wb=D+ = 14 + 2(X+21-4.61) = 14 + X+16.39u 7.54 ~

where X is determined from the parabolic equation after Y is determinedfrom assumed apron elevation. This can be sinxplifiedby making a plot ofx versus y for the parabolic invert drop equation (plate F-2).

Then -y = El outlet - S(Lf) - Apron El

= 100 - 0.21 - ApronEl = 99.79 - Apron El

TableF-1

~ c- tationa for Dete~ing 8aeiaApronE2avatiou(Caae1)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (lo) (11)Apron ktual

Q El Y x ‘b ‘1 ‘1 ‘2 0.85d2 d

Cf s mel ft ft ft ‘1 ft*s__— ft ft—. —— —

12,320 80 -19.79 107.84 46.96 89.55 2.93 9.22 36.76 31.25 20.2012,320 65 -34.79 l&3.98 56.54 95.01 2.29 11.06 34.73 29.52 35.2012,320 70 -29.79 133.00 53.63 93.25 2.46 10.47 35.26 29.97 30.20

O.K.Check jump with lesserdischarges

8,000 70 -29.79 133.00 53.63 71.16 2.10 8.66 24.65 20.95 30.204,000* 70 -29.79133.0053.63 59.82 1.25 9.44 16.04 13.63 26.2

m: See explanatory notes on page F-4.

F-3

EM 1110-2-1602Change 115 \lar97

F-3e(l)

●

●

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

ExplanatoryNotes forTable F-L

Design discharge (* Denotes partially fullconduitflowcondition,

Qfull= 4408 CiS)

Aasmd vtiue

C~ced frm

With c~tad

Y--x

of apron el

-Y = El outlet - S(Lf) - Apron

valus of Y (Step 3) cquce

t.e-~2(1.25V)4cosAe

X2

x

Solve by qudratic formuk, graphicallyor numerically

Width of stilling basin

2(X+Lf-Lc)Ub-D+—

AL

●

*

Flow velocity in stilling baain at section 1

solve for VI “ “eithergraphic82.Ly or nunrisally (cubic●quation).

F20u depth ●t section 1

all-+lb

Froude mmber of flow at section 1

‘1=1-=

(9) SaWat depth in st- baaiu ●t esccion 2

,*->(m-l)

(10) Saquent depth (d2) titipLied by 0.85

(11) Mtue2 depth at section 2

d - ?ailmter ●l - APron ●l

Saaults :

Sti21inS baain aproo ●levation - 70 ft aal

Sti3.2ing baain tith Wb - 53.6 ft

TrUition Langth - Lf + X . 154 ft

St- basin length LB - 3d2 - 3(35.26)- 105.8 Or 106 ft

●

F-4

F-3e(2) m 1110-2-1602Charge !15 Yar s;

(2) Baffle Piers. Since the stilling basin apron elevation wasset at 0.86 d2 for tailwater at the design discharge, two rows of bafflepiers should be used.

Height of baffle piers d = 2.46 ft; say 2.5 ft.(Check l/6d2 = 35.26/6 = }.48 ft ~. 2.5 ft o.k.)

Since velocity entering basin is greater than 60 fps, first row of bafflesshouldbe placed farther than 1.5d2 downstream from toe of parabolic drop.

Since 1.5d2 = 1.5(35.26) = 52.9 ft, place first row of baffles 60 ft down-

stream. This is based on judgment depending on flow velocity enteringbasin. Second row should be approximately 0.5d2 farther do-stream, or0.5d2 = 0.5(35.26) = 17.6 ft . Thus, place seccnd row 18 ft downstream frcm

first row. Make width of baffles and spacing equal to baffle height or2.5 ft.

(3) End Sill. The height of end sill should be half of the baf-fle height or 0.5(2.5) = 1.25 ft , and the upstream face should have aIV-on-lH slope.

(4) Determination If Low-Level Outlet. Check to determine ifconduit outlet portal is low tith respect to tailwater for low flows.Determine section in the transition where parabolic invert slope is IV on6H.

y = 4.01X - 0.00161x2

thusg = -().()1- 0.00322x = - A

6= - 0.1667

or

X = 48.66 ftand

y = -4.3 ft

Thus, invert elevation of section is 100.00 - 0.21 - 4.30 = 95.49 ft msl,and the local width of basin on the sloping apron Ws = 14 + (48.66 +

16.39)/3.77 = 31.25 ft . Computed‘2

elevations for lesser discharges

and the corresponding tailwater elevations are compared in table F-2.

The d2 elevations are well above the tailwater elevations and there

should be no eddy problems ia the stflling basin.

F-5

EM 1110-2-1602 F-3e(4)

Table F-2

TAILwAT22 2L2vAX0N -us d. ~ATxON mn r.ou mows

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10-1) (10-2)

v v, dl= d2~ ‘1cast 1 Caae 2

Qd v TUE1 TUS2* Cfs—&=& ‘1 ft

dzl -la=.——— —Esl *

500* 3.18 19.03 31.25 28.66 0.56 6.76 5.0$ 100.55 91.5 101.31,000*4.53 23.19 31.25 32.51 0.98 5.77 7.56 103.0S 92.51.500* 5.63 25.90 31.25 35.16 1.37 5.30 9.58 105.07

103.293.2 104.2

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

*

(9)

SxPticory Notes for Tshlo F-2

Lov flou di8t~rgc (* -tes partwy fdl flow edition,

Qfull - U08 efs)

No-1 dapth for ms~d disctirga(assumingn - 0.012)

Nom velocity, V - Q/A vhmre A h aru of flow for theCet$d llOml depth

Widthof tran8it:oo●t pointuhsre 2nv@rtslope●WLS 1/6

2(Af-Lt)U,-D+~

vinrex-48.66ft, Lf -21ft, L - b.61 ft tidL - 7.56 ft t.

?20utioti~ ●t tietf.onvlurm slops-s L16

6<+d-$+~-(~t~tel - M@rt ●l at section)

as

Solw for V, ●it2ur ~aph.iu2Ly or oumrit8L2y (tubic 6WC:OU)

Y2w d~th ●t aactiontire slopefargrrslopsWIS 1/6

.+dl, ● ,

~ -r of

v==1-W

s

Saqwat dspthof

●

F-3e(5) ~ 1110-2-1602Change 115 ‘.ar87

(5) Riprap Design. The average velocity over the end sill is

used in HDC 712-1* to determine minimum riprap size (W50 and/or D50).

~=:= 12,32053.6 (30.2 - 1.5)

= 8.0 fps

From HDC 712-in with specific weight of stone of 165 lb/ft3 and V =* 8.0 fps ,

’50 = 45 lb and ’50= 0.80 ft or 9.6 in. ; use D50 = 12 in. +

or greater. The extent of riprap downstream depends on local scour condi-tions and exit channel configuration. Details of the stilling basin andrecommended outlet channel configuration are shown in plates F-3 and F-4,respectively. “

f. Case 2 Desi~.

(1) Stilling Basin Geometry. From plate F-1, the tailwater ele-vation at design discharge (12,320 cfs) is 118.6 ft ml. Assume variousbasin apron elevations and make computations as in paragraph F-3c above andsimilar to table F-1.

Iable F-3cm rations for Decemining Baain Apron Elevation (Case 2)

(1) (2) (3) (~) (5) (6) (7) (8) (9) (10) (11)Apron Attual

Q El Y x ‘b ‘1 ‘1 ‘2 0.85d2 d

cfa Mel ft ft ft A &a AA_ fc—— —— —

12,320 80 -19.79 107.86 b6.96 89.55 2.93 9.22 36.76 31.25 38.6012.320 90 - 9.79 76.96 38.23 85.57 3.77 7.77 39.54 33.61 28.6012.320 86 -L3.79 89.53 42.10 87.21 3.36 8.39 38.17 32.46 32.60

O.K.Cheek j- ultb lesser diachargee

8,000 86 -L3.79 89.53 42. LO 63.05 3.01 6.@ 25.81 21.94 29.50b,DOO* 86 -L3.79 89.53 42.10 50.06 1.90 6.60 16.26 13.82 23.20

● Denotes ~~y fti flOU condition, - 4,608 cfa.●

Qfti

(Ban COle-olm description(axp2anatorYnocsa) as table F-1. )

Thus,

Sttig basin ●pron ●lavatlon - 86 ft mslstu* baati Vldtb Wb - 42.1 ft

TransitionLangth - Lf + X - 1.5D +X - 110.5 ftSti22.lngbash Zangth ~ - 3d2 - 3(38.17)- 114.5 or 115 ft

F-7

~ 1110-2-1602Change 115 Mar 87

F-3f(2)

(2) Baffle Piers.

Height of baffle piers = dl = 3.36 ft, say 3.5 ft.

(Check l/6d2 = 38.17/6 = 6.36 ft A 3.5 ft o.k.)

Since velocity entering basin is greater than 60 fps, first row of bafflesshould be placed farther than 1.5d2 downstream from toe of parabolic drop,i.e.,.

1.5d2 = 1.5(38.17) = 57.3 ft

Therefore, place first row 65 ft downstream from toe of transition. Secondrow should be approximately 0.5d2 farther downstream or

0.5d2 = 0.5(38.17) = 19.1, say 20 ft

Make width and spacing equal to baffle height or 3.5 ft

(3) End Sill. The height of end sill should be half of the baffleheight or 0.5(3.5) = 1.75 ft , and the upstream face should have a .IV-on-lHslope.

(4) Determination If Low-Level Outlet. Check to determine ifoutlet portal is low with respect to tailwater for low flows as for Case 1.The section in the transition where the invert slope was equal to IV on 6Hwas at x = 48.66 ft , y = 4.3 ft., and invert elevation was 95.49 ft msl.(Case 1 - para F-3e(4)). The tailwater rating curve for Case 2 (plate F-1)tidicates that the tailwater elevations for lesser discharges are consider-ably higher than 95.49, therefore, check

‘2elevation versus tailwater

elevations for several low flows as h table F-2. Since the tailwaterelevation is above the elevation of d~

IV on 6E for discharges of approximately* is lfiely to occur with these low flows.

along the center line of the trajectory.inverted V at a distance

‘f0.19D = 100+ 2.66 = 102.66.

elevation) = 16.66 ft and x =

cm

d~tream

at the section vhere the slope is

1100 cfs and less, an eddy problemThus, an inverted V is neededThe center-line elevation of thefrom the outlet portal is 100 +

Thus, y = 102.66 - 86 (stilling basin apron

89.5 ft from y’ = -cmX2

16.66= — - 0.0021

(89.5)2

Thus, the equation of the center-line trajectory will be y’ = -0.0021 X2. ~The trajectory is shown on P3.ateF-5.

F-8

*

F-3f(5) =. 1110-2-1602Change 1“C >!ar87.-

(5) Riprap Design.QAverage velocity over end sill = ~ =

12,32042.1(32.6 - 2.0) = ‘“6 ‘Ps

From HDC 712-in ,W50 = 135 lb, D50 = 1.16 ft or 13.9 in.

Use D50 = 15 in. or larger

Details of stilling basin and outlet channel are shown in plates F-5 andF-6.

F-9

EM 1110-2-1602lG n-+ Qn.2 “b. ““

I 22

120 -

118 -

116‘

114 ‘

doz

112

1-L

110 .z“~~ 108

z

d 106 Tuu: 104

a

2102

Lu1-a 1003

98

96

94 r

92

900 ~ d ~ * ,0 ,2 ,4 ,6 ,8

DISCHARGE, THOUSANDS OF CFS

TAILWATER RATING CURVE

PUTE F-1 .

EM1110-2-160215 oct 80

180

160

140

120

100

x

80

60

40

20

0

-y= -0.OIX-0.00161X2

/

o -10 -20 -30 -40 -50 -60

‘f

PARABOLIC INVERTTRANSITION CURVE

-- ..G. “,

zzum.

t ?

+,9’ES

ElaEfalao91au

EIEEE9QBBQE

4+4+4 ~

m“ w- 04

:h-

—a ,Ff

d

m. 1110-2-160215 n.+ Qf)

.

—

Io

zo>

—

.

+

6

cc0

ii

\

PLATE F-4

ELJ24.2’

v“-

-am

21x2

(TR

AJ

EC

TO

RYA

LO

NG

CE

NT

ER

LIN

E)

V=

-o.o

fx-

o.m

16

1x

2(O

RIG

IMA

LT

RA

JEC

TO

RY

)

3.5

’1.7

5’

ST

ILL

ING

BA

SIN

CA

SE

2

t- w,-

.,-

.

PL

AN

%>

EL

80,3

1E

L98

.0

EL

86.0

’L

hi’’

’’’’’’

”’:

-R

IPR

APA

ND

EXIT

CH

AN

NiL

CA

SE

2

EM 1110-2-1602 Hydraulic Design of Reservoir Outlet Works

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