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ALASKA POWER AU~ECEI1Y aESfONSE TG lGENCY CC~MENTS CN LICENSE APPLlCATIC~; EEEERENCE TO CO~MENT(S): I.lOS

A WATER RESOURCES TECHNICAl. PUBLICATION

ENGINEERING MONOGRAPH NO. _ 41

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AIR-WATER FLOW IN liYDRAULIC STRUCTURES

TK 1425 .58 F471 no.2905-1 05

UNITED STATES DEPARTMENT OF THE INTERIOR WATER AND POWER RESOURCES SERVICE

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As the Nation's principal conservation agency. the Department of the

Interior has the responsibility for most of our nationaUy owned public

lands and natural resources. protecting our fish and wildlife, preserving the

environmental and cultural values of our national parks and historical

places. and providing for the enjoyment of life through outdoor recreation.

The Department assesses our energy and mineral interests of all our

people. The Department also has a major responsibility for American

Indian reservation communities and for people who live in Island

Territories under U.S. administration.

ENGINEERING MONOGRAPHS are published in limited editions for the

technical staff of the Water and Power Resources Service and interested

technical circles in Government and private agencies. Their purpose is to

record developments, innovations, and progress in the engineering and scien­

tific techniques and practices which are used in the planning, design, con­

struction, and operation of water and power structures and equipment.

}O~irs( Printing: 19HU

mJS1I1ETRIC

ARLIs. AlaskaR

LIbrary & Jut; eso~cesonnationSe

An"hQr"8~,A.1askl:t IV1ces

U.S. GOVERNMENT PRINTING OFFICE

DENVER. COLORADO

For 5al(' by the SIl~rint('nd(,111 or Documents. u.s. Govemment Printing Office.

Wa~hinglon. D.C. 2U402.. or till" Willer and J10wer Resources Service. Attention 922.

P.O. Box 2;}()1I'i. Denver. Colorado 80225.

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Preface

The material assembled in this report is the result of studies extending overmany years by a large number of engineers. Ellis Picket at the U.S. ArmyEngineer Waterways Experiment Station in Vicksburg, Mississippi, supplieda reference list dealing with air-water problems. Personnel of the Water andPower Resources Service E&R Center. Water Conveyance Branch madetheir files and drawing on air design criteria in pipelines available for publica- :tion in this report. Prior to publication, the report was reviewed by EllisPickett and Ted Albrecht with the U.S. Army Engineers; and by engineers inthe Dams, Mechanical, and Water Conveyance Branches, E&R Center,Water and Power Resources Service. The many constructive comments bythese individuals and the assistance of Richard- Walters who provided con­tinuity and technical editing is greatly appreciated.

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ARLIS. Alaska Resources

LIbrary & Infonnation ServIcesAnchorage, Alaska

Symbol Quantity Symbol .Quantity

A Cross sectional area of water prism d Flow depth

A. Cross sectional area of airflow db Bnlked flow depth

passage de· Deflector height

Ac Cross sectional area of air core in a dn Nappe thickness

vertical shaft do ()ri£ice diameter

=Ad Cross sectional area of conduit d, Total depth of underlying and air

Ao. ()rifice area free zones

Ap Cross sectional area of penstock d.s Bubble diameter for which 95

Av Cross sectional area of vent percent of the air, by volume, is

a Ratio of bubble terminal velocity in contained in bubbles of this Iturbulent flow to terminal velocity diameter or smaller .

in still water E Relative width of the frequency .-ao Mean air distribution function spectrum

~a, Mean air distribution constant exp Napierian logarithm equal to

B Width of rectangular chute 2.71828, approximately

b ·Width of flow channel f Darcy-Weisbach friction factor

bn Nappe width G Gate opening

~b, Empirical coefficient accounting for Gg Mass velocity of gas

sand grain roughness G, Mass velocity of liquid

C Air concentration g Gravitational constant (acceleration)

~C. Actual air concentration H Hydranlic radius of prototype air

Cb Drag coefficient on a bubble vent

Cd Discharge coefficient based on 100 HI Fall height of a water jet

IIpercent gate opening Hm Head across orifice

CI· Local loss coefficient Hn Net head across turbine

CI Air concentration at d,/2 Ho Distance from channel invert to

Cm Air concentration measured by a .energy grade line

pitot tube sampler H, Total potential and kinetic energy

Co C>rifice discharge coefficient h Mean wave height

C, Drag coefficient on a sphere h. Height of airflow passage

C, Air concentration at the bottom of hi Distance from inlet to the water .-the mixing zone level in the vertical shaft

C Mean air concentration hi Head loss per unit length

c Waterhammer wave celerity hm Head across manometer

D Conduit diameter hw Allowable head rise in penstock

Db Smaller dimension of a rectangular Ke Entrance loss

conduit K, Singnlar (form) loss

Dd Diameter of water drop k Von Karman universal constant

De Equivalent bubble diameter equaLtoO.4

D, Larger dimension of a rectangular kr .Coefficient of roughness

conduit,:;. k .Sand·grain roughness,

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Letter Symbols and Quantities

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- LEITER SYMBOLS and QUANTITIES-Continued

I Symbol Quantity Symbol' Quantity

IL Length of conduit or vent r, Relative roughness of conduitLc Distance to start of self-aeration (rugosity to diameter ratio)Lr Prototype to model scale ratio S Submergence depth

IL, Distance between stiffener rings So Pipe slopeM Unit mass Sf Slope of energy grade line

c M o Maximum difference in elevation S Root-mean-square value of wave

Ibetween a wave crest and the height distributionmean water level Sw Root-mean-square value of 'water

;- m Air concentration distribution surface distribution

Icoefficient T Top width of flow passage

N Safety factor t Pipe wall thickness

r .n Manning's roughness coefficient U Free stream velocity: no Velocity distribution power-law Ud Velocity of water drop relative to

I coefficient air velocityP Energy dissipated Uj Water jet velOcity

f' Pg Normal distribution' function u Local air velocity

I Ph Probability that the wave height is V Mean flow velocity ,equal to given height Vf Terminal velocity of bubbles

f Pw Probability that the water surface . in turbulent flow

I is equal to or greater than the Pi Nappe velocity at impactgiven elevation Vm Minimum velocity required to

• P Pressure intensity entrain airP. Allowable internal pressure V. Maximum water surface velocity

Patm Atmospheric pressure V. Terminal velocity of bubbles in

• Pc Collapse pressure slug flowPin Internal pressure V, Terminal velocity of bubbles inPo Nappe perimeter still waterQ Discharge W Wetted perimeter

I Q. Volume flowrate of air x Distance from start of boundaryQc Critical discharge layer growth

r Qr Discharge from reservoir Y Distance normal to channel bottom

If Qw Volume flowrate of water (flow depth)q Unit discharge Y•. Distance from water surface

q. Insufflation rate of air per unit Yc Conjugate depth

I surface area Y. Effective depthR Bubble radius Yk Critical depth

Rb Equivalent bubble radius Y' Normal distance to the bottom of

I i Rc Radius of curvature of the, bubble the mixing zoneI, cap z ElevationRj Thickness of annular jet

I r Water jet radius

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LEITER SYMBOLS and QUANTITIES-Continued

Symbol Quantity Symbol Quantity

a alpha Angle chute invert makes E Elltvlls number - YD'

with horizontal 0

f3 beta Ratio of volumetric airflowE" Euler number /ill-

rate to waterflow rate-

l'J'"Y gamma Specific force of waterd delta Boundary layer thickness F Froude number - I'

£ epsilon Mass transfer coefficient I~I >1'"of bubbles P Prandtl velocity

~ zeta Air concentration ratio - Fdistribution constant 11,'/(>1"2

YJ eta Normalized wave heightI,,," Idp/dxl

fi theta Void fraction P" Poiseuille number -lC kappa Gas constant ~J1V

}. lambda ' Density ratioR Reynolds number 1'1)

Dynamic viscosity-

J1 mu v

II'J1. 'Dynamic viscosity of air

J1w Dynamic viscosity of water Rx Distance ReynoldsVx

,v nu Kinematic viscosity .. number - ,

VI Water viscosityv

~11 pi 'Ratio of the circumferenceW Weber number II

of any circle to its-

(o/,!/),'",

radius, 3.14159...

e rho Density

e. Air densityew Water densityeg Gas density

el Liquid densityem Density of manometer fluid

~a sigma Interfacial surface tensionTo tau Wall sbear stressTj Shear stress at water jet

U.tm upsilon Specific volume of air atatmospheric pressure I

u. ' Shear velocity1jJ psi Muiticomponent flow

parameterco omega Volume of gas bubbleco. Volume of airCOw Volume of water

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00 Infinity

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viI3'57788

101214161619191921222428

3637374141424444485152545457575757575759

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PagePreface ; . . . . • . . . . . . . . . . . . . . vLetter Symbols and Quantities .•...... '.' .......•...... ~ .Introduction ...•......•..•..•................................Purpose and Applications .Summary and Conclusions .•.........•... , ..•.........•...•...Open Channel Flow ......•.•...•.........•.••.•..........•.. '..

Introduction •.........•...•.....•.••..•...•.............•.Bubble Dynamics '.

Terminal Velocity of a Single Bubble in Still Water .Bubble Size in Shear Flows ..... : .....•..............•..Terminal Velocity of Bubbles in Turbulent Flow ......•....

Vertical and Longitudinal Flow Structure .....•....•...........Design Parameters ....•..•.. '. . . . . .. . . . .. . .. . . . . . . . . . .. . ... .

Location of Beginning of Aeration ..••...•.........•....••Location of Fully Aerated Flow •••.••..••.•......•...• '••.Air Concentration Profiles ..••••.•••.•...••.........•••.

Definition of concentration •..•••.••..•.........••••.Air distribution in the mixing ZOD .

Air distribution in the underlying zone •....••...•••...Mean air concentration .••••••....... '.' ..••....•....

Water Surface Location ..Effect of Air Entrainment Flow on Stilling Basin

Performance ......••..••••..•.......................Closed ConduifFlow '.' •.• '...••.......••.............

Classification of Flow ......• : .Flow in Partially Filled Conduits ....••.......•.•..•..........

Model Predictions ......•.•.................•.......•••Air vent not designed ..Air vent designed ..

Analytic Estimates .Flow Having a Hydraulic Jump That Fills the Conduit .......••.Flows From Control Devices , .

Flows From Valves ••••••.•.•.••••...•••.....•••••.•••.Flows From Gates ••.•....•...•.•.•..•.........•••.••••

Falling Water Surface ...••.••...•....•..••..... ; ..•...••...Air Vent Design Criteria for Closed Conduits ........•• : ..••••.

Purpose .Location .....•••.••....•••••••••••....•...•••..•••.••Maximum Airflow Rate .Structural Considerations •.••.•..•.•...•....••...•..••.•Physiological Effects .Safety of Personnel .•••.••......•••.••....•...•...•..•.

..\.Aontents

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CONTENTS-Continued

FIGURES-ContinuedNumlJer Page

36 Pipeline configurations ...........•.........•.........•.. 6137 Plan and profile of a gravity pipeline ....................... 6238 Vent structure .......................................... 6339 Typical irrigation system air valve installation ........•...... 6440 Vent location at changes in pipe slope ...................... 6541 Air binding in a pipeline .................................. 6642 Large-orifice air valve ...........•...•....•....••........ 6743 Performance curves for large-orifice air release valves ........• 6844 Typical small-orifice air release valve .••.•...."..........•... 6945 Performance curves for small-orifice air release valves ......•.. 7146 Typical frost protection installation ...•.•......•..•..•..... 7247 C;ollapsing pressure of a steel pipe with stiffener rings ........• 7348 Performance curves for large-orifice vacuum relief valves ....•. 7449 Specific volume and barometric pressure of air as a

function of elevation ......•...•.....••...........••.. 7550 Required air relief orifice diameter to prevent collapse

of steel pipelines .................................... 7651 Observed air blowbackin morning glory spillway at

~Owyhee Dam, Oregon ............................... n

52 Typical types of vertical shaft inlet structures .........••..... 7853 Vertical shaft spillway discharge characteristics ...••.••...... 78

~54 Breakup of a water jet from a hollow-jet valve ............... 8455 Water drop breakup ......•..........••.........".•....... 8556 Velocity distribution for flow over a flat plate, Bormann [11) ... 86

IAPPENDIX

~I-I Electronics schematic ...........................•....•... 961-2 Probe schematic . : ....•........••...•...•....••....••..• 961-3 Controls in utility box .................................... 96

III-I Definition sketch at penstock intake •..•.••...••.....•.••.. 114IIF2 Typical turbine characteristics of runner specific speed 230 •.•. 116III-3 Turbine loss coefficient ........•....•.• ~ ....••..•..•..... 117III-4 Air volume in penstock ........•.....••••••....••....••..• 118III-5 Water surface area ....................................... 118

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Introduction

In many engineering projects a strong inter­action developes between the water flowingthrough a structure and the air which is adja­cent to the moving water. Sometimes the inter­action produces beneficial effects. However,more often than not, the effects are notbeneficial and the remedial action required toreduce the effects can be costly.

Cases in which air-water interaction developinclude:

• Open channels with fast flowing water thatrequire depths adequate to contain theair which is entrained within the water

• Morning-glory spillways that must have acapacity to convey the design flood andits entrained air

• Vertical shafts that entrain large quan­tities of air at small water discharges

• Measuring weirs that need adequate ven­tilation to prevent false readings and toeliminate surging

• Outlet gates that require adequate aerationto prevent the development of low pres­sures-which can lead to cavitationdamage

• Emergency gates at penstock entrancesthat require ventilation to prevent ex­cessive negative internal pressures duringdraining or emergency gate closures

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• Sag pipes (inverted siphonsI' that can bedamaged due to blowback of entrainedair

• Long pipelines that require air release andvacuum relief valves

From these cases it is noted that air-waterflows can be generalized into three basic flowtypes:

1. Air-water flows in open channels,2. Air-water flows in closed conduits, and3. Free-fall water flows.The first type usually is called air·entraining

. flow because air is entrained into the watermass. The second basic flow type generally isreferred to as air-demand. The term air­'demand is both misleading and technically in­correct, since an air vent does not demand airany more than an open valve demands water.However, since the term has been in commonuse for over 20 years, efforts to improve thenomenclature seem rather futile. The third typeis referred also to as air-entraining flow.

'''siphon, inverted-A pipe line crossing over a depressionor under a highway, railroad; canal, elc. The term is com­mon but inappropriate, as no siphonic action is involved.The suggested term, sag pipe. is very expressive and ap­propriate. to Nomenclature for Hydraulics, Comm.on Hyd, Str.. Hyd. Div•• ASCE. 1962,

Purpose and Application

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• Effects of turbulence and air concentrationon bubble dynamics

• Fluid dynamics in the developing aerationregime of free-surface flow

• Effects of hydraulic and conduit properties I' /on probabilistic description of water sur- /face in free-surface, high-velocity flow

• Effect of pressure gradients on air flow inpartially-filled, closed conduits

• Bubble motion in closed-conduit flows forconduit slopes exceediIig 45-degrees

• Effects of ambient pressure levels oncavitation characteristics of gates andvalves discharging into a closed conduit

• Interaction between the air and a free jet

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The purpose of this report is to summarize thework that has been done on air-entrainmentand air-demand regarding the most recenttheories and to suggest ways in which theresults can be applied to design. The intent wasto produce a concise reference of material fromwhich design manuals, nomographs, and chartsfor specific applications could be prepared. .

Although many generalizations of the datacan be made, some types of flow conditions'thatare encountered in practice can be treated onlyby individual studies with physical models.These cases are identified when they occur.

Additional studies are needed in many areas.Some of the most critical areas requiring fur­ther research include the following:

Summary and Conclusions

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Methods have been developed to predict themean air concentration and the concentrationdistribution with open channel flow. A newdescription of the free water surface in highvelocity-f[ow'isproposeawhich-moreaccuiiitelL_representS actual conditions in high veio~ityflow. The effect of air entrainment on the per­formance of a stilling basin can be estimatedusing a bulked flow concept. A computer pro­gram (app. II) is presented with which themean air concentration' in steep chutes andspillways can be estimated.

With exception of a falling-water surface anddecreasing flow in pipelines, closed conduitflows require model studies. When properlyconducted and analyzed, model studies willyield accurate data for estimating air-flow

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rates. Experimental methods are discussed. Acomputer program (app. III) is presentedwhich cim be used to predict the airflow ratewith a falling-water surface. Design charts arepresented for sizing air relief valves andvacuum valves on pipelines.

The airflow rate in vertical shafts was foundto be extremely dependent upon the flow condi­tions at the shaft inlet. Equations are includedfor estimating the airflow rate having variousinlet conditions.

Factors influencing the airflow rate aroundfree falling jets are discussed. This area is iden­tified as one needing additional research. Equa­tions are presented from which the air entrain­ing characteristics of a jet entering a pool can beestimated.