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HYD-30·4

LOW-VELOCITY AIR TESTING APPLIED

TO HYDRAULIC PROBLEMS

BY

JAMES W. BALL

PAPER PRESENTED AT ASCE

ANNUAL �.EETING, CHICAGO, ILLINOIS

OCTOBER 13, 1950

LOW-VELOCITY AIR TESTING APPLIED TO HYDRAULIC PROBLEMS

by James w. Ball, Hydraulic Engineer

Bureau of Reclamation Denver, Colorado

INTRODUCTION

The title of my paper is "Low-Velocity Air Testing Applied to Hydraulic Problems." It \Ifill be preeent.ed from the viewpoint of the hydraulic engineer since my professional experience has been almost exclusively in thi� field of engineering.

Scope of Paper

The discuasion will concern the use of low-velocity air in testing closed hydraulic systems, or testing in which air can be sub­stituted for water without introducing any appreciable error due to compressibility. It will deal with the advantages, disadvantages, errors to be expected, and the cautions to be observed when the hydraulic engineer employs this method of testing.

Definition of Low-Velocity Air Testing

For the purpose of this paper, low air velocities will be considered those which for all practical purposes yield the same results as hydraulic tests. These velocities usually range up to about 250 feet per second or about 25 percent of sonic speed, depending upon the nature of the particular problem.

History of Air Testing

Air testing, or aerodynamic testing as it is commonly termed, in itself is not new, but the technique of using low-velocity air as a fluid in obtaining solutions to hydraulic problems is of fairly recent development. We find references to aerodynamic testing in the early part of the twentieth century, but these usually deal either directly with aircraft research or pertain to fluid mechanics research and not to testing of the type under discussion at this time. In this early research work the experimental data from tests using different fluids, including air and water, were combined to illustrate a fundamental law or principle rather than to prove that air could be substituted for water in determining the flow characteristics of hydraulic systems. It has been only within recent years that low-velocity air testing has been used in solving problems of this nature. Among the first to make use or this methOOt and a pioneer in this field, was Dr. C. Keller of the Swiss firm, Escher Wyss Company. Some of Dre Keller's work was

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published as early as 1937. In 1939 he was co-author of an article on air testing of turbines published i:1. the Escher :,:yss News and entitled, 11A Method for -DeternrL'1ir.g the Cavit"'ti,)n Factor by Air Tests." In the same year this engineering periodic.· 1 p..:b} 1sllr:id another article nNew Method of Aerodynamic Researr:h," �-.-hi"h cit.t,d some of Dr. Keller's work and discussed low-velocity air testing of hydraulic and steam-operated machines. Everything set forth in this article is just as applicable today when we find leading engine8rtng organizations, universities, and private industries using air testing as a low-cost useful tool to solve some of the Lr hydrau1 ic problems.

InrLn:r...c.nta, te.::t t;quip...ic.n�, anc.! meaE ..i.r�_ng techuiques are b�:ton, 1 the scope of this p.s.per but they offer no problem in low-velocity Rir testing because they have beer. highly developed through the exten­sive aerodynamic work pertaining to air�raft design. On the other hand, much wcrk still can be done towards defining the limits whrre aerodynamic testing car, be �ubstituted for hydraulic testing. Some of the limits already P-str,tli�hed v:ilJ. b� dis(!usscd later.

Increasing Use c·,nd Advantages of Low-Velocity Air Te3ting

There are numerous reasons why low-velocity air testing is gn1n1ng popularity with hydraulic engineers. The following advantages contribute mainly to this popularity:

a. Because of the low density of air the structural requirements of the test facilities are a minimum

b. For the same reason power requirements to circulate the test fluid are comparatively low

c. Absolute fluid tightness is not essential but more ..easily attained. Wetting problem nonexistent which permits use of a wide variety of materials

d. Atmosphere serves both as a supply reservoir and a catch basin

e. Test procedure usually greatly simplified., but requires certain types of more highly developed and sensitive instruments

f. Reynold's numbers can be made about the same for either air or water in a given model. Use of a larger model to test at a higher Reynold's number might be advantageous in some cases

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g. The relationships for non-compressible fluids can be applied with negligible error if the air velocities are ·kept below certain values (less than 1/4 sonic speed)

I am sure that you will agree without further explanation that all except the last item are advantages which reslllt directly when air is used instead of water for studying the flow characteristics of closed hydraulic systelll8. However, without proof you r:J.ght quo st ion whether or not the simple ·relationships for an incompressible fl�id are applicable when air is used in place of water. I will endeavor to supply this proof without going into extensive mathematical details.

Indicated Disadvantages

Before continuing with the discussion, however, it would seem appropriate to mention some o.fthe disadvantage5 of using air aa a test medium and to emphasize that the discussion today applies principally to systems of short length where friction is not a major consideration. Air has a comparatively low bulk modulus, it does not become discontin­uous as in the case of liquid& when the vapor pressures of the liquids are reached, and since it ie a gas there is no free surface. From these properties it would seem that air could not be used to replace a liquid where effects of compressibility, cavitation, and gravity are predomin­ating factors. Thie is not always the cas<- but one must be sufficiently familiar with the dynamics of gaseous flow .: ri order to recognize when such studies are applicable. The following discussion concerning the use of the equations for incompressible flow will indicate the l.iJnita where compressibility is of little or no consequence. A logical and valid conclueion without the aid of mathematics, would be that the velocity of sound for the test medium should not be exceeded in any event, since beyond this point it is not valid to assume the condition of adiabatic changes. A more elaborate theoretical treatment of the problem is required in such cases.

A pertinent question at this point would be, how near eonic velocity can the speed of the air be without introducing errors of appreciable magnitude?

Application a.nd Limitations of Formulas for Incompressible Flow

It can be shown that large errors are introduced by using velocities near sonic when the simpler hydraulic relationships are applied. This being the case, it would appear that the first proolem of a hydraulic engineer wishing to use air instead of water for testing a hydraulic system would be to determine the niaximum air velocity for his particular study.

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In most problems, if the test velocities are kept low and there are no large changes in pressure or velocity, it will not be necessary to make an evaluation of the compressibility effects. However, if there is some question as to whether or not the compressibility effects should be of concern this evaluation can be made as will now be outlined. The prob­lem may or ma.y not be easy depending upon how difficult it is to establish approximate expressions for the flow conditions as regaros the relation­ships for pressures and velocities for both incompressible and compressible flow. The maximum permissible velocity for the problem can be determined by setting up the expressions for incompressible and compressible flow for the pressures at two carefully selected points, computing the pressure change from one point to the other for both types of flow, and plotting these against the respective velocities at the reference point.

If the velocity of the air is kept within the range where the pressure difference between the two selected points is essentially the same for both types of flow, then the simpler hydraulic relationships Ce-J'l be used in analyzing the test data from a hydraulic system using air instead of water as the test medium.

The velocity of the air which ��11 give results within a given percent of accuracy in a given system can be found by considering the foll�wing two general equations for incompressible and compressible flow which are derived from the Bernoulli relationship between the two points.

and

h1 =1--1-ho 2gho

. h1 =� _ K - 1 ho L 2

(incompressible flow)

� K v2_v 2 K-r

_(_ 1

2 ° (compressible flow) co ....l

where h is pressure head, Vis velocity, g is acceleration of gravity, K is the gas constant, C is the acoustic velocity, and the subscripts o and 1 refer to the reference station and selected station, respectively. Fo� the type of testing now being considered all velocities are much less than sonic and all p�essures will be near atmosphere. Therefore, the term K _ 1 (V12 _ V0 ) will be less than unity and the right side

2 Co2

of the equation can be expanded into a convergent series by means of the bionomical theorem and may be written

h1 K .. 1 - -ho 2C�

4

K - 2 24

also v1

can be expressed in terms of V0 as, v1 • l3 V0, Where 13 is the ratio of flow areas Ao. Then

K V 2 1 - .,C 2 o

4, 0

or

since hok

C 2 0

,. _

g

also for incompressible flow

h1, - ho .,. - l... V 2 2g o

(A2 _ l) _ (K - 2) r 24

v4

J Co 4 Cf2 - 1/ .. 0

yi - 1)

Examination of these equations shows that the relative magnitude of the compressibility effects will be reflected only in the s�cond and subsequent terms within the brackets and that it depends on three factors: (1) the velocity of the air in the test system, (2) the sonic velocity at the pressure in the test system, and (3) the shape of the flow passage.

A quick estimate of the probable error introduced by using air instead of water may be made for a particular test set-up by substituting approximate values o! V0, C0, and,.e in the second term within the bracket. For example, let V0 = 250 ft/sec, C0 = 1000 ft/sec , and13 � 2. This

error would be 1 ((_ 250))

2 (4 - 1) or .1..64

n 0. 047 or 4.7%. The effect of 4 "�000

the third and subsequent terms is insignificant. Examination shows that error would be reduced to about 1% if V0 was limited to 50 ft/sec. How­ever , pressure intensity and pressure differentials might be more difficult to measure and more precise instruments required.

Examples to Determine Limiting Velocity

One of the least complicated examples for determining the permissible test velocity is that for steady flow past a solid body held stationary in a uniform stream such as a Pitot tube which might be used

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in making a test. In this case the points selected are in the undisturbed flow upstream from the body and on the leading edge of the body where stag­nation pressure exists. Expressions for this case are,

and

V 2 hs - ho a -2.... (incompressible flow) wherep = 0

2g

V 2 a ...2,_

2g V 2

+ ..:..Q.._ 4C 2

0

_ (K - 2)

24 :0: .J

0

(compressible flow at subsonic velocity)

The subscripts o and s refer to the station in the undisturbed flow and at the stagnation point, respectively. Assuming various values for V

0 (less than sonic), computing values of h

8 - h

0 and plotting the

(h5 - h0 ) vs V0 terms for both cases, the follo�Qng graph is obtained, (Figure 1). An examination of the graph discloses that the values for both conditions are essentially the same for velocities up to about 250 feet per second. For this type of study then, one would conclude that comparable results could be obtained with air providing the value of V0 was kept below about 250 feet per second and that reliable results could be expected from a .2itot tube for this velocity range. However, if other points in such a system are selected, it is possible that the value of V0 would have to be less in order to hQld the error to an equivalent minimum. Compressibility effects in .:1.uence the results from many test instruments. Flow through an orifice is another example. The accuracy of the formula for incompressible flow through an intake orifice will vary depending upon the pressures under which it operates and the refer­ence pressure used in ma.king the computation. The four lines on the graph of Figure 2 show the percent error in quantity for four possible conditions. The error is a minimum when the base pressure is that in the pipe downstream and results are compared with those obtained by the equation for compress­ible flow using the specific volume for the downstream pressure. �Jith the low velocities employed in the air tests now being discussect_ the pressure differentials are small and the ratio of downstream pressure to upstream pressure so near unity that the error is small in any case. I might add that the mean pressure could be used and would result in even less error in the case whe�e the quantity is based on the specific volume at the downstream pressure. It may be concluded from this illustration that the equation for incompressible flow for an intake orifice may be used without introducing much error if the pressure differential across the orifice is kept small, not more tha.n 1 foot of water.

Examples for stream tubes in general�and for flow in a venturi meter may be found in "Fluid Mechanics" by Dodge a.nd Thomp�on. The evaluation of the compressibility effects on the accuracy of data taken

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from the test structure and on any instruments which are to be used in ma.king the tests might be only the initial phase of a study in which air is substituted for water. In most cases the need for this initial work can be eliminated by keeping the test velocities as low as possible and still provide accurately measureable quantities. With a little experience the hydraulic engineer is able to recognize whether or not the initial investigation of the compressibility effects is necessary.

There are other factors not apparent in the equations which might influence the accuracy of the results or make them qualitative only. Specific examples 1dll be cited later to illustrate some of these factors which have been dincovered mainly through experience.

Hydraulic Problems Studied by Low-Velocity Air Tests

Air has been used successfully in hydraulic problems of the following nature:

a. Design of water passages and runners and impellers of hydraulic turbines and pumps

b. The study of operating characteristics of hydraulic turbines and pumps including the efficiency and cavitation factor

c. The study and determination of losses in and the capacities of water distribution systems

d. The determination of the losses in and the capacity of comparatively large water tunnels

e. The study of the mechanics of turbulent flow and its application to liquids (turbulence loss, development, and decay below screens)

f. The study of the hydraulic characteristics of large outlet valves

g. The study of the hydraulic characteristics of complex passages such as those of hydraulic operating systems of large valves

h. The study of the pressure distribution and losses for various shapes of penstock inlets

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i. The capacities and hydraulic characteristics of certain types of fluid meters (nozzles, orifices, etc.)

j. The study of the diffusion of air jets and its application to such structures as sub­merged sluice gates

Testing Pertaining to Turbine and Pump Design

The air testing in connection with turbine design seems to have been done mainly by German and Swiss engineers in the late thirties. A great deal of their work was published in the Swiss technical paper "Escher Wyss News," which contained the following comparison between aerodynamic and hydraulic tests. (Figure 3). The meth9(i seems not to have been adopted by manufacturers in the United States for we find these companies still using water for testing their models. The same ie true of United States pump manufacturers.

Testing Pertaining to lArge Water Tunnels

An unusual instance where air has been used instead of water to determine the flow characteristics of a system of water tunnels before they were placed in operation and checked by hydraulic tests afterward was discussed in papers given by two French engineers, G. Remenieras and P. Bourgingnon at the 1949 meeting of the International Association for Hydraulic Structures Research in Grenoble, France. The work consisted of passing air through the tunnels taking measurements of pressure changes, ascertaining the loss coefficients and computing the tunnel capacities. The agreement was very good when the results were checked after the Bystem was placed in operation. The air tests in this case actually proved the adequacy of parts of the system before construction of the entire system was completed as 'wOuld have been necessary for water tests. Such tests permit an on-the-spot check of such a system before the contractor has moved from the site and any deficiency could be c orrected at a minimum cost.

Testing Pertaining to Turbulence

Currently, work is being done at the University of Iowa laboratory to study fundamental laws dealing -with turbulence. Air is used instead of water because suitable instruments have been developed for measuring turbu­lence in air and instruments for measuring turbulence in water are still in the experimental stage. The diffusion of an air jet and its application to submerged sluice gates is another of the University's projects.

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Testing Pertaining to Hydraulic Out let Structures

The air testing of hydraulic equipment with �hich I am most familiar is, of course, that done in the Bureau of Reclamation Hydraulic Laboratory at the Denver Federal Center. This type of testing was first employed in the laboratory to study the flow characteristics of a diffuser cone. Later it was used to investigate the hydraulic properties of exist­ing and proposed designs of outlet valves to study the deficiencies and advantages 9f the physical arrangement and dimensions of the water passages

as regards capacity and possible occurrence of cavitation.

In one case there was a question as to the time required for the closing and opening cycle of an outlet needle valve when operated hydraulically. The speed of the 0:rcle was governed mainly by the c:apacity of the flm·: passages of thR operating mechanism. A very simple reprP-sentation of this mechanism was constructed of wood and sheet metal and tested with air. The results proved very satisfactory and were obtained with less work and in only a fraction of the time required for hydraulic tests.

Latest tests in the laboratory have included the study of the pressure distribution in the rectangular �ntrance to an outlet conduit having a radial gate for regulation, and t�e detennination of loss coefficients for a complicated systM of branching penstocka. Comparison of the results of these a.lr studies with water studies have not been made available to date.

Miscellaneous Items Affecting Low-Velocity Air Tests

Some very interesting facts pertinent to air-testing were brought to light during the studies just discussed.

In the initial air tests on diffusers, an unexpected discrepancy was noted in the results when compared with those of water tests, (Figure 4). The air tests indicated considerable more loss in the diffusers than did water. In an attempt to introduce an additional loss ahead of the diffuser to study its effect upon the action of the diffuser, a wire mesh wastebasket was held over the inlet to the test apparatus shown as Case I in Figure 4. A decrease in loss was indicated immediately. It was concluded that turbu­lence was almost none:x..istent without the basket placed in the incoming air strea.m because of the arrangement which used the entire volume of the laboratory as a supply reservoir a.nd thus flow conditions were not correctly represented. The apparatus was rearranged as shm�n for Case II and the tests repeated.

With the air supply passing through the screen before flowing through the diffuse:rs of the new arrangement there was a marked change

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in the re sults and good Agreemen t was found between the aerodynamic and hydraulic tests . This situati on of havi ng a virtually turbulence-free fluid at the beginning of the model , .which fi rst oo curred inadvertently in the air test, rarely, i f ever , i s en countere d in a hyd raulic problem . It is the reverse of the c ase in aerodynamic wo rks where th e tu rbulence­free co nditi ons of th e atmosphere c a.n be st be only approximated i n wind twmels . The plot of Figure 4 illustrate s the error which mig1 t be intro­duc ed by imprope r turbulenc e .

Several items of intere st were di sco vered in the ai r t e sts made in the Bureau laboratory pertaining to the d e si gn of outlet valve s. The te sts concerned, the Ensign Balance d valve , ne edle valves, and the more recent d evel opne nt, th e hollow-jet valve . In the c ase of th e b alanced valve , exten sive ai r t e sts were made on the existi ng design and proposed alterations to el iminate cavitation (Fig.i re 5) . The tests were completed before a hydraulic model coul d be put in operation and were use d as an e,q:,edient to obtain design info rmation wh ile the hydraulic mod el was being constructed . The ai r t e sts -were late r checked by water te sti ng of a sc ale mo del a nd in general foun:i to be in excellent agreement . When materials could not be obtai ned for making the indi c ated alterations becau se of war re stricti ons, the t e sts were use d as a guide in operating the valve s at openings which would pennit a. mini.mum o f cavi tali on . The ope ration at the se openings prove d highly successful in te duci ng the cavitati on damage. I could gi ve a di. scussion on the co ns truction of air model s , but thi s would b e a paper in itself . However, it might b e ne nti one d here that the u se of mcxi eling clay in this type of air t esting migit b e l ikened to the use of an eraser in drafti ng.

From the result s of the t e sts o n the b al anced val ve, it may be shown that very reliable qu antitati ve data will be obtai ne d from hydraulic systems in which the re is ll ttle chance for vapor pressure s to occur 'When air is used as a t est fluid. On the o ther hand, when vapor presen re i s likely to o c cur i n the hydraulic sys tem the data are not s o r eliable quanti tatively but are extrenely useful qualitativel y. Figures 6., 7, and 8 illustrate this . A comparison of p ressure r actors for computing pressure i nt en si. ties at given point s fo r v arious operating co ndi tione show excellent agreement in the oase of the streamlined dem. gn and si zeable discrepancies in the design where cavitation was a problem . The more gen­eral oondi ti on o f now l eading to d iscrepancies of th i s nature i s that where separation i s present .

Another intere sti ng fa.ct note d duri ng the s ame stu cy 'tm en t-wo small valve s were calibrated usi ng bo th air an d water., was th e importance of selecting the co rrect points for meaat ring pressure s or pressure drops whic h would represent the actual hydraulic conditions . In the c ase of

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t he hollow-jet valve shown on Figure 9 , it was necessary to install an additional piezometer in order to measure the effective head on the valve, mainly because the use of air actually represented a submerged condition which was not t he case in the hydraulic tests . Without this piezometer the results would have been misleading and would pot have compared with those from the water tests .

In another instance it was found necessary to remove ;,,hat off­hand appeared to be an essential part of the test valve in order to make it represent the hydraulic conditions which would be present in the field structure.

Conclusion

No doubt there are other factors involved in t he proper repre­sentation of boundary conditions which influence the application and accuracy of air test results that have not been discussed in this paper. Those presented here are either readily apparent from an examination of the physical relationships involved or those encountered by the author in his work or in contacts - with other engineers who have conducted low­velocity air tests for solving problems of a hydraulic nature. It would be interesting to hear from others who have had experience with or have knowledge of hydraulic problems being solved by low-velocity air testing.

In closing I would like to leave t his thought. Although low­velocity air testing of hydraulic systems is a very useful, expeditious, and economical method of solving many hydraulic problems , it is doubtful if it will ever be used extensively or result in accomplishments of a sensational nature. It is used mainly as a substitute for hydraulic tests and serves as an expedient for urgent or preliminary studies. The final proof of the design of a hydraulic system will, therefore, in most cases etill be its successful operation under hydraulic conditions.

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I 8 0 l---+-+----1---+------i1----+--+--J......;,..,��

iij I 6 0 1---+-+---+--+------ir--+--++------..e-+--+--='

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I- I O O r---+--+---+--+-------1--+---+r---a, ; � 80

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lAJ

m 2 o 1---�f--+----.-+--+---+-,,-;--

f o��e--+--"F-+-+-�-.+-

>------

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I

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--

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I I I I I

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--::-// /

- -3

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/ i II I

II I If

;'ti if,,' · t -

�,' i I I , -

- 1 - -- --t- --f--

· -Atmospheric pr�ssure - - 8 ,9 i _ _...:.-r--

t,Absolute pressure at E l . 5500 -28 ft. of water

- -r-- . , r - 1 1 1 r 1 1 ---&o0 2 0 40 60 80 100 0 20 40 60 80

\/ALVE OPENING IN PERCENT VALVE OPENING IN PERCENT

1 : 6 AERODYNAM IC MODEL 1 : s t HYDRAUL I C M O DE L

EX I ST I NG OU T LET DES IG N

SHOSHONE D A M 58 - IN C H BAL A N C E D VALVE

PR E S S URE S I N VA LVES AND CONDU I TS

100

"Tl G')

C: :lJ l'TI

....,

220

200

1 80

G:i' 1 60

0 1 40

e:.1 20 a: LL.I � 1 00 3: � 80

� 60

- 40 w

� 20 (f) w a:: Q. 0

-20

-40

-60

18', .!

.,/ .. v- ------20 - .. / .... _,. ,-

v,, , .,,..,..,,

� / ,:,,, / ,· ,

,\ , /,, , , / ' - 22 �;.''1 ,,,

h / / ,,� I \ /�..- :,.,:;,, \ \ ;� �1/1 -- --'i \ _,, ... -- / - .... ... - "' ' -7 �'j,1 , -,, \ , _,

--r, -1/ / ; / , .. a 1/r- _ __.... I ----

\ I I

\ I I

\ .- - '20

\ I

'• \ '.., ..,_

';_, / '_/

, -�/ ./

J '

.. - - .. ,7) / ,'

.. . ..

.

/2 � --

A __ .. �-I , ,/

,,�"9

e- - , 0 � . - -"- ....

V,,' _,, ... -� ,,_,, -(.:..f 1,,- -'

i� ,,

·C,1� /' / � .. ---- .., /

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I 'I I / /,1

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,

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I I I ,,, I _,.--I

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, / ' / // I I _ .. -" I

6' / v" - -Atmospher ic pressure _,, f .. � �,, Atmospheric pressure f , ,:

/ ,/ I

:'�Abso lute pressure at E l . 5500-28 ft of water t-Absolute pres sure at E l . 5500-28 ft. of water

0 l

20 40 60 80 1 00 0 20 40 60 80 VALVE OPENING IN PE RCENT VA LVE OPENING IN PERCENT

1 : s AERODYN AM IC MODEL 1 : e f HYDRA U L I C M O D E L

REV I S ED OUTLET DE S IGN

SHO SHONE DAM 58 - I N C H B A L A N C E D VA LVE

PRES S U R E S IN VALV ES A N D COND U I TS

1 00

1 .0 w _J 0 W 0. 9 la.J

a: 0 .8

: 0 7 LL

a::: 0 0 .6

u tt o.�

w 0::: 0.4 :::::) (/)

I 1 · --+--- -

.

r f-I I

/.,,_ Y �-

T I

i /

-f -· ;;,· � .' _/i z-/ f /1

-- -

f'J : �.....-

l ' i,____ .,_ __ � -

- -- -

--

--- � -i ... ---..... � r--o '-- j _ -+---

-- -c ! -· - - y

[ _ +-

I

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-,_

- - --I

i -�- - t

- - -....... _

--

�

Fu/Iv ooen -- � I _ J( � ' �

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I -- -

u

- -->- -- -- -- - -- -

X ,- 50 % oDen - -'-

i -- -

" , .......

>- -- --

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i

: -----0• -� -

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l j r

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2 I ---�/ ' (/) 0 . 3 w

0 . 2.

v�:_ --+- - ___._ __ -----4

: I I '

....... - � O

)<- ---1 - - - - - --

, ...... ....... - -- - --

+-·7 --- --

II 0 K = / : Bl Hydraul/c_ model

J : 6 Aerodvnamic mode · r-..... ""'. , 10 % o en -� · - -�Ii-+- - - -----------,--

' .. io

La.J _J

0. 1

s 0 . 9

: � =

I l

i

LJ �-------=-"'-

' l l l I ' I',, .

r�� -I � • ' . I

r - l t :

i I i I ' I

5 1 0 1 5 2 0 2 5 D ISTA NC E FROM i O F VA LV E " R " I N I N CH E S PROTO T Y P E

A. P R O PO S E D RE D E S I G N

! .

' " ;

V 7

--

- -

-

·-

3 0

z 0 .8 1----,----3!k:-__..--+_,....:..,,k----1--+---+--+--------+----lf--t--+--+--;---+---+---+-i--� a:: 0 _LL. 0. 7 t--,,__ __ _._-+ _ __..---1, ____ t--:::,,0.--.::::-----"f-'"'*'--

' I.L _ ___,___ -�- -+ -

a::: o .e t--:-----::::t:===,!;:---t--�---t--+-----::>��---:-;-��r.:-:-::-:-::-t-----i--H

� o.� h-�--------+::_...-"""9��1----.:?!o,.c----+------1----...j:.::�- o�o -oiw.::+---�

W 0. 4 ..... -.....,._::-'I' ==--+--=· ..... d--���+�---+-4-'"---t---+------4� a::: (/) 0. 3 11-,fl-----+-�----..::!lo,,,t---.......!1..--��----,.::�-....s.�+.-�,.,;-��..;-,;..,;;...,..,-.......a-==........_-1---1 (/) w 8: 0 . 2 1-----.......:_-4-2__._�___,_-�1-�_.__,�--+-......;::��.....3ii,r--f--+-----+-:::,-:::---d----"-----�

0 = I : 8 3 Hydrau lie mode x = / : 6 A erod namic model O. I 1----�__:::.._:,...:..;:,:....::...;.:...J....:...:...:..c.�.;...:::......,..:..:...:,..::..;;..;,.:..:.--4--__._�.._....-..31,...��

. I

0 .0 1--------- � P L U N G E R , - - X" , _ ' R

. '¼.. VA_LY E ·,:

_ , 1

- 0 . 1 �--_;_ _ __._ __ ___._.__.1.-____ _._ _ __._ _ __.�.L-...__�---'-----�'---' 0 5 I O I 5 2 0 2 5 3 0

D I S TA NC E F R O M £ OF VAL V E " R " I N I N C H E S P ROTO T Y P E B. E X I S T I N G I N STALLAT I O N

S H O S H O N E D A M CO M PA R ISO N O F PR E SS U R E FAC TO R S

PRO PO S E D R E D ES IGN A N D EX I ST I N G O U T L ET A I R V E R S US W AT E R

F I G U R E 6

'

-< !

' I'

<

cj

ci C) 0 "'

[1qht ribs

Travel • I. 200·

A. NEEDLE VALV£ 3.200" DIA. INLET · 2.574" DIA. SHA/:IP·EDGED EXIT

;:i 0 r-j

l. 665 "

Travel • ,.ooa·

8. HOLL O W - JE T VALVE 3.023" DIA. INLET • 4.662" DIA EXIT

A

cj

c:i ;..,. "' ..,:

10'. n: w "' � :::, z "' 0 ..l 0 z >-w a:

.5 X fO' r-----,

3.0 X 10' 1-------j

2.5 , 10•

, '\ . .

2 0 X 10'

. "

1.5 X IQ!,

0

d', ..

I.O x 105

o s , 10' �---� 41 .43 45

COE F F IC IENT OF DISC HARGE C 1N O • CA�

LEGEND • A I R 0 • WAT E R

.) 5 x 1 0 • ,-----,

3.0 X 10' t---�-i

IO: 2.5 X 10' f--<>----i

a: w

IO

2 :::,

z 2.0 , 10' f-----1 "' 0

..l 0 z

>-w a: I 5 , 105 1-------l

,0 .

1.0 x 10 5 i---0 ·----1

0.5 , 10• �---� 64 .66 68

COEFFICIENT OF D I SCHARGE C IN Q • CA�

ht • static + velocity head

DISCHA R GE C OEFFICIENTS FOR SMALL VALVES

USING AIR AND WATER AS FLUIDS

F I G U R E 9