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UNITED STATES DEPJ .. RTMENT OF THE INTERIOR

BUREJ. U OF RECLAJ\::f, 'l'I ON

HYDRJ.,ULIC Lf�BORJ. TORY REPORT NO. 100

ON THE VIBRATION OF VIEIRE'

BY

PROFESSOR R. SEIFERT, VDI

Translation by

H. G� Dewey, Jr.

Denver, Colorado October 13, 1941

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UtUrED STATES

IEPAR'01ENT OF THE TI'1TERIOR

BUREAU OF RECLAMATION

ON 'mE VIBRATION OF WEms

A Translation of

UBER SOHWJliJGtJNGEN VON WEBRllN

BY ffiOFESSJR R. SEIFERT, VDI

'

Fram Zeits. des Vereines Deutscher Ingenieure•

VoJ.. 84, No. 7, February 17, 1940, PP• 105-110 - - -

Translated by

H. G. DEWEY, JR. , ASSIST.ANT ENGntEER

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Under Direction or A. RUE'ITGERS, SENIOR ENGINEER

Q.nd

:r. E. WARNOCK, HYDRAULIC ENGIDEER

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Dem.er, Colorado

October 13, 1941.

ACKN01.'ITEDCMEHT S

This translation was prepared in the hydraulic structures

laboratory of the Bureau of Reclamation, United States Depart­

ment of the Interior, Denver, Colorado, under the direction of

J. E. Warnock, Engineer. All testing laboratories are under

the supervision of A. Ruettgers, Senior Engineer. The engineer­

ing work of the Bure.au of Reclamation is under J. L. Savage,

Chief Designing Engineer, ands. o. Harper, Chief Engineer. All

activities of the Btn"eau are tmder the direction of J. c. Page,

Commissioner.

Special aclmowledgment is due to I. K. Silvennan, Assistant

Engineer, for reviewing this translation, and to J. w. Ball,

Associate Engineer, an� R. R. Pomeroy, Junior Engineer, for

their assistance in editing the text.

UNrrED STATES IlEPAR'lMB:NT OF 'ffiE Th1TERIOR

BURE.AU OF RECLAMATION

Branch of Deeign and Construction Engineering and Geolog1caJ. COntrol

and Research Division Denver, Colorado October 13, 1941

Subject: On the Vibration of Weirs.

lNTRODUCTION

Laboratory Report No. 100 Hydraulic Laboratory Compiled bys H. o. Dewey, Jr. Reviewed by: J. E. Warnock

There are two types of we1r1 vibrations: one type occurs when rais­

ing an underflow gate, the vibration resulting :f'rom the compressed jet;

and the second type occurs with an OV'erflow gate, the vibration result ­

ing f rom the jet flowing over the gate and spilling into the atmosphere.

By means ot model studies, it has been possible to clarify the forces

acting in both of these cases. Thus measures for the elimination or

prevention of vibrations ware discovered in a model and were tried on

the prototype.

As long as the regulating devices at movable weirs, sluices, and

conduits were moderately large in width and water pressure, the flC7R­

ing watel' caused no dangerous vibrations. They occurred at first, how­

ever, as the dimensions and water pressures were considerably ihcreased.

Vibrations then appeared so strong that, disregarding the disturbance

to people living in the vicinity, the stability of the regulating gates,

of the power plants, and or the f'oundatiOn was endangered. In several

oases, failure of structural members had already occurred due to fatigue

l.rranslator's notes The German word "wehr" nay be translated aa "weir"

or "dam" as applied to hydrau lic structures. The former probably

applies to smaller structures and 1s used, therefore, 1n this transla­

tion.

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or overatrain. The groping attempts to remove the vibrations by sup..

plementary structural pa.rte, without taking pains to lm.derstand the mechanical. process of v1br�tion excitation, were sometimes successful; however, these attempts he.d other drawbacks and 1 as a result, showed in any case• from the very first, no m:ithod for designing structures free from vibrations. Extensive research on the causes or v1eir vibra­

tion are not practical on a prototype structure because the essential

conditions, such as the discharge, reservoir end tailwater elevations, total drop, and shape or weirs, cannot be changed arbitrarily and in­

dividually. Pure theoretical considerations also lead no further far there are vibrations even at rigid weirs, for example at the H.ameler weir. Thus there remains only the model study to clarify the action

of the 1'orces and, in this way, to el 1.minate or to prevent the vibra.­tion of weirs.

In the following discussion, only existing structures are considel."­

ed. The transference of the knowledge gained to sluice gates, conduit

sluices, and valves is possible without further ado. CAUSES OF WEm VIBRATION

Weirs may start vibrating when either the regulating gates are

raised a small amount permitting the jet to flow under the gate under

the pressure of the headwater, or they n:ey start vibrating when ovel.'­flow gates are lowered, permitting the jet to spill ffer the lip of the gate into the atmosphere. On 1930, vb.en the Waterway Administra-

tion at Hanover planned the new construction of the Doztverden sluice-way dam, demolished because of sand erosion, they turned, being warned by the failure of large dame of other administrations, to the Prussian

Research Institute of Hydraulics, Soils Mechanics and Shipbuild ing in

Berlin, with the purpose of conducting fundamental research on the pre­

vention of weir vibration.

The Research Institute undertook, first of all, obser\'8.tiona and

measurements on a large number of existing weirs, some of which vibrated

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with underflow gates, in order to become familiar vd th the forms of vibra­

tion and the manifold conditions for which vibrations occur in a proto­

tYl)e. The measurements were made partly with existing apparatus ( Geiger­

Collins vibration instrupent of the Cambridge Instrument Canpany, Pabst

Indicator, Askania-Werke moving picture camera, very sensitive aneroid

barometers, and others); partly with new apparatus (Waas recorder, E�ller

tuning fork) which had to be developed to measure, under the quite diffi­

cult local conditions, the frequency and amplitude of the structures; and

partly with instruments which had to be developed to determine rapidly "

variations in air pressure (Muller-Jahnke pressure recorder in combination

vdth a Siemen's oscillograph, and others). Similarly, it was necessary

to make corresponding self-recording apparatus for the model experiments.

VIBRATIONS PRODUCED BY l'NDERFLOVi

The first experiments on the model dealt with the vibrations produc­

ed by the underflow of raised flood gates. Observations on prototypes

had shown that vibrations occur especially for small gate openings, thus

exactly in the region of gate positions most frequently used in regulating

the discb.a�ge. The opinion proved to be incorrect that the vibrations

originated from pulsations of the headwater or from the waves of the tail­

water which struck against the structural members of the weir projecting

into the tailwater. On the contrary, the flow around the sealing beam

located at the lower edge of the gate was recognized as the cause C1f

vibration· whenever the beam had unfavorable shape.

For the clarification of the mechanics of vibration, a model caP­

able of vibrating was constructed. A two-dimensional section of a seal­

ing beam of a weir was constructed and suspended by springs to enable

the beam to vibrate vertical ly { the possibility of torsional oscillation

was foreseen, but was not exploited in the first series of tests)• This

model was placed in a glass channel 6.30 inches wide, with a tailwater

depth of 5.91 feet, and with a discharge of 7 second-feet under a head 0$

45.93 feet. The shape of the sealing beam, the ��te opening, and the

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modulus of the spring could easily be varied;. like,dse, the head, the position of the weir underneath, and the discharge could easily be changed. The vibrations were recorded me-ehanics.lly aoeording to

number and displacement,. The sealing beam rested on a s1,11 lying

flush in the approach floor, eoITesponding to the usual pretotype arrangement . The floor was connected by an apron on a l to 2 slope

directly to a stilling basin deepened to 20 inahes. The model then

corresponded to the Dorverden weir to a scale ratio of 1 tQ 3,8, In general, there were two tailwater conditions investigated, which were maintained by a series of superimposed stops in the outlet or the channel; later on sills of various shapes projecting above the approach floor, various sloping aprons and stillillg pools with modified slopes, a.pd various starting points for the slopes were also investigated, changes, which proved to be of considerable value.

At first the sealing beam in the vibration model was rigidly fix-

ed and the average pressure heads were measured far changing heads, tailwater, and gate openings. The appropriate discharge was also measur­ed in each ease. In the ease of rectangular � similar sealing beams

intense negative pressures occurred at certain points whieh caused, as a eonsequanee, a separation ot the jet (figure l); nevertheless. it was possible to obtain b

y

suitable curvature of the upstream edge ot the sealing beam• a constant and gradual decrease of the headwater pressure t& that of the te.ilwater pl"essure, with the jet throughout a wide range of gate openings cohtinually adhering to the sealing beam (figure 2). Under thi§ condition it is expected that no vibrations will occur.

The investigation on the v1bra.t1ng suspended sealing beam of the model oonf irmed this hypothesis. The rectangular beam which has pro­duced vibration on the prototype weir also yibrated 1n the model, It was observed directly how eddies in Bh�t. uniform time interval.a form­

ed 1n the region of the negative preesure1 and how they drifted away

after reaching a definite size, and1 for a moment, yielded to the nor­mal stream (figure 3) • This pressure change at the see.ling beam

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produced elastio deformation in the weir which, 1n turn, contributed

to the separating process of the flow and thus maintained the -rtbra�

tion. In this oase the nattn'al vibration of the steel struoture also

played a 1)$.rt (figure 4).

The vibrating seal beam s howed a larger discharge than the non­

vibrating beam, the former acting as a pump. The discharge eoe:f'ti­

oient of the square besro increased approximately 19 peroent when vi�

brating; the coef ficient depending on the spring tension, the def l�o­

tion, and the average gate opening.

A broader series of tests were conducted on a l to 10 scale,

6-f oot wide, complete model of a Havel weir which can be flowed under

f rom two directions. The results of.the partial model were confirmed.

After the action of the forces had been clarif ied, then exist�

ing vibrating dams could be made free f rom vibration by easy rebuild•

ing, 11nd new dams could be designed f ree f rom vibrations f rom t he start

for all important heights of 11ft. To do this, suf ficiently large cur­

vature is required at the inlet �ide or the sealing beam (figures 5 and

6) or, in the case of removing existing vibrations, individual addition­

al members are required a.t the exit side 1n order to divide the jet inte

several parts (f igure 7}. The edd ies in �his case break away in differ­

ent intervals of time, so that the parts of the eddies mutually disturb

each other at the beginning of' any vibration. In the case of weirs in

which the f'low sometimes occurs in one direction, sometime in the op,­

posi te direction, f reedom from vibration may be obtained by alternate

curvature of sealing beams on the upper <:Jr lower side. Such cases OC•

cur in inlet and outlet sluices in tidal regions. VIBRATIONS PRODUCED BY OVER!LOW

Considerable dif f iculty occurred in the clarifieation of vibra­

tions occurring with free fall jets at overflow slu1ee gates, drum

gates, and the like. Measurements with the apparatus previo«sly re­

ferred to were used, f irst of all, on a large ntn:nber of vibrating pro­totype weirs. Small-scale model experiments were then conducted on

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a port ion or a gate , which gave many ine i�ts into the phenomena in­

vol wd, but no c omplete knowle dge .

The first supposition was that the vibration of the flap ( Klappe )

was produced by fluctuat ing regions of negative pre ssure s in the jet,

moving 1n uniform intervals of time on the back of the flap causing

return f low and water rollers which disappeared and formed anew ( fig­

ure 9 ) . Vibrations would , therefore , so it was believed, be prevent ed

if the flap bad, as a result of it s shape , no such regions or negative

pressures above it .

This initial supposition proved t o be false . At a prototype struc-

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ture such flaps vibrated considere.bly without any regions of negat1ve preaeurea

being indicated. In any case varying pressure distribution on the tl ap

did not produce vibration , but at the moat promoted it. Model and pro­

totype studie s showed that the he lp of air under t he jet was esse ntial

for the occurrence of f lap vibration. A constant negative pressure with

re spe ct to the surrounding · atmoaphere wa s also detectable in . addition

to air -pres sure vibration and pulsating air flow alon g the axle of the

weir , similar to an organ-pipe vibre.tion. The ventilation of the jet

i'ran pier recesses appeared to be of importance , while breaking-in at

air in certain chronologi cal sequence stopped the flap from vibrating.

If this condition 1n the a:tr pressure is c ons idered as the cause of

the flap vibrating, then it would be a matter or breaking up the jet

in order to remove the negat ive press\ll'e and also the air-pressure

changes . The jet d ivider suggested f or this purpose by the Research "

Institute for t he 78-foot 9-inch weir openings of the Dorverden weir

gave good results ; 1n the case of the 1:38-foot weir openings the j et

divider also gave good result s , but not under all conditions , since tor

sone f lap positions , thickne sse s of J et , t ailwate r elevation s, and wind

condit ion vibrations st ill occ'lll'red . The working together or all these

variables , which can not be brought into action 1n the prototype as de•

sired , remained unclear.

Far that re ason the Research Institute bad to take up its problem

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1 n new mo de l studies when the Wat erway Admi nistration ot Bliinover re­

qu ested tha t their dam far the storage regulation of the Weser River

between Bremen an d Minde n b e absolute ly free from vibration. Suppor1i-

'. a d by its existin g knowle dge of flap vibration , the R esearch Ins titute

con ducted syst ema tic t ests o n a 20-foot wide mo del whi ch represented

t he flap shaJJ8 of the Dorverden weir to a scale ratio of l to 10 . Thus

the mo del correspon ded to a wi dt h of weir of 200 f eet ; howe ver , smaller

segments or the mo de l coul d b e s eparated for investigatio n. The height

of drop could be incre ase d by lowering the tailwa ter as much as 32 feet

an d the flap could b e rotate d to any desi red position . In general: , an

average, a low, and a. hi� fla p pos 1 t ion wa.e used. The flap was sup­

ported by rigi d, but changeab le, cylindrical springs which had different

t ensions. These i nvesti gation� brought fu ll clar1 t1o ation o f the :forces

o ccurring far an overflowing jet , e nd thereby o ffere d t he possibi lity-

of obtaining, by means 9t certain constructio nal arrangements, t he re­

quire d dam f lap abso lut ely tre e f rom vibratio n.

The resu lts of these studies have bee n revi ewe d by many repre­

s entatives of Governnxmt boards, research insti tutes, stee l constructio n

firms, etc. Al l were :fully convi nced. According to t he lmowle dge ob­

tained, t he flap vibration was reve aled as b eing a n automat ic coupled

vibrat ion i n which three common pa rts are invol ved: t he flap with its

water load, the tre e jet , an d a n air cushio n unde r the flap.

By means of the vibratin g f lap, the f ree j et beecmee rippled w1 th

waves which are0

parallel to the rim or t he flap (f igures 8 and 9).

These waves move an d accelerate downward and become larger a nd more

rapi d with in creasing drop h ( figm.-e 9). The ra nge of proj ectio n of the

jet changes co ntinual ly.

Posit ive and negat ive air-pressure impu lse s oeour alternate ly whe n

the jet waves meet the tai lwat er, and by means of t he air cus hion the

i mpulses are return ed to t he flap . In this way the vibratio ns are kept

going, but only if they li e in t he vicinity of the natural vibratio n o f

the flap with t he wa ter load and if' t hey occur on t he flap i n oo rrect

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phase . I:f we interrupt this coupled vibration by a horizontal. dia•

phragm 1n the a ir cushion, then no vibrations of the f lap occur and

no waves form in the free falling jet .

The vibrating flap transfers a certain e nergr to t he j et by

means of the lateral accelerat ion of the water. This energy produces

the pressure Change in th e e.ir cushion and thereby control s the pro-

cess of vibration. MOreover, the energy los s due to t he ext ernal re­

s istance ( friction, resonance , etc . ) must be replaced , so the energy

returned to the flap by the a ir cushion must be increased by this a­

mount . This increase is drawn from the energy increase of the falling

water. The air impacts also react on the tree movable jet itself; the

thinner the jet , the more it acts ( figure 10 ) . The size of t he air

cushion is also important , for the sma.J.ler 1 t is the harder are the air

impacts , and t he more defined is the c oupling of the vibration. The

movements of the nap increase or decrease--acoording to the phase in

which t hey coincide with t he impacts of the rippled j et--directly with

the variation of t he air pressUTe un der the flap. This pressure 1s only

slight in a prototype struct ure b ecause of the mnall defle ction of the

flap. In the model , however, the a ir-pressure variation is cons iderable,

wit h its proportionately larger deflection . Thus the fl ap movements

again affe ct t he fre e j et because t hey produce compressions in t he air

cushion. Consequently, numerous processes are involved. Ext ensive

t e sts on existing weirs are , t herefore , b ut slightly suitable tor an

investigation of the nature of weir vibrat ion , whereas the inf'luen.oe

of each variable is more readily determined in the model.

The drop from the headwat er t Q the tailwater has decisive im­

portance in the occurrence of vibration ( figure 11) . For each flap

positi on and• here again, for e ach jet t hickn e ss ( that is , for each

discharge ) there are, in general , several drop ranges 1n which vibra­

t ions are possible corresponding to the number a,r waves of the ripple«

jet . Ir we pass through a range of vibration by means of e. change in

drop, t he n the deflection and rat e of vibrat ion of the flap change

. s

approximately according to a resonance curve. The largest vib ration ·"

deflections occur in the case of the aj;ta.inment of the natural · fre-

quency of the gat e with its water load,

Th e natura l frequency decreases wit h increa sing hea d of overflow,

so t hat th e vibrat ing zone moves towe.rd t he side of gr eatest dro p. The

relat ion b etwe en drop and f requency within each zone of vibrat ion is

fixed by t he relation fVH= a constant . In thi s relat ion, " f " denot es

t he frequency and "H" t he drop; the refore, a def i n ite f requency b elon gs

to ea ch d rop. If th e :f requency of the f lap for a change 1n drop varies

too far f rom the natural f requency t he vibration ceases. The manifold

occur rence of regions of vib ration for a given dis cha rge is exp lained

b y t he fact that th e t ree jet poss ess es several waves on it s course ot

fal l f rom t he headwater to the tailwat er. If the lower jet waves o.re

cut of f comp let ely by the raising at' t he tai lwat er (f igures 8 and 9 ) , even t hen coupling condit ions are pr es ent , and a new vibration zone GO-

curs in wh ich the number of m0dui�t ing wa ves is reduced by one . The

zones of vibrat ion may be cl assified into a genera l va lid phase lnw.

If "m" is t he number of jet wave s an d if "k" is a cons tant , t hen

i' VH • m•k (f igure 12) •

The weir flap can produce two basic vibre.tions : those due to de­

f lection and t hose due to torsion. The coupli ng process is the same for bot h forms of vib rat ion, only t he natura l frequency and th e v1bra•

t ion zone , a re, in general , d if f erent from one anot her. In t he case of

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torsional vibrat ion the deflect ion at t he end s of the f la p is t he great - �_.; est ; 1n t he mid d le of the f lap t he deflection is z ero. By means of the

torsion, inert ia forces and t he f requency a re increased. If t he natural fre quencies of t he denection and t orsional vibrat ion lie close to one

another, , t he supe rimpoai tion o:t' both types occurs.

Previously, t he d iscus sion t reat�d exist ing vib rations . It my now

b e a ske d how vibrat ions 1)1.rise fro m a stat e of rest. In t his regard, it

may be said t hat it is a, question of an automatic format ion. An.y shaking

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of th e gate, a disturbance in the flow , a gust of wind on the j et, or the like , produces even a small natural vibration of th e flap. Thi s again changes th e proj ection distanc e of th e falling j et, ripples it, produces air impacts on the air cushion which in turn react upon the flap, and th ereby ripples the j et more intens ely. This coupling , which is started whenever th e drop and natural vibration follows the relation f ,/ii = ·m·k , requires a certa.1.n time befor e th e vibrations are in full progress. For that reason , in th e case of rapid chang es of j et thick-ness ( loweri ng of a gate) , or in the case of rapid chang es of drop ( filling a lock) , vibrations cannot form .

EXPERIMENTAL RESULTS The weaker the gate was suspended and the greater became its am­

plitud e of vibration, then th e smaller its frequency , th e more intense­l;r the falling j et became rippled, and th ereby th e exciting force of the

air impacts on th e flap increased. The thick er th e j et and the greater are th e oppressing water masses co-vibrating with th e flap, th e less the j et yield s to the pressure variations in the air cushion, and the harder th ey strike th e flap, but the flap exhibits greater inertia resistance against deflection b ecause· of its co-vibrati ng water mass . The moment of inertia of the flap itself likewise decreases the tendency for vibra­tion. Th e greatest deflection occurs , th erefore , for a certain drop and ceases for a certain thickn ess of j et. Th e amplitude and frequency are a measure of th e danger of the structure to failure by fatigu e of struc­tural material or settl ement of th e foundation.

In th e case of weir trembling or weir humming , a vibration which rarely occurs in rigid weirs. it is a question of a coupling between the air cushion acti ng as th e spri ng of th e vibrating structure and the freely falling rippl ed j et acting as the mass . There is developed, th erefore, a coupling b etwe en th e air cu shton and tb e flap with its water load. Th e audible vibrations are rapid and are caus ed probably by the air-pres­sure changes at th e point of separation. Since the j et int ermittenUy carrie s down air from the air cushion, such change s of air pres6U1'e are probably conceivable . Even in the model for a rigidly set flap, high ta1lwa.ter ( that is, small air spac e) , and a thick j et, a weir trembling

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with violent , rapi dly vibrati ng air-pressure va ri ati ons cou ld be pro ­

duce d. It i s not e ssential t hat the flap at eit he r end be i n open con­

tact with the out si de atmosphere , or be e nt ire ly c lose d off ; the refore ,

the assume d organ pipe vibrations do not appear to be operative. In

the prototype they were prob abl y c ause d by wind which struc k ob liquely

agai nst the pie r re ce sse s.

MEANS OF ELIMINATnm VIBRATION

.After the Re search Institute had sub stantially c larifie d t he me­

chanic al proce sse s of vibration, it was able t o procee d wit h confi de nce

to look for reme die s for prevent ing flap vibration. A di st urbance of

the vibration proce ss i s po ssible 1n practice only by affecti ng the jet

an d it may be brought about re liably only by formation s on the flap.

Jet di v1de rs sugge ste d by the Re searc h Instit ute prove d t o be a simple

an d sure method of e liminati ng vibrati on whe neve r they were put in sut­

f ioient numbe rs on the f l ap. The jet di vi de rs may also prove t o be ef-

fective against ice f ormati ons. The mode ls studie d f or the Dortmun de r

Bri dge Canpany an d f or t he MAN ( Company) likewise f\:tlfi lle d the demand

for f ree dom from vibration for all ope rati ng conditions.

The mode l f or the Dortmunde r Company consi ste d of a row of t eeth

with a lternate upright and downward bent surfaces place d on the e dge

af the flap. At t he points of impact s eparation plate s proje cte d up.

wards into the jet (figures 13 and 14 ) . By meana of this den�ated bor­

de r, the jet wa s di vi de d i nt o aeverel. strips with varying di stances af

proje ction, the separation p late s ai ding in di vi ding the jet . The mo del

with separation plates wa s f ree from vib rati on for all operati ng con di ­

tions; i n fact , t he higµe st g ate posit ion was not free from vibration

wit hout tham. The shape of the f lap and of t he deneoting surface s must

be correctl y dimensione d so that the jet pa rt s wi ll separate from one

anot he r 1n aJ.l flap positi ons and for all t hict:nesses of jet .

In the st udy of the mode l for t he MAN ( Compa ny), vibration s were

remove d by the const ruction of a so-cal le d " st urgeon back," by means

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of vm.1eh the surface of the f lap was placed higher in several· sections

{f igure 15) . The dentates of the " sturgeon back" rose the greatest

amount at the discharge rim and continually decreased to zero toward

the crest of the dam. The v1idth of a dentate was equal to the d istance

between two dent ates , eo that half of the flap surface was covered by

the construction ( figures 16 and 16 ) . The range of projection and thick­

ness of jet was changed by these dentatEJs , and for a sufficient rise ot

dentat e , the model arrangement was completely free from vibration , but

the discharge of the flap was reduced because of the dentates. The Re­

search Institute then developed , with the use of small and large dentates

an arrangement which obtained freedom from vibrat ion with the least amount

Gf dente.tes { figure s 18 to 21 ) . The sm.-faee covered in this case amount-

ed to only one-seventh of the surfaoe required for de ntates with spaces

between them e qual to their width.

Prevention of vibration in this manner also cause d an· increase of

water load on the flap because of the congested rim which, mor�over, in­

crea.sed the l ifting f oroes of the wd.nd. Nevertheless , rigid construo­

tion of the flap was an advantage because it decreased the deflections

and :produced a larger moment of inertia.

Further investigations were ma.de to clari fy the processes of dis­

turbing vibrations . Fundamental. methods were found ; the chief' one ,

vm1oh conoerna all methods of el iminating vibration.a . was the divid ing

of the j et into sewral independent strips having different ranges ot

projection. The action of the di vid.ers was not attributed to en equal­

ization of pressure , but was due t o the separation or the parts of' the

jet by changing its shape. The width of the undisturbed parts of the

jet were de cisive for the formation of vibration. The greater the dis ..

charge , the greater can be the spacing of the dividers or dentates ,

while the number of dentates rr.ay be decreased if the spacing toward

the cent er of the flap is increased. The most certain method 1s a com­

pl ete separat ion of the strips by splitting the jet which, without fail •

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must be done f or smal l heads of overflow. The prevention of vibration was not obtained by means of trough•

shaped depressions of the flap in the middle of the weir or at several

points, even though continuous changes would occur in the jet thick•

nass and d istance of projection, because no separated strips could be

obtained which would mutually disturb the various factors producing the

vibration.

Other explanations of flap vibration have been investigated, Thus the surtace tension of the jet was said to be a cause , and without wbich the mechanism of vibration 1n no way ooul,d be explained; however, t his force was a)>le, at the roost , to affect appreciably only a thin, skin­

like jet. Thie we.a borne out by the test of pouring ether, which has

a much slll3.ller surface tension ccmpared with air than with water, on a thin j et in order to eliminate vibrations . Another explanation of the

starting of jet vibration was sought in the waves which formed in the

tailwater on both sides of the falling jet and which occurred under cer­tain conditions in uniform fluctuations. In this case, h.owever, ca.use was confused with effect. These osci llating waves we1•e unable to im,pr.-ees waves on the falling jet, since the jet is, indeed, not rigid against

bending and cannot be deflected by means of shearing forces opposite to

the d irection of' -now. If small vibrations are removed occasionally by

sieves placed at the pointe of impact at the tailwatar , then it follows that the sieves supress rocking motions of the tai lwater which would aid in the starting of the motion of the flap by means of air impacts.

- - -

s ·,

i

)

I

:Mul ler, Otto

Fuhrmann, 0 •

Keutner, Chr.

F isoher, H.

F is che r, H.

BIBLIOGRAPHY . "

- S chw1ngu ngauntersuchungen an un terstromten Wehren,

Mitt. Preuss. Versuche anst. (Vibration Studie s

a t tams wit h Unde rflow Gat es, R e port o f the

Prussian R esearch Inati t ute ) ; Wass e rbau un d

So hiffbau, Berlin 1933, Vo l. 13. " It

Sohwingungsunt ersuchungen an ube rstromten

beweglic he n Wehran, Diss. Teehn. Hocheoh.

Be rlin 1934 , und Mitt Pre us s. Vers ucheanst.

(Vibration Studies at Dams with Movab le Over-­

flow Gates; Disse rtation Teohnioal Hochschule ,

Berlin 1934, and Report of the Prus sian Research

Inst itute ) ; Waeserbau and S chi ffbau, Be rlin 19349

Vo l. 16. ff " " "

- Die Stromungsvorge.nge an unterstromten Schutztafeln

m.1t scharfen und abgerundet e n Unterkant en (The

Flow Cond it ions a t Unde rflow Sluice Oates with

Sharp and Round lower E d ge) ; Wasserkraf' t tmd Waaserwirtsohaft , Vol. 30 (1935) PP• 5 - 8 and

p p. 16 - 21 ; and Zeitechrift de s VDI , Vo l. 79

(1935 ) , PP • 1419 -20. - Die Be seitigung van Schwingungen an ub er-tmd

unterst romtan W'ebren, Mitt Forsch-.Anst.

Gut eho:ftn (The R emoval of Vibrat ions at Dams

w1 th Over- and Unde rflow Ge.te a , Report of

Gut enhof fn R esearch Inst it ute) ; Vol. 5 (1937 )

PP• 75-88; and Ze itscbr ift des VDI, Vo l. 82

( 1938) , pp. 27-28. Die S chwingungen an unterstranten Wehr and ihre

Besai t igung, Mitt.Forsoh,-Anst. Gut ehoff'n

(The Vibration at Dams with Unde rflow Gat es

and its R emoval . R eport of Gute hof fn R esearch

Inst itute) ; Vol . 5 (1937 ) , PP• 125 -34.

14

Mul ler, Otto

'' Mul le r, Ott o

Muller, Hans

Pet rikat, K.

.,y,

Wittmann, H.

Schwingu ngs untersuchu ngen an einem unters tromten Webrmo del l, Mitt . Pre uss . Versuchaans t. (Vi­

b ration St udies on a ·Mod el of e. Dam w ith Un der­

flow Gates ) ; Waas erbau und Sch iffba u, Be rlin

1937 , Vol. 31. • ·,

Dae bei Uberfall s chwingende Wehr als

s elbst erregt es , gekoppelt es S ystem unter "

Beruoks iohtigung gewisser Analog1 en zum

Rohrens ende r unt er zur Zunganp f eif e, Mitt .

Pr euss . Vers uehsanet. (The Vibrat ing �

in the case or Ove� low as a se lf -excit ing Unit ed Sys tem un der C ons i de ration or C ertain

Analog ies vrith Respect to the Valve Trans­

mitt er and Reed-pipe , Report of the Pruss ian

Res earch Inst itute ) ; Berlin 1937, Vol . 33 - Beitrag z ur Erforschung der Schwingu ngser-" "

soheinu ngen a n ubers tromt en Wehren (Co�tribu-t ion to the Research on the Phe nomenon or V1-

bra t1on at Dama with Overn ow Gat es ) ; Wass erkraft u nd Wasserwirts chaft, Vol. 32

( 1937 ) , PP• 61-64. " - Schwingungs ercheingungen an UberfaJ.lstrahl ,

Mitt . Hannov. Hoche chulge m (Vibratio n

Phenctnena. for th e Overfall Jet, Report of

The Hannove r Hochschule) ; Ha nnover 1937,

Vol, 17 . Dtech. Wasse rwirts ohaf't { Germa n Water Contrg l) ;

vo1 . 34 { 1939 ) , PP• 346-55.

15

I ' l ,

· \ ·

1. I

• 1 :, ; I,

I . \ ,

!

\

\

PRESSURE SCALE IN FEET

--------------- 12!' --------------

Positive pressures lie outside and negative pressures fie inside of cross section.

:i I' 1\ I,

:1 \• I I

+ , (See a/sa figure 3)

FIGURES I, 2, 4 5 6

PRESSURE SCALE IN F E ET

------------12" - - ------------

F I G URE I - PRES SURE ON SQUARE SEA LIN G BEAM FOR VARIOUS GATE OPENINGS

FIGURE 2 - PRESSURE ON EL LIPTICA L SEA L IN G BEAM FOR VARIOUS GATE OPENINGS

HEAD • 16.73 FEET MODEL SCALE RATIO I: 3.8 HEAD • /6,73 FEH MODEL SCALE RATIO /o 3.8

0.60

"' o.�o UJ ,: l) z ; 0.40

UJ Q :::, � 0.30 ..J 0.. li .. w 0.20 ..J en :::, Q Q 0. \ 0

0

• • -Natural frequency af structure .. ·� ---� /

�- \ .1( ·Estimated / - -o-\ --r-

,+ . ./ .-"l' i I , i f \ I . I � i ' I i �. J �:\ I ,.

I 1 \ I I' . '

\\ '\ Ii/ / i I,.- 1'., // h -+ ... 11 I

1., b/c /Q

;,,,� ·:� I . �:,iJ i 'j'--�

, .. ,__g,'-,

i I j,,.,,

., d 8 \

/f i''· i " �'

-", \

-o--

� i

(!:)'•

... ,o "',

.. .. - -Natural frequency of structure

? -� ' . I_, --.. \ - -fp<-o b-�,\ -"

,-Estimated t -� � l\..t. Ii

\;' " � --� \ \'·· · .... \.,

··\ .. .. x

..._ ··. ',

c L•-+., . \ � ', \

,, ! I· I , , 1�.

· ii1

\ j' .

I \ ;t '

-:� ',!..xi...

/r

1

......_

· I\ b, +\

.

�\ 0, 't lr�,o \_

i � � ' \('i) ', ',

/ / ''-9 ----�

E . I st,mated

''f ·.\ '.'.\ <?� "' '· �:� r--:, '

'+,. ', ' •" I I

,1, \ . rroll spri7g tensia7 Average spring tension I i I I

Large spring tension I

4.e a e.a s s.a 7.5 e e.5 9 9.5 10 10.5 1 1

F R E QU E N CY

FIGURE 4 - A M PLITUDE VERSO,,S- FREQUENCY FOR DIFFEREN T SPRIN.G .TENSION W I TH . , SQUARE SEALING BEAM IN M ODEL

GA([E OPENINGS :, a • 3./5" ; b • 3.94"; c • 4. 72" ; d • 5.51'; e • 6.30"

', --Horlzantol

Verti6al ···· FIGURE fJ - VIBRATION O F AN U N D'ERFLOW GATE

WITH SQUARE SEALl�G BEAM,

•. (

Harlzantal • · '

..J Time scale � .,

Vertica, .. • • FIGURE 6 - VIBRATION OF AN UNDERFLOW GATE

WITH ELLIPTICAL SEALIN G BEAM

Figure 3 - Flow Pattern for Square Sealing Beam in Model

( See also Figure 1 )

Figure 0 · - Vibration for 7 .87" Weir Head ( See aleo Figure 9 )

Figure 18 - Back of Flap with Reduce� Dentates ( See also Figures 19 to 21 )

FIGURES 31

8 , 18

Q Flow ......

FIGURES 7 9 TO 17 19 TO 21

. · -Headwater ""'"'"""_"""_·�-------------l

(See also : , figure 8/ I � :

' I

-!

FI GURE 7 • R E M O VA L OF VIBRATION WITH ANGLES ON TH E DOWNSTREAM FAC E OF SEA L ING BEAM FIGURE 9 • B OUNDARIES OF UNDULATED JET

BY RAISING THE TAILWATER TO LINE "o"

,· Flop motion only, ,' b ·

Time scale--··

Vanishing point-,

, Superimposition by \.. secondary influences

FIGURE 10 - REA CT/ON OF FLA P MOVEMENT "o" ON VARIATION OF AIR PRESSURE "b" UNDER THE JET

WITH PHASE DISPLA CEMENT

V) "'

H I G H FLAP POSITION · DISCHAR G E 1.55 C. F.S.

i'.; o.40,--.--�==rr----.--,---,---,

:!: 0.30 t---t--t-----11-'r-+----t-,f'--t----t:-----i

A COMPLETE WAVE IS CUT OFF

Range of first vibration condition\ � 0.40,----=-,=

f'

:7'"""�-..-::�-,--�,-;;;;;,i�===�-,;::;::---,--,

� /\ "' 0

::, � 0.20>-----\, '---------�-

0.. :Ii <l UJ 0. 1 01-----+-- ---'1-----+-----+-----"--+---'-----+�-l .., ID

::,

0 0

Q • D.90 c. f.s.-·'

�',-2

------',.----�2""0 ____

2,,..

4----�

2'"'0

____ 3""2- - ---:36

-�

D R O P I N I N C H E S

FIGURE I I - A M PLI T U D E V E R S U S D ROP FOR VA R I O U S DISCHAR G E S A V E R A G E FLA P POS I T ION, AERA TION CLOSED A T BOTH ENDS

MEASURE:ME:NTS TAKE:N AT CENTER OF DAM

YI c:;:J CJ "'

0

i: 0.201----11---+-FIGURE 13 - D ENTATED FL A P

:J mk • 5.65 I : 0.101---+-- --+11---l---+- · -

/ Second condition "' , .., ,' � �;....--'---!,e--�,,.,....,__�.--�.--�.--O D I S C H A R G E I N C. F. S . 0

D 1 1 D IJ FI G U R E 15 - DEN TA TE ON FIGURES 16 AND 1 7 - BACK OF FIGURE 12 • AMPLITU DE VERSUS DISCHARGE

AVERAGE FLAP POSITION,AERATION CLOSED AT BOTH ENDS, DROP • 29.92"

f • FREQUENCY

FIGURE 1 4 • S ECTION X·Y B A CK O F F L A P FLAP WITH DEN TATES AS IN FIGURE; 15

k • A CONSTANT m • N U M BER OF JE:T WAVE:5 FORME:D

�c iifil i19'69 1:- -39.37-''.L .393 7''. ....,__39_37".J k --- '- - - - '1'- -19.69'-- -

3.94''wida , ._l 07� j

�

rn . I " I I " -� '""'� 1- -J.9,J -'" �

/ G U H 1 9 TO 2 1 - D IMEN I ON S O F BACK OF F L A P ANO O N T A 'rltS

A I N IGUH IIJ