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V E NTU RI M E T E R P A T E NT E D B Y 6 C L E M E NS E RSC E L Ȳ D R A U L I C E N GINE E R A N D B U I L DE R S I R O N F O U N D RY M A D E B Y B U I L D E R S I R ON F O U N D RY FO UN D E RS A N D M A C I N ISTS PR O VI D EN C E, R U s A PR E F A C E I n the papers that have hitherto been published by us concerning the Ven turi M eter, ( copies of which will furnished application be u p o n have we, given a ore or less technical explanation of the physical laws governing the action of the eter, and called attention to th to which it could e u ses be The ob applied j ect of this paphlet is to again state the facts relati ng to the operation f o th eter as briefly as possible and to show by e,, soe illustrations how it has been applied in actual uses B U I L D E R S I R O N F O U N D R Y PR OVI D E N C E, R January 1 I 8, 9 8 T E VE N TU R I METE R The is naed for th I talian philosopher Meter e O ri g i n of na e Venturi who fi rst called atten tion in 1,, to the, relation between the velocities and pressures of fluids when flowing through converging and diverging tubes The consists of two parts Meter the Tube Pri nci p al p a rts, through which the water flows and the Register which eter,, sus up and indicates on a dial the quantity of water that has passed through the tube The Tube is fored of tw o tru ncated cones, Th e Tube, us Shape' j oined at their sallest diae ters by a short throa t piece A t the upstrea end and at the throat there are encircling pressure chabers that are con nected with the interior by carefully drilled holes, and fro which pressure pipes lead t o the register See Figure I The operation of the Venturi M eter is due to the the fact that when water in any pipe passes fro a s tate of rest to oveent, or fro one velocit y of flow to a greater velocity, a certain aount of pressure agains t the shell of th e pipe disappears, and that the d isa p Velocities p ea rance of pressure, or loss of head, is entirely dependent upon t h e velocities of flow past the points in the pipe at which pressure is taken Therefore, at two points in a taper pipe, or Venturi tube, as at U T, Figure I, because of di fferent sec FIGURE I SECTION A L VIEW OF VENTURI METER TU BE A ND REGI S TER ti o nal area, different velocities an d c on sequently differ ent pressures ust exist whenever there is any flow through the tube The d iflerence in pressure at the two points is always the sae for the sae velocity of flow, whatever the total or hydraulic pressure ay be ; and by exhaustive experien t has been shown to be nearly equal (in feet of water to the square of th e velocity o f flow ( i n feet per second through throat of eter tube ; o r, in other words, to coincide closely wi th the fundaental hydraulic forula for the head corresponding to any velocity of discharge fro an ori fi ce, i n which h corresponds to the di fference in pressure at U and T, V the velocity of flow through throat, and g the acceleration of gravity For de onstration of th e precedin g state en ts, see erschel s Rowland Pri ze Paper, Transaction s of A erican Society of Civil E n g ineers, Dece ber, Reprint furnished on application Merri an s ydraulics, Article 7 1, ( Reprinted here wi th I llu strations of th e Theore of B ernouilli under y dro ech anics, o th E di tion E ncyclop aedi a Bri tannica, or reprin t f urnished on application, and al ost an y odern text book on ydraulics The di ff erent pressures existing at th e upstrea R egister end and throat of the eter tube are transitted by sall pipes T U t th register o e ( Figure I, where, they oppose one another and are balanced by dis, placeent of level of two colu ns of ercury i n cylindrical tubes on e within the The inner, other ercury colun carries a float J V the position,,, of which is dependen t on, and as previously explained is an indication of the velocity of water flowing through FIGURE 2 REGI STER lined t h e tube The position assued by an idler wheel carried by this float, relative to aninteritten tly r e volving integrating dru I, de terines th e duration of contac t of gears G and F con necting dru and counter, by which the flow for successive intervals is registered I t is a coon but erroneous ipression that water fl owing through a con tracting pipe brings an increased Coon error regarding loss of head pressure against th e entire converging surface which it eet s reverse of this ipression is true The The pressure of water flowing through the Venturi Tube decreases fro the inlet to the throat, and increases fro the throat to the o utl e t The di fference between pres sures at inle t and outlet ends of the Tube is the friction head or loss of head caused by its operation, and under ordinary circustances is i nconsiderable The a ount Loss of head of this loss in tubes with throat area 1 9 of ain is inconsiderable stated in the accopanying tables and shown by dia gra, Figure 1 B y adaptation of the tube to r e q u ire ents, desired aount the loss of head ay be liited to any Th e re is n o liit to the si ze of the eter tubes, nor the quantity of w ater that ay be easured The Advantage of eter no liit to size largest that has yet been ade is 9 feet diaeter, with axiu capacity at the rate of ore than gallons in 2 4 hours U sually the eter tubes, for si zes un der 6 inches diaeter, are ade of cast iron, with bron ze- throat pieces, but for special service ay be ade of wooden staves, sheet steel, ceent concrete, brick or other aterial, with suitable etal parts for throat and u p stea pressure chabers and is The tube is usually laid as a part of the pipe line not in j uriously aff ected by water haer or not Meter affected by water haer or sub stances the i n water 9 FIGURE BAC K OF REGI STER th e ost violent fluctuations o f velocity or pressure, and requires no ore care than the pipe line itself The e ter cannot be disarranged by fi sh, gravel or other substances carried through the pipe line by the water The e ter ay be said t o have created a fi eld f General useful usefulness for water eters which did not previously T1 655 exist I t accoplishes with little d ifli cu lt y what o therwise is done only laboriously or approxiately and clusily I n water works, this eter enables a record to be kept of the total quan ti ty consued, also, of the Special ad van tages for water w ork s quan ti ties consued by large users, such as ad j acen t towns and cities, the several districts of one and the sae city, railroads, factories and the like S ee Fig I I A s it can not be disarranged by substances in the Fire service water, it is especially desirable, when th e water it easures is liable to be used for fi re service I t can be used as a waste water e ter, keeping a record of the quantity passing th e e ter at any tie I ts use in the detection of wastes and and as a easure of th e slip of p u p s j and the action of fi lter plants, akes it v ery valuable to all works for a pub lic supply of water A siilar line of service can be done by this eter in th e case of sewerage systes, any of which, as Special ad van tages for sew er a g e syste now built, are constructed and operated for the j oint benefi t of several towns and cities, with the cost of operation divided pro rata between the, according to the quantity of sewage contributed For irrigation works this eter can accoplish what has hitherto been desired but has not been practicable Special ad tages for irriga va n tion works I t enables water for irrigation purposes to be sold strictly by easure, and with practically no constraint as to the tie when it ay be drawn See Report of , W ater Co issioners, Clinton, Mass TS ee Report of Bureau of W ater, City of Philadelphia, I I I n the case of water powers, this ete r is valuable i n deterining the quantity of water drawn by tenants of water- righ ts for power, or for wash water and other purposes other than power I t o ffers to ills and factories a eans of checking a nd actorieso charges for power, or for ascertaining the aount of power used : Figure 5 I t can be suberged in a flu e or penstock, and enables large bodies of water to be easured regularly and accurately 4- INC VENTURI TU BE, S PIGOT END S M E M O R AN D A Colun of water foot high at I 62 F lbs Colun of water foot high Colun of I M er cury high at 62 ins, F 1 Gallon 2 1 cubic ins 1 cubic foot at 62 O F bs I litres 1 Cubic foot of water gallons I Cubic foot of water lbs at 62 F Flow at rate of I cubic ft per second for 2 4 hours gallons fi g l / Q g I S ngineering July ee E Vol News, X X XVI I I Pioneer lectric Power at, No 2, E Co, Ogden, Utah 8, I The P lant of the 1 2 FIGURE 5 ONE OF Two 54 INC VENTURI METER S PO W ER ST A TION PIONEER E LECTRIC POW ER CO OG D EN, UT A F I GUR E 6 I N C V EN T UR I M E T E R TU E I é - B FIGURE 7 2 -INC VENTURI METER TUBE Meter TABLE SO ING OF W Q ATER PASSING TROUG UANTITY W VENTURI METER UBES OF T DIFFERENT SIZES (T ROAT AREA OF MAIN 1 9 IT CORRESPOND W, OF TROAT EAD ON I NG VELOCITY FLOW I N, V E NTURI, A ND F RICTION E A D a le EAD ON VENTURI is the difference of p ressure, at r, at hr at an i n feet of water, at throat and u p- strea end of tube RICTION EAD F is the di fference of pressu re in feet I D, of water, at u strea p- re and ends of tube or s a strea down-, the LOSS OF EAD due to I n EAD due to introduction of eter tube Quantity 11 C bic Vel throu g h Quantity in Cubic Feet per Second ead Fatii throat in per ft second 1 - inch 1 Meter Meter 2 - inch 1 5 -inch 1 6-inch 1 8 -inch 2 -inch a Vegr i in feet, pp r oxi fee ate Meter Meter Meter I To eet special re uireents as to Capacity or Friction with throats of q ead, any area less than one-fourth the area of ain pipe Meter Tubes are ade I 9 TABLE SO W ING Q UANTITY OF W ATER PASSING T ROUG VENTURI METER TUBES OF DIFFERENT SIZES ( T ROAT AREA 1-9 OF MAIN , W IT CO RRESPOND I NG VELOCITY OF FLO W I N T ROAT, EAD ON VENTURI, A N D F RICTION E AD a le EAD ON VENTURI is the difference of pressu re, i n feet of water att throat t and w a u, p- strea end of tube RICTION EAD D F i s theh di fference of p ressure i n feet, at u tre and ends of tube or p d strea down-, of water, at u strea p- the LOSS O F EAD due to introdu ction of eter tube Vel, Quantity in Cubic Feet per F i a i thro ead lf throat second on l eag n I t y F in feet venturi aidez t, per sec' 2 h h I h h 6 h _ fi lviéiifr éfgr h 1 ' X Meif n MOTEL feet i ate ~ To eet special re uireents as to Capacit or Friction Meter Tubes are ade with throats of any area q less than one-fourth the y area of ain ead, pipe 2 Meter TABLE SOW ING Q UANTITY OF W ATE R PASSING TROUG VENTURI METER TUBES OF DIFFERENT SIZES (TRO AT AREA OF MAIN 1 9 IT CORRESPOND W, ING OF FLO TROAT EAD ON VELOCITY W 1 N, VENTURI, A N D F RICTION EAD ON VENTURI i s the difference of pressu re, i n feet of water, at throat and u W er at h ro t strea p- end of tube s t RICTION EAD F i sthe di fference of p ressu re i feet n, at p- of water, at u strea Strea p- and strea end s of tube or down-, the LOSS OF EAD due to introdu ction of eter O F u e tube Quantity in Cubic Feet per Friction i n F e d Second 1 ead 5 Venturi feet on 9 a ea 5E ; 4 8 -inch 54 -inch 6 -inch i ~5 R Meter nch 8 -inch f t 66 a pp r oxi ate Meter Meter Meter I eet special re uireents To with throats q as of a n y to Capacity o r Friction ead, Meter Tubes are ade area less than one fourth the area of ain pipe 2 1 J J A C C U RA C Y The accuracy of the ete r has bee n full y de o nstrated by nuerous tests, and when these have bee n ade with the care that should be exercised in any hydraulic experient, ost satisfactory results have been obtained N o better deonstration of the accuracy of the Venturi eter can be presented than the continuous perforance of thirteen eters on the works of the E ast J erse y W ater Copany That Copany has a contract with th e City of Newark, N with no t ore than 2 7 %, to supply it illion gallons of water per day The Copany controls the water shed and plant supplying this water, and is allowed to dispose of the balance that the works supply to other cities and towns I n this way it supplies at the present tie Je rse y City, the City of Bayonne, the Township of Franklin, the Town of Montclair, N consuers A ll the water is sold b y easure, through, and other ten Venturi eters, and daily records are kep t of the quantities delivered to th e principal consuers, wi th weekly and onthly records for the saller consuers D ail y records are also kept of the quantities deli vered to the conduits through receiving eters at the intake The of arrangeent th eters is shown b e y diagra and the following table copiled 1 1, Fig, fro o ffi cial records of th Copany shows coparison e of Recei ving and Selling eters for seventeen onths Fro this table it will be seen that in seven teen 2 8 S 8 D N : E a % 9 v N : v 6 w e N 2 M M a J ZM M w 5 N o s / V S w N 8 8 c 9 «w v 4 u z E Q 6 6 i V 6 % 1 ; ṃ o é MM F 2 O Z A u fi 7 : o e g E S S / : a E 6 : Q 6 w w w w c o Ḥ 6 w «; F M S U Z Z SM U M N E O Z O O O E s w s a q A 5 M E S 2 2 : 5 a S M Q : $ z z d # W E Ḥ 8 onths gallons of water were delivered into the conduits N o s I and 2, through two inch intake eters, and reeasured thro u g h ten selling or outlet eters, varying in si ze fro 1 2 to 4 8 inches, with a di fference of easureents between the tw o sets of eters of only of I per cen t Considering only the onths Noveber, , to J uly, , during which perforance of the eters was not in terfered with by irregular u neasured drafts ofwater for test ing pipe lines, etc, it will be seen that I 2, 99 6, 5, gallons of water were easured by the intake eters and reeasured by the selling eters, with a di fference of only gallons, or of I per cent I z - I NC VE NTU R I ME TE R TU B E, S PI GOT E ND S 2 6 should be frost proof, and not less than 6 ft X 6 ft SE T TI N G O F ME TE R The eter tube is set in the pipe- line, wherever ost convenient See Figures 5, 6, 7, 8 and The 9 ster is usually placed ten feet or ore below the regi hydraulic grade and not ore than feet fro 1, th The tube and register are con nected by e tube two lines of inch brass lead or lined pipe and tin-,, as a atter of econoy are usually placed as near one another as possible The register ust be properly protected fro freezing, and when a gate- house, puping station or other building suitable for the purp ose is no t available a vault or register house ust be provided This i nside ; but in other respects ay be built t o suit the tas te and requireents of the purchaser Figures 1 2, and 1 6 ill ustrate a few th at have been found entirely satisfactory D rawings for that shown by Figure 1 4 will be furnish ed when desired W hen the eter ust be placed where frequent readings can not easily be obtained, the registrations ay be autoatically transitted by electricity to a secondary or ofli ce dial, fi gure 1 7, which ay be placed any distance fro the register FIGURE SECON D ARY OR O F FICE D I A L T E VE N TU RI W A TE R METE R MAN SFI E L D ME R R I MAN s YD RA U L I C S A RTICLE 7 1 I t has been shown by e rsch ep tha t a co pou nd tube provided with p iezo eters a y be u sed fo r the accu rate easu re ent of water Th e apparatus, which i s called by h i the Ven tu ri W ater Meter, is shown i n outline in the acco panying fi gu re, and consists of a copou nd tube ter inated by cyli nders, into the top of which are tapped I L J D AT U M P L A NE J the piezoeters : and, S u rrou nding the s all sec tion d e is a ch a ber into which fou r or ore holes lead fro the top, botto and sides of th e tu be, and fro Transactions Aerican Society of Civil E ngineers, , Vol XVI I I, p 2 2 8 9 at the sections ch, which rises the piezoeter 2 Th e flow passing through the tu be has the v el ocities 721, v2, and a 2, and a, and these velocities are i nversely as the areas o f the sections W hen the pressu re in (1 2 is positive, the water stands in the central piezoeter at a height 2, as shown in the fi g ure ; when the pressu re is negative the air i s rare fi ed, and a c olun of water lifted to the height Izz I f E is the he i g ht of the top of the secti on a : above the d atu, the value of 2 for the c ase of negative pressu re was tak en to be E J zz Th e apparatu s was constructed so that the areas a t and a were equ al, while (1 2 was about 1-9of these To deter i ne the discharge per sec ond through the tu be, the areas a : and d e are to be acc u rately fou nd by easu reents of the dia eters ; then ( the quantity pass ing is equal to the area Xthe velocity or Q = a 1 7/ I, r = fl 2 7/ 2 r u / I f no losses of head d u e to fricti on occ ur between the sec tions a t and a 2, the q uantity h ' in the for ula of th e last article is, and O 72 2 I v I _ 2 T 2 g I nserting in this for vi and v2 their values i n ter s of Q, and then solving for Q, gives the resu lt Q v a x a : _ 2 2 VZ g K r which ay be c alled th e theoretic discharge D ivid ing thi s expression by a : giv es the veloc ity and d ivid i ng it 1 ' This e uation is deduced fro the known law at the q th su of velocity and fric well- tion heads is constant 6 is the for ula for the actual d ischarge per second by an giv es th e vel ocity 71 2 Owing to the l osses of h ead which actually exist, this expression is to be ultiplied by a co - effi ci ent c ; thu s : a t [1 2 Reference i s ade to erschel s paper, above quoted, for a full descri ption of the ethod of conducting the experi ents Th e discharge was actually easu red ei ther i n a large t ank or by a wei r and thus being ; 9 k nown for observed piezo eter heights and th value of was I 2, e c co puted by dividing the actual by the theoretic dis charge F o r exaple the saller tu be u sed, had the areas a : a 2 square feet ; hence the theoretic d ischarge is Q : 2 g ( : 2 and the co- e ffi cient of d ischarge or velocity is 9 Q I n experi ent No I the valu e of : was , while l b was feet, and th e actual discharge was cubic feet per second A s E was , the valu e of 2 is feet Th e theoretic discharge then i s Q : X D ividing by this, gives for c the valu e F ifty fi ve experi ents ade in this anner, i n all of which negative p ressure existed in an, gave co - effi ci ents ranging 7 essential part of the apparatu s and a y be o itted, in val ue fro to only fo ur being greater than and only two less than Th larger tube used had the areas e a and : squ are and the pressu re the central a at 2 feet, piezoeter was both positive and eight Twenty- negative experi ents give co - effi ci ents ranging fro to the highest co - effi ci ents being for the l owest velocities I n this tube the velocity at the section a, ranged fro 5 to feet per second e sall variation i n the co - effi Th ci ents for the large range i n velocity indicates that the apparatu s a y i n the futu re tak e a high rank as an acc urate i nstruent for the easu reent of w ater U nder low velocities, however, it is not p robable th at the arrange ent of piez o eters shown i n the accopanying fi gu re will give the best resu lts ; i n order that : ay correctly indicate the ean p ressu re i n (Zr, c onnection see s to be req uired both at t h e botto and sides of th e tube li k e that at a I t is thou ght, oreover, th at the elevation E should be easu red to the centre of the section rather than to the top Th e lower piez oeter is not an althou gh it was of valu e i n the experi ents as showing the total loss of head
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