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'■' '"• '■'•'"' Friilti/^ Mai/ •lath, 1894.. rius -paprr is, in tin- main, ,i compilation from _^cattcred memoirs (m.istly (Jcman) „n the sohj-cts i„ ,|„rstion, and, savu for incidental novelties o{' treatment, contains iiotliiiiL' oriiri„al. It isoffered to t.lii. Society first, heeanse the secretary informed the author last week he wodld he pleased t- In applyin- llie>e prineipies, iliue ar- llir. e ,litf rem nja.s.ses of water, the etreet> ,.( wh, >. ii,, ni., aie i,, |„ eoii-ideiv,!. (-') A weight of wai.r <: A ,1 , Hlueh eolers tie Mielie,, p,,,,. fnipj the well while the plunuer d,,~enl«s ll„. -paee- ,/,, . an') reeeives the velocity « tthieh ,,bla^t,s n, tl„i pipe ;,, i!,e instant eon-iderMl. A work ill loot lbs. cp.ival.nt lo C .1 ,r ,1.,- i> neeo.-sarv to elleel this, and ,.a,. be perfonne,l by a loree U .1 ,„ ' ,„ovi„u' tliVo„;,l, , disMnce '/./. -.'/ ion St (h) The weielu olwat.r I : „ I Hbieli is Contained in the suctio pipe of a ..inule acliiifr pun.p without* vaeinim vessel which is at les at the hefjinnin^ ef thi' -iruke If there be a v.ieuiiiii ve.-el, W,,; wiler .•ontained i,, that part of the suetM.npipe between thi~ and i he uell i. eonlinun,|.|v in nmtion. while tliat part which li.^ hetwe, n p.iii.p .•! amber and ^aeul„n ve.M I eomes to re,si ,|,ninL' ihe ,eii«„ -ip.ke II ,|,e ,,,-, .eeeleiulioi, be ' "'"' "'^'' "' 'I"' 'l""l I" l!i' -.er,„„ pi|,e ;,, ,1,,,, (he, work (1 „Jn ./.r, inu^t I.e expeinf d win].' ih, pi„ .^.er de.enbes the di^-tance 'J ' ' , ' iLr. This IS p( rlin nie'd liy a loiee (,' ,i I „ .'/ ''■■) '■''"■ "''f^'" "'■ » '!"• '• -I I ' • ■ .V) contained at ll .ment in the pump .■liambei- nmsl als., be aee, j, rai.d, and ;,ii an t:- 'J A (.(■ ( e ,V) '' ././ looi ll,s oluork most I xpende.j wlole (he plunder travel:^ the distanei' ./, , ''''"' '■'"■"•'• ''' ■' (-• ' ■ '^'l '■ "■"">: Ihro.ejb ./, will accomplish thin. At the instant considered, then, tliei-e is leipiired .in amount of work to ovureoue the in rtn ol' the I'li'.- iin.2) an integral which can be easily found for certain kinds of motion of the pluui^er, as we shall see. ^Jhe forces which must at any instant he exerted on the fluid during the sucti^ stroke is obviously G Ar u' ~7~L 2 ■f (t + !•+ c .9) y J where u, x, and v are variables. .Section 3.— work against hydraulic resistancb. The prejudieial hydraulic resistances acting during tho suction Stroke occur: at tho outranoe to the suction pipe; atjhe foot valve if any; by pipe friction and variation of section or direction in the suction pipe and the pump chamber ; and at thy suction valve. II hr be the total head lost in resistances, then a force G a hr must be exerted on account of these resistances ; ami since, while the plunirer travels u distance dx, this force will have to move throu'fli .1 iLc,, the work then done will bo G a hr Aj.lx — G A hr ilx K hr may also be put equal to f "^ ; where f is an experimental constant, and is made up of the following five compflO^nt part* : f, for entrance to .suction pipe, fj for flow through foot valve, fj for flow through suction pi|)e. f^ for flow through suction valve fj for motion In pump chamber. « The work reijuired to overcome these resL^^lances may thus bo written : and for the whole stroke : for the travel dx av,^ = «-.(v,^))j;^ .(3) section 4. The pressure of the external aimosphere must he capable of over- corning all tlu'.se opiKjsing forces at every moment ; or at all events the work done dnrin;.' the stroke by tlio atmosphere must bo at least equal to the sum of all the op[K)siug (juantities of work. The distance moved through by this atmospheric liiroe during tlie suction stroke S is S~ ' a s<: that if /( be the pressure in [Kjunds per scjuaro inch correspond in ' to the lieiLrhfljf the barometer, we'viust have G n„ kS ■' > (A', + y. ,- /' )"a' II - .1 / . or G I! A S':l G A (A + S) S Ix 'M (f, ^f, +f, t ny domont he c(iu;il to or greater tlian GA(h^ + .,.) ,. ^1 [-„^.,(/ + ^_., s^) ,.J.^ Jj^p (f) J,^ (5) Obviously Jo = „„ ; ani .lii = nn if the law of continuity holds. The cotiilition oxpre^si'd in (5) is best investigated ^rapiiioally ; and Icir, this purpose we may writi! it thus , -•: ■ 'J ' ^ ... " ^O (5a) (l + 2(r)) --1 ^O (JK,)* ^-[(''. + x) + + ,<; + c ^' In Fi-. -1 let J/} represent the sin.ke of ilip, plunj,'er and let A be the lowest position. We may now >hr\v i;raphieally the values of the terms in expres.sion (5rO by'Vettini: up Irom AH their numerical ' amounts e.\i)re.ssed in feet of water; po.-itive quaiitifii's upw:irds, ne- gative downwards. 1 lie constant atmnspherie pre.ssure is tiist represented by the straiirht line drawn so tliat .;./ = /}A' .- H. The lift (A -i- .r.) will be rep"re- sented by the slightly inclined line, when Ad = h and UIl =■- (^, i ,S'}. The term involviiijr -. ,lie aec.d,.ration of the jilniiger will be shown by sueh a curve as CDE . while that involving-H- and com- posed of resistances at entrance and dnriiii; transit tluough the suction ' pipe by the graph AF/I. v , ' . For any given piston position, as Q , if .1//^ 1„> taken e(iual to the sum of V-S, V'*. ^lU'l . then .V(J represents the excess of the force due to atuiosidierie pressffrf over the resisting forces of i^ravily, inertia, and hydraulic resistance. If A A' he tfie locus of all su,di jioihts as .1/, it rcprcscBta the resultant curve of pn'ssnre on the under side of the plunger. So long as all the p.iints in J,X lie above ..1/?, (,-)„) is sa- tistied. If .the curve intersects .liJ as in Fig.'!!, the jilutmer loaves ■ the water behind as at T . and is struck a blow by it when it catches up agaiti after //. In Fig. 4, the aecetcration force is ,so j..reat that the water is unable, even from the beginning ,.f the stroke, to fdlow up the piunuer. 'llie smaller the lift the le.ss is the fear of the suction colu mn brctiking. The greater ". thr an a ..f the snelion pip,., thesmaller the importance attaching to tlu' eurvrs CDE and AFH. for the (|uantilies they represent diminish as the scpiar.' of thr increase (if „. Honee the .spt'cd of the pump may be inrrea-ud by inoreasin- the diamelcr of th.^ auction pipe. The gieater / is, the li'nirtli ol' thu lift main, the smaller must be the .speed of th.' pinn-rr. Will, hiuh piston sp. rd and a not very excessive pressure in the fcM-ce main, the pressure '„> the pnm|i chamber may, towards the I'lid of the slrnke, Ix'come s,i crr.at as to open the discharge valve and force water to flow through, before thr plunger gets to the lop of the stroke. Ti.is i^ re[)risi.nti'd in Fig. 5. Fn (Irawing tbi'se eurv.s for a ernnk driven pump, it is usually •suffieiently accurate' to n.-leel the obli(|uity of the eonneetin- rod, when CE beeomes -x straight line, ami .!/■'/< a curve of sim's, as slioWii in Fi''. t>. From the above eoiisi siderahle portion ol tl beginning of the suction stioke liir ll 'U4e mass of w;it<'r in tin- lilt main. 'I'ljis ii rations and diagriinis, h is seen that a coii <■ availj^ li' .itniospluTie li.ad u rci|nired at tin- purpose ot merely accelerating fact del.'rmims the ma.xi- mum plunger speed with givm values of iho prtnip dimensions ; and l\ loiiL' l ift mai ns the aili.wablr ^pcd npi-t b r v ery Hmjiil. — To overeomo this iliflienlly, a v.ouiim vess-l is inserted in ttir ill order Id Insure an inflow from i| Tlie mass of water lo hi' aec- Irralci main ■ wril as nearly ^Irady as possible, al llir eoiiimeneement ol ihe suetion I stroke is then reduced to that between this vesgel and the plunger ; so that instead of I in the above equations we must insert / (the distance between vacuum vessel and plunger), which can usually be made very small. ■ If the vacuum vessel be sufficiently largo, the pressure in it will alter but little during the-doubk' stroke, so that the motion of the entering fluid between it and the well becomes very approximately uniform. The work expended on the inertia of tiie water entering the suction pipe is again given out at £lie vacuum vessel ; and then is effective in accelerating the fluid between it and the pump clianiber, when it eomes to rest at the end nf the down stroke. The work necessary to overcome tlie inertia of the water entering the suction pipe with uniform velocity u" is obviously (r.4S (u")' IfZ, be the length of lift main from vacuum chamber to well, the work spent against hydra-ulie re.sistauee will be GM.S' ?"(«")" J where f" = f, )■ if, I- f"^,_ + f'-; refers to the length/,, In the length U between vaeuum vessel and pumji chamber' an amount of.work J" 2;/ must be spent ; since here; n ' is vaiiablo. ALsoheje ^ ^ ^\ + f' + f, -,- f. whore C, i.s the coefficient of resislanee at the ontiaiiee to tlie pipe loading from vaeuum to pump chamber ; f', for the IViotion in the latter eorrosponding to the length When a vacuum vessel is littod, wo liave only to change equ. (5 a) into the exjrression ■ B- Uk -. s) V ^si±^^A ;■ . (1 4 f//,ioi + p (uy -J L y -':/ 2(j J ■ ' llo (56) Paht II. — Valves. In this paper wo eoncoin our.-elves only with automatic valves: those, i.e., which open and oloso under the influenee of fluid pressure. Puring the lifting of the valvo and after completion of the stroke, water flows thmugh tlu' opening so made, by reason of ihediffereuoe of pressures niiove and below tlio valvo, and keeps it open. If now the velocity ol iho water diniini>hos to nothinL', ilie valvo should gradually elo.se, :ind should touoh its seat exactly at the mt)inont when the speed of the water becomes nothiiijin othorwi.se a return flow of water will take iilaee lliron^h the unolosed valvo lor an instant. This is to be . . . '^ . . avoided not only booauso of the diniinuti-eribod a short distanci' .r of ii> rolurn stroke before the valve touohi^s its seat. When 'his dor- happon, tho disehargi' valve has to be struck open :ind Iho mass of water on the other snle of it aeecderatod ; and since tho aooolir^iiido is a maximum with orank driven pumps at tho end ot the siroko, tho i ffoct of this deserijrtion of even a small value ol'.r will produoo a blow in iho pump eliamber, which will hi' tho more severe tho later the suolion viilvo closes anil llio groator tho ma,ss of water to bo ncceleratod, A similar, if not usually as grout, etioet is prwUw^edwlien the delivery valve closes after tho phuigir has bognn to perform its return stroke, III order to obtain -a timoous closing of the valves other forces must be introduced besid es those of fluid presguro ; and three kinds of valves may bo di^tingui^lled : ((() (Iniviti/ loailid valupi, when gravity alone acts ; {!)) Sprimj lodiliil lalrct, when the ehistieity of the valve itself or of iinother body is employod ; and 5 rih ('-•) Oravili) anil fpring hailed valre>, when both kimls of Corco are .'essential. A valvo spring loaded only properly spoakirif; only exists when the specific f^'ravity oCthe vulvc is unity. Gravity can often be made to effect correctly timed closure; but when heavy v;ilves arc in (|UC!-tion with large incrli:! cffeefs recourse must be had to .sprinL'S. SKCTION 1.— (llt.vVITY VALVES. At the moment when the valve begins to clos'-, it.« wi'i^ht in water, H', must be a little greater than P. the difference id' the lurces exerted on its sides by the fluid .-titaniing past it, which we •-hall call the ratvi: head. I P IS a funoliun el' (.-ee Fig, 7) a ,a (the ii^iier and lower areas) ; Pi, p., the lilt /(, the v. lucily », with which the water i^ flowing through i^, at the beginning of closure ; of the si/.,' and shape of the valve box, and of coiisiruetiun and linish of the valve. The pressure in the fluid between valvi and seat is not known at presi'Ut ; hut assuming it to'be but litth' cliffcrcn.t from/;., and that the valve box is large enough to fave m, influence on /', we may write with sufficient accuracy for ilie vAe head I' "^ (/',— y > ", =■ I' ^'r (i- the difference of the lower and upper pro-ui'.s aetin- on the area of uuder.-idc of valve, together with the t«rce reiiuired lo change ihe momentum of the water flowing.through. hi Fig. !-!, if u^ and >■ npreMiir 'he initial and final velocities of the water passing the valve, the cllaiije ot' velocity is represented by ii. If a mass of watei- .)/ im|iiiige against the valve jier second, the force required to give this a voKK'ity " in a svMiid is /■' .^ "" lbs. The .7 vertical component of this force is y Mu " , .)/" Mil . sirferlinfriiri Jl. ttnd wfiprr tfieretimi tfow from .-f rSlTier ^ tends to lift or jam^the valve than lo close it, is by all means to be avoided. The kinetic energy per pound of the water pas.«iing between valve C !■! ^m and scat is !r|_ if v is its velocity there. Now this kmctic energy consists ofAit ,- that partof i«,-whiohitstill retains, and/j, ^ p^ *'^'^ ^- W ' Q head equivalent to the diflfcrencc of pressures below and above. hence „ = c- yl'k~^7^^p^ where C,. is ihe coefficient of velocity. Assuming tlie co-efficient of contraction in the urea oj, under the valve to be unity, we shall therefore have ['S ". =cqm[l^a, ^ + 2/'-rZH-| Where c is the co-efficient of disch:ir -i' '-■'■? ^ ."JlitTION 2. — SPRINd AS WELL AS GRAVITY VALVES. 1. Opening. — At the instant of opening the forces acting on the valve are a ,;,,+« y; upwards (where (/ ^ _^' (''!~'''") and /) is the mean pressure in the space between valve and .seat) ; and n-i p-i + \V+ F downward (wh.ro /' is the (brcp due to the spring; and \V the valve's weight in watur). Tlie equation of nuuiun of the valve is therefore a\ (/M —pi ) — , —p., (since the smaller this is,' the greater may the suction head be), aid constant, the time re(iuired to lift the valve a given amount will be shorter the smaller its mass, the kijs the initial spring-load, and the smaller the valve seat area. The conditions for e((uilibriiim of the valve are obtained by putting ' a=0 in (i;i) ; then ) —W—F = -^^W^^f^' a ^xw p^ — /),j may be called the oaloe loud. ^ AfeBM^HlaaHiiHl >r Section II. — IIydhai i>(; Ktsi.-TA vces'wiikn open. Tlic^ llydraiilic re.4i,-*t:iiiccs ii|i|io>"(l liv tlic valve lo tfu' piisH;i;;i! of tlii' fluid, thu suTrt of wlroli w;_.'ill th ■ i-'h-r n-.i^i in,;\ may li-' ciiiiiuir- atod UH follow,^ : TliJRt cau^od (<( ) liy tlu' c'liaiii;.' lit' liin ctidii lit' tlic sti'oaui. (i) liyllir cliaiii;!' "I vrlocilv ncca.-ioiic il iiy )ia,-siii{; troni aira k , to ' area /oy. ■ • ' ■ (c) l)y triclii)ii aja'ii^tr'illii' uii'lri>idi of tlio valve ami valve soat. ((/) by (dianiir nl'iliiv c-.tioii and >eutiniiiW ;iiea ill the valv(anee .i,~. cdii-i.-iiniL: ol a |pait |»rii|ii.rtional lo the vtdocity-head ii' and .inojhei larl |.r"]ini lion.d \" ihe vilcitv bead r- -V' ' '' -'c •*ojbat the l^otal valve re.-i~taiue will br iiiea.-nied by ,a ' ^ ?:;-?!/•?..;; ^ '' (i^» where f'i^ the eo i IHinent ,d' re-i.^iaii ■ ■ ot tin' valv . .ind ^i and ^, exi criuiei t^il ro-i fliiienl-. Now , . ; ■ '''>■-'!'' ,.,A, . where e,. i.- the co idrieielil nf n-ntr letinii. henee (1.')) may b'Wrilleii: For the v.dve,^ here di^eu.vse^l ii\ tt ■!- , iii I loi \al\es irnided on lop ij :z= TT (/. lieliee ( 1 li ■/) becoifie.s ^^ ' ..ii,,.'^ h ' , -^^ l'uttii1<;/3 for N^ ., ^ i he ^" ''' ■ •• -?=?. ■■ •'{'[)' ; ■■ *'^' iSECTIo:< 111. — \AI.VIslei.\'l> Ol; V.VI.VE IIe.Mi UlllEN ol'BN. ''~ I'sintitlie ,i,|uarM''ii of rM||tinuii\ of tluw we ujay similarly simplify ' e((U. (lli) tirr ill.' v.iive bead, wfieli beeeiin- : _ ,,. - /--..;.[,.; (,;V.1. ■ ' ^^^v • - -V „ r- F,(|uatiolis (dS) and .( I- " ^ werr lir in l'^'^:!; and they wmt .■xperiiiu'dtally le>ted as t.> ihi'lr validity, and foi the deirnui '.atien ..rdieir eo efficients by him in IS.St. <4k I'.Mlf Ijll. ll-\' ll> K.M'Kltl.ME.NT.S. In this section a >ieeinet aeeuiHit-ol ibe v. suil- id' Ifudi'.'' ex.)ierinient.s is f;iveU ; loi Llivi»''tbod- iiid .ipjiai alu< ii-'d li\ bini, .mi- his tn-atise '■ Versiicbe lii'Or Vi ntilbeslaliiici ii. \ cntitwidersland," licriin, .lulius Siiringer, 18«4. •) "" ' (:iiiiliH' vaKe with larger seat area was used to deti^rmiue •\\\c effect of this i|uantily ' The -*Hniensioes wne i/ =^..")ll mm . i ..3^155 {'^y c.<...".... riOu). (Ii) Valve coneave ilo\vii\vanls, yiiiilud above, as'sliown by Fij;."12, ill thus ease iu Ciiuiitiim (12ii) we get /= 2.34, and c ==0.63. For FIl'. 1 1 we il:.(l '- ,., f — 2.5 anil (■.:_=0.t)2 ; so tb:it u^j^Wthat under similar conditions Fii;. 11 requires- a somewhat <;ieater valve load than Fii;. 12 con- tiarv' t'l wiiat wo should have expuctrd. With this vilve ^1 beeomes :::z: O.JiS and /^ — 132, so that oom- pariu- with r(|u:aion (20); it is .si.;n that f, -i.s greaterMind B less with -a euncMVe tli;in with a flat valve. On the winkle, -tiie coefficient of resistance fcumesniit s'liailer, I'oi- Hits from , tu , for concave than »- 10 4 ibr plane valves. ' ■■ i/ (c) \'alve convex downwar>ls ; JMded above. ^ , Here the coefficients in ecjuation (12((> :ind (18) are almost identi- cal, witlrtfiTise iiii- a flat biiuonied valve given in eiiiAitions (19) autf (2((). 3 (i/) Viilyr> with guiding libs below, as shown by Fij;. 14. ' Here the area lliiough the valve si^at is diininislied 12.*9 percent, by thc^uije fealhys. " / ' If the number of libs be j, then /) = ttc/ — is, so that «qu. (12a) becomes : — > ^ ^i/L _ \ch(:^ d-u)j J. ^- '. ■■ -(ai) and ibeeonstanisobtaineil Irom exjierinient were/= 2.18 -f Cri=. 0.553 Also instead nfe(jn. (1^>) We have here • ' • : K^-K..Bi:'[x'-*-- ;--(22) - ^ (^(/-/»)/i / . ,„. anil fur or. lering lifts we may writ' f, - 1.35 and, /i i 1.7. , SEcTlli.N 4. — PltACTlCAL RULES. ■ Taking /' as the .valve liiail, ,,^ ,|,^, c^rCe with which the opened valve most be loadeil .in opler tn niaintaiii>ts ei|uilibrium -against the streiuning Hnid: — , . • I ^ dia of valve seat (v,.'i-V. LI) - '^ In - Trti:i=: area llirougti do //( = lift (if vahf. r^ {= number (if guide'rih^, for ehiek valve "F~=" breadlti of s.'ime (v. Ffg. 4y T ■ li - radial breadth of valve or seat fijcing = i'(''i '— '0 (Kig. 11) .- « = speed of flow through s)h ) J .(II) ^ = ^i*+l3( d ( •;, )' f=r. + fi{ d' (ttiI- ix) It •(III) .(IV) W'ith the Ciljowini: values of conMants 1- — FOR I'l.ATt VAI.VK AS IN Fid, 11. I" E<(U. I, tiik. J 5 I- I'j i-ti;-,,/- '' from ,1 d '!■ Iirc'.'idihsof to d O.tKt to 0.t;3. II) " '••qu JII tak Si --(\\d K" ith I Any dt'vialioM from a plan.' un.lrrsi.le makes but little differenee on le CO-, ffieicnts ; but it may ii,. not.,) that f, ,. Mualler f.r the valve i„ V'.'l- and iai-eil,,,- Ki;;. i;{tli:,i, f,r Fi^. 11. The biva.llh ofv.-.jve or; ■It f,c.' IS much 1 e influential than the form of the low. r surface oft tlie V;ilvc -lOH I'l.ATK \ AI.\K.> WITH (lUlDK Kills, AS I.S FlO. 14. L'S Kqn. II valves iiiii.led al; .t-Toaler tlinn i witii \alves ol /.iii.l nCr 10 p.c. le-s than for thosf' f/>r I\' Willi I valvrs of f, from 0,8 to 1{,6 urea (rom 1,'i effi nil iliose 10 4: 1 cniK s|„,,Miin- i,, ,, .liminutioo of si very cousidi'iably -reairr wiili lit M <'*"!»<-. 1 • « ■ r .. • _.- . - ^^v -., -e : . ^^^_ \ ■.«^...-^.-..-..^.....-^..-... - --^--^--- ^---- :---^--^ \ " f^f^^