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(All rights reterved,
ADVANCE PROOF— (Suhfecl to revision).
Tins ,,ro,,r ii, .sent to you for discussion only, and on the express
u.i.lcrstandin,,' that it is not to be used for any other purpose What-
ev(r._(>Se« Sec. 17 of the UonstitiUion) .
(^aiKidiai; ^ocidij of ^ioil (^nginceos.
■ INL'OKPUKATEU 1887.
TRANSACTIONS.
N.B.-Tl„s Socioly, as a botly, ,loes not hold Itself rosponslhla for the facte
and opinions slated in any of it.i puhliciition.s.
THP]ORY OF TlIK .ACTION OP PtlMPH.
!!y i'roC.ssur J. T. Nic,ii,.s«ff. B.Sc, M.C'an.Soc.C.E.
'■' '"• '■'•'"' 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<i have ■.^ paper for this evening •
and seeondly.l.eeausel'.i.st President .Mr. Kennedy ihou-ht it would be
of value to have Hach s felehrated e.xperiments /eeorded in the Society's
proeeedin-s. They are .yceordinirly eiiibn,|fi.d in Sect. Ill: It ig
proposed to -ive an arconnt of Bach's aiTt KicVjler's later experiments
on pump, ihem.seives to the S„cjeiy jn .i future paper.
/■, avi rai;e f irce reijiiired to act on the plunder in order lo over-
e.inie iiii'ilia
Fi iiverii:;- fnie.' h ij^iired t i iiel '111 111,' piiinj;er in order to over-
eonic Irielinii
1
The work .lone by the atniospltcro while forcing tiie fluid Up tlic
lift-TOiiin during the suction stroke uotisists of tliree- part^ ; that
rc(|nired to raise the water merdy ngait.st L-ravity ; that required to
overcome the force' of inertia ; and that required to be .expended on
prejudicial hydraulic resistances.
Vabt I.--TnK Suction Stroke
, SECTION 1. — WORK Ad MNST QRAVim-.
The work expended per stroke in merely raising tiie water may be
estimated as follows : ' "
'J he foree aetiiifr on the suction jiipe is C ii (h, + .,), and acts
through a distance -,/.,; wle n llie pluii-er rises the amount dx.
It
The work done durin^,' ttie upw.ard stroke is thcrelor<!
^'i '^' - I' O' .!(/(, ,-.-■)./.': ^- a A S [u, + ''''y.i..(l)
SECTION 2. — WORK AILyiNST INKIITI.". (•'OIU'ES.
■, it the watiT in the suctioit pi|.e is arresi.arid then receives a vel-
ocity,/, an amount of work eqiiivalint to ■_"!'" ro(]t lbs , the kinetic
-'J
enerny ,il ih,. mass of water J/, must be expended. If it have initially
a velocity «, and this is to be inerea,-ed to ".,. the amount ol' work to
be expended must be the ci|nivalent of ihe diffei'eriee of the kinetic
ti:er-ies before .ind aftrr alti'raiion olspeed of the water , or in symbols
-V
■Should », be ureairrthaii »„ work need oot be expended 'upon,
but will be done by the tiiiid, and if »., » , , no work needhe do„e ' •
_>-
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.<M ol' Mm 1, is fdliwi
or sinoo A .^ = a ^ ,
G[Ar ,1 ^iUx^cS)^ 1
3 '- - J ■
, Tlic work done during the wliolo. stroke is therefore
^'^-^ i'o{"l\^'^-' /'^^ivl^? >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
<ir . ...^4)
i
The force GAB must at c\'cry >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 <J(> . 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<ni of delivery thereby ocea-
sionod, but also on aooount of it-^ off'oet In destroying smoothness of
working.
If it be tho suctionvalvo which closes too late, the plunger will have
(le.>-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<i (in
Thi-may be shown a< tbllow~ :
'fhe forei' tending to keep up ihe valve 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 .
<J " 9 .'/
In other words, the force actinu' on this account on the vnlve is that
required to destroy the vertical speed ol the water passing. Now,
Gil , » , ■■
-n — where » is a co-efficient allowing for friction.
Hence F,
etc. Putting- A' -- 2« We may write
., " , '
F. A „' a^i,
■'
which justifies the form of ill). A' beinu ;i co efficient tube determined
by ex]ierimenl, and depending Inr lis value u|)Oii the limd direetion of
the stream, the breadth of the valv ' ,-eat, and nature of ilu; v.ilve.
'I'he greater the weiuht of tie valve the more readily it will close ;
on the other hand, the less it will lift ai iiia.xiinum flow, and tlr" i;reater
resistance will it ofl'er to the pa-s.,ge of tir' water. When Ihe distance
from valve to well is great, jironipt eiosure must mi this account he
somewhat saerilieed in ord. v to ilin)iiti-li llie prejudicial liydr.iulie
resi-lance. A return flow is tlieii inevitable through the valve ; and
what must be carefully attended to is the securing of as direct and'
energetic an action on the upper sideof the valve due to this return flow
as possible.
Such an arrangement .is shown in l'"ig :l, where the wat»'i is diseliarg-
erf ffirbngh t1i> 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<re and y = wdi
Hence
Suhstitiitin.,' ill (11) the'-valve hciid ia^
''=<•"••■ 'Tr[(.-:V)' * *•-'■]
Or puttioi;/ for A'- /.-, the weight of the valve in the fluid,
"C [(,:») = -/] 0^)
>
-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 ) — <i ip, ~ji) _ 11/— f^
If + G V
s r
-I
WluMv a is the aee,.lerat,o„.s ao.l K the v,.lumo of the v.lves and y
is the speeifio gravity. /'
lIen.o if JL J^ be denoUd by M, the following is
for the aceeliratiim
"I ll'i - p .. )
[^0-
7-1
< +
an expressJon
^1 .(13)
MA
M -" ^ } 7
■ From wliieh it is s vii that the accLloralion increases with difference
(if'pressures (yi, — yi.j ) ; and diiniu'shes as the nia.s» of the valve, the
spring loading, and the area of valve seat increase. The last only so ^
long as//., —p is p.witive, whieli is probibly the case with high speed
pumps as a vacuum must nbtain for an instmtwlion the valve lids
quickly at tirst.
Assumiug as small a value as possible for ;>, —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
<ii (/'I —pj—o ( ;) J— ;> ) —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<! box., «
aii4, (^'1 in till' case of a valve ^uid'd Iroill lirlow, by lite clianuo.-i ul'
dii'oction, and sectional area of .stre:ini .i.'< well a,~ the frietiuii against the ,,
surface.^ of tjie ^uidiiiK Imdie.-. »
Till' [ireseiiJ ^t:lte uf the -^ei. nee el' hydro 'iyiiaiiiies is unable lo t;ive
rational exinis.-^ion.-^ ler ti.e-i ai tinii- .- baiately,. we luiisi be content
with a sHnjunariMiliiin.
For any Liiven valve in ]iro|H rly i "i:-triiete 1 .si ai and bi'.n. Wi' may in
thi.s way lake the n.si>(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<l -ivi'ii liy '1! leh in a troati-e on
' Fife KiiL;iiie> 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. •) "" '
(<z) Plat'- c Ive, jinded .Wove, an i plane under si.le (I'di;. It).
With this e..n-t'i urtioii olvaivi \\, re -slj/^enoined the intetdependenee
of valve loaii, vahi le-it.iiic' . and ,valv5 lifl, •nhlTthe lehitions
" 'brtWcC'ti vaivi'Tnatf nriH f!fr<''t ciT wafer. ^--^ ~ ' ^ "^
Anotlitr >:iiiiliH' vaKe with larger seat area was used to deti^rmiue
•\\\c effect of this i|uantily '
The -*Hniensioes wne i/ =^..")ll mm . </. fiD nun ,'i/.. '---90 nun. ■
■ ' TliL^ variutidH.of 1' with the lift A when the bead under which waU'r
8
r .
^
r\\
m
— ^fe-,^ -
.^
\ •«»
r .
6^
r:\
: , ' - .. - . . •
Q flowed tlirou},'h wns kept constant, for viilucs of h between d and d
' .» W T
luny be oxpri'fflL'il by ^
« 2y L . V 4 X 0.62A ) J ^^-^
/ beinjj =.2.5 diid/^ (M 0.62. ' „, . '
The variation of f wiiji tbo lift /i .iref^^cssed by equation (18);
" witb fi ~0 5.i ami /i — 0.15;.sotbal ■ ," -^<.'
f =((.55 + 0.15 C'lLy ..; .(fO)
^ ^ ft ■* . • " -
" I'or.oniinary values of the lift between (f and (<.
{ ' ' 10 r ■
.For a va^ve a« in Fii;. 11, but with the dimcnsiong tZ ^ 60 mm.
''■ ~ ^ i^n., d^ = IftD min. thai is a broader seat-area:
/= 5'.]!i.aml c = p.i;05.
»so tlkit (ID) is
7;.iooo,.,;; E^i^* Qr^)'] (^^»)
Also fi bcoonifs 1.1 and /:i .0.1 r)5 no tliaJt(20j read.s
^ - f=>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 <i. ^
g = aceeleri(tiuu due to gravity =32.2
(. %■
..^
Itt
■
H
Hlf
■
flttuMl
?=
cooffi. of resistance of the valve; so that head 1
;liroufj:h tlie valve is "^ u-. and ^'^ /3, 7,/
wt by lestfltiinoc
experimental coefficients.
Then with the foot and the pound'as units wi' haVe:
(0
2g L V c{7rd->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 -<l. 16 to 0.1
^, 0. 55 + 4 l>-(\\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 <ti(/iial
to :^0 p e, , and vi
III' f-i from 1.7 to 1 ,75,
eo-eflieient ol' resi-tanec f is o|
valvesL'Uii
Ih'Io
eniir,<i> very cousidi'iably -reairr wiili
lit
M
<'*"!»<-.
1
•
«
■
r
..
•
_.-
. - ^^v
-., -e : .
^^^_
\
■.«^...-^.-..-..^.....-^..-...
- --^--^--- ^---- :---^--^
\ "
f^f^^