Centrifugal and Axial Flow Pumps. Theory, Design and Application

249 Pages·2016·47.95 MB·English

by  Stepanoff A.J.

Centrifugal andA xial FIow Pumps
Centrifugal Flow Pumps
_.-
- u -
l u -ft
urE
THEORY, DEstGNA, ND APPtlcATloNN Y W,
A. J. Steponoff,P h.D.
MeluilteM ed,alistA, .S.M- E'
I nge r soll'Ra nd'C o mPanY
KRIEGERP UBLISHINCGO MPANY
MAI.ABARF, LORIDA
SecondE dition 1957
Reprint Edition
Preface
Printed and Published by
KRIEGER PUBLISHING COMPANY
KRIEGER DRIVE since publication of the first edition of this book, the application'of
MALABAR, FLORID A 32950 centrifugal pumps has been extended to new fields. At the same time
the ranges of head per stage, total pressure, temperature' speed, and size
have moved. to rew high levels. This advancement presented new
Copyright @ 1948 by Alexey J. Stepanoff problems-hydraulic, mechanical, metallurgical, and manufacturing' A
Copyright @ 1957 by John Wiley & Sons,Inc. considerable progress was achieved during the same period in the theo-
Reprinted by Arrangement. retical aspects an"dd esign procedure based on a better understanding of
the flow processes through the parts comprising a centrifugal -pump'
All rights reserved. No part of this book may be reproduced in any form or by any 1'nu, u r# edition of this book at this time seemed well iustified'
rneans'e lectronic ormechanical, including infornrationstorage and retrieval systenrs The theoretical treatment of the impeller action and casing perform-
without permission in writing from the publisher. ance and the method of presenting experimental information as used in
NProin ltieadb iilnit yt hies Uasnsituendt eSdtw atieths oref sApmeectr itcoa t.lte use of the infornrction contained lrcrein. tthimee f irvsetr ye dwiteiolln. hAatv eth bee esa.tm reet atiimneed .a sTuhcecsees shfauvla ep wpliitchasttiooond otfh teh et essat moef
techniqul to the field of turboblorvers in the last decade has furnished
FROM A DECI-ARATION OF PRINCIPLES JOINTLY ADOFIED BY A COMMITTEE added assuranceo f the soundnesso f such methods of attack' A number
OF T}IE AMERICAI{ BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS: of new topics dealing with theory, design, and application are included'
This publication is designedt o provide accuratea nd authoritativei nformation in regard to the on the other hand, a number of articles were eliminated or condensed
subject mattcr covercd. It is sold with thc understandingt hat the publisher is not engagedi n
'e-"n*r"l'5a ri-- lr-v-6.q1r r q-^v^v^vu..r-rrlul-r^E ,r v^r- u^uelLe-l - -P-r^ufl^s-lt-l:s-lg--n-at l S--C -fv-l-Ct-C . tffn rlcgal aOVlCe Of Ottrcf expcft
assistanccis rcquire4 the serviccso f a competentp rofcssionalp erson should be sought.
Llbrary of Congress Ca taloging-In-Publlcatlon Data
rCr.e-p-.^u-l-ugr l, AArt(-'^-e--y- -f J. \/A^tre xey Jr oaKrr.m)
centrifugal and axial flow punrps : theory, design, and application
I A.L Stepanoff. -- 2nd ed.
Odginaily pubtished : New York : Wiley, 1957.
Includes index.
ISBN 0-894&-723-7
1. Centrifugal pumps. I. Title.
T1919.5651 992
621.6'7--dc20 92-LOL7
CIP
1 0 9 8 7 6 s 4 3
Not€: Figuresl 3.l-L3.4,1 5 .7-1 5.8 , 17. 3, L7. I4, andl 7 .20: uel ocatedi n a
pocketi n the back of the book.
cavitation criterion is introduced in chapt er 12 to correlate pump be-
havior with respect to cavitation when pumping liquids of different
p-Lr--r-J:^s^Ir uar a^-rl ru rrr.-r rlel'rnL ap,rlo perf,res. New charts are glven in uhapter g
relating to impeller design for any dischargea ngle. At the same time a
procec| iure t' s esrt aab !i.t stneilto seibct the caSin$d eSi$ne lemenfs to suit im- Contents
pellers. An improved method of the inlet velocity triangle construction
is offered in Chapter 5.
A great number of minor improvements and refinements will be found
throughout the book. Old chapter numbering and titles were retained
for easy reference of readers familiar with the first edition. The first
edition of this book has been translated into Japanese and arrangements
are in progress to translate the second edition into German.
r am indebted to Ingersoll-Rand company, Mr. R. H. Johnson,
President, and to Mr. Hanns Hornschuch, Engineer-in-charge, Blower
Chopler
paonsds iPbulem. p PEronfgeisnseoerr iAn.g HDoelplaanrdtmere not,f twhheo sCea sliufoprpnoiart Imnsatditeu teth iso fv oTleucmhe- I Selected Topics from Hydraulics I
19
nology and Mr. H. A. stahl of rngersoll-Rand company have furnished 2 Definitions and TerminologY
numerous correctionsa nd helpful suggestions. 3 Theory of the Centrifugal Pump Impeller 29
proAolftsh,o uergrho rsg mreaayt cbaer dei hsacosv beereedn. e xI esrhciaslel adtp op rcehceiactke t iht eif mthaensues acrreip cta allnedd 4 Vortex TheorY of Euler's Head 53
to my attention. I also invite criticism of the views presented in the 5 Specific Speeda nd Design Constants 69
book or suggestionsw hich may lead to its improvement. 6 Design of Mixed Flow Impellers for centrifugal Pumps 90
A. J. S. 109
Phillipsburg,N. J. 7 PumP Casing
r38
8 Axial Flow PumPs
g Hydraulic Performance of Centrifugal Pumps l6l
l o Leakage, Disk Friction, and Mechanical Losses t62
204
I I Axial Thrust
12 Cavitation in Centrifugal Pumps 225
l3 special Operating conditions of centrifugal Pumps 269
14 Special Problems of Pump Design anci eppiication zvJ
l5 Shaft Design for Critical Speeds 325
352
and Axial Flow PumPs
17 specialP roblemsa nd Applicationso f centrifugalP umps 377
l8 Centrifugal-JePt ump Water Systems 4Oz
l g water-Hammer Problemsi n centrifugal Pump systems 425
459
Index
vll
ap er
from Hydraulics
A theoretical treatment of the florv through hydraulic machitres is
very difficult because most of the channels comprising such machines
have variable and irregular sections and a curved mean path' some
of the channelsa re in a circular motion with power applied to-or taken
from the flow. Si*pt. relationships established in hydraulics for ideal-
ized conditions, if applied directly to such flow,_m ay not only give an
incorrect quantitati',r. unr*.r but may also result in a false qualitative
mental pattern of flow.
An oversimplifiect view of some of the flow problems in hydraulics
has, in the past, resulted in a number of fallacies which still persist
although there is ample experimental evidence to prove the erroneous
reasoning behind such views'
In this chapter a number of subjects are treated which are either
missing or not sufficiently emphasized in books on hydraulics' In sev-
eral instances limitations of principles established in hydraulics, when
applied to conditions of flow as found in centrifugal pumps, are stressed'
^ r^,., ^f +l-o mnqt r,^nnmon fs,lla,cies are clarified.
fI I i' IY L'I UIIV IIIVU W
1.1 BERNOULLI'S EQUATION
When Bernotrlli's equation is applied to the florv thlough various
part,s of h.Ydraulic machinesits limitati<lns arc freqttently overlooked'
Rernoulli's equation,
uL-
n + ? + : E : constant (1.1)
^l 2s
represents,the energy per unit of weight where h is the energy of posi-
tion (or ability t,, tol*ork rvhen situated h f.eet above the arbitraty
datum plane), p/l isthe pressuree nergy,a nd u'/2g is the kinetic energy,
or velocity head. All three u.u .*p*ssed in feet. The quantiLy E is
the total energy in foot-pounds per pound of liquid' It doesn ot depend
on the specifrc rveight oi ttt. Iiquid, r. When applied to two points of
thc same tubc, Bernoulli's equation expressest he law of conservat'ion
t
CENTRIFUGAL AND AXIAL FLOW PUMPS SELECTED TOPICS FROM HYDRAULICS
of energy for an idealized liquid. rn actual liquids, variations of E forcesa re developed. streamlinesd o not maintain their relative posi-
between different streamlines occur and changes of ttre value of E may tions; secondary. ror, flows appear;a nd the liquid may leavet he walls
hc nrnvrl$tstnvavuA LvrJr t {u}''vo @^ ^v+u:r^r-J ' r^Jfr -v.ri^D^U^U-:Dr-r-u y. ,r'rrr-url - r-ocr rrrowrng paragrapns deal oIe [rIlI e - U-Lrl-t-lr-lr^tltil.
with the limitations caused by actual liquids. U) Euen when to the aueragef l,ow of the wlr'olec hannel, Ber.'
(a) Equation 1.1 is obtained from the power equation in motion, becauselo cal pressuresa nd, uelocities( as measureda' t two points)
may d,iffer greatly from the auerageu aluesf or the wh'olefl ow. Besides, the
Qth * Qp * q, !: constant (r.2) .,r"lo.iti'head it ietttoulli's equation based on me&n velocity does not
2g
,"p..rurrt the true kinetic energy of the flow which is equal to a summa-
I
by eliminating Q (volume per unit time) and 7 (specific weight of the tion of the kinetic energy of individual streamlines and
liquid).
Elimination of Q from equation 1.2, when applied to two points of u*2 t'-w tlz
the same stream tube, requires that continuity of volume be satisfied. ,o
This means that in a closed conduit no liquid escapeso r is added be-
tween the two points. Therefore, when Bernoulli,s equation is applied, This expression means that the square of the mean is smaller than the
to imaginary stream tubes or streamlines, this continuity requirement mean of the squares. This can be verified easily by a numerical example'
maltes it necessaryt hat the two points of comparison lie on thi sa,?/Lsetr eam-
line becauset'h e constant in Bernoulli's equation is not necessarily the same L.2 REYNOLDSN UMBER
for diferent streamlines; as, for example, in straight pipe flow the total
energy carried by streamlines near the center of the pipe is greater than Reynolds number R : ud,/v, where u is the velocity, d the diameter
that at any point in the pipe section. of piie, and y the kinematic viscosity of liquid, is used as a criterion of
(b) Elimination of 7 from equation 1.2 is possible only if 7 is con- the flow in closed conduits. The type of flow (laminar or turbulent)
stant at all points of the flow. This means that the liquitt must be incom- and the velocity distribution are similar for geometrically similar tubu-
pressible. ft is not sufficient that the product Qy be constant. because lar sections, and the same friction coefficient / can be used in Darcy's
this product represents the weight of the liquid which is constant for formula
gases. Bernoulli's equation, as given in equation 1.1, does not apply h: IeL zuzt
for gases because it does not include thermoclynamic changes r.r.r[!sl
take place in florving gas. From the above it follows that Eernoulli,s
equation cannot be u'sedi n casesw here the gasesa re liberated,o r absorbed, if the Reynolds number is the same irrespective of the nature of the
along the fl,ow path, as either processi nuoluesa n energll change. i"iJ o, u.turt velocity or pipe size. A considerable amount of data on
(c) A streamline is defined as the path of the liquid particle macle u1r friction losses for rouna pipes has been accumulated and correlated
of prevailing flow direction from point to point. A fluid is in steady with Reynolds number as a basis. Evaluation of the pipe roughness
motion rvhen its streamlines permanently maintain their position and is the ohly factor which makes the resuiis uncer'r'ain to within + 10
relative arrangement and velocities at each point on the streamline are per cent.
the same. Bernoulli's equation applies only to a stead,,fAlo w. (c) Hydraulic Radius. For conduits other than circular, it has been
flow in a mouing channel, dependoinngL uo rnc athne form of the c.h aInnnreel and caunstdom taor y seiecI0t thues € fricurtlitot n rlJc\uocleurfrficient from round pipe data for d : 4nL,
the nature of its motion, energai s either applied to or absorbedfr,o m the the existence of similarity of flow pattern under such conditions being
flow. Thus the constant in Bernoulli's equation varies along the stream- assumed,. There is no theoreticatj ustifnation for sunh an assumption
line and from one streamline to another. becauseg eometrical s'imilarity is the first prerequisite for $rn'ilarity oJ
(e) With actual liquids, Bernoulli's equation is not applicablc to curui- flow. Thus, for laminar flow it has been shown theoretically and proved
linear motion becartse inertia forces come into play and centrifugal experimentally that the friction coefficient for a rectangular channel
+ CENTRIFUGA]I, AND AXIAI, FLOIV PIINTPS
have never been determined and are different from those established
section depends on the shape of the channel and is different from that for a straight pipe flow. Fortunately, in a modern pump' hydraulic fric-
for a round nine.2
tion losses are but a smaii fraction oi i;he pump powei' inpii'u and a'frec*"
64 little the laws of similarity governing the head generation which are the
basis of the PumP design. I'or reason
64 ma.r,iona bout fryarr"fio lossesi n centrifugal pumps has not retarded
.f :0.89-R for a square channel appreciably the progress in their design'
To summ arire:,i,t can be stated that the velocity distribution, the loss
'f : 1 . 56R-4 for an annulus, or two flat plates oofr htuerabdu le(fnritc) tiocna nnaontd beed dy losses), afnnodm t hthee paknttoewrnl edogf ef loowf R(elaymnoinldasr
Schiller 2 investigated the flow through conduits of different sections- nouf mflobwer thine rceu irsv inlinoe gaer,n edriav"lerltyrug baelcni.cht,e. dpo tre dc odnevfienrigtieonnt oflfo wR.e ynFoolrd ss ot mneu mtybpeers;
round, square, rectangular, triangular, and star-shaped-and found
tnhoatt ctohien ccidoee fwficitihe nttsh oosf ef rfioctri orno u/n, dp lpoitpteed. oInn tthhee btuarsbius leonf.t d ,r :e g4iomn, thdeo fino r( aco )st hecenorsnsev, ceporrgmoepmnetor tniJalysn duo sf DeRdive efyorngr oetlhndets cnshutramanibgnehertl shp. aipveeF ifngloeuwvree' r 1b.e1e ins dreepterormduinceedd
difference is not great and, for lack of better means, round pipe data from Nikuradse's work a to show the effect of channel section variation
may be used for flow in channels of other shape as &n approximation,
although the theoretical justification of such procedure is lacking.
(b) Curvilinear Flow and Channels of Variable Cross Section. AnA-
thi,ng that disturbs the uelocity distribution of flow, such as a change in area
or direction of flow, changest he pattern of flow through a conduit, and the
Reynold,sn umber basedo n the auerageu elocity of steadyf low ceasest o be a
0.8
criterion of the flow in the senset hat it is usedf or straight pipe flow. That
is to say, the same Reynolds number is no assurance of similarity of
0.7
flow because the change from laminar to turbulent flow may take place
at vastly different Reynolds numbers when the pipe axis is not straight.s
0.6
There is no way to estimate the friction coefficient / for such a flow;
in fact, in some casesd etermination of the exact channel length or sec- 'l"Eo .u
tional area is impossible (example: impeller and volute channels). More-
over, the skin friction loss becomes secondary to additional eddy losses
incurred by the disturbing element. The eddy lossesf ollow laws dif- 6 Negativec onvergent
6 Positived ivergent
ferent from those followed by friction losses. In a straight pipe flow a
0.3
iength oi 20 io 40 pipe ciiameiers (or even more accorciing io some in-
vestigators) is necessary for the flow to assume its final velocity distri-
0.2
bution. No such length is available in the channels comprising a cen-
some are statior&ry, and others are in rotary motion. There are &
number of Reynolds numbers that can be assigned to a given pump,
depending on what channel and which section of a given channel are 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
t
taken for calculation of velocity and characteristic length for the Reyn- 6
olds number. Each of many possible Reynolds numbers, if used as a Fra. 1.1. velocity distribution in convergent and divergent rectangular channels;
criterion of operation of a given type of pump, will reflect the summary i i, l.U of width, c is location of the point from the axis of the channel
""" "harrrrei (Nikuradse {).
effect of all channels comprising a pump. Properties of such criteria
qENTI!IFU-qLL--AND AXIAL FLOW PUMPS SELECTED TOPICS FROM HYDRAULICS
on the velocity distribution. The most uniform velocity across the pocketsf illed with eddies( Figs. 1.4a nd 1.5). such behavioro f liquid in
channel is obtained in a convergent channel. The beneficial effect of a turn is causedb y inertia oitft. flowing m&sso r centrifugalf orces' fn
nvnvngrvravFrd6avn^f^ v ful^vtvt,v irop u*-rJQ^ sv "u-E^ v u^fr :r*i. r Ll^r^r:i-$-:r-S uurg - r:-u-l-l-J er-rlerr approacn cnannels aclqr llt'l,(,) n.t rU-W--O- U--P!r-I^'ill' I UIt'DD-ur-G'vlv^ "' *rr^tv{iunrvn^cru
for the purpose of producing uniform velocity distribution. The author appear in the stream which are di- Top
taper, an indication that the bad effect of an elbow on the velocity dis- tw Efa; lUlV \r o1f Ill thUeIrv tu^^rrrsns'v antd along the side
tribution is fully neutralized by the steadying effect of a convergent walls of the PiPe, toward the inner
channel. wall of the turn (Fig. 1.6).
1.s FLow rrrRoucrr ELBows AND BENDS f vevloactnitay la ,0n -dhp arse sosubrtaedi nisetdri.b," u t.i:oitntt ielux"-
(a) Velocitva nd PressureD istribution. The majority of investiga- | ;;il;;G -Hi!h *itn a shndard 6-in.
tions on flow through pipe bends and elbows were concerned with ihe I ;il. p*.r"". and velocities
losseso f pressure through these parts. A theoretical | *e.e observed at the outer wall by
pattern of flow, ?rr: constant (where a is the verocity t the end of the g0o turn, whereas at
of a strea,mlinea nd r is the radius of curvature of its I tl" beginning of the turn high ve- T\.,- 1.4. velocity disiribution in
path), was generally assumed. However, more recent I tocities and. iow pressures occur at the middle of an elbow; velocities
studiessh aves hownt ha,ts ucha pa,tterno f flow exists I l;; i;""r wall of the elbow. Five in metemp ers econ(dN ipper't) '
only at very low velocities or where the ratio of the I feet beyond the turn pressures are
mean radius of curvature to the pipe diameters,r /d, I A;t*, but it takes up to 10 ft to restoret he normal pipe velocity
is very large. At high velocrties,o r low values of i aistribution.
trc. 1.2. Di.recrion r/.d,, the flow shifts toward the outer wall of the I T;i";i ob""*"d higher velocities and pressuresn ear the outer rvall
i" elbow in the second half of the turn (Figs. 1.2 and | .r Trr" t r.r, to" t"_iou" flow, very large radii of curvature r/il (25, bo,,
"erl"bt"o"rw_ r(iN.* ipper"5t" ) . 1.3). with ideal liquids a change in the velocity t ;-;-J 10-0), urd Rey"oH" numbers 1980t o 8220. The critical valueso f
distribution is followed by a changei n pressured is- |
tribution in such a manner ihai an increasein velocitiesn ear the inner | -Td-5\o;l\
walls is accornpanied by a pressured rop, and a reduction in verocities I
a&tE tr hnee oouutreerr wwa&lrlr oofr tthrnee tl uurrnn i$s ftoolllloowweedd bbyy aa pprreessssuurreeii nnccrreeaassee.. ssuucchh I+ F93]h4..N..\\}N 4 Ttoopp
a velocitya ndp ressurdei stributiobae. sinuto 'upp"u"l o tt upp.o""l
gG5lg
to thet urnw irhl owv elociriaensd h ighr /it ratio. " I lN
EEFlg
I hu)l
I N ll lll Bottom
; [-.LrlLUl -f -|
. i '
Ir
!IIi' uIIt'' rr"unlilj'b . u1trr.'iU Uo,K t n iPII n 'oIl ueEDaDeDDrnUurrr r o e vvl br\\.'o:rrlr\i)w)e- ' Fglcr.a m1 .o6.f sDpiiar-al
| "-* i prersureg shown sxe in croes flowe in an
lpproach ---+F- Pastt urn meters of water (Nip- elbow.
FIo.1'3.velocitydistributioninanelbow;developed(Nipped6).
In high velocities and sharp turns, although high velocities shift velocitieso r ratio ',,fir /d, at which the theoreticalv elocity and pressure
torvard the outer \,vall,t he pressured istribtrtion is affected little by this distribution is destroyed were not definitely established'
change, and the nxarinlunl uelocity and pressure both exist at the outer In centrifugatp umps, qll passageisn the impeller and,c asing &rec uruit
wall of the bend. The low pressure zone extends somewhat downstream, linear and, uelocitieitr e high. Thereforea theoreticaul elocitga nd pressure
resulting in a separation of flow from the inner wall and the formation of distribution is hard,'!,eyu ere rlnowtpred,
- - 8 CENTRIFUCAL AND AXIAI, FLOW PUMPS . SEI,EETED TOPICS FROM .HYDRAUI,ICS
(b) Several Turns in Series. When the flow of liquid follows several use of the energy gradient concept simplilies a number of problems con-
turns in successioni n the same direction, which are located in different nected with the flow through a pump and will be elaborated further
planes as shown in .tt'ig.1 .7, the liquid acquires a spiral motion which is in later chapters( Figs. 1.9, 1.11;F ig. 7.11).
superirnposedo n its forward velocity.s Such motion does not cause
additional lossesi n a channel with a circu-
j;|;:l: 1.6 TRANSTTIONO F PRESSUREIN LTQUTDr N MOTTON
:=0- ffil:; lT'.',""T;,:i*l':i'fl :r,
In a stationary body of liquid, pressure intensity is transmitted
/ ,/ if the channel is square or recrangular, equally in all directions. In moving liquids, a difference in pressure
l<-'/ losses of head result because of excessive may exist along the path of the flow and also across the section of the
l.r<;. l.z. Sever.ael lbowsi ' eddiesi n the corners. In multistage cen- r;hannela s a result of the dynamic forces developed by the florv. Pres-
seriesin ducev orLexm otir.rn. trifugal pumps of the volute type, such a sure changes along the path of flow are a result of a change in kinetic
successiono f turns is found in the cross- energy as given by Bernoulli's equation, the total energy of each stream-
over passagesf rom stage to stage. Round sections for the major por- line remaining .c onstant.
tion of the crosso\rerss hould be used to reduce the losses. Variation of pressure across a channel, howeuer,c an occur in such, a
n'LanrLetrh at some streamlines will increase their pressure without decreas-
ing their uelocit'ies,t hus increasing their total energA, or the constant in
L.4 ENERGY GRADIENT
Bernoulli's equation. But, since the total energA of the f,ow across the
To start and rnaintain fl.ow in a channel, stationarA or'rnouing, there channel section,r emains l,he same, such an increase o.f pressure energy of
must be a drop in total energAc ontenti n the direction of flow below its initial one group of streamlines takes place at the efrpenseo f the pressure energlJ
leuela t zerof low. The graphical representation of the total energy along of the remaining streamlines. When the transition of pressuree nergAt akes
the path of flow is the energy gradient. This should be distinguished place in this rnanner without actual miring of streamlines,p ressuree nerglJ
from the hydraulic gradient, which shows only static pressuresa t dif- ercltange might be called "conduction" by analogy to heat conduction.
ferent points of the path (Fig. 1.8). The hydraulic gradient may have Both pressure energy and heat energy are due to molecuiar kinetic
a local drop and rise along the path, but the energy gradient drops con- energy and are interchangeable, as is well known in thermodynamics
tinually and it determines the direc- of gases.
tion of florv. In actual pipe flow the Energyg radient When the pressure energA erchange is efected by sh,ifting or mining of
errel'gy g--r---a Ll:r-r-1e rrL u-lr-u-^l-J- reljres-e-n--La-S rLl-y-- SLt TeAfnL1X' TLeS Lt7n- e- p'ro0e$$ 7'E ti'LTrL'LLu'r L0 CU'tLueCL'LU'tL. I llel-e IS SIJlIl. aIlOIJIlef
draulic lossesa long the flow path. Hydraulic mode of pressure transition which takes place without exchange of
gradient
An idealized flow can be imagined particles or mixing of streamlines, and that is by means of traveling
to be produced by hydraulic (or pres- pressurew aves. Pressurew aves follow all water-hammer phenomenaa nd
sure) gradient drop with the energy are treated in the extensive literature on the subject.
Frc. 1.8. Energy and hydraulic
content remaining constant; for in- The florv of pressuree nergy from a higher to a lower level takes place
--^ l:^-a^
stance, the discharge from a vessel Br alurtrrr u$. naturally like heat flow from a higher to a lower temperature, whereas
through a nozzle. But in every caset vherer eal liquids are concernedt he the flow of pressuree nergy in the reversed irection usually takes place
processw ill follow the direction indicated bv the enercvs radient droo. under the dynamic forcesd evelopedi n a curvilinear or rotary motion.
The presence of a pump in a system of conduits produces a jump in As soon as the tangential component of the velocity is taken out of
the energy gradient, but the flow is still maintained by the energy gra- the florv by special means, such as guide vanes or a straight length of
dient drop ahead of the pump, through the pump, and beyond the pump. pipe, pressuresa re immediately equalizedb y a natural flow of the pres-
In a mouable channel, surlr,a s an impeller of a pump, the energy gradient sure energy from a higher to a lower level without mixing of the stream-
drop is referred to the energAl euelw hen there is no flow. When the flow lines. Conduction is responsible for the constant pressure across the
starts, energy is absorbed by the flow at such a rate that the total energy section of a channel with a steady florv assumedi n hydraulics. Examples
remains, at all times and at all points, below its zero flow level. The of conduction and convection of pressure energy follow. Figure 1.9