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Chemical engineering applications of a modified Archimedean screw

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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Hftjor Sobjoot Chamteal !agJ»©®ri»g
Iowa State Collog®
1941
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UMI Number: DP13111
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am m m m m
In a n c ie n t tisass m. number o f slew moving devices were developed for
r a is in g w ate r for irrigating field® and pimping out the. bold# of ships*
th e A rt* imedean screw said to have been in-rested hy AreMsedes la igypt
was one o f -fee soet mmmmful slow spo«& pumps.
Xa modem times these
slow speed pumps hare almost e«8fl#t«Jf disappeared perhaps beears© the
induct ion m otor, a high speed device, is used t o d riv e asst pumps* We
now have s in g le «ad doable w »
gear speed reducers that provide large
speed re d u c tio n at high pww r traasaissloa efficiency*, la chemical plants
th e re mm a la rg e number of testsaees-where speed reduction u n its are
necessary f o r o th e r e f u i p w a t *
l a swefc case* A reh iM d eaa screws could be
installed for paapteg liquid® to moderate e le v a tio n s reliably and t»ex p e n s iv e ly .
A systematic Investigation. of the Archimedean screw was begun, at
Iowa S ta te College is 133$ * Hebi (1 6 ) built a screw and found that the
performance was erratic#, the sntHergenss of the lower end of Hm screw
in the w ater seemed to affect the capacity*
In 19358 lolls*® (It) dis­
covered th e so-called "th e ml§%m effect,* and developed two venting
methods to overcome it*
venting ©f th e Archimedean screw has
cleared the way for the present studies of a p p lic a tio n s *
A p p lic a tio n s of
the Arehlwedean
th e present tre a tm e n t
ser««F is
doe* not attempt
Archimedean screw fwsp# a re
a very
t o cover
la rg e subject, and
the field* S©«? note® on
included, and the subject® of Archimedean screw
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
aerators and ehajaiaal fmp&ttimMg i«r?t©.#» are oensli#r*4 in detail*
§mm additional application# «?© anggaiitad Sa the .final ##©ti«a ©f the
thaaia*
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ii,
wmim qw f s i u i m x m x
A*
Ar$fe£»ed*«
Otter ihm the nmmmm g>i©ri#s fats#d down to m eonearning the
m & m o t& ix m r ? originality ©f Arolilm tim - m
tfe* wm
»- to m r d ln g t« ffmtli (tt) A m
h & m littl® Information about
wfl» W « k « o f Arohi3a©d®sw is w r y
A l i f e of Archimedes m s written by on© I«r»©l#M«a, bet
this Mop-Aplay few not mrrlvwd, and m e b jjartimlar*. as are
Im m m h a ve to fee @©Hooted f w » m m j different sources. Accord­
ing to Tsetses be died at toe age of 75, and as be perished in
the m e k of Syraouae (B .C . 212), it follows that he was prob­
ably b o m about ft? is*C. He was the son of Fheidla* the
astronomer, and he m s oa intimate tents with, if net related
t© King i i i e r m and his son. Ueloa* It appears frost a passage
©f Diodorus that I» s p e n t & considerable time at Alexandria,
where it stay be inferred that he studied with the successors
of Buelid* It stay hare been at Alexandria that he made the
acquaintance o f Canon of Samos (far whom he had the highest
regard both m a aaifceiBatieiaa and as a personal friend) and of
Iratosthenes. To t»*e former he was in the habit of eeaw uaieet-'
tog his discoveries before their p u b lic a tio n , ami it is to the
latter that his famous C a ttle -p ro b le m purports to hare: been sent.,
toother friend, t o vbos he dedicated several of his works, m s
Dosithous of Pelusium, a pupil cf Conon, presumably at Alexandria
. though a t a date subsequent to Arehf»d@e sojourn th e re *
After hi® return to Syracuse fee lived a life e n t i r e l y
devoted to sathesiatioal re s e a rc h . Incidentally he sad® h im s e lf
famous by a variety of ingenious sseehsnieal lavention-s* These
th in g s were however merely the ‘diversions of geometry at play,*
(P lu ta rc h ) and he attached no importance to tk©». In the word#
o f P lu ta rc h , *he possessed so high a .spirit, so profound a soul,
sad such tre a s u re s of a e i e a t i f l e knowledge that, though these
in ven tio n s had obtained for him the .renown of more than human
s a g a c ity , he yet would n o t deign to leave behind him any written
work m . such subjects, but, regarding me l.ga#fel® and sordid the
business of mechanics and every sort of art which is directed to
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
vm *®d
lie placed bis whole smMAiaB to those specula­
tions 4» %
%
tm
e beauty Ml, subtlety there is no admlxtare of the
common needs of life** I» fact he wrote only ess suefe meeh&aleal
book, Qq Sph®r®-«king
Some of his mechanical inventions were used w ith ?reai effect
•faixart the Romans during the siege of Syracuse* Thus he con­
trived catapults t o in g e n io u s ly constructed as to he equally
serviceable at long or short ra n tea, -machines for discharging
shavers of aisslles tbrouch holes mode in the wa.11 m, and otten
eastsJusting of long moveable poles projecting beyond the ■walls
•which either dropped heavy w eights upon the enemy** ships, or
.grappled the prows by means of an iron hand or a heal; life© that
af a e ra n e , then lifted t*-exa in to th e air and 1 st them fall
again * Mare® Hu s is said to have derided his own engiasers and
a r t i s a n s . . . j bt.it the exhortation had no effect, the Soman* being
in such a b je c t terror that, *if they did but see a pie®®, of rope
or wood p ro je c tin g above the mil, th e y would ery, *there it is
■again,,* d e c la rin g th a t Archimedes was setting some eagin® la
m otion a g a in s t them, and would tu rn their backs and run away,
Insomuch that !& rc e llu s desisted from all conflicts end assaults,
f i t t i n g a l l h is hope in a long s ie g e .’
Archimedes i s s aid t o have requested h is frie n d s and
relatives to p lace upon his tomb a representation of a c y lin d e r
circumscribing a *$&ere w ith in it, together with an inscription
giving th e ratio which th e c y lin d e r bears to the spherej from which
w© m y I n f e r that he hinself regarded the discovery of this ratio
as his g re a te s t aAieveswni* Cicero, when quaestor in Sicily,,
found th e tm&h im a »gl«cted s t a t e and restored it.
Beyond the above p a r t ic u la r * «f the life of Archimedes, we
have nothing left except a number of stories, whisk, though
perhaps not literally accurate, yet help us to a concept lea o f
the personality of th e most original m a th e a a tie ia a of antiquity
which we would not willingly have altered, ffctts, l a i l l u s t r a t i o n
of hi# entire preoccupation by his abstract studies, we are told
that he would forget all about his food and such necessities of
life, and wowM be drawing rcometrieal figures in the ashes o f
the fir®, or, when anointing himself, is the oil on Mo body, Of
iho same leind is the well-known story that, when h© discovered
in a bath the solution of the question referred to him by fliere®
as to vh e th s r a certain crown supposed to have been made of gold
did not in reality contain a certain proparti on of silver, he ran
naked through th e s t r e e t to his heme sh o u tin g , *eureka, ewrefca**
According to Papua it was in connexion with his discovery
of' the solution of the problem To move a given weight by a .given
-for o©-'that Archimedes u tte re d tS»"’
p|a®#
I can move the e a rth . ’ . * ...
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• if*
There are only scattered references to the water screw (ale® called
Icochlias) wfeieh Archimedes appreatly tewstei in IfQTft, for the purpose
•f Irrigating. fields*
It m i else »#ed f«r pumping oat the hold ©f ships
according to Beatfe ( 11)*
I*
types of Screws
According, to tk© Boor
IttcydcfiMMtia th e re are two forms
o f Archimedean screw*, the ©pea form cosslstlsg of ft helix attached to s.
core which re v o lv e s l a a. stationary c y lin d r ic a l ©mslag (usual ly cal led
the- Bwfca.fc s e re s ) « i ifa* dosed form Is i& ie lt th e casing fits the h e lix
tightly tod re v o lv e s with it* The open o r Betels, screw Is also deaerlbed
by £**«©» awl others, sad it las been treated foito thoroughly" ly Hereh (12),
Muyaken (if)*, mad % l m t {t.d} • ft© Stibefe & m m ir become the w e ll kmmm
screw econreyc? whoa used for moriaf solid®*
Screw eetreeyor* can fee oper­
ated wrti es lly according to th# tiak-ielt Oempany {15}*
Hawkins (10) m
hm
s a cat ef a® early closed screw reproduced Is
Figure 1*
la t h is cenmetlen he *ay&.
The Kosmn screw delineated upon the opposite pegs* if
act the earliest hydras11c engine th a t was composed of tabes,
o r is tho construction, of which they were introduced, is
c e r t a in ly th e o ld e s t one known of th a t d e s c rip tio n * in its
mode of o p e ra tio n it differs e s s e n t ia lly from all other
a n c ie n t tube machines} in t h e l a t t e r the tubes m erely mm
m conduits for the ascending w a te r, and as such a r e ..at rest;
while in th e screw i t is th e tubes themselves in action that
ra is e s the itfuid*
Butler (d) and C-olyer (#) describe installation® of the dosed, screw,
and Krohnke (1 3 ) tofts treated it ia considerable detail*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sutler (4) # « *« rib M t ttsjmms eataaplea of mesha# s w « r fora® praps
'Milled h© © a lls Arohtswieaa paipst ©sue ©f ih « a ecmsist# of rigjit and left
hand screws meshed to -prevent refers of the fluid within the pufsjs easing*
f liis is r e fe r r e d t© *«■ the, ®<4«iat©a &vehim€mm. thruster ©f Aaoriefe
o rig in *®
k double eaie# w s
present day engineers *
on o f this is the (feiiaby P»*P f a m il ia r t©
Sutler** other two mesh screw pssap® here an
idler gear wheel end & ©liaia gear eo®b f & r th e meshing elem ents*
one having a eb a ln ©oatfe is referred t® wader the name Trlebea*
The
D espite
the m m s these Idler elem ents are probably e e l led ©a f o r a share o f th©
pimping d u ty .
These meshed serer pmp» a re n o t tru e Arofelaadeaa screws*
An internal ribbon conveyor mamffcetur*# by the MsJe»B®lt Company (14)
•es be eowiderei a development of the eloeed seiw*
Figure 2 illustrate*
this eanveyer which has.no ©ore*
®be Herding* (9) ««mter*ea*Tweds elMsifier, Figure 8,. is similar
t© th e ribbon ©o»v®y©r set at a s l i
t a&gl# with th e h o r iz o n t a l.
the
published d e s c rip tio n states?
Tlie m a te r ie l to be c la s s if ie d is .fed in at the lower end
above the pu lp l e v e l , and as the classifier r o ta te s , the ©oar®#
p a r t ic le s th a t s e t t le out a re moved forward by the s p ir a l and
-are re p e a te d ly turned over i n the forward motion...* It© fine®
and the wash w ater overflow through an opening in the opposite
end o f fee c l a s s i f i e r . The sand or oversiae is des&tered and
discharge#**.* ft?© internal s p in a l f l i g h t s have a v a r ia b le
pitch end depth, fee pitch, decreasing and fee daoth of the
f l i g h t * in c re a s in g toward the discharge end* The volume b®t»**a
succeeding troughs forced by the spiral decreases as th e over­
size discharge end is 5-.pproacb.ed and as the settled solid* are
moved into the s e c tio n * of decreasing volume, fcbe liq u id is
fe ra e # te- flow over the top of the f l i g h t s le a v in g the sand t©
f i l l th e last section...* The size ot particles allowed to flow
o u t a t the fin e s or overflow end is ©losely controlled by
re g u la tin g the speed for a given c a p a c ity , dilution of the pulp
In its® settling p o o l, and the depth of the s e t t lin g pool*
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Conveyor
Internal Ribbon
Link-Belt
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Hardinge
Counter-current
Cicssifier
-1 9 -
Re produced with permission of the copyright owner. Further reproduction prohibited without permission.
m$Q*
1m i» d e o f th e #«v#lo p ® E ,i i n which a e e B t r if u jp l
Mention should
fo re s f i e l d i s a u b s tiie te d f a r th e g r a v it a tio n a l f i e l d *
t h is kin d o f
A rte ime dean screw has been developed by B© 1ewer sad asso ciates ( t ) { 8 )
f o r us® as a ,91s eonpreasor l a
r e f r ig e r a t o r s *
the Arohijaedete screw*. te e r e f e r e * ha# taiergon© a continuous dsvslopasst leading to- the away different ferns o f paafa described above*
the
closed mrm haa h&mi n o s t p o p u lar i n Sssrpt wad the ie d ite r r a a e a s c o u n tries
and te© Bwteh s o re r seems to i»m te e s mmore recent form w e d estensive**
I f In H o llan d * England, and # 1© Scandinavian e oontri.es*
Archimedes, h im s e lf* f a i l e d t o a©a t lam the s o re r fftssp i a may o f h is
-w ritin g s th a t s u rv iv e d *
So probably considered i t o f l i t t l e
i«f© rt*m e® *
f o r it® i® tmowa. t© b a te regarded p r a c t ic a l a p p lie s t i sms © f jsatheasatics
as m amusing d iv e rs io n *
C . T h e o re tic a l &asu& d e ra tio n s
1.
C a lc u la tio n of e a p a e lty
Aeoorcfing to Kr&mfce ( IS ) it is p r a c t ic a lly im possible to devise as
expression for the. theoretical ©ape,city o f either the- olosed screw or*
ssswsiag t h a t there Is as leakage*, f o r th e Hatch screw.
So did n o t
el&bomts 1it« reason for t h is o b s ervatio n * bat Rollrawa (19) has e x p lain ed
■teat a l l attem pts a t fo rn aX iategratioa lead to tran scen d en tal equations
which must be solved by trial* % ! s reduce® t e e s o lu tio n t o praphi&al or
auasrieaX t e te g fn tie n * & new a m l y s is being re q u ire d for each s it u a t io n *
It will be shorn later tean an a n a ly t ic a l integration can be p e rfe rs a d
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*8 1 -
f o r the special ©as# of ft aerew at zero angle of operation,. a result of
i»p®rta»«# o n ly for parfos*# of
Kretaft*** (IS) swrthod o f ovalaatiag oerev cfijaeltj omelet# of
determining t * » length o f th e sujaaerged © m te r llB e * HHltiptytsg by th e
w id th and depth of th e wrap and then % the awsber of tubas la th e screw.
ffei® Is obviously an. a g e m i n a t e so lution . b u t * g ro a t tim e s w r l » prac­
tise! e s tia & tln g *
Instate#*’® equ ations ftr© ft® follows*
I f E * ra d iu s o f th e ea s tin g
r • ra d iu s &£ the oor©
/& m ( R - r ) / & m rad iu s of the tub# © e n ie r -lta e
a * number of tubes or threads m the s c r w
t TTr tea ft * pitefe
f * angle of r e v o lu tio n from the vertical plane
^ * angle of operation of the screw
*» voitoaetri© .©ape-city per revolutioa
withrespect to the horizontal
'H u m s in y /' s> taa PC t*a/2
(1 )
(2 )
V, *
f ' °°%V - f
(s)
Q * (yrf » ^j_)CX* * **) r W ism «•
f o us© th e t l w
find th e v a lu e of
(4 )
from e $ a * tie n 1*
This
*epr©ee®,ts tit® angle of th e overflew point on th e lew sid e o f the serew*
th en f in d th e two a n g le * Y I «®d
re p re s e n tin g Mi# aebmergenee and
onergm ee p o in ts on the tube c«nt«r~M*» by trial.
Finally substitute
those values in th e f i n a l equation 4 t o find the © apaeity*
B o lls a a (19) suggests laying ©at t h e e le v a tio n of m » tube of as
Archimedean screw* drawing is Hi# w a te r -lla ® end picking o f f the drawing th e
eubnerged p a rt of the © m t e r - lln e *
figure 4 shows hm this is done*
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“ 22«
Casing
B
Eollman!s Approximate Method of
Integration of the Liquid Slug
Figure A
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Ctely the lower flight trace e» the esa® and the eest®r»Iis® need b® l w »
is togofchor with tbs mter-llws*
Perpendiculars are dropped, from the
sutaergenoe jwiat S and the ©serges©® point 0 to the screw axis and the
lengths of these s e p « t 8 CS an# Bf are »®asur»d« Weir* a© Krcfcrike (IS)
Its already she»ra# the length of the sttfcaerged «®ttter**line is proportional
to th« -m im e of liquid slug*
¥ * X £ C tt )
SFhea L *
1^. *
1|, •
V »
(§ )
leapt}, of submerged eea-ter-iis#
total length of center-line per rev®Iwfcicm
total velsae of one revolution ®f the tut®
volwaae of liquid in th e tale
The length 6C of ©«ttter*liae is i
%0 *
C % /S 6:0 ) a r e
®o® Cc^t?.}
(6 )
***® eos 0 " * / l )
(? )
Where 1 » ra d io s o f the ©eater-lte#
®\© length S3 ©f e«st©r»liae is*
%2 *
Cl isassigned a positive sign heeaose it lies above the axis. DF i*
asetgaed a positive sign if it 11®® above the aadL* or asgativ© ifbelow
the a x is *
%CCW h / 2
it
t
TJ
* % 0 0 *»
+ Lqjj
„ IS# ♦ ar@ ees (C'%^) ♦ ar# ©oe (Sf/S)
'
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-2 4 -
fb® w l w
of
« (f 77-l){oyoss-®##ti«al area of the tube) ©an be obtained
by t&rm l in te g r a tio n *
Let B
P
r
$
- radius of the tab© center-line
» pitch of the m t m
* <®« fee I f the d iaten ee between cor® and. easing
* aepexetiffia between ed^eeent flights
€h®o#e x, y#; *®si * m m
as shews, la Pi pare S*
The equation of the ssMisg let
x® ♦ y® * 1 * r)®
(9)
The equation
of the core Is#
x® *
• {& - r)®
(10)
th e equation
o f th e lamer f l l r h t - i t #
*
*
th e equation
of th e tapper t i l ;ht l e t
*
*
(.
? '
:
Y ‘
e re ban **
(1 1 )
&r« test X * $
(i£ )
4? * ds % d *
dx 4y do
t
fy(B - r )
- r
- »
* 3
ebt 4y 4s
?t •
U F B H fc rS )
(II)
Bat since (2 r S ) is th e e ro s e -s e e tio s a l e r e * of th e re e ta n g a le r tab®#
f| • {2XS)(oros.s-»®#ti®*l ferea of the tab©)
There a re eeeerftl g rap h ica l methods' of determ in ing t h e o r e t ic a l
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(14)
-2 5 -
i
Nf
'V
u
> -i
C;)
•C
r
.l;
+5
r
0)
4^
o
o
•H
C--
-P
r:
M
X-Axi;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-
a .'
Jh
r*
-2 1 .
eap & eity* ' Figure 8 shows the method o f fjrlmi (%%)*
hollas p ro je c te d ©at® «
e le m tie s a As a s in * eery#*
the tra c e of a
fher© o r * f e w such.
e»rv©t required. to rep resen t one tub© ©f &a Arohimedosa s e m , two on the
core end two on the easing#
Tbs Cwm water surfae© lies at the ang le of
operation to the serssr axis and t©agent t© th e highest point on t h e curve
re p re s e n tin g th e tr a c e of the upper fe e * ©f th e lowest f l i g h t ob the eo re
(tfe@ overflow point,) *
Tyltmi d iv id e d the screw into & series o f p lan e*
guarpesulieular to the a x is an# a sixth o f a t u r n apart*
Any other separa­
tism of plane* t o M be all right hat si* per -tern are p a r t ic u la r ly e ® «
v e n ie n t
because sinV s
one half and a t h i r t y - s i x t y degree t r ia n g le
ten b* used to lo c a te th e lower flight tr a c e *
A series of e r a * * e e e tie n s
fttft now draws as# the- twitted areas p ro je c te d from th#
If
Aq, A j.* Ag,
«* wetted areas of tee respective pianos
h * distance between adjacent planes
& * nvmkmr of tube® or threads on the screw
ft * capacity per revolution
Application of iisfioa1® rule leads t© th e equation.* when s is even*
ft •
^
* 4 ( 4 ^ 4 Ag ♦ Ag * — } ♦ 2 (Ag + A4 ♦ * - - ) (If)
Muysken (17) divides the sp&es between the eoro and easing into- a
s e rie s of ooneeotrio cylindrical elsiamt* of which only on® is shown i»
the end view ©f figure f... IM, and 81 represent the trsee of the water surface
m . the flight® os tee low side of th# tub#* and XJ and FI nr© th© traces
«
tee high side.
Ifceee lines ars nearly straifht and can be drawn as such
without appreciable error*
fh© angle D( j (ft®) is now measured fro® the
points where th® lower teaees cross- the ©enter*!!®# of the element and
G(g (MOP) from the points where the upper traces oross#
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-2 7 '
Water Line
Core
Plane 1
Plane 2
Plane
7Z
Plane 4
i
i
Plane 5
; Plane 6
7
1
Tylvad's Graphical Integration of a Liquid Slug
Figure 6
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-2 8 -
•H
•H
■A
-p
-•i
■
P
M
M
O
•H
'a.
vfl
w
o
l_t
to
jg
r<3
a
*-■e*
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
a
r-<
&
•H
«*®§—
& »t S »■ d is a s te r o f the sonwr easing
* • twice th# masher of ©lews(its
T m radius of th* center-line of »*eh
<r » ratio of pitch to diameter
a. » number of tub*®
Q * capacity per revolution
f * r/b
.* ,)
(1 6 )
When figuring th* capacity of an aerator*wMehvill
b® described
later* it i® desirable to know act only the volume of afull
slag of
liquid bat also th# volume of the slag as successive i»or®®»ts are drained
o f f th® surface»
To avoid prf©raise complete- numerical integration# at
each decrease in height it is helpful to «et up iaerewnts either parallel
or perpendicular to the water line so volume* can be calculated at various
heights without repeating the work*
Rollawa (19) w*o* tfeo method of p**#iag plane* through th© screw
parallel with Ha# m t o r lint*
figure 8*
th# intsraeetlone of th® ooro
and easing with these seotiow are all elliptical and they are exactly
alike*
Sue traces of th# flight* **« projected oat© th® sections sad the
wetted areas Measured with a plastaeter*
these trasses are net quite
straight* but little error results from making them straight*
If suit­
able means of identifying the traces with the proper ere*# seetioa can be
worked out* they m y all be projected onto the ® m ® section hut this
.really multi plies the e-hauee of error many tines*
ffee wetted area# are
then multiplied by the distance betjwwm planes end added together to get
the volume of tfe# total liquid slug*
fs get the 'volume* of slugs at ■
successively lower height* just emit asetles# erne at a time beginning
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-30-
o
*i]j
3
rH
00
•d
•H
•H
o
•H
c
CO
Figure
o
•rj
"5
rH
o
•H
oj
H
a
i
jq
H
O
03
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
■*‘51**
with th® t©p. Jtether scheme for using pimm ferpmiioulmr to th© »tsr
Its# will be em*i&ere& l&i«r*
S*
Hethedg o f v e s tin g
As e a r ly as lift frototes flS) recognised tfc«t a closed screw mast
be. vented to th e ataes^h ere is order to assu re r e lia b le o p e ra tio n .
1#
reeosseads that screws be- design®# te operate la. soeh * wtam&r that
31§**iil s lag s So act «©•&. « f f th© sir ptssags by coming i» eeatftefc with
th© n e x t h ig h e r f li g h t *
la $«a«ral. this fraeeiwre teds to soae sacrifice
o f flftffceitgr Wrought
ift w w ro a l ways s « & as a high an g le of oper­
a tio n . s sm all c o re , te g - p itc i , s a l few er tabes,
fh® effect of t h is
I k it H i M S ’ will fceeoo» apparent ft* we discuss optimum e e n d itie fc * of
o p e ra ti oru
la I S M ft patent issued to f* f. Sayier (20) for c e rta in improve­
m ent* te -to© Arehlmedeaa fterew dealt w ith the m a tte r of ve&ttog*
T h is iftWBtioa rs lftts s to p ep ® or water hoists o f th e
A r& ift« i» s » type. sad it has for i t s object th® p ro v is lm o f
means whereby th® air spaces store th© bodies of water supported
by th© s e rio u s convolutions of th e screw o f ife® bodies o f the
h o is t will he smstmtly in eoawsitoiitien w ith th e external
atm osphere, thereby p reve n tin g {pftvitsrfcioE of th e ©oatwats of
the h o is t to th® level o f th© supply.,
The p a te n t fa r th e r s ta te s *
W ater h e is ts o f th is iy fc swell as h e re to fo re construct®# have
employed minut© &pm$Mg# e««e©tisg. a c e n tr a l air space with th©
spaces between the ocmulwtim* to. order that Biphonio a c t! on
iwr re tu rn flo w of the ®l»mtei w a te r, m ight be prevented but I t
ha® been found, in using ©nets devices, that tr a s h . »«eh as le a v e s ,
tasrigs, and o th e r fo re ig n substance© have been carried into tti#
in a c c e s s ib le p o rtio n s o f th e h o is t by the water ft»d h a w clogged
the f t i r opening, th e re b y preventing t!i© escape of air to or
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•5 1 -
trm. tfe# e x te rn a l fctsmepfeer# wad* th e re fo re * p re v e n tin g th e
p re fe r *p e *ik ti« B of th e a p p a ra tu s . As here inbefore stated*
one o f th e fwrfsoipl# objects of this in v e n tio n is to provide
neon# whereby t h i # ofe^eetAeaabl# slo g g in g of th e air m a te is
p reve n te d .
& © means referred to consist®. of a spiral slot im a # eore just
below each flight.*; This oomwst® the apaee between slags to the hollow
core which is open at the upper end end eleeed at the bottom*
ffsat this
scheme m s not completely sueeaseful i* disclosed by the .following' quo­
tation from the patent*
A fu rtli© r o b je c t is to provide neane a t th© low er end o f
tli© screw f o r cheeking th e daws flo w o f f lu id w ith in th e h o is t*
whereby f lu id * a f t e r once e n te rin g th® h o is t,, can o n ly escape
by passing upw ardly through the o u tle t a t th® upper and th e re o f*
Furtherm ore th is check, by a c tin g a a a w ate r re ta in in g means,
prevents th # screw from re v e rs in g under th e a c tio n o f th e w a te r
supported th ereb y*. rh an pm»m is dim oom aeted fro ® th e screw .
T h i# discussion in d ie * te e that th e p a te n te e had a oonsidorabl®
acquaintenee with th# Ar#hiUs#d#«a m r m $ but it sswst* probable th a t M s
a e d e i d a w loped troubles 1® had not a n tic ip a te d *
It say fee im g ia e d that
the w a te r ran Sat© th # cor® whea th # s a w * m s operated at oilier than
q u it# high angles eal deseen&ed to the lowest wrap vfcere i t r m back
into the tales and over the overflow point into th e pond,
This probably
f r o n t e d him t o in c lu d e a ©heel: v a lv e a t this point claiming that th is
would prevent the screw from waning laelasmris i f released.
In o rd er to
prevent the screw fro ® re v e re lag under th# aotiee of th® liquid slugs
which it eaataS as* eheek valves would he n #e e*#a*y at e v e ry turn as will
be e v id e n t when we develop th e for®# system on a liquid slug later on*
But to eoahtaij® w ith th # p a te n t I
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The w ate r h o is t c o n s t!to tin f. th e —«*» i a w a t i w i® to
to t i l t e d p re fe ra b ly a t an an g le o f 45 degrees alth o u g h * w ito
th® form b e reto b e fo re d e s c rib e d , w a te r *
b e b e la te d w h ile
th e apparatus is bold v e r t ic a lly *
I t 3m® been fo u n d , t o w n w ,
t h a t the g re a te s t e f.fie ie n .e y can be obtained by su p p o rtin g
the heist at th® an g le stated*
It
is e v id e n tly expected th a t th # p e c u lia r Shape of the flig h ts w ill
safes i t p o s s ib le to l i f t Met id to a vertical position* Bow erer, this
co n stru ctio n . cannot
possibly «*•»%» eapss&ty at an eagle above the angle
o f no c a p a c ity unless
a e ea fc rifu g d l fie ld i® u t ilis e d *
S olliaan (1 9 ) probably was the first to describe e le a r iy the siphon
e f f e c t , tfce cause of erratic operation is closed Archtoedean screws. He
used a spiral of glass to illu s t r a t e this ^ e a m R ffit.
how th e slugs of liq u id should be distributed*
F ig u re 9 shears
F ig u re 10 shows one slug
w hich has Just been c u t off f r « a e e n s tm le e tie n wito the pond by th e ®s®rgto g tube end*
t it t le
lifting: hm eeeu rted end both ©ads of th® slag are
at the saws le v e l* Figure 11 shows the sane slug after i t has been, l i f t e d
slightly sad th e ta to ©ad is ready to submerge*
slug being formed.
Figure If shews a see end
The water is flowing tote th e open.'end of th® tube
and try in g to seek th e lew! of th e pond outside«
the first
sin g has been rising steadily te n d in g t© lengthen the air space between
to e s lu g s *
Since this space is tout off fro* the a ts a w flie re , expansion
takes plaw and the excess preeeinre of th e a ta e a p h e r* ever toe air slug
poshes both slugs of w a te r up to te th is spa.®®*
situation as toe tub# end sstergee a g a in *
F ig u re 1® shows th©
Ttoless the air epaee between
form ing and rising slu g s o f liq u id is vented to th ® atmosphere tois siphon*
rising n o tio n is cu m u lative and. can cause com plete loss o f © o p acity*
It
turns out that whea the lower fa c e of th# screw is submerged to th e pond
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-3 4 -
’roperly Formed
Liquid 81u /is ■
The Screw Picks up the First Slug
Figure 10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-3 5 -
F.eady to Pick u;i a Second Slug
Figure il
The Second Slug Being Formed
Figure 12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-3 6 -
Two Ciufs Torned und Siohon A c t i o n befirn
Figure 13
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to J«#t th # proper «*fe#afc th# •© te a l ©#.p#©itgr approaches the th e o re tic a l
c a p a c ity .
th is #xp:toia« th© ©rrati# ©fes,riM»-ta§r o f mush- o f th # p©rf©r*a«a##
d a ta i n th©
Figures 14 -and l§ B h m two «#thods of ven tin g developed fey t©li«s»
which do n o t affoet th® screw design and do sot spill liquid,
Liquid
rus# out into th e oxetut tubes « r up between th© sid@ws.lls m the low side
of the rotation but* sine® th##e ©attend up th® old# to a point above th#
water line, th® liquid i'd## sot spill feat rams hook into th© wrap »t th#
high side of th® rotatim*
3.
Speed of e p e ra tio i
Irsteak® (1 $ ) *ay# that fo r olosed screws there is « dofiait® staxiaxus
to th e speed of eooaoaloal of®ratios*
Me sett a peripheral v e lo c ity of
2.2 to 2*$S a e te rs .per second as th©' ,as*im» advisable,
C<grv#rted to
re v o lu tio n s p er m inute th is gives#
.
|r
“ B < |~
(1 7 )
where
B • e»#lag d io p t e r is ssiters
n « revolutions- per s to u t#
Mmy&km (1 7 ) quote# S u it® (sour#® a e t gives) as reeosw m diag*
a «* Jp-
(1 8 )
Although Kuyeko-n was ooasidoring th# Putoh sorew, it 1® probable that
B u tte la te M o d equation 1-8 to- apply t© th e elo#ed serww or else adapted
it fo r th e open screw based os exp erisn ee with toe closed screw, beeaus®
#11 toe other oxproMioss for th® Botch mrem een t& ia easing iianeter to
sos© power le s s than * « - *
These «**-$
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-3 8 -
Venting b r Veens of External Tubes
Figure 14
Venting by Henris of Nested Casing oics'*&ilfa
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
**3f§*»
( 19)
(to )
(21)
&utah screws t a th® larger *1*#® e r e subject to greater losses end em
probably be operated a t
falser speed* tefor® th e loos of c a p a c ity due to
-c e n trifu g a l action becomes ap p aren t*
Sollawa. (It) using «. preprly vented screw for which S * 0*462 meters
plotted volumetric effioieney against velocity,
th is screw should oper­
ate at 93 Tmpmw a« #■ maziwm i f eq setie& s I f and 18 a re e o rre e t* y e t It
«h«**ed 100 fear c e n t volwaetrlo e ffle ie a a e y s a ly a * high as 18 r*p*i»# m d
reached zero o&feclty at 4f i »p*m*
It ih m m iem appear® th a t screws vented
with, tubes or nested s id e w a lls ©a th® o u tsid e are a ffe c te d adversely a t
lo w er v e lo c itie s ttasua th© s e lf seated serees o f Krohnfee*
% # mimiawa self
v e n tin g angle of the above screws- is ?4 deg ree* a»d it m s ©prated at-
69°-S0* * If perifteeral v e lo c ity is the limitxr
faster «® Xrohake says
th en e x te r n a lly vented- aero** sitemM act be ©prated ia e x a m s o f*
{■tg')
4.
Ratio- o f ©or© to easing s is e
The © p tiaua r a t i© o f ©ore to eas in g e ls e is en@ h a lf m n e a rly as
could be a-seorteiaed from th e s w p e rie a l In te g ra tio n o f £6§ ic rw rs © p ra tin g
under v a rio u s o o n d itiM as, acc o rd in g t o lo lls t a a
(19)*
Jfete rati© holds
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**411*only fo r screws im v in g a pitch etgs&l to o r lees than th© ©ptiuM m l o ®
for eaeti angle of ©j»ye.tim*
Other r«e©m»ndatiens ore:
fy lm d (fg )
a r/l * 0 *1
(28)
Mayafcan ( I f )
r /l
® 0*48
(2 4 )
toreh (It)
r/l • 0*25
(SS)
Rrehs&e (15)
r/k * 0*55
,
(86)
A e r#
x * rttiim s o f th e eore
1 » rad iu s, o f th® easing
Irofcake*'® reeoan«Bdatien ie determ ined p rS m rlly by h is d e s ire to p ro *
yide a ecmtixmems s ir fMtssag^w&jr a t eg&imw; angles o f o p eratio n fo r © elf
P itch
f o r o p tia n w .p lte lt saw*
Erehnfce (1 8 )
p * If® S>
{ 21 }
Sfuysken ( 17)
|> * 1*2 B
its)
f jl m d
f
(2»)
( 22)
0*t 0
where
p « p itc h
» * easing -«H «etw r
These are probably intended to apply to s s b is operating in the vicinity
of
Magnitude*
eagle# o f eye ratios slnee th ey giy® data f o r angles o f th is
Sellnaa (IS ) has stems* fo r two thread screws having a ©or®
to easing s is # r a ti© ©f one half* th a t & definite ratio of p iteh to easing
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•41-*
diameter i t optimal fo r. each a ig is o f o p eratio n *.
H a fin d in g ® sr®*
p * 1*07 I) at 3,0°
(30)
p * 0*625 ®,at 45°
(31)
p * 0,375 ® at 60°
(SB)
f w i w ©pemted ■«* high «a§le* h u m lower ©apseity for the optima® pitch
than at lew angles*
Soila n t (If) ha» pointed oat that mx Arohis»d*aa screw when proper**
ly wonted ha* greatest eapaeifcy at ser© angle of operation and tftis
capaeity deorwuMMt at the angle of operation increases until the aagl# of
a# e a p a o lty is readhed,
this angle in determined by the point whore th*
imterseation of the flight with th© ©aging fceeesaes horizontal*
Fi'ure 16
shew#, that there 1* a© capacity at or beyond this point for all the other
parts of the flights slop*. downward*
th* angle of bo capacity is given
by*
where
1 * radius of tlie tube ©enter lime
r m mm half th© distance between core sad casing
T * pitch of the flights
I t is e v id e n t th a t th e work l «
% a screw ptasp depends n o t o n ly upon
th * c a p a c ity o f th® pim p, b u t a ls o apoa th * h e ig h t to w hich th e liq u id is
lif t e d ,
S in e * c a p a c ity decreases as th e e a g le o f o p e ra tio n in creases m i
sine® work don© is a i l a t th e h artsen fcai and a g a in a t th e an g le o f bo
c a p a c ity , th e re aaagt be sea® opti®w» a a g le o f o p e r a t ic fo r e v e ry screw*
Shore seen* t o h© mo d iscu s sio n o f th is sayNftero la th® lit e r a t u r e *
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o th e r
-4 2
Angle of No
The Angle of No Capacity
Figure 16
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#4S»-
'reeossaesdatiwas eeaeeraiag optima* eagle of operation are*
Moskva (it)
m®
T y lm A (ft)
*T®
Krsfenk* ( IS )
80®
Probably these tiff#**1heesaas of mrJatleas la. th© dimensions of their
screws*
It trt.ll be shewn. later that the epfciMss eagle of operation is la
this vicinity*
7*
Boater of tabes
"She g m t t r the a«b#r of tubes th# greater the eepaoity per revela­
tion#
iaoh tab# added G-oatrlbutee leee tfeea the last one, however* end
the eost of construetioa and the spe-o* oeeupied by th© additional flights
soon offset the added rapes!iy*. ?h® ©phis** arra».g#aeat is difficult to
ereiaaii without detailed production costs but more than six tabes are
probably seldom justified*
leeoswesrtations in the literature arej
fylvmi ■(11)
8 tabes
M«y*1k#a (If)
„
.
.
fwta*®
® tubes
- 27Trtsaa
(13) » * _ r 5 _ T d
sin f
* ten « tea/3
, ntX
(34)
(55)
where
a « number o f tubes p erm issib le
/3 *■ an g le o f o p e ra tio n
Zirr teaaK * F ** p ite h o f th e f lig h t s
d
th ic k n e s s of all the in te rv e n in g flights'
ffce equetie&s 84 and 35 were derived m th® teals that & continuous sir
passageway he provided for self vesting*
Slace eigu&tlen 34 is a little
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cuafeerftom© i t aliouM be noted th a t i t m & be simplified by ro*rraag® »E t,»
. l £ £ a aA . « . | . d . s
S • mvunx • SJfl.
(gel
Y TT
where
S * separation between flight® or .P/at less th© tbiotees®
of tbs flights
f© ms# -fe e sbor# s fa a tio a # f i a t th® w in # o f V fvm m
as© e q u a tio n M
ie te r a ia e th # irdttiisaat m la # o f S.*
to
estisates fretaak©
m
the
g iv e ®
f o llo w in g
r u le s * f «
a
?®
$5
sad t h « a
a id l a preli»isaftry
s « w » fe a r in g
a. pitoll
eq u al to th# easing d ia m e te r* ft ©ore me th ir d the casing s is ® , and an
sagl* of
o p e r a t io n
of
S0 ° * .
b a s in g d is a s t e r
less than0.376 meters, Z tubes
Casing d iam eter .from 0.176 to £.336 meters, 4 tab#*
faring
d is a s t e r g r e a t e r
If tli,® screw is w a M
r a le s m e &
®*
thus 2 *556
e s te r s *
§ tulw e
la the mammr' r#e«®end®d by Bollasstn, fflrsiaak®**
s o t b e a d h e re d to *
■Sffluency
By v e lu n e tr ic e ffic ie n c y of an Archimedean s«r«*r i s m e m * the r a ti®
o f actual d e l le e ry t© the th e e r s tie a l..
ir©ta#t:«s, who seems to be th e -only
one o f th e e a r ly in v e s tig a to rs to a p p re c ia te th e im portance o f re n tin g *
speaks of -fix© necessity ©f assuring & eaitiaaoas sir passage t® iasare
that tbs screw carry liquid to th# full ©xbsnt of its capability (IS).
Soils#® (If)
fo u n d
that
s c re w *
properly
v e n te d
mad operated at slew speeds
g m very nearly 100 per cent voluBetrie efficiency*
On tests of his
So* 2 aerator th© four tube® gay® tOf.3 per sent,. 93*8 per cent, 166*6
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
,per cent*.
psr cen t or as average ©f 100*7 per c e n t.
This v a r ia ­
tio n is quit© evidently due to im o e a ra e y of © c s a tru c ti on and -consequent
error in
Ha© in te g ra te d c a p a c ity *
Overall e ffic ie n c y is the r a t io o f useful output to power input a t
the d r iv in g engine or motor*
Xrefeafce
(is ) reported
o v e ra ll e f fic ie n o le *
o f 88 -per cent end St per cent for Wooden d o s e d screws and a n tic ip a te d
higher m l see f o r stool «e»ws# Its designs wore hosed upon &a overall
efficiency o f §4 per ©safe*
%® tftte of Erofm ke*# paper in d ic a te s that hi®
eoreea s w » operated by etewa englse# rwefcg a t slower speeds than th#
in d u c tio n motor# used toisy*
W itt* ittduetiaa m otor trim worm gear sp«®€
reducer® a re practically eeaestl& X *
'M o d t» worm gear apeed « t o * w
©an
he d e s ir e d with a power tran sm issio n e ffic ie n c y as high as 97 per s ea t
prevl&ed th e reduction. Is not to o g r e a t.
$h# Ma1fe«Belt catalogue- indicate®
th a t 96 per eeu t e ffic ie n c y in a speed reducer having -a re d u c tio n ratio
o f 4 i/1 6 asd as low as 85 p e r eenfe -e ffic ie n c y a t a re d u c tio n r a t io o f
100 ( 1 5 ) *
With such high grade speed reducers and a a t ifr ie ilO B bearing® *
o v e ra ll e ffic ie n c ie s o f TO p er cent - 90 per e#»fear@ qpctte p o s s ib le *
9* Us# of the centrifugal field .
A p a te n t issu ed to Cagle-.aw l C agle ( 8 ).*
s * la te n t
d u ly 4, 1916 * mugpwted operating a closed Archimedean -screw ia a vertical
p o s itio n at c e n tr ifu g e i speeds*
v e r t ic a lly a short d is ta n c e *
la. th is m y liq u id is prestaaably l if t e d
.%» d ev ice 'would.seem to"develop’k in e tic
energy Is th e liq u id wl ich i® largely m e te d .a t th e discharge- end of th#
p»p*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Tbs**® is a way in whlefc ft eentnlfegal fore# field ca® he substituted
f o r a gravitational fere# field to ©perat® m Archimedean m r m
c c c w n tio n a l a w g r * '
ia th®
To do till® th# whole screw must he Srept on one- side
of the a x is of rotation. Sueh a device would have little value as a
-liquid pump, b u t it also pwsps fas alo n g with liquid a t ang les below the
minimum s e lf venting a n g le *
ia# eoKprsesors using this principle have
been developed by Be Bemer and associates (?) (8) • figure 1? shows th e
latest model (8)*
I t e m s ie t* of an Archimedean screw one ia c h in
d ia m e te r, eleven inches long, inellned at an a n g le of 8 degrees to the
a x is of rotation so as to pump m r m r y toward the rotational axis.
Inlet
and outlet gas connections a re colled into holies to allow for the neces­
s a ry flexing*
The screw does n o t turn on Its own axis b a t only wobbles
about the a x is of rotation of a 1750 n*p*»* Indttcti® motor*
One and
one th ir d pounds o f mercury s e ts as * series o f liq u id pistons to pump
th e r e fr ig e r a tin g g&e from th e low prsaaure side to the high pressure
side# Use mercury th e n run# bask through an orifice s m all enough t o
m ain ta in a supply o f a e re u ry a t the h ig h pressure side.
This d e v ic e
permits the Assign o f d o a e s tie refrigeratiea ays tones that ean be sealed
with out including the m otor is th e a aa lsd space*
■ ■
®*
Commercial Installations
1. 'Pumps
Butler (1 4 ) describes an Installation of Archimedean screw pumps o f
tremendous sis® for ir r ig a t io n purpose*#
Be says*
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
*« *.T h g la r g e s t, anfl also th e o o s t re c e n t, p » |« « f this
v»*y a n c ie n t type were set up at K a tatb eh , Egypt, so recently
a® 1861| tut in this ease, how ever, w ere socaa destined to be
replaced by the asore econom ical centrifugal pump* This
is®*a®« installation, consisted originally of ter. Archimedean
pu&ps, each s e t being designed to ra i« e 5 ,0 0 0 pralions
25 tons o f w a te r per revolution.,, which at 6 revolutions per
miasfc* equal® S,0 0 0 tons per hour a g a in s t & total head o f
12 f e e t , and rep res en ts 120 'W«H.3?* per screw. Bach o f these
* Iteston-A nderson? Archimedean pumps cor;sisted of a tub# 11 feet
is d ia ra e te r by 43 f e e t long, in c lin e d at an ang le o f 12° with
th e h o r is o n ta l, the tern sets being arranged parallel to one
a n o th e r, and to draw from* basin of 1-50 by 50 feet e«»ual©ati«g
d ir e c t ly with th e K ile *
Seme co n sid erab le d if f ic i- .lt y was soon experienced w ith the
w orking of those mammoth c o n triv a n c e s , owing in a great Treasure
to deflection caused by the immense weight of water e a rrie d in
the tubes frosa t h is , therefore, and other cause®, find in part
dwe; to t h e ir g en eral in e ffic ie n o y , seven o f the® were e v e n tu a lly
rep laced by vortical ’ f& rc o t* p w p e , which were the. largest and
f i r s t c e n trifu g a l pumps put down to be worked by a vertice1 shaft,
trouble again was fro ® the very onset experienced with the new
installation, due to the inadequate provision for the great
weight o f the im p e lle r , shaft, and fly w h e e l, totaling together
50 tons, this w e ig h t being earried by a water-cooled bearing with
forced lu b r ic a tio n , supported by the fixed shaft..#
Thus at this installation seven of the discarded screw pumps
were .replaced by five c e n trifu g a l pumps of the type referred t o ,
the oilier three Archimedean# being put into working order and re­
tained as a stand-by..,, the capacity of' each o f the F&rcot pumps
being equ el to a discharge of 77,000 gallons per m inute* against
& total head of ten feet at a speed of 52 revolution® per minute.,*
I t is apparent that the o»iy sense of inefficiency in -Archimedean
screws is l&ci: of proper voteting.
This eeaelu s im la supported in this
ease by th e 1m an g le o f o p e ra tio n , 1 8 *f alth o u g h the pitch tod number o f
tube* in each screw are not. state#.. It is probable feat if the screws
had been p ro p e rly vented-and the desif® strengthened to support the large
quantity of-water co n tain s# is fee screw th is in s t a lla t io n might have
been sere successful.
The In s t a lla t io n o f c e n trifu g a l pumps was evidently
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
* 49 -
b©tter engineered*. bat trouble* develsjwd s w a then*
S«i# that the res­
tating parts of the e«br I#ttg8»l pwtp* weighed SO toss*
load had to b«
This tremendous
by a sisgl# bearing,
Oelyer fi) dsserihea th# Arebiiaadean »er«w of the M r y And inderson
Company*
His 4©s#rijtie» follow#»
The p&tttat spiral or sore* pump is an apparatus bywhioh
liquids are. ®er«sr#d, up an inclined plate at & lo w velocity sad
without th® Intervention of pistons or valve® of any Mud.*. The
duty $ » r£ & m * & Is h ig h e r than, is possible f o r lew lifts, with
any ether arrangement of pwsjw,*
&p#riaseats have shorn that 8 B t of useful work eaa %# r®all*#d,
and M th e larger pumps, worked by compound c eadeiwisg engines,
water has been raised with less than 3 lbs* of coal per hors# power
of water lifted per hour. The construction of the pump is very
Simple, and consists of a sheet iron cylinder, down th# center of
which runs ft core. Between the two &r© wound three or more spiral
blades of a peculiar fens, made of sheet iron.* Si® ends of th#
cor© terwinat® in gudgeons of .suitable ©oastruettm, sad revolve
in f^ds®tals, the lower one is fired underwater, th# upper, cm®
on A bridge spasming th# delivery opening* The pimp is generally
drives by a spur or bevel wheel at the top attached to th# easing,
and geared into a pinion and shaft, which may b© driven in m y
e & m m ie n t manner, either by a portable or fixed engine* M
dibf&ragm rsak#s a water tight joint between the upper end of til#
pump and the delivery canal. The water level on the inlet side m y
rise and fall above th© iciniawn level without affecting th# #f<*
ficleney of th# p®ip, but on the delivery side the water ss«#t sot
rise above a certain height, nor can it fall much below it without
lota of effect, hence these pumps are not applicable whore there
is j£r#*t variation of level on the delivery side. Th# pumps ean be
art® of any. site to deliver from 1,500 gallon* to 38,990 gallons
per minute, but th# height for ##®h lift should not exceed 20 feet.
3h# patent spiral pumps deliver very nearly the .mm- par
revolution whatever speed they are ra t at, ken#© they m , k# accurate
meters. It I® only necessary to fix a counter on eaoh pump in
order to have a complete record of tfe# quantity of water raised
in any given t l m *
lb® p*ps do net require ffearging, «ed say be m
at very slow
speeds.
The d e s c rip tio n does »#t state what lo sses mre 1mlttded in th# 80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
per cent e ffic ie n c y *
ft® fu e l emevmpttee. fignr® represents very lew-
o v e ra ll e ffic ie n c y m would be expected of the la rg e »«tber of power m®*»
v e rs io n wit® involved.
The statattent that efficiency i® u n a ffe c te d by
ft® inlet w a te r le v e l i « not e x p la in e d *
The Mails*® m t e r level on the
inlet side 1® oresumhly th* highest p o in t on th® cor© a t ft® lower face
■sine#' c a p a c ity drop®' below this level*, ft# m t e r tight f r ic t io n disc at
t h * apper end of t h * p » f pewits ft® nairiUnsm lift to be r e a lis e d *
Th*
d e s ir a b ilit y o f th is armagesent depend# upon w hether ft® increased lift
o ffs e ts f t * f r ic t io n loss or net*
f*
A e ra to rs
Wmllwm built two a e ra to rs (If) consisting of Arohiaedean screw®
w ith s id e w a lls extending upward fr o a ft® flights and ta p e rin g outward
s lig h tly from the screw sods*
Those nested sidewalls* at the lowest point*
extended to just a little below ft® liquid le v e l, and ft® water that s p ille d
o f f was allowed to res down both fa « # » of sow* radial fins*
f t # f in #
war® attach ed to the top of the sidewall® and extending outward p erp e n d icu la r
to ft* screw axis*
The tteifhb of the s id e w a lls m # decreased r e g u la r ly
is o rd er th a t the liquid slug aight b e «3rlsao»d p ro g re s s iv e ly , th# fInal
s e c to r of f i n being supplied with the f in a l Incresmt of liquid*
The ju s t if ic a t io n fo r t h is elaborate arrangem ent is th a t a'liquid
s u b je c t to b a c te rio lo g ic a l o x id a tio n -can b * lifted a minimum d is ta n c e
and d is trib u te d a v e r a fix e d su rface that will retain th* bacteriological
fila in c o n ta c t wlft t h * air*
f t # first cost of this d evice is high*
b u t savings in space and In paping costs ©f large in s ta lla tio n s should
b * co n sid erab le*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
to llaaq a’ s final a e ra to r (IS) had the fallowing e h a ra e te r le ile a *
§ laches
18 l/S Inches
M am eter ©f core
Internal disuset e r of easing
lumber of flints
4
18 laches
P itc h o f f lig h t s
Initial b e i.^ .t of sidewall
16 f / 8
incites
tegl® of inol.irj.ation
The o r e ti c a l c a p a c ity a t 22 r * f* m *
44*6 g*p*3B*
T o ta l len g th of the core
7 fe e t
Length o f core covered by fins
t® fo eh e*
laaxirnaB w id th of fins
Si 1seh.ee
T o ta l f in a re a (both s id e s )
S78 aqaar# fe e t
IfS i|tw« feet
E f f m M m fin area (e s tia a to d )
V e n tin g —* V ent tubes at quarter turns for the first turn.
lotto aerators wore tested fo r rate o f oacygaa
tion o f fe rro u s iron, and r a te of water © o e lin g *
pond $ and eo-oliag tower
r a te o f esdda**
1 ecwparisoa w ith sp ray
t M t e a t a i th a t these a e ra to rs were
act ®ne«gh better to j u s t if y t h e ir greater f i r s t cost#
F ig u re 18 shews
Hollnmn* s final -a e ra to r*
I*
1*
Swwfery o f th e C h a ra c te ris tic s o f th e Arctoto^deaa Screw
OptSjnaa design
The design of *». Arehim & f& m strew passf for ©ptiRW -c o n d itio n * of
e p a ra ttim is based vspm a aafeiaftostory wethed of venting it*
I f . vesting
is. accomplished ia ta m a llv th® © K i M B a tta in a b le s a p w lty is redneed
msmmimb over * eerwr p ro p e rly vmtei, by sea® other weens*
totemseade~
t i« « » developed la « » lit e r a t u r e are presented in the following tablet
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-«s«
type of vesting
In te rs **,! s e lf v e s tin g
jgxtern&l ven t duet#
(iolXssm)
(SrohnJc©)
Speed o f o p e ra tio n
Core to easing rati©
P itc h
Angle of o p e ra tio n
lusher of tu b e *
■Overall e ffic ie n c y
Y o lu m etric e ffic ie n c y
43,/®
n
i » D/S
p * D
» SO
a
-
8 /S )
d
p * 1 . 0TD,
*
*
D /2
« SO0
, • 45®
0 *6 2 5 0 ,*
* » 600
» to 5
■60
loops
lOOfl
© b aracteristi® ® .
Archimedean s crews era 1cm lift h ig h e ffic ie n c y pimps of large c a p a c ity .
They deliver & s e rie s ©f slugs o f liq u id , one fo r each tub© per revolution*
They have a© mlves end a© fr ic tio n ® ! surfaces such as s tu ffin g bores*
They operate as equilibria® devices, and th© a&Xy losses are s kin f r ic t io n
and bearing Mid p m m r traasjaissiom losses*
Aerators ©*m be constructed
th a t w i l l d is tr ib u te liq u id u n ifo rm ly over r a d ia l f in e , and these operate
at very higjh o v e ra ll e ffic ie n c y *
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0 *$ ? ®
in ,/
uttsussmx s m m fw p s
km. T h e e re iie m l # « a id # ra ti© » ®
1* Wm&ismm th**g*tl**l ©apathy
It has already beast ©xplaiJwi that *11 attempts at f m m l tot®gr«fi©«
o f capacity for the g e n e ra l m m
head to tmasewdental ®f«ti©a* which
must be solved by trial « M error* thin is sot. tru e to th# special case
where to# sagl® of ©pwmiiaa i® ssrcf I*®,.* with the screw axis boriaontal*
M though to is is sot a prftetiool «**#, this ©af&city is to# twtxlww toward
which toe ftctoi eapealty tends &s th® eagle of ©psratios is deareaaed*
Kith reference te Pi '-v.ro ISt
r * r&dius of to# ©or#
8
X
e
/»
9
P
»
ra d iu s o f th e easing
m p o s itio n v a ria b le on the v e r t ic a l a x is
*
*>
•
»
p o s it! ob v a ria b le ©a to * screw a x is
rad iu s v e c to r ab o u t th # a a x is
ang le o f ro ta tio n , beginning a t the %a x is
p itc h o f the f l i g h t *
8 « separation between f l i n t s slang to® z tad.®
Sanations. fo r th© m rfm m a re *
Th®. plus# of to* » t » r line
* » r (rw etfeiig n lar ceo r& in fttes)
t a t stows#
/>#oa § * at
r *■ /%©© # |c y lin d r ic a l c o o rd in a te *)
(57)
fb e h e lix of. th e low er f l i g h t
( 38 )
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fb@ t o ll* : o f th e ttpp@r f l i g h t
a *
l i f t s
.
C s t)
fit# eyiiiwtrteai «#r#
/ •
r
(4 0 )
ff» cylindrical easing
/«
t
(4 1 )
The mximtun v®lmm o f liq u id s lu g I # g iw a 'by*
L „.(/,/,>]& ^aM* <tt)
f
/•/»•* f«-r
r«-#*s
,
,
»
!
{ V * a rc # •« ( f /r ijf & y ?
• 77S(S2 * r 2) - 2 i r 2 |
[ { / > > ) a rc «#e ( / / r ) J
( d /> ) /r
- r 2 } » Sr2 [ ( y » /r ) 2 a re see ( j> /t} - ^ y * / r ) 2« 1
•
2.
7fS (E 2 - r 2) * SR2 a re see ( f / r ) ♦ Sr2 / ( S / r ) 2 - 1
(4 3 )
llB -iataa s e lf v e n tin g suagl#
At h i#
an g le o f o p e ra tio n 4fe#r# t« a c ontinuoue a i r passageway open
th rew *#o n t th e screw* b u t a t low an g le o f o p e ra tio n th e liq u id slugs a re
con fined between a d ja c e n t f lig h t ® , and te n tin g » a s t be accom plished by
sons e th e r means*
An exp ressio n f o r the- a a g le a t -which t h is change occurs
would be w ary u s e fu l,
'l#f#s*ri»g. to F ig a re 20 s
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I
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£
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C
U
|C
\t
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-s t-
* radius of the core
* radius of th© msia g
* pitch
** separation between f lig h t ® alor»-~ th© serew a x is
* position variable of the vortical axis
* position variable on the screw axis
* angle of rotation beginning with the x axis
/3 * m in im m s e lf venting angle
C » Intercept constant for the equation off th* water lin e
r
E
P
S
*
2
#
The eq u atio n o f th© low er f l i g h t (s « b « :© rljii#i 1 ) Is *
277*
a
*1
W
w
She height of its trace
x
45 *f~ * 1
©a th® core is*
» r eo« ©
er
x ® r ©os JpTg.
T~ m
i
“
(45)
Biff«r#ntiating gives the slope o f this tree©.,
H | * » JL|pu sin |j~
( 4 i)
The equation of ihe water line (subscripted g) is*
a* « »
1
+
taa/3
c
When x * 0,. sg « P /i + S /g ,
to
0 « P /4
*
S/iS beeemse ©f symmetry*
* f
(4?)
x * (P /4 + S / i » * g ) t a n ^
D if f e r e n t ia t in g gives th® slop® o f th e
(4 8 )
water l i n e .
~jZL m • teaayQ
( 49)
At the overflow point ( a ) the coordinates are Identical so equating
4.8 and 40*
r cos
* * {$*/* + % /t » * ) ta n /3
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(SO)
<•!»§**
Also s t th e
point (a) the slopes are equal so © qaation 46 and 40*
(5 1 )
I t is aeeeeeary to fin d ^ and * fey .solving sisittlteneeusly equations 50
and 51.
th is arnst fee aeecssplishsd fey t r i a l . .
As a rough e s it u a t e the
fo llo w in g e x p re s s ly any fee used*
( 68)
f h ls r e s u l t from
the
that the overflew p o in t a is a t the
f e i n t a* end th e s e a lin g p a in t b
is « t b * *
So® Figure 20*
E ffe c t of. f lig h t thickness <aa c a p a c ity
S.
I t has te e n customary in the prior l i t e r a t u r e to n e g le c t the t h i c k of the flig h ts o f an Arohinedean screw when figuring th® c a p a c ity *
ness
I f th® screw i s large this dees sot in tro d u ce a p p re c ia b le error but in a
m a l l scree th e re
is a la rg e d iffe r e n c e e s p e c ia lly at low angles of -oper­
a t io n .
shows- th e c a p a c itie s a t v a rio u s angles o f operatic® fo p
F ig u re 21
single# dou ble, and trip le th read screws wbm the f l i g h t th ic kn ess
s n a il
is neglected.
Obviously a double th read screw offers a good. iraproveswmt
in c a p a c ity -over a single thread a t a l l u s e fu l an g les and a trip le thread
screw is even better*
ance
Figure 2 2 , however* sham what happens when a llo w ­
is mad® fo r the space ossified by th® flig h ts.. A double thread
screw is as. ijfiprovesnent over & s in g le thread throughout most of th# work­
in g
range# "tat a trip le th re a d screw is d efin itely in fe rio r to a double
th read
except a t meccacsloallj" hig b angles.
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Form E 5
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ft
a
m
*
1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Form E 5
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ift:
3^
£1
i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
«*S2*»
I t has a lre a d y been p o in ted « t that th e re w » t b# «o optimum. ang le
o f opsration a t which Hi© w ate r
ptaap*
hors# pevrer is a ss®ail®«« for any give®
this mxiwua work output is e b tftis fth l* as the h i # i point is the
curve o f the product of ©apacity and d e liv e r y head.
f o r p r a c tic a l purposes, p ro p o rtio n a l to th #
t io n since the seres? length
is a e & is ta & t*
Th© delivery head i©#
sis® of the angle o f opera­
the capacity at th# various
:#sgl## K tw t be gotten by <sm of the graphical o r n w a e ric a l » tb o d e pre­
viously d e s c rib e d ,
Ihe deteralsation of the ©ptfaraa an g le o f operati® as outlined above
is a la b o rio u s procedure,
la e®m©oti«s with the desip. of a ehei&Ical
p ro p o rtio n in g d e v ic e to b« described later, a fm such curves were 'marked
o u t to f in d th# optimum a n g le ,
figures f® and 24 show hew the ang le o f
operation, a f fe c ts the o utput of screws designed for optimum perform ance,
fig u r e 23 gives th e e q u iv a le n t output of s in g le , dou ble, and t r i p l e th re a d
screws when th e f l i g h t thickness is neglected* Sine# th # flight thickness
i s n o t n e g lig ib le , Figure 24 was prepared for s in g le , double., and. triple
th read screws o f the same sis# except that the flight thickness is allow ed
fo r*
These curves indicate that the eptlmwa eagle o f operatics lie s
between 3G and Si degrees, and longer pitch screws would have s l ig h t l y
lo w e r optimum angles#
In gen eral
the ©ftlsa® ang le o f o p e ra tio n probably
lies between 25 and 45 degrees la all but a few cases*
5#
Free body analysis of a l i q u i d .slug
figure 26 shows three view# of a liquid .slag in an Arohiaedeaa seres*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Form E 5
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I
S
fi
Hi
liiiitlin
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
fo rm E 5
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Sii
i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
These show t h a t th® mmtvr of gravity of the ii<pM s la g is not directly
below ft© axis h u t to mm sM« o f i t .
This system c o n s tit u te * a. couple
testing to tu r n t h * s#r*>* backward and eapt y a l l the liq u id out ©f i t *
As f t # s c r w tu r n s , th© l i f u M
flows doww&rA seeking i t ® rnn l e v e l , and
t h * coupl© remain® s u b s ta n tia lly e o a a ta n t u n t i l th e l l f u i d is discharged.
This is a dem onstration t h a t th # A re h im & e m »© re* is am e q u ilib riu m
d e v ic e »
I t move® s lo w ly ©sough so th a t In t e r n a l f r i c t i o n is n e g lig ib le ,
and th e o v e r a ll pumping e f fic ie n c y i s H a lt e d only by th© loss#® in th®
hearing® and d r iv e u n it e *
B. l&Kperlmstal Data
1*
Apparatus
The Archimedean screw used in the pwap tests m s built on a standard
2 -in e h black iron pip© as a e a r # *
i l i , ’ us were made up f r e a doughnut
shaped discs of mm sixteenth inch m i M steel plate, cut and welded t o ­
g eth er i n continuous spirals.
These were stretc h ed over the cor© and
brazed on ftro u fd ie u t th© entire length.
c o n s tru c tio n .
Figure 26 show® th # screw under
The casing consisted o f two lengtha of s to re pip® rolled
and seamed th© correct diameter for a snug fit*
over ft© f l l # t ®
These lengths were d riv e n
one from each end, and the Joists were soldered s h u t.
I n o rd er to sml -any leaks between th e f l i g h t s and the casing th® screw
was f i l l e d with a h o t water s o lu tio n o f »di»tor sealing expound,
Then
w h it# p a in t m s diluted and poured down th® flights of the screw .
A d is ­
charge U p m s soldered over the 'upper end ©f th© casing to prevent th®
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
co n s tru c tio n
under
A n t o i x m screw
m*
Figure
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
dlacliarga from, yeaning d®m the e a tin g *
Measured dissensions and e»le«~
latasMl p .r« s ® te rs of th e eospletedi s®r#wr ay® as fo llo w s t
Casing d ia ia e te r
Core d la a a te r
P itc h
Ho. o f tubes
S e paration between f l i g h t #
Angle o f m c a p a c ity
Mini®xaa s e l f v e s tin g ang le
C ap acity p er re v o lu tio n
a t tS®
a t 60°
* t 43®
a t 30®
a t 16®
a t 0®
4 ,7 2 in«h»#
2*34 inches
2.875 inches
2
1.229 inches
ff.S ®
42. S®
.
0 .0 4 cab le Inches
3 .9
sab le inches
11*8 e«M© inefeee
1 8 .S cubic inches
10*3 cubic laches
24*0' cubic inches
Vent tubes 8/S t»«h pipes at q u a rte r turns for th® first
two tu rn s * ■
t h is screw was a&tmted i» a e r& tle o f h a lf inch pipe pivoted a t the bottom
m tb© angle of in c lin a t io n ® « M be v a rie d *
A q u a rte r hers© power motor
w ith a speed o f 1S00 r.,p*m * was d ir e c tly eoaneeted to a worm gear speed
reducer w ith a r a t i o o f S 4-4*
th© c ra d le .
f il ls d riv e u n it was mounted crosswise on
th e scree m e turned by a one h a lf inch p itc h r o lle r chain
o p e ra tin g on two sprockets*
tee o f these was a 40 to o th s p lit sprocket
m th® screw, and th e other was one o f n ix iBterehaageabl® sprockets m
th e speed, reducer ,
this, .gave a choice o f 2 0 *8 * 25., 2 9 .1 , 3.3*8,, 40,. or
SO r .p .!8 . f o r th e screw pump, fig u re 27 shows th® c ra d le and d riv e
arrangem ent*
2.
Procedure
The feed tank, for the pump was arranged with as inverted siphon
overflew ., and the task was kept overflowing a little is o rd e r to keep the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figaro
2?#
Brlv®
and
or&dle
of
propertlo&er
p tn f*
«6 9 *
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
submergence a t any d e s ire d level.
W ith th® an g le a d ju s te d ,
th# discharge
was caught in a ta re d pail f o r a coasted amber of revolutions and weighed,
Th® r,p *m . was
vsry reliable is#©®!#® th#
th® d riv e was p o s itiv e ,.
load on th® motor was low and
Accurate aMMumre&enfc o f th e angle o f o p e ra tio n
from the
was accomplished by suspending & flu s h l i n e
screw in to the
water*
*®a«*arwa«at o f th® le s g iti o f th® plumb lia ® to the w a te r surf*®® and
the len g th o f Hi® water eu rfa® * from the screw to th # plumb lin e gave
the tangent o f th e te g l# o f ® f» ra ti« o *.
S*
ttqjs>ria®ntal.. r e s u lts
& e performance
Table I *
of the above
as
a
water pusf is tabulated in
Theoretical capacities were obtained fros th®. curve of
Submergence means th®
ly in g in th® lower
wetted
C apacity
28,
Figure
©f the most nearly vertical diameter
f r a c tio n
fas® of the screw*
0,
1*
screw
Ms®u»«i«m
of lesult®
characteristic
The data o f Table
I have been plotted on Figure 28* and the
curve
was drawn w ith reference
to the experimental points as well
c a lc u la te d p o in ts . -When
the curve was drawn only through the calculated
a® th®
points* volumetric efficiencies as high as 108 per ®#nt war# noted., With
th e present curve
the volwsetrle ®fflei®ney
q u a te ly submerged t e s t s varied
6 2*8 degrees wfeer® the
ffpa 97 per
of
properly vented end ad®*-
cent to
102 per cent except
at
S-6 per cent figsr® was due t@ serious leakage down
the screw casing*
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Form E S
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- u t t .
<3)Q ;Q
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» f 5—'
2*
Befe&vlor o f animated .sorwrg
When th e fe e d ta n k a t th e lower t n i o f ifee pomp was f u l l , performance
was e r r a t ic a t angles 'balm tfea mStfiwas s a l f v e a tia g a n g le *
I t was tra c e d
t o th e f a c t t h a t t h i a t!complete” sateergeaee drowned the ven t ta k e s *
lo w e rin g th e submergence t o a f e i n t between 75 and 10# p er cent produced
r e l ia b le r e s a lts at- f u l l c a p a c ity *
ft® t e s t s from So* §8 to So* 88 show that th e capacity is u n a ffe c te d
by speeds up to SO r*p*»* when th e pump is properly vested »
fhe tests
fro ® B e* 67 to !©*-- 78 m i 1®* 82 ted Be* S3 sheer th a t SO p e r e s e t submorgens* is better than eemplste mhmrgmmm for ®a unvested screw*
Approxim ately 76 per e a s t submergence is meeessary for f u l l capacity with
this screw*
In numerous eases when Hi® screw was unvested the capacity
w»® observed r is in g to a w m i m m end then dropping off again*
fh e series
of te s ts from Be* 19 to So* 28* So* If to 1©* 29* mi. Io* 48 to 1©* ®4
show this trend* In other eases the ehenge m
rapid enough to b® noticeable
w ith o u t measurement.
Bom o f the data presented by S©ll«iR» (It) in Table ? o f h is th e s is
in d ic a te d tfcai capao i t i e s in. excess o f th e t h e o r e t ic a l could be r e a lis e d
by proper r e g u la tio n o f th e « l»erg e» @ » o f an unvented Archimedean screw*.
I t Is tru e -teat an unwanted screw picks up more than a vented screw when
■fee submergence is w r y low* b u t regardless of the submergence an undented
screw cannot deliver as n»eh as a vented screw which is adequately sub­
merged*
T o lu m strtc efficiencies la excess of 100 per sent are therefore
m eaningless.
Furtli#r«ar©, the c a p a c ity of a properly vented* adequately
submerged s ©new o p e ra tin g a t low speed ©tenet exceed the theoretical
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*#yih*
c a p a c ity *
The f a c t t h a t some .of lolltam*® results do exceed th e t h e e r e t ie e i'':-
ia&leabes m error I n e a le u l& t t m *
A c a r e fu l eM«fe of th e integration for
the angle 53° 4S* disclo sed a© error, ©xoept that the rest passages'- w*#b
have bm m la a g e r th a a his diagram in d ic a te d ©r the e a te r would spill o a t ,
( l e e Figure ES»)
As e x te n s io n of Test® o f the same s is # to a point above-
the water lime would provide acre then the indi cated capacity*
Bespit® the above discussion there a re indications that tit® c a lc u la ­
t io n © f the capacity o f an Ar©M»i«a» screw ®&y he as saaefa as 10 per east
is error*
In an e ffo rts t o aeeount for this the various g ra p h ic a l and
num erical methods already mentioaed m m eaapared*
.is e x c e lle n t agreement ^vrlthia 1 per cen t) *
The results were a l l
A f m refinements* such as
allowing f o r the thickness o f flight®, h u m been outlined above? b u t th e
p r in c ip a l soar®® o f error s«®»s to 11© in in a c c u ra c ie s of c o n s tru c tle a *
th e eew w wfelek was b u i l t and te s te d for use ms a s h e e te e l p ro p o rtia n e r
had v a r ia tio n s in the pitch of the flights msomting to on© fo u rth inch*
t h is happened despite e.etmiimmhl® oar# la its m a s t m & M m *
At h i #
angles of o p e ra tio n this variation can cause a surprisingly large v a r l a *
tic a i to capacity*
That laaecuracy of eosstruetiO B is a f a ©tor in building
large sewnrs as well as s w e ll ones is show, by the fact that the four
tithes of the screw vsed as as a e r a to r varied fros PS*5 per cent to 107.3
per e ea t of the calculated capacity*........ .
S.
g fflc ls & e y mad ooaveoleaee
The overall efficiency of Archimedean s crew installstioa® ha® heea
re p o rted a® 84 per ce n t (IS)*
The r e m r n for this has been considered
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r .
*•
Q?2 r i -
fQti
C°miM o Wner
UC,ion P'0hlbit
* '" ’<>« Pem,
rniission
'
*•78*
faro© the s tan d p o in t o f th e equilibrium o f forces on a liq u id slug.*
ffe®
quest!* naturally arises a# to h e r It happen# that eueh &» e f f i c i e n t
prcsEp faa® gradually been supplanted by the centrifugal pump*
A p p aren tly
it has Men mom a miter of emwenieace than of efficiency*
la early
ttsn the BOtiw power was men ®r animal#! later it m s the stem engine*
Both o f these were inherently slow i n speed, and slow speed p a p worm
n a t u r a lly .required* Witt, modern electric motors o f th® indue tie ® type
speed* low er than 1750 r*p«su are .®*e#fti«ial*.
To operate a slow speed
pump from aa in d u c tio n motor c onslderabie speed red u c tio n is necessary*
I f a s in g ! * wait is d e s ire d , « warn f® « * w a it is test.
But good speed
reducers a re exp ensive , and poor ones are inefficient*
Therefore, despite
the c u r ta ile d e f f ic ie n c y , eezm m ieuee usually dictates th® use o f a
centrifugal pump directly eesses-ted to an induction m otor*
Applications
©f the Arofcto&deaa screw pomp a r e likely t© he most useful where alow
speed power is a v a ila b le .
B.
Summary o f the Archimedean Screw Psasp
la additions to th e © h a r u e te r is tie * s m t i <med in the literature and
summarized i a the preceding s e c tio n the fallowing eonsMerati caas are
p resented.
. I*- The optimom angle of ©p&retlom of Arcltiwdesa screw pumps lies
■between 25 and 45 d eg re es.
The angles between SO to 35 degrees are best
for screws designed for optimum capacity*
g*
Abets the minimum self went lag; angle which is given approximately
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w'T’®*"-
by .aare •tea
3.
a# special f r w i t l m
is m .m m m ry for vent tug tb® screw.
l a oalettlatiag th e capacity of am IrAiwifsa screw* p a r t ic u la r ly
a sm all ©a#*, allow ance stamM be med* for tbs span® occupied by the flights*
4*
l a e<»etam@tiag s. sow*’ m m t m l atteatios should b® paid to
getting the p itc h a a lf e r » if th e c a p a c ity is to match th e design*
S*
f e a t tub®# should be larg o and mwmtmxo enough to carry th e sen t
gas w ith o u t pressure less* m i the subaorgene® isust not be so great that
all the ven t tubes are submerged*
6.
Tim © ester ©f g r a v it y o f & lisjtiid slug is an .Archimedean seres
i s os th® lew side of the screw axis* ant tfc@. screw fu n ctio n s as m
e q u ilib riu m fieri©#.*
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••Hew
If*
AHSJtflOJ®
A# Hater feeling m a Rotating Disc
1«
Apparatus
Hhea th e eagle o f operati©a or th e speed of aa Archimedean a e r a to r
I s v a r ie d , the w a te r disehftrg# r#.t@ ©has go®.*
It was d e s ira b le t© be able
t© sake these eha»gs® without a£f««hl»g the water feed rate*
f o r t h is purpose a « lre u l& ? d is e braced ©a the basic to present it®
springing, m s ®eust®d m a s h a ft terning is a thrust bearing*
t h is bear­
in g m s fastened t o the table with a hinge in order that the angle of
o p e ra tio n might be mried,
fh® r o t a t in g dise m s d riv e n wit*, a sixth
horse fwwer motor mounted near mm edge*
Speed red u ctio n was accomplished
with a f r i c t i o n drive betmeea th e lower side o f the disc rear the edge
and a piece o f rubber tubing slipped over the «ad of the motor shaft*
W ater was supplied to a point close to th e ©eater o f the disc from a siphon
which to turn drew from a steam heated tank* later tem perature# were
measured w ith thermometers placed under the siphon discharge and in a
shallow catch pen tes»diat«ly under the low er edge o f tti® rotating d is c .
Wet and dry bulb ttermoiaeters were mounted in f r o n t of a small e l e c t r i c
fa n *
% is fa n was also used for in s r# a # i» g the a i r velocity on some ©f
the te s t® .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tm .te a iy s is o f c o o lin g r a te
Evaporative u » te r cooling Involves- v& pnrlsfttlon as w a ll as d ir e c t
tr a n s fe r o f b e a t between » t « r and *ir»
ftsa a rate eq\:atior. must be
w r itte n f o r each process*
L et
V « weight of water *»f©ri*®4 (pounds)
9 * tim e (hours)
Q • quantity of sensible heat (B*f*®*)
A * a re a o f c o n ta c t between a i r a»J w ate r (square f e e t )
T ■* water teasperatttre ( eF«)
t * air t®»p#mteir# ( ° F . )
m saturation humidity at water temperature (pounds per pound)
I « air haaidity (pounds p e r found)
V * water feed rate (pounds per hour)
X • la t e n t heat of v a p o riz a tio n (B .T ,tJ . per pound)
h * sensible km% trmeter coefficient for the air fils
( i * f »tJ* per hour per sqt* are fo o t per ° F . )
k*g ■» mass t r a n s f e r coefficient for the air flla (pounds per hour
p er square fo o t)
s * humid h e a t of waist air
per pound per °?*)
Badger and MeCabo ( l ) give m boat t r a n s f e r rate equation 134, p * 271*
| | * hA(T - t )
(53)
and also a m m transfer rat# equation 116, p>* t§3*
H | **
M b# ~ H)
The rat® of heat renew al by s a p e rls a tio n la
-1 )
(5 4 )
The total ra t® at which water I s cooled i» Wdf sincethe heat capacity
©f w ate r is u n ity *
This is equal to the total rat# at which the air re­
mores h e a tj i«©«, the sum of eq u atio n S3 and 5.4*
» f * hA(T - t)
♦ k% A A
(|^ - 1)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(58)
* S f*
Fo r i t t i f v»p o r b/k*Q * s aeeording to Badge? and MeCabe, p , 264 ( S ) *
k*# • .V®
(56)
Combining equ ation 55 w ith equation if give®.
WAY • hA [(f - t) *
>/»(.% » H)]
(57)
Tills can be integrated if fesmaing the Arivtag fo rc e * ay® constant and
equal to their average v a lu e s * •
W A f * hk J~(f - t ) 6Te^+
V « (H - E )av g J
(6 8 )
i ‘ }E ” j
(s 8 )
or
" ‘
This formula gives th e v a lu e of th e heat
transfer coefficient. The m s s
tr a n s fe r coefficient is related to the heat tra n s fe r c o e f f ic ie n t by
equation 56,
These coefficients are net n e c e s s a rily constant •
w ith the e ig h t te n th s power ©f the air velocity*
They vary
Should the air reach
s a tu ra tio n d u rin g the process, reeoadsnsatioB of water vapor occurs rais­
ing th e air tem perature5 and ataoyaally lew c o e ffic ie n ts w i l l result*
8,
Analysis; of c o o lin g ..rungs
The preceding analysis gives s® in fo rm a tio n about what happens if
the ang le of operation, th e speed, or the si.se of the rotating disc were
changed*
It appears frost eq u atio n 66 that the## param eters have no e f f e c t
except to change the area of contest*
th e cooling rang#*
fa s ts showed th a t they do affect
The following a n a ly s is was wort®# out t o shew the
effect of these v a ria b le s *
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Choose* as a b a s is , ©ne pound ©f w ater,, sad rearrang e equation ®S
th u a t
4f • hk ( f •
t)d ©
+ lc*
A
>(% - S)d»
(60)
S u b s titu tin g equ&tien §6 in to #0 and in te g r a tin g givess
A t * h m [(f * t)w #
* A/«(i • h ) ^ , ]
(ei)
the eosliag rang© A f 4# here- proj^tioaal't® A* th e surface & r m
o f co n tac t between earn petiM of water ted th e air and also to the. tie®
o f contact 0 .
The obvious way to g e t & large cooling rang© is to spread
the w ater as t h in ly as possible and keep i t this way as long as possible,
totatiag discs end Areh &»&<£*«& aerator# e re ideal for this,
fh e for©.# of
gravity acting m the water filw in a fixed direction and th e centrifugal
fe r e e d a tin g radially eonhiso to predwe® e» excellent spreading: action,
With such, f is® spreading actios It Is possible to reduce the w a te r feed
r a t e until the cooled water reaches th e w et bulb temperature,
It probably
Is not e e e n e a ie a l to eoo l water this far,, but th e arrengenent is q u ite
f le x ib l e *
la order to sake use of equation 81, A and ® west be related t®
Hseftsurabl© quantities*
Ckxe m y o f doing t h ie is to relate them to the
average thickness of the rnter ftla*
Let
/>*»■ ieaslty of water (pounds per cubic foot)
d * aweraee f i l m thickness ( f e e t )
%
Then
ft -9Bf
The analysts of the k©M~np tisae 0 is -.sore difficult.
Inferring t©
Figure IQ let
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
* 84 **
* * angle o f operation of fche axis o f th e disc (degree®)
/ * angle o f rotation beginning atth e low est p o in t
o f th e d is c (degrees)
x « r a d i a l v a r ia b le ( f e e t )
g * acceleration of gravity (feet per second^)
cu * rotational velocity (radian® per second)
/ * * viscosity of w a te r (pounds per foot per second)
§ »
(hours)
k *
a constant ©f proportionality
1 * radius of th e disc (feet)
r * radius o f the hub (feet)
The force of g r a v it y acting m any eleaw nt of water on the fa c e of the
disc is fSxdx&ff g. cosD( , and it aetw toward the low side of the disc as
shown la Figure SO,
everywhere radially*
the centrifugal feres.is /> <fx d x d ^ xtu^, and It acts
the re e is ta a e e to flow is viscous friction*
Us®
forces are resolved ia tfee ©ire«f«rea%'i*i direction tims*
K « .« U W
She c irc u B ifo ren tia 1 velocity 1®*
^
.
{gsj
th e cire u ffife re a t ia1 jsotim e o n trih u ts s nothing t o the fioM**wj» tiw e bat is
resp o n sib le for th e spreading aeti w . that is aeeessary for wetting th e
satire surface*
Stoss force* are resolved in th e r a d ia l d ir e c t io n thus t
/o S x & m p (xtJ * g »©« a.cos
ix&dl |||
ix
* ~J££$2L£
the r a d ia l v e lo c it y l a *
dx
^
n
{x o 3E * g cos*, cos $
th e heldwup t in e i s *
»E
f
»B
d#, i 4
/*«
f
Jr
_ ------------ £ ---------------( " * * g oooKoos / )
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(64)
I
-8 5 -
g COS 01
An^i/sic of 1iquiu Uiu_u-up on u RotafciRg lit.c
figure 30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Uhen tli® average tfeletoess of th e t i m i n g f il m o f -ra te r is 1mm& 9 can
he saieulated fro® eq u a tio n ®S *R i A f r e s eq u atio n 62*
Bqustien '61 earn
than be nsed Sa eoraparlsce *i J- equation Si to establish th e w & lid ity ©f
1 iiis analysis*
4* fepertawttfel results
Tii© ’
tost results of the 'eater cooling performs©© of the rotating
dine w e totoletod i» fable 11*
She ©©efficients la this table were
e a le u la te d by the eoelSjig rate method using equations 59 and 56*
The
arltoaetie swan water te a ^ ra to a re m s need is the m lm ilm fA m of both
tem perature difference and Humidity difference*
As a matter of eon**
-real©nee the feed water temperature was fcwfrfc at If2® P* is so©t of the
tests except l a tests Is* 40 to So* # 3 inclusive* where the average water
temperature was miataiaed m m m l j *# possible at 122° F *
The area of
the disc was 4*0 square feet* «s? th e rain# of h/% used was 4*260*
All
the tests were eontinued for a t least twenty minutes to insure equilibrium
condition®*
Bie c o e ffic ie n ts obtained ta.Sfcble 11 were not c o n s ta n t*
•v a ria tio n occurred when to# w a te r ra t© m s changed*
the principal
Figaros SI* 32* ©ad
33 show th e -yartatim in th e heat transfer coefficient as th e w a te r r a te
-varied*. F ig u re Si is for the- an g le Tl# 64* j Figaro 31 is for 63® 51’ 5
and F ig u re II i s f o r 46° 3#*,
th e ecNtffieimte drop off rapidly at low
w a te r r a te s * t h is m s quite uaexpeeted, and the feet that tfeey do appears
t o in d ic a te seme shortoomtog o f th e toe ©ret leal analysts*
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
*87*
ti
le w s !* * a# W ater §9»ttm « * • » * m t i m Mwa
M»0 m mf
M
§**■
fm t m*
t
f in d o f K r a ft
fe a p e ra tu re e * F*
Water I n l e t ( f i )
Water O u tle t (fo >
A re. Water (7 )
A ir * Kry Bolb ( t )
M r * Wet Bulb
S a t*a . B o a id liy ( % )
A i r Hum idity (ft)
{B» - «>
V*<H w - 1 )
(7 - t )
■}:
f:
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41
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85.8s
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1 0 .8 7 :
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is # .# :
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18 2 5 .:
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s
2 2 1 0 .:
5 2 6 .:
15 8 5 0 .:
8 .3 6 :
3 2 .8 :
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43
Fan
1 9 9 .8
1 2 2 .0
7 6 .1
# 4 .4
.0861
.0 1 0 4
.0757
3 8 4 .0
4 5 .9
3 5 9 .9
1S12.
6 3 .0
fat.
184.
11600.
4 .8 9
2 4 .6
T ab le I I
(O o a t.}
R e s u lts o f Water- C ooling on a R o ta tin g m s s
Angle o f O peration 71° 54*
f e e t So.
Kind o f D r a ft
Temperatures ° F .
W ater I n l e t (T )
W ater O u tle t p r )
A w . Water (T ) °
M r , Dry B ulb f t )
M r , Wet mOM
S a t*n . S ttB ld ity ( H j
A i r H um idity (H)
(a - ®
> /i( H • H)
(T » f )
(T - t ) * y a { % -H )
A f t i v t ) * v « ( a « -K)]
( % - T# }
Water l a t e
eo. per min.
Itea* p a r b r . (wj
WCfi. - ToJ
* v
*■
e
.
s
i
•
i
t
s
i
i
:
:
:
5
1
t
I
I*
**
S.
:
:
44
Fan
1 2 2 .0
106.2
1 1 4 .1
7 3 .4
6 5 .3
.0669
.0113
.0356
2 3 8 .0
4 0 .7
2 7 8 .7
1 , 5o7.
1 5 .8
4 ,0 4 0 .
1 ,0 3 9 .
1 6 ,4 0 0 .
1 2 .1
4 6 .3
»
s
*
45
t n a tu r a l t
J.
■5
:
lit.#
1
1 1 3 .0 *
:
1 1 7 .3 :
:
7 3 .4 s
s
6 5 .3 s
i
i
.0750 %
••
.O H S *•
.0637 s
*
tft.f
:
t
: .
4 4 .1 s
s ■ 3 1 6 .# s
1 ,5 5 2 . ' i
-.i
9 .0
s
:
3
4 ,0 4 0 .
:
3
1 ,0 3 9 .
s
1
9 ,3 5 0 ,
t
t
6 .0 2 3
?
r
S»«* 2
46
fa n
urn.®
108.2
128.X
7 3 .4
57*8
.0 6 3 6
.0062
.0674
2 4 3 .6
3 8 .7
2 8 4 .3
1 ,3 9 3 .
1 9 .8
3 ,4 8 0 .
888
.
1 6 ,2 7 0 .
1 1 .6 9
48.®
1
47
2 S a tu r a l
1
1 2 2 .0
2
1 1 1 .8
S
*
1 1 6 .6
:
7 3 .4
5 f.®
t
*
•fw
.0072
2
.0688
S
2 8 1 ,6
t
4 3 .2
<
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3 24 .8
a
1 ,5 9 2 .
s
1 0 ,8
:
2
3 ,3 8 0 .
I
797.
s
8 ,6 1 0 .
s
s
8 .4 0
*
2 0 .8
*
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T e b le I I
(C o a t.)
R e su lts o f l a t e r Cooling on a i t b s t l a g ©tee
Angle e f O p eratio n .91® 84*
$a«t S *
M a d o f D r a ft
Temperatures
*
W ater I n l e t (T^)
W ater O u tle t ( To)
A te , W ater (T)
A i r , S *y Bulb ( t )
A i r , l e t Bulb
S a t* n . H u m idity (H )
A i r H um idity (E)
f c
a i Hi
(T ~ t)
(T - t ) ♦ V a (H Vi •• H) n
* 0 » “*3 + V®Tfi - H j
{T, -T 0 )
w
W ater Bate
oa. p e r ffiia.
lb s , p e r h r , | l )
« { T i - To)
h
k*
a
t
J
t
:
5
f
:
1
S
s
s
;
t
*■*
«
A
*
s
s
*
s
48
fe n
122.0
107 .6
1 14 .8
7 4 .3
61 .7
.0686
.0090
.0598
8 5 6 .1
4 0 .5
896.6
1 ,4 5 4 .
14*4
6 ,0 8 0 .
1 ,4 3 6 .
2 0 ,6 8 0 .
14.88
-54* f
1
49
*
t la tr n a l *
*
*
%
1
2
2
.0
s
s
1 1 3 .9 s
:
1 1 7 .9 *
*
7 4 .3 s
:
6
1 .7 t
S'
.0759 i
s:
.0 0 9 0 «
f
.0669 :
1« M .8 t
4 3 .6 . *
s
338*1 t
4.
S' / I , 6 1 7 . s
8 .1 *.
s
s
6 ,0 8 0 .
s.
i
1 ,4 3 6 . t
t
t ll,« iO . s
s • 7 .2 0 s
8 7 .7 s
S
«
*
*
50
Fan
*
*
.
51
ia tu rs l
1 2 8 .0
9 0 *9
1 0 6 .3
7 5 .2
6 2 .1
.0585
.009©
.0435
1 8 6 .8
1 1 ,1
a t,i
1 ,0 6 4 .
3 1 .5
$
s
1 2 2 .0
ft.f
1 1 0 .7
7 5 .2
6 2 .6
.0602
.0092
.0510
2 1 8 .3
1 ,2 0 0 .
883.
8 ,9 1 0 .
8 .3 7
S f.I
i
:
I
;
s
:
I
s
s.
S
$
s
s
s
s
;
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ma
2 3 4 .0
1 ,2 4 4 .
2 2 .3
1 ,1 4 0 .
B it.
6 ,0 6 0 .
4 .8 7
1 8 .7
Form E-5
-9 7 -
1
-a
m
i
i mHLa-j;
Heat.jransfbr'Ca
i* I i
i;l? m 3i j
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
fo rm E 5
-9 8 -
s
::
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Form E 5
j!:-
^l\v..7Z
la' a f l a
r
I:
g3
i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
*•1 0 0 *
Figures. 31* 32* and S3 alios th e ass.gaitM « o f the change i n the h e a t
The upper
tr a n s fe r coefficient when the air v w le e ity was in creased ,
curves were taken when the n a tu r a l esnvwetien m i supplemented by the draft
from ea e l e e t r l e fan blow ing d i r e c t l y a c re s * the dise*
the a n a ly s is of c o a lin g range require# s»wr#iw»t of the average
thickness of the flowing film ® f w a te r,
There are several way® in which
this could have been done* tat after some d is a p p o in tin g trials the fol­
low ing method was chosen,
A four foot round shallow pan was supported on
a s n a il platters sod© aafter the rotating disc to 'weigh th e r w a -o f f ,
d is c was set 'la » M « # and the r a t # of flour m # measured.
The
This was
accomplished by catc h in g the feed water is another c o n ta in e r for a measured
length of tta© « M transferring the w a te r to a la rg e graduate to -b e
measured,
Since th e scale esuM .act b# balanced and th e water feed shut
o f f e is m lta n e e a s ly * the tim e between these two occurrences wm mmmm&
with a stopwatch*
At th e m& o f th re e ©r four minutes the r u n - o f f m s
complete, and the final w eighing was made,
The SEtsunt ©f water accumulated
before th e feed was out off m s c a lc u la te d from the feed rate and the
elapsed time end sub tracted frees the t o t a l .
hold-up,
This gave the instantaneous
The average film th ic k n e s s was. determ ined by dividing the hold­
up by the density o f water md by th e area of the d i s c ,
A amber o f such
tests were made a t different fmi. rates, see Table III*. The film th ic k ­
ness wsasurwaents have been c o rre la te d w ith w a te r feed rate is Figure. §4*
B e sp it# the mm. of mme&mmnb the d ata scatter badly saUcing th e curve
difficult to locate closely,
In order to simplify calculation of the coefficients by the cooling
range method «fuati<as #2 end 6§ were combined and simplified thus*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
*•1 0 1 **
fable 1X1
L iq u id Kold-up of t& e B o ir.tia g Disc
Water Katsy*
:
L _ *
t
:
?iae u iCC’’r 'u :-•*
bojLf
■ .
t 11 <r
: fo ia h t
: ve ln - t : Volvic ;'!v 1 r ' t , ea
%.......«*.&*.....».s a .tl3 t«
835*
75.
340*
135.
<60.
14.4 *
70.
932.
3X0,
310.
585*
870,
'5^5.
540.
6 .2 5,
655.
626,
750.
540.
745*
475*
-365.
71 0.
I ii? i?
tO .C :?»* 39.6?
*0.
tC* i, 30s
96,5s
56. 8;
t O . . i 5;
9 6.5*
; *i . I / 1
*4 *
; u . j'6 v » i
4 3 *6 ;
:0 .6 3 6 * 29.UO*
t0.250 s 11*.5?
s0.225 ; 1 0 2 .0 ;
;0 .3 3 1 s 150,5s
.*0.681 ? 309.0s
s0.4j.25; 378,Gi
?0 .2625s 16/;.6 ;
s ).a < 5 # 147 .5*
i 0 .4 3 7 : 1 9 8 .5 :
1v.4<5 1 iy 0 *7 *
;0 .4 1 2 s 137.0*
*0.325 * 14?• 5*
s0.410 : 186.0?
s0.283 .* 130 . 8 s
;0 .288 * X w ), 8 s
; 0.3625s 164*7?
ji
& *—
3»C ;
3«~ :
4 i,6
4 .0
.:
t
'*5 .r * 0 . KJ'jO? s o . . io?2
35*6 sO.'JO
57
3 *- *
v:.6 ;
1?.0
5*7
:
:
79*5
?0.0 6 .>74
51.1 * 0 .JO.805*0*
3*3
4*4
5*0
5 .0
4,0
2 .8
—
6 ,0
3
6 ,0
6 .0
6 .0
/.0
5*2
:**■•
4.U
u.O
7 .0
4*5
if.O
14*9
5 .6
77,6
t
s
;
:
:
f
s
*
;
5
s
1
:
:
?
:
t
$
?
*
24*8
1 4 .5
38 .5
c"7.0
.0
54 .0
6 0 .6
8? ,3
'7 5*0
6 8 ,7
5w*0
f.= . 5
i ? .6
^ .6
53*2
*
;
s
j
s
;
s
;
;
s
:
t
s
:
s
s
?
*
8 3 .5
04* 5
37*8
2 12 ,4
: 0 . >4:95 sO.O « 0 2
* 0 »*“ X sO.*,*. .4" >
s i. . ; <1 ';© :o .o
5
;Z . w /3 x t o . 001522
88*7 J1.00314 sO.OC-.
87*5 * ,. . > 3 0 9 * 0 . .
? 2.0 ;')..}I/125 ;O .C K j64j
222.0
sO.OOl'53
196*0 ?C-.0>39? s i. X /t'jl 4
1 1 0 .6 sC.00591 # 0 *0 0 -/9 8
8 5 .0 tC.90300 sO* ^uu'12
1 1 1 .2 s i . >1393 sw.
1I 7 .7 ; 0 . 30416 sO.Gov... 49
118.3 ii.O C .U ? s v .O 'x -H
93*5 : 0 . 4 ,330 *0 « 0 . >6 /3
I I 3 .5 sO.j-0401 tQ.Outf.l?
91*2 *0*00322 *0,000657
88.2 sO.00312 s0.000637
111*5 *0.00394
s0.OOO804
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Form E-5
'U 'i ;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
w here*
k * 6
* 0*00045 (pound s p e r foot per second)
/> • 62*4 (potmd* par © tilts fo o t)
(Aim r r (radian© per seeend)
1 * 1 ,2 5 (feet)
r m 0,08 (feet)
g - 32 .2 (feet per second^}
K * 71° 54*
cos <x - 0*301
cos p - « 1*0
fhem
_
14,2 x IQ**11
A© » ———
<f
Also*.
V ® « 4*280
(6 7 )
Squailoa 61 a»y be rewritten lime*
•hA9 *
v
'STOi
? "w
—
4m%*
C®8)
fa b le I f shews the ealetil& tto ® e f th e coefficients f o r #©sae of the tests
from fable II,
The average film th ia k n e e * <f» a obtained from the curve
I® Fig u re 34 and th e water fee# rate*
the mass transfer e e e f f lc is n i k*g
was obtained from equation if ueing a ImwiM heat wlae of
h old-up d a ta fo r teste So* 37 and tfe*
choice o f th e value S
0*26,
The
38 are "*iren in Test lo* 88* The
for the coefficient k was eased upon preliminary
o a n p rla c B with result* of th e ©edling. rat# method. % analogy with
viscous flow is pipes th e value o f k is 8 j so i t is a t le a s t of the
proper magnitude,
figure 88 shows th e e m p r is e ® between h e a t tr a n s fe r c o e ffic ie n ts
e e lo u le te d by the two nethods, c o o lin g rate end cooling range.
There is
some scattering, but the observed agreement is quit© rewarlrable consider*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
♦104-
Table I?
O d im la iio a o f fee u o ei'fic io a ts by fee C o d in g dug® m r n lja is
Angle o f Operation 71 ° 54 *
Test So,
fin d of p r& ft
T«Bi.p&ratur6£5 °F,*
V e te r In le t
P a t->v - r j e t ( f 0)
A w , fei> r (T )
i,ir» Pry Salb (t)
Mr, let Balb
Ss,trn Hui>id i ty (^ 1
A ir Ife fi c-tty
6
1
:
2
:
t
4
? .5
3
:
:
%l & f e m l: l a t u r a l : fe t e x d ; Satural r fe tu r & i; la t e r a l
*■
:
:
s
?
I
112
.
0
:
1
22
.
0
: 1 2 2 ,0
122
.
0
s
122
*
0
:
122.0s
•
86
.
0
:
102
,
2
: 102.2
t
iOr.O:
35 . I t
6% 3 :
1~
102
.
6
:
112
.
1
:
d • -*A
t '
103 - 5 : 10 / . 0 : U .‘ . 0 :
*t7-*2 /. *^
73. 4:
7 4 .3
t
7'
7 4 . 3:
7 4 *3 ;
57 * 2 ;
57 ,
'$ 8 . 1 :
560
55. 4 :
5r O
t
0 . 0 1VO: 0 0 .90 : 0 . 0630 : O.Oo35 : c .o ' : 5
t
t ' O.C” ’'7 : J*. ■53 : • d * : o ■0 . 0068 : 0 , 1X500: O .fe O
1 ’0 *C * 1?} 0 , 0437 : L.O/,.45 : 0 . 0562 : 0 . 0575 : 0 . 0 0
C «w " H )
y/t (% - h )
v ,6 . 0
t 17c . 5 : 103 * 0 : J 90 . 5 : 240 . 6 : 046 *0 :
//# -$
, 1:
3 7 .5
*
(T - t )
2d ? :
37 - 7 :
>7 * 0 :
" d : 2 f e . 3 : 2 0 . 0 : 2 S3 * >-•
(T - t ) * tys(H * - H) ; 20 >*?:
/ #
<0 . 3 :
.. / • ‘...'I
:
3B.7t
; ’' . 0 :
16 . 9 :
( % - T»)
s 0 . J> 1 : 0 . 173: , . i ) ,5 : • 0 . " 7 l a : t . j -9 - : 0 . d
fc A 9
f& fe r ' e i e e c ,/» ir i,
1 d»;
fe d s
: <• *
tb
1160 .
:
PiJ ? Ihigkness {(T)
:Q*0 GOo ?; 0 , 0 ’d 7 d , , 03070 : 0 .-J 322: 0 . 0022 : 0.0 0 2 2
7*vg { * •*#
<f3 ♦ tO1^
y / -,/*.
i
3el * : 10 , 700 : i 0 , 7 O
374 . :
0 * ™ ^ *. * 0 . 0378 : . O O ,0013261 Od 324 : . d l 24
A ©
*
h
:
0 7 :
4 . 56:
5, 4 3 ;
d
/
3 ,0
1 6 .0
k *s
*
1 7 . 55 : 4 5 * 23 : 20*86: 20.27; 20.27
.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
‘
l am© I? (Coot.)
Calculation of the Coefficients by the Cooling Range Analysis
Angie of Opera ci n 72° 54*
fosb fa *
i
fc
■ae
Kino of f-
7
8
:
0
:
1
10
*
■
;B
J
S
O
. OKliiU
fen/:-' i o n e
,.00or Inlet {%)
:
1
:
1 2 2 . Or
:
6 1 . 7s
:
11
;
12
h r u r a lr 4 G
ert-i
:
;
U7.0:
1 2 2 .0 :
.1 2 2 , 0 *
6 2 .6 :
r-5.3:
6 6 *2 :
83.3:
91.?:
92*2:
?.' * J£
94*0:
102,5:
:
75*?’:
75*2:
?6 . 1 :
77*0:
■54*5:
57.2
Sst’n Humidity (Hw)
Air Humidity (If)
*
•
•
:
•2*0215:
(B« -H )
_(Hf - H)
ol 5 / ,
:■ 0
•
*
1 - „»
i
U r "iUst (f0)
Avs. F«.tsr (T)
Air, T'r;/ ’xtb (t)
Air, so Bulb
:
V s (i%
- If)
’1'i -
his
O e./r.iru
7hic_; - • . t ( * )
x lir'''-'
A 0
h
in .
:
55*4:
55*4:
O.o;e'):
3.035''-:
1,0155:
0,0475
■\oj43:
0 . ) <53:
0 .0 0 4 6 :
-52:
0 . ,0 5 2
G, . „
J.33 '-*• 0.0413;
n, O
i, 03
/ I:
£
*
1 /. 3:
d* ^0 :
*3.0>:
* .42
U. .,’7 :
o«6b?:
1 7 7 .0 :
in * . 9
17.- :
25.5:
, e. )
l vj ,3:
149* '£
202.5:
2-7.0
55.6;
345, 7 *
37.8
!
( .37- :
0,191:
0.1:3
.1 i'»# * t
1 0 ).:
* . „v
' . 0 >0 2 .6 : G.v
*.
X-s.
A
V*-4*
32«:
J.-07.
-;
i, ^ , -i«
0 *4*“ 0 *
;
*
a
t
77.0
54.5:
:
:
64,2
1 0 3 .0
0.0354*
1 . i ,j t
rO*«Ud. : :
1 2 2 *0
57.2:
1 i/.o :
i
M
*
bn*.::
0 . 4 5 .-:
♦
:
k L d .i
qi+0 *
,„ x : 0 .<
0 0 .,, 1 : 2 . hO7Q:u*G~’-7 3
f 7 *v :
3* 5*;
3x5.
V**4 --J
-*
0,451;
0 .0 4 1 1 :
o .o u i
1
^* -..i. *
0 .7 0 6 :
4 .6 4 :
4*46
,.1 4 :
3 .0 2 :
1 7 *8 6 :
17.13
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table I f (C o n ti)
Calculation of the Coefficient s fcy th e Cool lag F&nge .Analysis
Angie of :Verft4oii ?1° 54*
T
e s t
|8 k > .
K J n c *
o
T o -
f
C
' T t
I s
v
t e
"
I
i r ,
i r
R
(E *
V
-
-
t )
(1
-
t )
»
*
61
:
9 5 . 5 s
♦
«
9 2 * 4 :
( t )
i
u i b
( H w
)
( H )
-
H)
#
0 . 0 ? 7 0 :
{ . .
0 . 0 3 1 2 :
0 .
4
*
3 -1
+
A /s (t *
*
a
- r
c c . /
r t d ^ k n e s r
< f 3
L O
a d n .
( « f )
*
•
*v
<* *
'
-
4.-* 9
* *
u
*
:
*«
K
i^ 3 :
m
•' 7 3
- *
«
«*■ *■ * .*
• /
*
P e n
1 2 2 * 0
,
,
A
i - * . ( ■, s .
IC O . 9
7 7 . 0 :
O '?
y
9 9 . 5 :
79 * e
100.9
»
I
rs ’
- *
*
* 3 *■
7 3 . 6 :
7 « . 9
:
3 3 , 5 :
»
w: *
* W *
1
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Table IV (Ooivt.)
Calculation o f the Coefficients by the Cooling Range Analysis
ingle of Operation. 45° 34*
33
39
Tost So
3? *
* Safcural
*
Kind of Draft
* Fan *
j
. -atures ° f .
t
.0 *
* la...0
Inlet (TH)
t
«r ’
utiet (T0) **
9?.5 * 11.0,7
.ill•3
i'-ra, ,U r (T)
t
>
Air, Fry Bulb (t„) #
*
73.1
73-4
61-7
60*3
Air, <’0 Bulb
:
9.0720 :
Sot*a. Foffiidity (Hw) : o.:3o<
*
.■*■*, *
Air Humidi:,j (H)
*. .
0,0630
i 3.320
(H* - H)
169. ">
£
1-.5
Vs Oif - H)
-*
-n
P
:
4i
f*
‘*//
,>7*.
(’•• - t)
(? - t ) + >/«(% - ff) *
311-5
i) *'
1
*
(?1 - To)
J3625 *
* C.CO 'O
hA0
i&j S.VAW*
*5.'Tutor Rate ce*/mia* : 2»l6u .
rpv 11 ^
:
lelrbn lbs.
:
O
*r'
Weigat
■
*.
#•
*./
Tine u-->o.
»*v)
Accu jo...,tion gitt-.
i
«
«
*
Holo-up gas.
*
*
t
Mid-’jr.) OU.ft.
* r* 1 ,
*
Pilr
?kness (<f)
i
S .Lf :0 »
J
<P x 14'"™
t
l O.OOtal f G. 00622 Iv#(A*9*
A0
*# 13-99 i
5.® :
h
«
22,10
1
k*G
1 53-1 i
.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
.Form
E■!
-1 0 8 -
■+t;f -i; 4U-4 ,4:4
5
; w
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ta g the f e e t t h e *
$$ c o n ta in * th e film th ie lm ### cubed*
ffeaa
th e * a a l y * t * o f e o e lia g r * §» is. » t le a s t m ®.mwr&t # a® th e c o o lin g ra t®
a n a ly s is *
The © ooliag range a n a ly s t* has the a d d itio n a l taer'it o f p r o -
d ie t ia g th e e f f e c t upon i& e c o o lin r jrenge o f change* i a the e a g le o f
o p e ra tio n , the site of th e disc* ftM th e speed ©f r o t a tio n .
B* Ar©li»e#w» Aerator
1*
Apparatus
Th» aerator built fey Bellmen (1 8 ) v m used for th e e x p e r ta e a te l work
o f t h is section*
Before it m e tested* the f i n * were removedf ead the
s id e w a ll ooatoar vam ehaaagsd#
® M # was done in accordance with the f o l -
low iag se c tio n is o rd e r that all the f in e m ight re c e iv e a share o f the
w a te r i a proportion to *8»ir §!##*
Ihes tfe® f in s were re p la c e d , they
were mmmbted fey tab# c a t is the fine a# w i l l he e xp lain ed presently*
Seeastse o f th e & a m g«# is. s id e w a ll ecntonr Si© envelope o f the flas m s
no longer & fn o s tra s of a cone* 'hut it had a d i s t i n c t double curvature*
After the changes th e a e r a to r had these d h a rfte te ria tie e *
D ier-eter of core
Diam eter o f easing
Pitch, o f f lig h t s
■t inertias
II inches
If inches
lumber of threads
I n i t i a l sidewall height
Length of f in section
Total length of cor®
Maximum width of fins
Mnisuas w id th of fin®
Capacity of screw
4
§*§■ inches
38 la c h e *
T feet
11 .iach.es
6 inches
2,01 galle& s per rev.
$0 degrees
la g 1® o f o p e ra tio n
T o ta l f i n eroa
378 square feet.
Seating «* vent tube# at quarter turns for the first tu r n *
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
2 .
S id .e w e ,II d e s i g n
Tfe® moet o-omreaieat jaethofit for g r a p h ic a lly integrating the liq u id
• tu g of an aerator a re to take sections cither p a r a l l e l o r p o rp e n d ic u la r
t© the w a te r M ate*
t o U m n (1®) chose sections parallel to th e water l i n e *
H ils m s * .lo g ic a l c h o ic e , t e m w
of the fact that a * the water discharges
th e surfa©* low ers; awl integratiott at m m h new Is?®I is memplished by
emitting m o tio n s tssgtmlag at its® top.* Ilafortumtely t h is procedure is
de© active % It 1® d i f f i c u l t b© w e ig h t p ro p e rly th e successive sections as
ths water recedes,
Tbs m th e d © f taking «#etii»s perpendicular to the w a te r line has the
■advantage that it is p o s sib le to e s tim a te th e weight ©f th e end sect'- oned i r e c t ly front th e f ig u r e *
r e SS .shows the se c t toes taken in this
m a n o r f o r th e Arehtaedeen aerator,,
f t # wetted p a rt of eae-h s e c tio n
was d iv id e d In to h o riz o n ta l s t r ip s of uniform width, and th e len g th o f each
s t r i p m e measured*
fable V shews h e r th e moasurejaemts are e.©«feined t o
give the integrated vottsae at nine d i f f e r e n t liquid le v e l® *
The esocimn sidewall height* t| inches* was determ ined fro ® F ig u re 36
and checked by am a u re a e n t in th e a e r a to r *
Tit© c a p a c ity o f the m o le
screw m s 2*01 g a llo n s per r e v o lu tio n * end th e t o t a l f i n a re a ms 7,708
square inches*
The f i n a re a m s © a fti la ted. % form al in te g r a tio n fo r
each q u a rte r t u r n , and these are tabulated is Table ¥X*
The o ve rflo w
m s apportioned in r e l a t i o n to f is a re a * the water r e m is in g in the screw
m s tabulated ia the next coltum j and ft® s id e w a ll h e ig h t m s made propor­
t io n a l to- t h i s *
ftie final aoltssn shows the separation between fins at
each q u a rte r t u r n *
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-111-
D
C
H co
>C
M
O'
-*o *0
Graphical Integration of a Liquid
Slug for Aerator re s ig n
Figure 36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
*4 M m
Tab le T
Graphical Intcgr'ticm
of tie
Liquid
Slag
of an. Aerator
eecfc.S:.Sect*A:Total Vol.*
Full liamd tG; (r' iBCf' •<?■jf-.s !■ }
*
* 0,66 £
* a.52 s 0.15 t
Arv 2*. 0,52 : —
v*vo
« 0*78 5 A
:
) 2 0,$2 : --- s
s;
.0.85 j
£ 0,93 : '>.65 : 0,54 *
3
t
*
* 0,20 j -— - j
* 0.9& : *! H *
j
• 1.04 0 *;'i ;
5
•
6
J 1.06 j Ail :
fM. *» G . ;
A
* V*G©
7
G
* 0.50 : G: 5 :
■f
rti-ft-MMnr"-*. J -.0 • ;
.#• 7./}A .
..i4.;7(
5i\.. ’ *11..5
nf.
t .)•15 2.
Am..........f 0.35 :
S tri.j* >: 8* > : 40 :
..i.f.rlfi.1.
.*■.2*823} . 3 .0 O s...::,.07..a...
..
"*2.30.?..
«H J r.lt.. JLulU. GI7.G.,iGQ3i
Area
Volume * 0. 302: i,50: .OvA * a* * 0 *a^0
0
1
K
Sight int '*v:enta Gj|_tx liquid slug
i 0.78 : GOO : O.5, : ---j
£ 0,35 s aGO : 0.52 : --- :
1 0*93 » 0 .05 : 0*54 : --- :
3
4
£ 0,98 : A 71 : 1.20 *, — — :
: 1*04 j 0.S0 : „™,_ • .*«»». j
5
J
J
6
: 1.06 £ O.ol :
ef
*
•
«
,
«
*
.
»
.
.
;
0*36
;
*
0*44 5
a
>
k
,
j
,
»
™
~
.
*
8
«
.
«
<
*
.
^
*
£ 0.50 :
<
--*
0.00 s
— .9... I
Totals iJLGO : 4.09 : 1,78 :.
:
atc.
* 0.375: 0*45 0.445:
.
4‘-r,n * 7*5 ...: a,*0 1 ...1*3..s.... .s.
* 6.561s 1.60 :JU552s_... j .
*
Area
* 0.547: 0.3‘
JO; 0*13 :
:
Voliaae .f 0.274s Q,450fi 0.065s
* 0.489
X
2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
i'&bi© y (c e n t.)
Graphical Integration of the liquid Sing of an Aerator
O rriicste: t e e t .D i Sect. .C: Sect .B:
T o ta l Volume
Seven inoronsont. high liquid slug
.85 : 0 .6 0 ; 0 ,5 ;
*
3
0 .9 3 5 0 * U # 0 .5 4 :
0»98 j - .7 4 * 0 .2 0 t
•
4
«
.
n
oK
.inn.nw
nnir- *
♦
>
1 .0 4 t w«.lAi * ■
•• 1*06 i 0 * e i : m
-fiTTT.*™
.1.H1 *
r-t
:*uir.*<. #* 0 . 3b : 0*44 5 n*am
i
•*
'•
«
e
* 0*50 : W* fb,^f .*
'#Ov * TM.nmrr^
. 9 ... *♦ 1 * o0 * W
\ ,■<f ’
**- A9*.#0 •*
J*.mfJCr %
** 0.3 9 : ...51 : jfc- »*w M
Aire*
- ,»•
I * <v
# S trip s * 6 .5 *. r*
■
*#
1—, * ,1a'J2 j l " i . l T T
.....
.
.
4A v»
• 0 „ ■' , ; .r\ * *,,.**w** .T3.*q.q0 ;
Vc.io&e ** 0 . 111: w«
* • \i*S
* V
S ix in e r un-uae 'Vi^A U.X
* 0*93 : 0 *a5 :
:
& **
7' ♦ ***>* tr * 9
V* A
7M
• A
r •. ‘\Jf:* ’-.s-* «
Vi-f
•
• -*»* a
-nw
unc. m
* 1.06 : *3i i uju-.TW
|
% 0.36 : >.//+ % —
J
'.2 5 i
% 0.50
*■
*- -- --- |
■
*. . r.^ * \J»*
5 5.37 : 8.49 *
** 0 . 395* 0 . 499s
.i
n k *
0
*
H**.
...J... 3 .0 % **.#!> *
• 4*92 j y .99 s
Area
** 0 *41 : 0 * / 2O* 0*01.61
?oltai€
0 . 205* 0 * 125: 0 *013;
0*435
sing
->
4
5
6
7
8
9
Totals
Avo.
# S t ile
0*353
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table ? (C o n t.)
Graphical Integration of the Liquid Slug of an Aerator
OrdinatesSect.lsSeei.CsSect.B: Total Volume
Five increm ents high liquid slug
t 0*93 * 0*74 s 0.20 s
*
t 1*04 t 0*80 s
: 1.06 : 0,61 t — . i
: 0*86 : 0*44 * — __ :
i 0*50 i 0.25 : --- :
*
I
t 0*00 5 —
* 4*44 : 2*84 : 0,20 t
Ave,
: 0*888s 0,474* 0,20
# Strips.? 4.*5 s 5*0 :-P..5.?
..:
.....4.00..:....2.J£Li_ 0.100s
Area ....sjkm.syiaz:. 0,008:
Volume i 0.167? 0.099? 0.004:
0,270
4
5
6
7
8
.....9...............
Totals
Four increaents high liquid slug
j 1.04 s 0.80 s rffl —».i J’
5
*
6
: 1,06 * 0.61 s
——
J
.
j 0*86 : 0*44 *
7
_
*
8
: 0.50 : 0.25 :
s --- : 0,00 s — I
.9
T o ta ls t
1 2,io t ........... J .
Ave.
t 0.865s 0,420s
i 1
•
•
# S tr io s : 3*5 : 4 *0 :
s 3.025:.1,680:
*
■
*
Area
*
s 0.252s 0.140s
0.196
Volume s 0.125* 0.070*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
~u&*
Table ? (C o a t*)
Graphical Integration of the Liquid Slug of an Aerator
OrdinatesSect,B;Sect.C;Total Volume
Three increments high liquid slug
&
{ 1 .0 0 : 0 ,6 1 ;
?
:
0.36 s u.44 s
8
: 0.50 : 0.25 *
O.Oo
Totals :
1.30 :
Ave.
t 0.308: 0.325:
if Stripsj 2*5 : %0 :
2.02 : 0.973:
Area
t O.lSfi: 0*082:
Volume : 0.084: 0.041s
«
0.125
Two increments high lit.uid &JUig
7 t 0.36 : ;).41 z
&
j 0.S0 s 0.25 :
5.00
Totals 1 j-*JB
0*69
.
.
*
>
•%/
•"%r\ *3 -J*
Ar&,
: 0 .6 8 : ;
# Strips: 1.5 : 2,0 t
* 1.02 : 0.4)6 :
*
Ares
: 0.085: 0.038:
Volume : 0,042: 0*019:
0.G61
One increment high 1:
0.50 : 0 .25 :
B
9
s
J 0.00 ;
Totals : 0.50 : 0.25 :
Are,
; 0.50 t 0,125:
§ Strips: 0*5 : 2,0 :
»
•...O.s.25.s 0.25 :
Area
: 0.02 : 0.02 :
0* 010z 0.010*
0*020
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
lie *
fa M e V I
A e ra to r S id e w a ll Besign.
for O verflow is Proportion to Fin Area
Quarter?Fr&ctionaijFraciionaliKr&ction. sSidewalls Kn
Turn ! Fin arca *
• uverfLow :Remaining; Height * ;
Separation
*
■.... &&U... * ins* ♦
# ins*
I sseu. in. •* !gsA* *
90.4
1 S
2 • 114*9
3 S 26-3.6
A #• 195*9
5 • • 247*9
6 •« 290.2
7 : ,45*9
8 ••
600.4
9 ! 465.9
10 *•
539*9
11 t 6-0912 t 693*
751*
13 i
862,
14 i
15 ! 894.
16 *. JUQ38......
Totals .«* 7*691.0
E rro r *
17.0
Totals .*. 7.708.0
»
•
*•
«
S
s
*#
'
t
s
s
*
♦
0.02S
0..0300 *
*
0*0426 !
0.0511 :
*
*
0.0647 •
f
0*0758
0.0902 X
0 .1)64 •
*# 0.1215 1
J O.lijOl !
0.1585 *
s 0.18(6 S
#
*■ 0.1956 t
: 0.2193 %
*
* o .;iqo 1
*■ 0.-700 **
**1
.. 1*2933.;...•T
# 0.OJ67 -*
*
»
•
**.
#•
*
Saaple c a lc u la tio n !
I.9764 s
1.9464 :
1.9036 »■
1.8527 :
1.7^ 80 :
1*7122 *•
1.6220 *•
1.5156 *•
1,3941 *
1.2539 !
**
1.0354 ■
0.91S I
0.7190 %
0*6997 *
0»,:?t>7 *•
V* */WOf t
9*36
9.23
9.02
6.80
S*49
8.12
7*71
7*20
6.62
5*95
5.20
4*35
3.a
:
:
!
•
*
«
*
1
*
**
:
1
*
j
!
2:98
2,85
2.79
2.78
*c. d9
2.63
2.59
2.49
2.142
2.33
2.15
2.06
1.965
1.937
2.375
1*312 i
0.037 ** .1.725.
* ... 3£*12L_
*
«
0.0067 * ....0*037. • . .W
....
0,0000 <** U* ww ,-v. m
.
•
0
* -0.0236v "SI*)
» 9*38
3*0 -
(9*50 -
9*3-8}
*
2.88
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
<& 1U
Si® o r ig in a l method of mounting th e aerator f in s w
n o t s a t is fa c t o r y .
Th© o v e rflo w was ceasid esab ly g re a te r than could be d e fle c te d to th e beck
o f th e f in s by s u rfa c e te n s io n a lo n e *
method o f mounting th e f in e *
F ig u re S7 -ahowe th e m odified
A lte r n a te tabs ea the fins were best upward
to d is p la c e half o f the overflew to th e back ®f the fine*
fid s was a
completely satisfactory method so long a® th e aerator was r o ta te d at 22
or 26 r*p#»* At 12*6 r*p*m * th e water on the under side of th e fins
f a il e d t o spread and r»n o f f rapidly*
under, surface became w o t*
Some tins® elapsed before th e entire
4 h ig h e r ang le o f o p e ra tio n e « M
b© expected
to aggravate this condition*
Although the fin s of the presen t aerator discharge into a catch pan
80810 distance above the water level in the feed teal;* good practice re­
q u ire s that Hi# f i n * sh«sM discharge at th® wmm level as the food ta n k *
T h is permits a maximum fin width for ® give® a n g le of operation#
Test® were mad® o f the perform ance. o f th e Archimedean aerator as a
w ater cooler.
Table ¥11 shcnr® th # data fro ® these tests and the calcula­
tio n s o f th® h e a t tra n s fe r.a n d bums transfer c o e ff ic ie n ts using the cool­
ing rate method. When the aerator operated at 25 r*p*su* both the front
and hack of th e fin® war® well covered with water*
Shea th© speed m s
changed to 12*6 r *£*»*,» th e M o t sides o f th® fins were p r a c t i c a l ly d r y .
W ater was diverted to th e back side® of the f i n s * - but it f e lle d to spread
properly and ra n o f f ia ribbon# or dropped to Hi© front sid e of the n ext
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-118-
\ Fin
Diversion Tub
Fin
Method of Mounting Aerator
Figure
l-'in
a
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•*1 1 9 "
Table VII
later Cooling Tests of an Archimedean Aerator
Test No,
Kind of Draft
1
2 s 3 : 4 : 5 : 0
xNaturalt Natural:Natural:Natural:Natural5Natural
♦
#
Temperatures °F.
t
i
.5
Inlet a&ter (T]_)
t
73-Bx 100,1:
99.8: 104.8: 100.3; 1X0.3
Outlet later (T0) t
104.6
73-6: 97.9: 97.4; 100.5;
Ave. later (T)
: 73.7i 99*0: 98 .8 : 102 .6 s 105*6: 107*4
Air, Dry Bulb (t)
: 73*Oi 70*0: 78 .0 s 76 .0 : 78 ,0 s 78.0
Air, let Bulb
J■ 57*51 6 1 .5 t 6 1 ,5: 61.5: 61.5; 6 x.5
Sat'n. Humidity (Hw) s 0.0181: 0 .0113 . 0.0413; 0.0463: 0.0515: 0.0547
Air Humidity (II)
: 0 .0 1 O: j.Ollys 0,0117: O.oU 7; 0.0117: 0.01X7
t O.JUcllt J.0308: 0.0298; o,o;.;a.* 0.039S: 0.0130
(Hw - H)
V s (H# — H)
5
31.7: 132 .0 : 128 *8 : 150,4s 170.5; 184.1
*s.’ ir
:
o*7: 21.0: 20,8: 24 *6 ; 27.6; CO
(T - t )
35 ,A: ip3»0: 147*4; 175*0: If.i.l: _ 2.18.5
(T - t ) ♦ Vs(Hw - H) i
....,5 -*o*
AgT-t)
• h)j :13,3a).:57,o 0 .:55,750.:66,200.;74,700.;I1
2.2:
2,4:
1
0.2:
5*5*
5.7
4.3:
A - To)
r.p.m,
5
:
25.:
25.
25*:
25*:
-5.:
Wafer Kate (W)
:26,150,:26,15.;.:26 ,150 .526,150 ,:06,150.:
W(Tx - T0)
: 5,230: 57,5jos 82,750;112 4001136,600s149,000
h
5
0*39: 0.99: 1.13s 1.70: 1.85: 1.85
7 .11
s 1.50 : 3*«2: 4.32: 8,53;
k'G
*
•
* ;•
»
~ ... , J .
,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
r-"'
,
»
-320-
Table ¥11 (C o a t,)
later Cooling Testa of an Archimedean Aerator
Test Mo.
Kind o f D ra ft
Temperature® ° F .
In le t f la ie r (Tx)
O u tle t Water ( I 0 )
Ave. l a t e r (T )
A ir , Dry Bulb ( t )
A ir , Wet Bulb
Sat*n. Buiaidity (Rw)
M r Humidity (H)
(Hw - H)
V s (H * - M)
(T « t j
,
(T - t ) ♦ V s(H w - H)
A & 'T -t) * Vs(H ^H )J
(% - Ttt)
r .p * a .
l a t e r Rate (W)
W(Tx - To)
h
k»(*
11 *
12
8
S
10 ;
:
7
s
9
:
• n a tu ra l: M&iur&l t ::a tu ra i j n a tu ra l s Fun : Fan ■#
*
s
1
*
t
i
s 123*0s 134*5; 140.0s 158.0:
97.7* 101.0
t I1 4 .0 s i-t. .Hs 129.1: 3.41*0:
96,2
93.4*
; U S . 5s
6: 134.6: 149*5:
‘9 5*6:
9 8.6
t
■?8»0t
■7 6.0
7 6 ,us
78.0;
74,0:
76.0s
61.5s
s
6 l* $ i
c l . p:
t.5 s
59*5
59.5s
i 0.0770s 0.1060: O .I28O; o .208?s 0*0370: 0.043.0
*. 0 . 0117s 0 . - H 7 : 0.0117: 0.0117s 0.0070; 0 . 4 70
: 0 . 0653s o .m 3 s 0,1163: 0.1970s 0 . 0300; 0 . 0 ’ M
s 077. 5s 40/i.» -: /•9b.Us 844*0* 108* 51 145,5
22,6
50.6:
“6 .6 . ■ 71* 5 s
19.6 ;
•
Ac,5 *
s 300. 0 s ig4.6! 654.6s 915.5s 146.1: 168.1
s ill,0 0 0 s 171, sou: <cOv,5‘;0 :346,000: 56,000; 63,600
.
7 .0 :
4 .8
i'0,9: l?.0s
.11.7:
4 .3 s
25,s
i
-M*:
25.;
25* t
»
***
25*
: 26,17): .6J‘.f» 2b,lpO; 26,35»: 26,150* 26,150
:235,200:306, 40 s285,000: 444, -"Os 415.,500:125,500
<. 76:
S'
3.94;
1,36 s
1.^8:
2.01; 1,97
5
7 .40;
6 * 1/ :
7.7,3:
7*57
I *M :
5M3:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T ab le ?1J (C e n t.)
Water Coaling fasts of an AreBi* t/:.cs.n Aerator
•*
*
*»
Test Mo.
Sind o f C r a ft
T b i, . -
e
r a
i m
° F .
e
r
*
( T x )
O-Jtiet rtter (T03
Ave, t a t f - r (T )
A ir , C r y Bulb
A ir , Wat Bulb
Sat*n--H um idity { % )
A ir Humidity ( ! )
( % - H)
V s ( % - B)
{ %
( T
( T
*
)
A fiT -t).
-
K )
+
V ® (S ^ )]
( T i - T0)
r . .«&»•
” s-t^r fe te (!?}
?.(% - w
h
k *G
1 4
t
F a n
s.
:
f a n
:
J 6
:
»ii
:
1 ?
:
:
Fen
:
. 3 :
3 9 - 5 :
9 3 . 6 :
9 5 . 1 :
•*<r
X f e V * X •
I ,1J
U* 6
9 7 . 3 :
1 1 7 *
*
*
1 0 2 . 3 :
1 5
I O
C
:
1 1 7 . 4
1 1 0 . - 2 :
1 0 9 * 8
1 1 4 * 2 ;
1 1 3 .6
7 6 . 0 :
7 6 , 0 :
? 6 * 0 :
7 4 . 7 :
;
5 9 . 5 s
5 1 . 5 :
- v . 5 :
5 0 . 5 :
; 0 . 0Lf'tol
: O.fejTO;
*. O .rio b ;
« Ax
s
4
j . b
:
1 7 6 . 2 :
0.4395:
1): 0.00?0:
0 , 0 4 0 5 :
O . C "
0 . 0 7 5 5 :
0 . 0 3 2 5 :
0 . 0 7 0 3 ?
0
.
la jti'fi 139.0:
-^#4-*, U S
> . 6 ;
Ja -
'"i
l 6
o * 5
:
* w
&%#■»> *
2 1 . 3 *
s
3 0 6 5
s
0 . 0 7 3 $ ?
-jr*.
<
t
7 4 * 7
0 * 0 6 8 0 :
58.5
0*06o2
0 . 0 0 6 5 :
O
0.0615:
0 . 0 5 ) 7
2 6 3 . 4 ;
*
#
F a n
1 1 6 . 3 :
97. B:
f-s
I S
*
:
t )
{ %
a n
x
s
*
/ ©
W
9 7 - 2 :
t
>
1 3
•*
f c )
♦
■
. 0 C ^ 5
255.5
3 9 » 5 :
3
^
. 9
:
3 8 * 9
2
%
.
4
X 6 6 , 700 : 6 a , 6-70: 6 0 , 7 ) 0 : 1 3 5 , 0 3 0 : 1X 4 , 500 : 1 X 1, 2 )0
3 . 1 :
7.6
1 .4 :
t *■;
X
4.7:
5.1s
%
*
"
*
*
4
t
*'
2;)
.
:
2 5 .
2 5 . x
2 5 .:
3A-<~k
-JwX 2 6 , 1 5 0 : 26,130: 2 6 ,1 5 0 : 2 6 , 1 5 0
t 7 6 , 1 5 0 : AO- •'L
I
1
900:115,0-00:177,SOD: i l l , 8 00 :198,700
1
.
9 6 :
s 2.00:
1 * ./"*».
1 . 8 5 ;
1 * 7 9
1.89:
5 . 0 4 :
7 . 1 1 ;
:
■ 6 .3 8
7 . 2 ? :
v . ’fe:
v.6 9 :
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
faMe VII (Coat.)
W a te r
C o o lin r
te s t Ito*
o f D ra ft
Temperatures °F ,
I n l e t ' a t u r (T x)
O u tle t u t t e r (T 0 )
Ave* W ater (T )
A i r , t r y Bulb ( t )
A i r , lo t 'B u lb
S st*r*. H um idity ( l w)
A ir H u s iu iiy (H)
'H« - H)
(Hw ~ H)
(T - t)
( t „ t ) + A/s(Hw - K )
K in d
A
[ ( f
-
t )
♦
\ s
( B
w
-
T - * b©
■ t'
B a te
i
I
i
**••
*
*
$
»
*
*
;
*
*
19 :
l i j . c t
1 1 -6 ,9 :
U C . 4:
/ e r a to i*
20 '* ' 23, ? ' 22 ' : ' '23 '
*
*
•>
■
**
(? f)
*
*
4>
i
112 . O t
106.0
109.0
7 5 *7 :
7 .% 7
5 9 -/:
5 9 .4
0 . - v’>0s): 0 . 0 5 7 5
€.2 5 5 ’ 0 . 2.71
0.0521 ♦« O . u 5 - 0
iii. a :
id 7 *
X U c >*0
•>>-* J .
P l> 0 *
*■!
a a
’i
4 . ‘, :
j»/-, » c »
1: ,
*7 \
1
91 r
'1 :
/
A. 7 0 *
212 . 5
1/ , ^ 2
0,0
l i .6
! 5? */ ' " |
S ''
1', \
3,70-
0 . 5/.
11*|,l.r ♦ ****
110.8
»■
1 <-<7 <-•
1 0 7 *5
1 0 4 ."
75.7
59 . i
0.0565
5 9 .4 :
5 9 .4
0 .0 t? 5 2 :
0 .0 5 1 5
I . O d '/ l
;.2 d ? 2 :
0 . 07 *
0,04 7
u» ‘
•7 5 * 7 :
48 , ;
7 5 .7
^ .
.6
d
2%, 3 * 4 :
*9
.,2 * ^ .4
2 1 1 .9
i|6 , l o o
4 4 ,9 0 0 ?
15 , 5 5 .
66,6 j . ’
t
.6
6.6 :
1 :V£,
12. 6 ;
33 330* 13,210
0? , ; .0
iw.v.-V* •* JL *
*
H>]
V-(Ti - To)
h
k *G
A rc h i m edenn
m
tlfc tu rr l: ! is t u r g ij la t u r a ii S a tu r& ltS a tu ra l
( n - To)
r.o .m .
te r
of
.
v
2* 7 .6
2 > ..4
1 .K J
l *
? * -4
7 ,5 4 ;
ri h
3 1 .8
t
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4 4 ,7 5 0
1 -9 8
7.62
Table Til (Coat,)
later C o o lin g Tests o f m Archimedean Aerator
Test Mo*
?
H a d o f D ra ft
Tem perature s ° F *
I n le t *'te r (T|_)
O u tle t r L,er (T 0 )
Ave. s,:U r (T )
slaturaltMat.uralsJfetiiralsNaturalinatural
Air, frw, 'Ixlb (t)
Mr, -■r-+ !tjlb
Sat’n. H iidlby (Ew5
A ir H u m ility (H )
Hw - H)
« ( % - I-!}
(f - t)
v
(T - t ) + .Va(H» - H)
A[<T - t) ♦ Ve(fiw (Tl - T0)
y ,p *su
¥ & te r B ate (W)
W{tL - To)
fa
k *G
t
24
:
s
25
I
:
2&
s
s
.2?
:
28
t
Up. 2! 103 .2 : 122.8s 121.5: 116.®
97.6: 113*9: 113*2 : 108*8
78.5
101.8 100.4: lio*4: 117*4: 112.8
rtf?- r'f
75.7: 75.7: 75*7: 75.7
* ,
*
1*
✓,r>#■f
59.1: 59-4: 59-4: 59*4
<
^ ?^/**^5* 0.04pp: 0.0770: 0.0747: 0*0648
W•%■#^4u. 9 U 0.0077: 0*0072: 043072: 0*0072
U* w ~ 9.0363 : 0*0698: 0*0675* 0.0576
j/.A.O: 1'5*4: 298.8: 239*0: 246*5
14.1: 24 .?: 42»7: U*?:
37.1
190.1: 1"0.1: 341*5: 330*7: 283*6
• 34,075* 64,550: 62,650: 53,650
8.3:
8*0
_5-6:
8.9:
6.7 12.6
12.6: 12.6: 12.6: 12.6
1O AAA- 1?,330s 13,330: 13,330: 13,330
iA, 74,600 ;128,600s:110,600:106*600
' ' Jpe-'/V
r> * '
1.84: 1*76: 1.98
8*38: 7*08: 6 *76: 7*62
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-124*
lower fin*
The coefficient® in Table 'V II w#r® calculated on the basis of
the wetted f in area, 3?8 square feet at 25 r * p * » * and 189 sqvere feet at
12*6 r»p*m*
The valu® of h /n m s taken as 4,280® t * per wait huaidity
difference.*
Figure 88 shows the beat tra n s fe r c o e ffic ie n ts o f Table ¥11 p lo tte d
a g a in s t average w a te r tem perature*
Wham the a e ra to r was operated w ith
n a tu ra l draft at fS r .p *m * , e o e f fie im t * were abn orm ally low a t low
average w a te r tem p eratu res.
A pparently th e a ir was no t c ir c u la tin g ra p id ly
enough* f o r a p p lic a tio n o f a larg e e le c tr ic fa n ra is ed th e c o e ffic ie n t® *
At 1 2 .6 r.p.irs. the fan was unnecessary*
Since only ©a® sid e o f the fin ®
was active at thie speed* the air say not have reached s a tu ra tio n so
rapidly as at £6 r*p*»*
The data ia fig u re M also shows a s lig h t decrease in th e h e a t tra n s ­
fe r coefficients as th e tm p e ra tu rc ris e s *
This doorcase apparen tly was
duo to the e ffe c t of v is c o s ity m the h o ld -u p ti» ® of the w ater film*
Ecua t ion 65 shows th a t the h o ld -u p tim e is pro p o rtio n al to v is c o s ity * end
the v is c o s ity o f w ater is n e a rly p ro p o rtltm e l to th e trend of th e
c o e ffic ie n ts .
The power transmission e ffic ie n c y of the a e ra to r was quit© low p a r tly
because of excessive fr ic t io n less ia th e b e a rin g s , but p r im a rily because
i t was off balance.
Seme power m e eensured by the water flow ing over the
fins| b u t, since there seemed to be xto s a tis fa c to ry way of e v a lu a tin g th is *
it was neglected ia c a lc u la tin g th e w a te r hers® power*
tJsing a l i f t o f
3 feet as the average d e liv e ry head and us.tug a cap acity o f 26.4 g*p*m* a t
12*6 r .p .s u the output was 0*0 2 w ater hors® power*
TJnder the same e ® «
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
fo rm E-5
-1 2 5 -
-i i!
jlE h t:
ie e e
i h - i - l - l i i l l : :-rrf : 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
"
M
.'Its *
dltions tli© electrical power input measured with a watt-hour raater wag
360 watts or 0*483 hers® power* Although this is a very low power trans­
mission efficiency, the hulk of the power transmission less was seeh&irle&lf
the power emeuwptlea was S40 watte when the aerator rm empty*
C ♦ Discussion of Results
1* Variation of heat trissfer ccteffioients
It is mot known s h a t caused th e h e a t tra n s fe r coefficients to approach
gero as the w a te r rat® m s decreased*
ap o asib le for this*
A single factor earn h a rd ly be r e *
It may b® that a eom binatlott of th e assum ptions in ­
h e re n t in the analysis are a t f a u lt * . B jm tio n 56* which makes h e a t and
m s s transfer coefficients i^ o p o rfc taa al* is p r e tty g e n e ra lly accepted as
correct f o r a ir -w a te r vapor mixtures (Badger &Bd McCabe* p. 254) (3)*
Thus w hatever ©fe&agee mm. coefficient w i l l change the other on© in pro­
p o rtio n *
fto rtfte ra a re * th e Bittwt-Boolter eq u atio n (Badger and. McCabe*
p * 134) ( 3 ) shows that sir velocity*, v is c o s ity # density* th o r m l c<a«*
duetivity# and ft® g eo aetry (tf nearby solid surface® affect th e h e s t tra n s ­
f e r coefficient*
Of these last parameter® osly the air v e lo c ity change*
sufficiently to be regarded as a v a r ia b le *
It is hard to e v a lu a te th e air velocity whan natural convection it
'th e principal means o f c ir c u la tio n * but it Is c e r ta in ly lo w *
A larger
d iffe re n c e in- ieasperaiw re between th e air and the water should increase
th e c ir c u la tio n *
At M > water fe e d ra te s lb are is a larger average
temperature different© wnaeh eeu ld a f f e e t the c o e ffic ie n ts in the observed
d ir e c tio n .
The natural oenvecticrs was augmented by th e draft from an
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
«4*T*
e le e t r ie fa n blowing directly across th© 4.1m tn tb s hops that this won Id
minimise variations do# to n a tu ra l m m w m is ^ m .
All th© © © e ffic ie n t* w ere
ap p ro xim ately doubled (see F ig u re# $1* 3 2 , and S3)*
A s a final effort th#
tests So* 40 to So* 43 la fable 11 were rim with ©©sst&at average mt e r
te m p e ra tu re , hat th e variation. I a the oeeffloiest® did n o t charg e.
A t low m t e r feed rates where tfce eoeltag range Is large the fr a c tio n
of the feed mte r th a t Is lost by .evaporation eowld bee©®® a p p re c ia b le .
In v e s t ig a t i on o f this possibility .la th e ease o f tests
I©.*. 7 msA No. 8
.shewed th a t o n ly 4 *8 p ar cent of th e feed mt e r eva p o rated .
While the
aaount i# a p p re c ia b le ia this ©xtresae -© *•*> the c o rre c tio n is the co­
e f f ic ie n t s by a© m m A rfb m § » 9 ik e tre a d ..
A t high w a te r fe e d rates the eo eled m t e r m s hot enough to hare lo s t
some a d d itio n a l heat a f t e r leaving th e rotating disc b u t b e fo re reaching
the therraosaster,
f© misslsls© th is the catch pan was emptied fre q u e n tly ,
and th e therwowter m s often held right in the overflew a t the edge o f
the disc,
fh® dlfffer«J«e *©#a»d t© he less than that o f the v a r ia tio n in
the discharge m t e r Itself *
l a »®&-adi&b&ti© h u m id ifie rs sack as m t e r cooling © m e te r* sensible
heat tra n s fe r is proportional to the tcssperatur© difference- between the air
and th e s ir mmi the interface *
the tta y e ra tu r# o f the sir next the inter-
fa c e is very nearly o$uaX to th* water im p s ra tu ro *. because water has a
v e ry la rg e heat capacity*
fapcrAsatiaa proceeds ms rapidly m t im sapor
can be removed from th# in te r fa c e .
fh« rate ©f vapor r m o r a l is p ro p e r*
tlo n a l to th e b w i d l % ilfferea.ee between ft# air and the air at th© in t e r *
fa c e , which is n a tu r a lly saturated at that tsjaperaiur®. "Mm wh.m the air
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-m *
b® cerates s a tu ra te d w ith mpm# em •mmM n a tu r a lly eaepeet 'm p e r l m U m
ssas* fo r la c k « f ft h w iM ifey d iff a r e s # * *
to
I f th e procsss Is M fi^ d lftb a tie ,.
' t a t t w , ft h u m id ity d tffs r s n e * s t i l l
bstwssn s ir s a tu ra te d a t -Hi®
m t e r tem perature and « 4 r s a tu ra te d e t a i r t s ^ s r t t w * ' V a p o ris fttiB n w i l l
eoatim t© as usual ssccspt th a t th # «##:#» w p a r m is t r t e a ie f ls s .
th is eo n -
d itie n e«® %
mr s a i l l j f w a s mm& w i l l be .re fe rre d t o m stse& is g *
Steaming
is «a ixeportant p u r l o f tb s c o o lin g process aw l should s o t h® in elu d sd
w ith windage loss«
.So s a tis fa c to ry »»tho4
lift:®
fesss
< £ *? !*« &
for determining h e a t tra n s fe r
om fttelm t* t o allow f o r «tsM si»g act ft r o ta tin g d is c or «
a e ra to r *
Arohtoedoan
%t»litftt4.wly# h m e m r$ r#©©»d«n«»ti#» of m por o ro lro s h o s t*
m& th s a i r temperature acust r is e fro ® this mm® as w e ll as Pros sensible
heat transfer t t m th© w a te r*
StsiwiBg was obsorccd w w a s n a il p a rt
of th e 4%so ob E’
.ost of the tests*,
fhi# eotM proiue® low c o e ffic ie n ts ?
h u t, sines only a j&ft of th e s u rfa e a was mifooted* th® fiw r tg # f o r the
w hole di«© should n e t h a w bens greatly redwood*.
Although no on© of th© abow m i i m t» appears to h a w been responsible
for the -variation of the feeftt % m m i m
isight hare been*
all of the® together
Bower©r, tit# coefficients e&loglate& in this way are «»
•jcperimantal faotf so dosijp.® based upon the plotted coeffloients are Just
as acew rate a» if the theoretical analysis were correct*
Z*
cooditiona for cooling m t e r
Sju&tios B$ shews th a t the hold-up t in s in ersasss a s the r o ta tio n a l
speed deereaeest the logarithmic tea® is of secondary Importance,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
'Si#
fa c to rs in v o lv e d in th # logarithmic tmrm d©
not affect
te # hold-up tim e
much, bet th® best .spreading action ftps»r#nhly occurs shea th® -c e n trifu g a l
fore® at- the outer edge #quals th© grd'sitati-oaal fore® along th® fa c e ©f
th® fins*.
Stas® th * saws o f th # water As identical ia both eases, this
iae&aa th a t u»% should eq u al g cos K #
- Whoa this was
th© case ia th© tests,
tit® throw-off mmrr®& at or mm th # bottom of the fin®.
If either A
o r g cos <\ preiosiastes th® water does sot spread properly over the f t a s *
A longer hoM-«f tin® ©an he «s»«ct®€ with good spreading actim than
with th® aerator o p e ra tin g at a high a n g le « f In c lin a tio n *
fin s nearly, h o ri zo n t& l j if mkm
th® gravitational fore#
This mates tee
sm all %and it makes
IMs was v e r ifie d e x p e rim e n ta lly , f o r
possible a slow speed of rotation#
th e sum s# re p re s e n tin g th® heat tmaster c o e ffic ie n t# are higher for the
h i^ ie r angles o f o p eratio n #
In
tee
case of
(So® Figures 51* St, and 33*)
an Jarchtatadesn
a # ra t# r
o p e ra tio n f o r t e s t a e ra tio n m ast b#
optimum angle of o p e ra tio n
for
tee choice of a high
©cefromlsed with
the- se-rew pump.
of
an g le
th# 25 to 45 degree
Furtherm ore, a
high rotational speed gives th© test capacity f o r the screw f and low ro­
t a tio n a l -v e lo c ity
i® host for aeration*
S in g le
thread
screws w ith abort
pitch f lig h t s can b© designed ter ©pttw® © fe ra tie n a t 45 deg rees, b u t
aerators should perhaps s o t be designed ter much h ig h e r an g les *
An
Increase
In
the rate of
c o o lin g
water can fee aeh ieved by increasing
the a i r velocity over th© fins#- fh # 0ittus«BQ#lt«r eq u atio n (3) uhms
t h a t the tner®a®@ in the
heat
e ig h t tenths power of th#
air
tra n s fe r
v e lo c ity *
coefficient is proportional to
Sine®
th e f r ic t io n
th e
loss is pro-
Re produced with permission of the copyright owner. Further reproduction prohibited without permission.
.portion® ! to th « sir v e lo c ity is th e viscous region ( 3 ) , the cost of power
must he %m if high sir v e lo c itie s my® to he profit®*!#*
fo rb u len ce is
t» be avoided, because ia ibis re g io n f r ic t io n loss is m a r ly p ro p o rtio n a l
to th # square of th# air velocity |S|*
The co o lin g raags o w r whieh »a a e ra to r is to b# operated depend#
p r S m artly upon the condenser s y e te a it ie t# « r w ,
he In c re e e e d by enlarging the fit
fh e c o o lin g .range ©an
o r decree sing, th e water rat®-*
It
he® bees pointed, out th a t the water rat# can be decreased until th e water
cools to th© wet bull! tem p eratu re*
It is probably act econom ical to co o l
water to less than th e dry bulb ta n p e ra tu re , t o » 8 W «
■to
Archimedean a e ra to r eea be operated f o r c o n sid erab ly le e # th a n »
spray pond or a c o o lin g tower, for th e e f f i e i ©taey of c o n ta c t with th e a i r
1® h ig h e r*
Ih e e a rin g # in p e e in g co s ts may b e c o n s id e ra b le *
th e
Archimedean screw doe# have & h ig h e r overall e ffic ie n c y th a n a c e n tr ifu g a l
p m p , b u t this advantage m y be lost la its® speed reduction units*
How­
e v e r, w a te r must be pumped to a height of 20 or SO feet for a c o o lin g
towerj and it must b® pwaped to a pressure of ? founds per square inch for
a spray pond ( 5 ) .
An Archimedean aerator pumps mter to an average height
of only 2 to 4 feet*
Qti the o th e r hand, an Archimedean aerator oosts th re e
or four tim e s as mush a s a c o o lin g tower aads&ny tim es th® c o s t of a spray
pond, table fill shows th e costs o f a meefeeaieal draft ©©©ling tower
designed for co o lin g about 7,000 g a llo n s of water per m iante (1),
Fewer
was fig u re d a t on© cent per kilowatt h o u r, mad th # d e p re c ia tio n was taken
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Tata© n i l
Cost o f Operating a M echanical D ra ft Cooling Tower
Height
Length
W idth
20 fe e t
73 fort
25 fe e t
te s b e r
W ater
o f
4
Fans
7 , 000 g *p »st*
20 years
40 $
.300 days
1*01 per tew*-hr*
R a t©
Estimated. L ife
Pumping E ffic ie n c y
Annual Operation
Cost o f Poorer
In v e s tm e n t
Tow er
Cost
ip c tn .U e d
w ith
|'L2 * 22G*
fe n s
iwstore and swltehboxe®
T o ta l
| 2 0 * 740.
A n tm l O perating Costs
D e
• ~ ® c ia tio p .
o n
In v e s tm e n t
Cost:, o f pumping w ater
Cost of blowing a i r
T o ta l
Annual Cost
a t
5
g
$ 1,037.
6 *6 2 0 .
$ 0,
$ 1.155 per g.p.ffi.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
m
S per cent. fh # annual o p e ra tin g cost m th e 'basis of m e gal lea per
aiawfes is #1*16§*
fa b le IX shows th e costs of the Archimedean aerates"
which cools 11*8 gallons p©r mlaut#* fie p re e ia tle e m e taken as 5 per ee n t
to t h is ease*
th e r s b » 1 o p e ra tin g cost ia |l*2S S per g,*p*m*
Thas an
Archiraedes® aerator earring; snail water c o o lin g re fu ir# w n .ts is only
s lig h t ly less ©com saieal than a e e o lia g tow er h an d lin g #00 t im e as ««eh
mter*
Furtfeeitsere* I t is probable that enstage to toe first c o s t of an
Archimedean a e ra to r ©aa be B*d« when it is fetal I t to
0*
1*
$tsso*ry of Aeration
A flat circular d3.se
to rotate shoot an inclined a x is
m s set op to study empir&tim m t e r eooltojj as applied to th© fin s o f
an Archiiso dean aerator •
2*
A low .speed o f rotation is desirable to order to a t to© h o ld -u p
bo as high as p o s s ib le *
Best spreading n o tio n occurs *@ b th® e a n tr ifn g a l
a c c e le ra tio n at to® edge o f th e die© and th® a o e e le ra tlm o f p-arity across
th© face of to e disc are of th e saae order o f m agnitude*
I M s ©alls few
a h ig h angle of operation*:
S*
The discharge water ©as fee cooled, ■ m r j close to the wet holfe
temperature if the water feed rate is reduced ©a©»gh#
It is probably not
©aonenleal to cool below th© dry fenlb temperature*
4*
CffinsotiO B heat tra n s fe r « d isms transfer © © e ffic ie n ts ’ drop off
sh a rp ly as to® feed rat® approaches aero*
to is phaaoBteacn i s n o t wader.s te e d *
5*!3he design o f e id e m lla and th« aethed o f coniieetlag fin s to th e screw
o f an Archimedean a e ra to r w ere im proved*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-ts® ~
T&hl© I I
Cost o f 0 '© ra tin g an Archiseede&a Aerator
fin' Area
Angle o f Operation
Speed
Average Lift
Water Sat®
Estimated L ife
Pushing E ffic ie n c y
Annual O p eratio n
Cost o f Power
400 sq.ft.
60 degrees
17 r.p .m *
2 feet
-
11*8 g»P*a*
20 years
60 %
300 days
f .0 1 per 1sw*~hr.
Investment Cost
f296*00
Annual 0r c: s tin g Cost
Depreciation on investment at 3 |
Coat of operation (-pussplng)
Total
‘
.Amaial Cost
f 14*80
.53
I 15.33
| 1 .30 per
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6*
Th#
K m m t operating ©oat
s l i g j h t l y m o re t h a n
o v e r s ix
th a t
of
& fo re o d
of
aa Arehisssdeaa
a e ra to r
draft ©©©ling towor
is
o a p a b le
h u n d r e d t ir o e s a s m uch ’w a t a r *
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o n ly
o f h a n d lin g
?,
mmmmmm mnm
A.
« o i» « f io ia s
Bttoi n asd Construction
1* the m r fa Me s affeetiag capacity
t h * same eapacity for *aeh
fh® Archimedean screw posf
re v o lu tio n and is th e re fo re useful for * p p li« * tto n * r®%wlrimg accu rate
m eterin g o f chemical solutions*
Any p o s itiv e strive mri&bie speed tra n s ­
m ission ©an be used to adjust accurately th * rate of dosing a fluid stream
•whose rat© o f f l m
does mot vary* A nother m j to adjust th© dosage rat®
of aa Archimedes® *e r« v is to alter th® «sgl# of operati cm*
barge ©hang*.*
in th * dcs&g* rate can b# and* by plugging s u e e o s s ire ly ifc® tubes of a
m lt i p le th re a d lr©liis®d«*i» -m m * *
Z,
A v a ria b le p itc h mwm
la ©as® -mry slight ta n g o s la: th© dosage rat© are desired, an
Archimedean
screw which ha* mriabl© pitch ©«n be built*- Such a serev is
Illustrated in F ig u re 5S*. A tb.ro® tarter inch copper tub© m s wound In
the form of a spiralj vest tabes were s o ld e re d .to th e lowest two tarns.
The fig u re shows th® a©row smutted m a light fram e*
th e low er -end was
clamped to the fra*ee# end th e ah o le spiral can be palled sat in tension
to th e proper pitch and ©leaped with a C-el&af*
Ms a d ju s tin g w heel
should perhaps be arranged to -Bale® adjustm ent e a s ie r .
% is screw affords
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
screw
pitch
A variable
39.
Pifmr®
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
•
137*
a rosy ©lose control of the discharge providing it is rotated at a con stan t
speed.
S*
t o autom atic .p ro p c rtie n e r
f
If th© m ain fluid stream toes n o t fle w at a constant rat© sons a rra n g e *
« e n t m a t be m&m fo r altering the tosag# rat® p ro p o rtio n a te ly .
There
are- several p o s s ib le ways o f doing this,, bat the s im p le st seems to be
based on changing the a n g le o f ©per&tim *
th e Archimedean screw pump ©an
be- operated in a pivoted ©retdl# whisk ©an be raised or lowered w ith a. rope.
Th© m ala f lu id stream can be run over a w e ir , and th® rope tdiich changes
th e ang le o f o p e ra tio n o f the eoroar ©an be operated by a f loat behind th®
w e ir .
The weir plats m m t 1m m a s p e c ia l shape* for th® c a p a c ity of m,
Archimedean screw bears no simple r e la tio n to T i m through a weir*
the Arcfcii»d«am screw used f o r this p ro p o rtic n s r wag described in the
s e c tio n on the -A ro hi»dean screw pim p*
c h a ra e te r ia tic o f litis screw*
Fipj.ro 2S shows the capacity
F ig u re 40 shows th® dissuasions of the a rra n g e *
n e a t by sfoieh wwwmt* o f the float were tr&stisasittea to the c ra d le of th©
screw .
In Table X the g©©s»irle r e la tic n s obtained from Figure 40 were
used to c a lc u la te th® len g th of the rope CS corresponding to v a rio u s angles
of th e cradle.
Sine® th e jUrehlmedean screw shut off at 79*5 degrees* th e
liq u id head on th e w e ir h had to be aero a t th is a n g le * and th e differ­
ential change to th e head m s th e same as th e chenge in th e length. CD.
The c a p a c ity o f th© screw taken from Figure 28 m s also en te re d in Tabic X .
A convenient dosage r a te was chosen* and the eorrespendlitg rat© of flow
o f th e main f lu id streeia wa® entered ia the ta b le .
Figure 41 shows th e
c h a ra c te r is tic of th e d e s ire d weir plat©-*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Float
Control
for the automatic
Frooortioner
-1 3 8 -
Re produced with permission of the copyright owner. Further reproduction prohibited without permission.
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Form E-5
-1 4 0 -
%
rLtt
S
m
I
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m a t.:
t;
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
• M l*
Sines th e r a te of flow through efteh # l « « t of a w e ir is proportional
to th e square ro o t o f the flat# head, o u t and try methods mm entirely
te e tedious.#
Consequently te e following n um erical ssethod was dev®loped*
R e fe rrin g to fig u re 42 let*
c * ©ontmetioa coefficient ® 0,45
g • aeeelemtiso* of gravity (inches per minute per jaitm te)
h *» fluid head m the weir (in c h e s )
ft « t o t a l q x irr.tity o f flow (c u b ic inches p e r m in ute)
'v * fluid velocity (in c h es per m in u te)
x « width of th e weir (la s h e s )
y » depth ¥«lo«r the fluid swftct (in e h e e )
T * e / 2 gy'
(6 0 )
^ * Jo Yw iy • o V l i
* /y " d y
(7 0 )
|| * ■© -/Sg x yy*
(71)
(n )
?S2 ■/j’
o y i^
A ft * (d % % ) A y
(7S )
H ie v e r t ic a l distance on th# weir plat# was
divided into ©onwniemt
ineresam ts* end th e e a le u la ii« B o f th e successive widths was accom plished
in th e fo llo w in g Benner#
equivalent 4 ft/4 y ,
fee slope dft/dy m e replaced hy its p r a c tic a l
With tia® f lu id fesai at the low est increm ent th® c o r*
responding w id th was e e ls u la te d u sing eq u atio n 72#
The fluid head was
then shifted to the second lneressent* and the q u a n tity flawing through
th e first tmerewat m s e ftle u M te d for
73.
this q u a n tity w
this heed using
equations f l end
subferaeted tr&m that which was required, and
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-1 4 2 -
zn zzzzzm
Numerical V.eir Plate !• si;-n
Figure
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
'»M S~ ■
th e r«H»iiia8r vm used to calculate th e width of the second increm ent
using eq u atio n 72 as b e fo re *
of th e. w e ir was c a lc u la te d *
C ontinuing ia this my th e com plete shape
(See 'Table XI.)
c u la te d shape m e half full e ls e *
F ig u re 4S shows th e c a l­
H ie heart shaped h o le a t the bottom Is
mot e x a c tly c o r r e c t, for the c u rv a tu re is promewaoed t n this re g io n and
dfy^dy differs somewhat f r m
A Q /A y*
When t h is m s fin is h e d , the proporfclomer m s aseev&led using ball
bearings in the.pivot at the lower tad o f th e c r a d le .
The d r iv e mechanism
has heoa d es crib e d ia the section. «® the Archimedean screw pump#
It was
then d isco vered that the affair could n o t be counterbalanced by loading
the float*
This should have boon obvious, for the load of th© sw inging
s o re r on th e rope changed with th© an g le a t which it happened to be pull lag*
C ounterbalaneing could beat be accom plished by m ounting th e screw to
pivot about i t s mn c e n te r of g r a v ity *
This would have required e x te n s iv e
r e b u ild in g , and problem s such as mere adequate vesting sad provision for
n o t dunking th# m otor would lav© arises,
Th© counterbalancing usethod that
was used is shows in tie picture, Figure 44.
k steel beam was pivoted
about a point directly above th e pivot of the screw c ra d le *
The upper end
of th e screw c ra d le was suspended by a red of* adjustable len g th from m e
end o f th e beam} th® other end of th e beam was supplied v d th .an adjustable
cou nter weight*
the beam was arranged ia such a way t h a t it was parallel
to th e screw a x is a t a l l tim e s , and th e cou n ter weight was adjusted to
counterbalance th e screw regardless o f i t s p o s itio n * Sail b earin g s were
used a t a l l eonaoctiag poiati o f th e lin k and a t th© beam pivot*.
Hxeept
f o r a co n sid erab le nsowat of in e r t ia this m e entirely s a tis fa c to r y f o r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
*144*
fa b l® I I
Design o f th e 1 % ir P la te
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---------- —
Tab le X I (C o n t.)
Das:
U : y t h-y
:
inches:insl rJixches
IX,0 • j.2.0 : o.o
w
* 11.5 : 0.5
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i
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:
12,0 £ 4*W ; 8.0
:
ix,o : 2 .0 t 10,0
:
12.0
0 .0 ; i2 ,o
of The Xeir Plate
* 1;A& i
X
‘ 4& 1
: A j : V T :Vy 4?:
:inches
:
..'.-Mr..i. .In. ,, inches:
i.
l 3*11 T~^o37o *67 1->2
'j* i
I
I
; 78.C 0.5 : 196,0:
:
: 5*3V ; 174.5:0,232
:
:
i 206 .
0.5 : 592. :
IX4.I
:
: 3*32 j 503, ;0*668
0 .$ :l£?0. :
122?.?
:
j 3.24 *. 993 . a. 320
:
:
:1c. ', : 0.5 :3£15* :
..,1vX:
:
j
3 .3.6 i 0 ,...:0 ,.
as?/*:
£
i £5.0 : 1,0 5 25.0:
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2862 ,:
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t 3.00 : 128,0:0.0170
:
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: 3041 .0 : 384. :
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: 2 ,43 : 152,0:0.0176
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35'94»:
: 922 ,
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4016.:
: .j. « •w : 340,
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4v
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-1 4 8 .
Shape of the V.eir
(one-half full size)
Figure 43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
p ro p o rtio n ***
ffao autowktie
44*
Figur©
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-1 8 0 *
ootm terb alaneing th e j® p ty pump*
The water which th e pusp c o n ta in e d *
however* was greater at. lew angles th a n a t h ig h ones*
Si is was taken c a re
of by arranging for th® rope to poll nearly vertically* as illustrated*
Thus* A o n the ©crew operate* at low angles * the rope pulls w ith a. fa v o r­
a b le mechanical advantage\ when the screw rises* th e advantage becosies
lo ss fa v o ra b le ,
B*
Operating Results with the Autos* tie Proportion©?
1* ArohiBtedoan screw pcyformaee
The date, cheeking te e c a p a c ity of th e Arehiioedeaa s e n t were pre­
sented in th e section o f th e Archimedean screw pwsp* fable I shored t h a t
th e a c tu a l c a p a c ity equalled th e theoretical when the fo llo w in g p recau tio n s
were ta k e n *
She screw mast b© ad e q u ately ven ted } th® submergence must be
over th e cor© a t the lower fa c e b u t not so groat as to drawn th e vest
tu b e s f and te e speed o f r o ta tio n suet b# low*
§.*.
P e rfo rm a n c e
of the twir plate
Table X I I shows th e perfesnftaee o f
th #
first weir p la te *
The actual
c a p a c ity does not matter a* long •« the perform ance fa c to r stays constant*
The perform ance factor o f about 1*8 in d ic a te s that te e cont r a c t ! on co­
efficient chosen*. 0*46* should have bees. 0 *7 2 *
The p erfo rsaaee of th e
first weir plat# was not considered satisfactory,
This was to be remedied,
by filing the edges o f the plat© s lig h t ly t& th© right places.
v e ry difficult, sad the first w e ir p la t© was mined*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
This proved
-lil*
The second w e ir p is te was la id out ead c u t sore a c c u ra te ly th a n th e
f ir s t .
A 'im te l -c u ttin g power j i g w
» i nw d on th e c u rv e s , and the
fin is h e d plat© was chew ed w ith in on© f i f t i e t h
shews th e per form a© e of th is w e ir .
o f an in c h .
Table X I I I
Yfcwn the head m th e w e ir exceeded
1*92 toshes th e fa c to r of p e rfo rm n c s is w ith in 4 per cent o f it s m m
W ith th is w e ir plat® the co n tra c tio n e o # ffie i© s t* 0 .4 5 , should
m in e .
th e p is te does n e t fu n c tio n p ro p erly a t heads below 1*92
h am hero 0*S *
in c h e s .
4 1 }*
la th is re g io n th e c h a ra c te ris tic has a p e c u lia r simp© (see fig u re
In th e num erical ie s tp s th e increm ents ©feosea were to o larg e to
fo llo w the c u rv a tu re e lo s e ly .
Parfeherme-r©*. th e o r m te r ® is so sharp
th a t th e design method would h am r e t i r e d n egative w idths* which a re out
o f th e q u estio n on. any p r a c tic a l p la te *
If a siaiatsa rat© of flopr o f six
g a llo n s per m inute is s u p p lied * th e w e ir w i l l he s a tis fa c to r y *
When, the
p r o p o r t io n e r m s
i t was tried out
as
T h e h a r d w a te r u s e d
a n a ly s is r * m
in.
&
e e m p le ts m 4
for a lise-seda,
c h e m ic a l fe e d e r
had th e
a c c o rd a n c e
f o llo w in g
th e e le m e n ts
composition a®
with Jerome
B ld r x d
e
had
ash
he«a
water
d e te r m in e d
-tested*
s o fte n e r *
by frequent
and Mai Imxm (2 1 ),
P*P*SS*
IS*P*€
As C»C%
Temporary hardness
Permanent hardness
Total hardness
Cartas dioxide
HsgneslusL
300
150
450
31
38
17.4
6.7
26*1
l«-0
2.2
Sine© no ta s k o r sand f i l t e r large enough t o handle the output o f the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
*4fi»
T ab le I I I
Perform ance o f th e F ir s t Vsoir P la te
Head inches
Weights lb s ,
j l^S 'ir~335T**5^S W ~9'*8b
t
i
t
t
132*10:36 *50;7?.<5:71*75
s 6.25s 6.25*. 6 .25 s 6.25
j25.S5t80.25;73*00:65.50
: 1.00; 1*00; 0»50: 0,25
Grass
’arc
Kot
Tire "ioutes
Discharge cm.in./ain, ;
Actual
Theoretical
perforaance Factor
:
1
:
s 715;2,220; 4,040:7,270
; 630:1,300s2,350:4,730
: 1*66; 1.71; 1.72:. 1.54
Table 1111
Perfojw ar.ce o f th e Second Weir P la te
Hoad inches
0.90; 1.57*. 1.78; 1792: 2.02; 2.01: 2.39
Weights lbs.
Gross
Tare
Net
Time arinut.es
Mscharge cti.iri./ain.
Actual
Theoretical
Performnce Factor
Head inches
heights lbs.
Grass
.
'rare
Hei
Tim© ,nr*rrat "
lp,4 *>
.#
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■•*.^',*» <
»
•■
«
*»,•V
*.S
/«
*.«i.W
>-,**■
#"<■’?***
Actual
Theoretical
Performance Factor
;
;
:
;
;
:
:
;22.7C;U.17 “2*60. \5.?5; 5/.60:60.40*6 3*75
r 6,25: 6,2>* 6.26: <».;-*•; 6.*5; 6.25; 6.25
U 6 .66; jS. 25 :6 6 .2>:JW. 50 ;57 ..5 *.54.15:57*50
: i.Ou; j,)0: I.')'1; J.2 .J* 2,<)u: ..00; i.OO
;
'f/o;1, v24: 1,'5?0;1,480; 1,500; 1,595
750: 750; 800
*. 3.25: .2.7 j; 2 . .‘ L t i.,9fc>: 1.07; 2.00: 1.99
;
ft-: >50: 6>u-0 ”'50:
: 2*30; 2*76;
3 .2 6 :
i.*08: 4.75
s
:
;
:un*2G;-JO.20:72*>0 :6 }.20:77«Ji/;93*25;94»25
;
1
s ' :
; 6.^5: 6.2$; 6.^5; 6.25: ^*10: 6.25: 6*2>
:6q .55:73.95:63.25: 56.75:71.05:67.00; B8.00
: i.OC; 1.0.': 0.75: 7.5'H 0.50; 0.50: 0.25
*
*
*
•
»
.
*
.
*
;l,70r.;r»G50:2,450; 3.160:3,940:6,830:9,760
; HU :If2-0:1,250:1,- J ? 2 M ;
6,850
t 2.03: 2.01: 1.9o: x.94; /.J7: ^,.oQ: 2.01
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-IB S -p ro p o rtio n © r
wa® amil&bl#
doa«€ w a te r
th e
allowed to stand
ta k e n fo r on© rainute in t e r v a l* * . The sea p le a were
fo u r h o u rs, and then th e y
long ru n * These
shortage
beh avior
slowly t©
run*
carbonate sludge
lint® was originally assumed
was
-considerable excess
that
for*
The
th e p ro p o rti oner
proportdester
has
tin* is m m m & r y for an increase
screw f i l l s up at a
low er a n g le *
s te a d ily throughout
S h i* must have been
allo w ed
flow rat®* ?h®
son© a d d itio n a l
decreased rather
first
th e
water analysis the correct
fjs«
sudden changes in th e
th e
and
tem porary
lit p*f*»* of soda ash (t®^ SagCOg)
-(§.2*6fS
inertia* but
aaaen t hardness
hard
tw e n ty *
of soda ash end a
cverdoee
hardness r e f le c ts th e fa c t
the flow rat® while
o f th e te s t
of the
b asis
She
shews th e result of
there m s m
th a t
CaC-SlJg, and &
of the total
c o n sid erab le
in
the
S&fcle XVt
dosage should have bean
co n tain S-6^
re a c ts
Ga
p.*p*s* o f lii*
and 46®
to
data s h m .
of lise*
theoretical
w»r# filtered and analysed*
i#ten»iwd*
t o t a l hards©*® wove
Samples were
» s discarded*.
due to the
The p e r-
the hour and
accum ulation
a
half
©f calcit®
In the tank®* fludg® is knesm to promote the rate of
th s p r e c ip ita tio n re a c tio n s *
Table®
XV
through
JtVXXI sliwr the
re s u lts
of successive w a te r
lag run.®# Table. XV shows a large ©hangs in tli® dosage*
when
the w a te r
found to be
rate m s
out
changed*
of step with
th e
This
and
hardness ess bs
T a b le .X V III
produced.*
with & considerable
excess
occurred
m s traced, and the screw was
weir* Tli® ro w
was too short* Tables XVI
w hich
s o fte n -
eozrnsoting
Xfll shew th a t mter
.shows q u ite
with
s o ft
lew
to
th® f lo a t
tem porary
mter
obtained
of both Its® and soda ash* In all sf th ese
runs th® sarples showed very #rratl© behavior* Sow of this was traced
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
*im *
M L © Xtf
W ater S o fte n in g w i.th t-b# Aufccasatic P ro p artlsm er
Archimedean Screw Soead
50 r.p .itu
Mb * 1 r i** if®
Lime o S .v t C/(T;.-)
Soda Ash ;} %
SimolQ
No.
Bard
1
2
Change Hats
3
4
5
Cti&ng-e Rate
6
7
8
Chcnpe Rate
9
10
11
12
13
14
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15
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16
17
18
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192
204
164
198
174
•138*
T&hl® X?
later SoftaKisg tan So* 2
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Wafam Seftwrlag i « 1®* §
Sffctowr i:#*®.§e
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586 p .p .® .
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50
so
26
6
SO
0
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—189—
to Insufficient agitation*
Table XfTlI shows a mere or less steady increase
in the excess ilsse and a decrease ia the excess soda ash. The lime prob­
ably settled la the slurry teals until the concentration got high enough
to carry it surer, the agitation couM sot be increased -wwy much* because
the air used produced & wry stall© .foam* which drowned Si© vent tube#
of the .screw.
Is order to make longer rums p o s s ib le the speed of th e Jrcfcimodeaa
screw c m changed from 60 r*p *m * to 20.8 r*p*H U * and th e soda ash was
em itted fro®
the slurry* fa b le # SIX end XX shew the results obtained*
Hie w a te r was purposely underdosed* asl the cample# sheared much more re­
lia b le results.
The improvement m s probably due to the slower speed of*
'idie screw* for Table XXI shews that equally consistent results were ob­
tained using both lime and mSm. ash*.
0*. piseussiea o
e
dts
1* R e lia b ilit y fend response
The tables of o peratin g , results <m th e au to m atic proportion#!* indicate
r e la t iv e u n r e lia b ilit y *
Tables X IX *
XX* and H i show th a t fairly good
results can be secured if .operations a re e o ra in w d long enough to p erm it
the es ta b lis h m e n t of e q u ilib riu m c o n d itio n s *
These
last three runs show
that th e hardness varies less th a n fo u rte e n p .p * » * fro® the mean v a lu e *
Although
this seems p oo r, much. o f the e a r ia tio a would d isapp ear is the
s e t t lin g
chamber o f a eossflet© water s o fte n in g in s t a lla t io n *
A. settling
task large enough to handle the output of the p ro p o rtle n e r wee act a v a il­
a b le f o r te s tin g this # however*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
.*180*
m tsi® x u
W ater Mftmtmg Sim. S o. 6
W ater to n g ®
C o s ie s t! d ta r r y
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168 p.p.nu lirne
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258
214
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m i#
ix i
H a t e r I© f% # B in g S t® S o * 8
later dosage
Mffi©
Soda ash
Sample
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•163.
The data presented In Table XXT show that the p ro p o rtlo n e r does
n o t follow sudden change® in the food ra te very r a p id ly .
Ten or fifteen
minutes a re re q u ire d .for the dooag® to reach e q e ilib r itm after a change*
Table S I
a h a ** that fifteen m inute intervals e re s u f f ic ie n t for the tie-
y ie f to-reach, ajproodm ate bmtmcfa wh&a i t
is operating properly* A t a
flo w r a te o f tw en ty g a llo n s per minute three hundred gallons of o f f tre a te d w a te r would flow into th e s o fte n in g system in f if t e e n m in u tes*
A-
s e t t lin g b as in large enough for a four hour d e te n tio n tim e would hold
about sew n thousand gallm»*
$hia would p e rm it about 4 1/3 pur coat
variation in te e hardness o f the treated w a te r*
If the settling basin
wore replaced by mm o f the mm Spaulding p r e c ip ita to rs {Z)t the treated
w a te r m ig h t v a ry a s much as 10 p er cen t*,
th is in d ic a te s th a t the r e ­
sponse of the autom atie p ro p e rtlo n e r needs to be improved e ith e r by de­
creasing the f r ic t io n a l drag of th e bearings o r by reducing te e inertia
o f th e counterbalance or both*
Zm M o d iil c a tio n s
A new model chem ical p ro p o rtlo n e r should be designed w ith a view to
red u cin g th e inertia of the screw *
An obvious Improvement could be .made
by pivoting tee screw carriage in th e m id d le ,
fh e v e n tin g of the screw
must be- changed p robably by p ro v id in g nested sidewalls for th e entire
low er h a lf o f th e screw*
A s m a lle r .and; lighter screw could be used., and
th is , would a llo w the use of a lig h t e r m eter and speed reducer*
W ith these
changes the response should be c o n s id e ra b ly im proved*
I f an ac c u ra te c o n tro l o f the feed rate is neoess&ry* a continuously
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
«164*
v a ria b le speed reduo-lag tran sm issio n should, be p ro vid ed *
The tin k « *B e lt
variable roller iris# ( W S ) ( IS ) i# * li'-'-r, duty tmit? but It provides
oily a Moderate speed rednetlea,. and its. weight is perhaps too
m ue h
to
counterbalance* A- variable friction dr tee unit can probably be i@si.gned
that is light and insspeasive*
$ueh a unit should bare a positive drive.
Ibis can perhaps be accomplished by spring leading the friction drive
surfaces.
P.
Stssafery ©f F re p o rtio n in g
1. Since the Archijaedean screw delivers the seme quantity o f liquid
each revolution* it is sell adapted to ehemical proportioning,*
2*. For feeding ohssdeal s o lu tio n s in to a f lu id flowing at & ocn staat r a te a variable p itc h m v m was d evelo p ed .
Variation of th e p i boh
makes possible m inute v»riatis» in th e chem ical feed rate*
3#
For a fluid flwrtsg at * mriftbls rat© an autoimtie proper'ticner
w i developed*. A specially shaped weir plate is the main flew stream « «
used to actuate a float which in turn set the angle at wl-iich the Archimedean
seres', operated*
4*
%i9 ttutoaati© proportioner was used to dog© hard water vtitb a
ash solution*
tae device was disappoinl _
1 slow in respond*
lag to changes* but the reliability was developed satisfactorily*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•10®**
?x*
m m mwuQknmn m f i t
A*
1«
$mm
A m.% f%m$pQSK(r Design
\
Gas d e liv e ry c a p a c ity .
At angles helosr tbs »teim» self venting angle provision mast fee
m & » £ o r vent teg the spsse festwwm liquid slugs as they fora at the lower
end of th© screw.
If tele venting is limited to- the bottom of the screw,
the liquid slugs act e® pistons end deliver the vent gas is a positive
manner*
So eeKprsssioa ia the ic r « is possible unless the sis# of the
wraps progressively decreases, feat tfee ier« » y fee nssd to proportion
p.s and llqeld *ln*i Into a vertical pipe for esunprsssisn fey fhs Impact
of th© falling liquid slugs#
Sueh a device is illustrated in Figure 4S*
Per tlii® purpose the procedure to deterwtoe the gas delivery is of inter­
est.
A number o f jwstee&s fo r d eterm in in g te e volume o f the liq u id slag
h *v» been d e s c rib e d * Equation 14 I s an a n a ly tic a l espressios fo r the t o t a l
volume o f on© wmp o f * screw.
fit© d iffe re n t*© featwaoa th© t o t a l volume
•a d the volume occupied fey th® liq u id slug is the voltes© occupied fey g&g,
i f a© pressure is feeing b u ilt up in th e screw.
One c f th e most d ire c t
methods o f c a lc u la tin g the g&s d e liv e ry c a p a c ity is o btained fey a s lig h t
rearrangem ent o f eq u atio n 8.
Ws « ^
If f§ is th e gas d e liv e ry volume
iso + are
e o * ({3 0 t)
- arc
©o«
fBP/l)
• Z7TR(oroBS s s e tl& n ftl are a o f th e tu b e )
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
.(74)
(1 4 )
-1 6 6 -
Hoad
Archino' oan
0 crew
H
Inlet
T>
T7,
7/
Outlet
A G.-U:> Connressnr Lesion
Figure 15
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
*1672m
The Math lascm qyataift
F ig u re 46 show®' how the ©ompneam r 'works *
fhe Archiraedean poap
l i f t s the liq u id from th e fe e d hoy,: to fe e foeed hoxj a t th e same tin ® gee.
• is m arried alo n g in a fix e d re,tie t@ th e liq u id *
liq u id eosqarees th e gas t o fe e f in a l p rees u re*
fta> falling slugs ©f
A c o o lin g Jacket around
th e pipe max he ©f aosse h e lp in pre’spsmtin^ th e tem perature rise Avm to
eoarpjreeslott* . th e pressure built up 4a the s e p a ra tin g tank supports a
■©©iwart of liq u id le a d in g t o the feed box which is at in le t p ressu re*
Suefa a pm p as th is s ig h t be u s e fu l to handle c o rro s iv e gases f e a t would
r u in a co n ven tio n al eorapressor*
.1*
d ucke ted P u s p
Am Arohiiaedean mrmt jn»p mu easily be Jacketed for handling, viscous
liq u id s that »ast he kept, hot*
the Jacket «aa he cylindrical is shape
c a te rin g fe e entire easin g of fe e screw*
The steam lin e e»» be run in
through a s tu ffin g box is th e upper b e a rin g , and th e condensate pipe can
be c a rrie d out at th e bottom bearing*
The slow speed of th e A rfelm edean
screw is also an advantage Is h an d lin g viscous liquids, for there is less
power loss'at slow speeds*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
*& §8<e
m i*
e o fc m io s s
la a d d itio n to th e c h a ra c te ris tic ® developed l a th e previous l i t e r ­
a tu re o f th e Archimedean screw*. th e optimum an g le of o p e ra tio n was
lo c a te d as betog to fe e s » i ghborfeooi o f t h ir t y d eg ree**
Th® sub,-feet o f
w ritin g was advanced w ith e q u a tlm a fo r d eterm in in g the ® ia i« a s e lf
v o t in g a n g le *
A fre e te d y a n a ly s is e f a liq u id s la g m s mad® to show
th e e q u ilib riu m n a tu re o f th e Archimedean aerew p a p *
A discu ssio n o f
th e accuracy o f eoruitnaotiott in d ic a te d th e sources o f p rin c ip a l e r r o r
to c a lc u la tin g ; c a p a c ity *
too analyses o f the e v a p o ra tiv e water o oo ltog process as a p p lie d to
th e Arch is® dean a e ra to r fto* w ere mud**
te s ts sad# m a r o ta tin g d ls e
showed to e e f fe c t o f s iz e , speed o f r o ta tio n , and ang le o f o p e ra tio n
upon to e water c o o lin g process*
fhe im portance ©f good, spreading a c tio n
and of h o ld -u p h i® * was in d ic a te d *
to® chem ical p ro p o rtio n in g pwaps w ere b u ilt * .
The f i r s t m s a v a ria b le
p itc h screw s u ita b le f o r a preelse ad justm ent o f th e fe e d rate*
fh e
second p ro p o rtio n e r was an au to m atic chem ical fe e d e r capable o f dosing
a stream o f w ate r u n ifo rm ly mmn th o u # to e flo w ra te v a r ie s ,
fh®
au to m t ie p ro p o rt io n e r m s te s te d f o r s u it a b ilit y as a fe e d e r on a ltoesoda ash w a te r s o fte n e r*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
>M§»
S o i« ra pw ptiag wad hyArmHe m.®mmry+ pp» $i&.g $58.9 Gh&rlm
iriffia mm Co., IM * 0. fULlftfelfhift* M U *
A 4 « *e rlp ti< m o f
types o f wished serew fwtps including
right and l e f t hand «#*#»« and # # * * * *
w ith a g ear and w ith
a'©hate gwar corah*
A detailed dftfteripti#**. ©¥ if*# te n BastmwAadtaraera ArehIjsedeaB
screw ;p»jje. #®t «p «t
Igyft# they were eleven feet ia
dliweter ®s*d forty feet l«a§». ead they hand lei 1»«ahy-fiv# t o e
of water per revolution.
S u tle r , I *
iayeiag,. 1 * J * #.* Jr«ev« ter ’
bepa.liBf- van de m inst# J»«gt® *aa de ktiif
vea #e» v * i|t® la e l« to gemru fi^daehrift w s hot I« lo k :liJ k
In s t it u t vwsj In g e rie o rs * S o ta le n 1851-2 * pp. 17 9 , 1 8 8 -7 *
B#»erife#s the o p e ra tio n of a ®o4©l o f th® Dutch screw .
C a g le , R* I . and C a g le , K *-L *
J u ly 4 , 1916.
F ta p ls g seehis#*
This i® « elosti Arci iweHteaai « e « w
Id #
1 * S. Brfcest 1 ,1 9 0 ,2 1 8 .
vsrtieally at
speed.
C o ly e r , F* Ptaaps and ptsspififg s a A i^ e ry * pp* 8®**?# E * and ? , 1 * Spoa,
Load eta* 1889.
Peeerihos Hi# Airy m & Anderson p a te n t spiral pw»p* T h ia is a
closed Archtoede&n • * * « * feawiag a f r ic t io n d is c at the wp$#r end to
m k e discharg e #f water at ih® highest point fosslM*.
Constant, 1* 1* i»hri©*M#s d*un aoiil# powr pieces a t e r m * les spires
des ©lev&teurs & vis i%reMm«I#* la le w © 4® fonder!# K®4«ra®:.
.2 7 *1 -4 .
IfiS *
ffel® 1® * i»f»il#i JaaarlpticBi for- tedMing a wooden pattern
for use in foundry casting*
JtaGayffl*?, K* S«r 1‘eaplei d ’une vi® d*Ar«lii»«-As mue par use sachin® a
mpmr porn* 1 ’ a l linen ta tio n da e a p a l A# ioaetiesa 4 # la S«safer@ a
■ 1 *0 ! s e . te a a le s des Fonts e t Ctifttt#®##®, $* s # r i t , '2 # s e w t t r e .
6 * So* 77 1-1S * 1843.
A J w e r tp tio s o f th e e e ® « tr« ® tt*. »ai. f® rf« r*« *e # o f a s te a »
d riv e n Arcfcliiei®*®. screw. Q a lt# » ii« f » « t © r y f»rf<wr»ane# «a« ob­
ta in e d , and 1fe« devie© should he mere e jtte a s lv e ly med in I r r l f f t t i o n *
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-I?0-
SeJtaaar, 0, G* A mrcurj compressor evolved frost th# Archimedes screw
jaaap. R e frig e ra tin g Engineering* 13tlS8«€f* 1926*
th is d escribes th# slew speed te rm of th # lelmer com pressor.
I t c o n s is ts of an A rto toedaan serew S§ toehes is d ia m e te r o p e ra tin g
a t 20 degrees to l i e w r t i e a l axis of rotation*. the eom to rb elen eed
screw ro ta te *, about the axis at 380-4® r,f«*** but is. kept from
tu rn in g by the paaoake spiral# of the in lo t and o u tle t lines . This
compressor re q u ire s 12' lb* of imrmury*
DeRemer* J. 0*. mad Btaftw* G. W. Eeee&t improvements in th® mercury gft#
eOBprwwwr*. B e fW g e ra tte r S sg taeerto g * fS iSOf-lQ* 1913*
A d e s c rip tio n of an improved fora, of BeResser compressor c m s la tin g of a I t o . * 1 1 |n# Archimedean screw o p e ra tin g at an angle
o f 8 degrees to th e h o ris c n te l axis of ro ta tio n of a oeatrifugal
f i e l d * f h i * model is directly connected to a 1760 r ,p * ia . e le c t r ie
actor* It contains o n ly 1 1/3 lb# of m ercury, ftai the paneftke
spiral inlet ftsd o u tle t lin e a are replaced by helical coils.
Beber das forder%««atua d e r vasseraetm eeke* Hannover Z e it s c h r if t d «* A r to ite e te a wad to g e a ie u r*
1813*
This is an a tte a ^ t to develop the theory and calculation of
capacity o f as A y eh ia«d **a mrm*
©rate* A*
Or®®!* Arthur it** dr* Pwaptog ssaohtooiy* p* 14*
1m York. 'lill*
A brief descriftiaa o f a tutoli screw*
dote Wiley and Sows*
Hftrdtoge lo »
H ardinge ©omt#r-»urr«t classifier* B u lle tin . So* S®A,
York, Pennsylwaato* 1936*
This is a closed tocfcis»d#a« screw without a cor® adapted to
perform as & sand c la s s if ie r .
Hawkins, Reheaaifih. Rasp* and h y d ra a iie s * V o l. 1 , p* 83* Thee* Audol
and C o ., I«sr Yeffc*. IS IS *
A o u t and d e s c rip tio n . o f a® e a r ly fe r n of closed Arehtoedean.
screw*
H ereh , J . C * frm.£mm$agm met eeas w a te r v ijs e l. In g e r le u f* S it Be* 49
9 4 9 -5 4 . 1916. ' '
A ia te h screw ms- ta s te d under m rio u ® co n d itio n ® o f o p eratio n
to d e te ra to # th® r e la tio n s h ip o f th® e s e h a a le a l e ffic ie n c y end to e
output to th e v e lo c ity of -fee screw moA th® h e ig h t of th.® ■water on
the low er fa e e *. flm r e s u lts a re a t r i f l e e r r a t ic .
S u e t, A * YerbeterA e to r lc h tto g .van v lja e la a le s i* f ijis c h r if f c w r h a t
le n t o k lijk In s t it u u t m » la g e s ie e rs * K e tu lau Amr V erg ard eriag en
18S7-18S8*
§3-88.
G eneral notes os th # e m « tr u e tlm o f la tc h screws*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-4 7 1 lopefe®, C * W b e r d ie eonsbraebion e in e r a tie fe a hmgebTi’ cke* Hannover
l e i t s c h r i f t des A ro h ite c te n pud In g e n ie u r* 6 s2 5 8 -7 2 . Its © *
Cte th e o ry and e a & m l& tio a of capacity ©f Archimedean screw s.
Krohnke, S.*. l i n p w p fo n a s le a f a r «J®» b *« von m tsoraobnscksn.* Ssuteehe
B te M itia g * 1 0 15 7 7 -9 j 386*9« 18T«*
T h is is a very eom plete discussion of th e closed screw . I t
notes th e d i f f i c u lt y o f o b ta in in g an analytical solution o f c a p a c ity !
i t g ives equations fo r t r i a l solution o f th e approxim ate c a p a c ity .
V en tin g Is emphasized* and the d e s ire Is arranged for a continuous
a i r passage throughout th e full le n g th o f the screw* Seise perform ance
data on ty p ic a l screws, is mentioned*
L in k -B e lt Co.
C atalo g €0 0 *
p* 715,
Chicago,
1934.
fhe L in k - f e lt Internal f lig h t conveyor is a closed screw without
a core*
l o h l, 1* I* A study o f the Arohlm 4 m m screw as * pump f o r chem ical
e n g in e e rin g purposes# Bnpohliehed
2* thesis* Library, Iowa State
C o lle g e , Ass»%. 1 « » *
IS 3 6 .
la Ar©hl»«d©*«i teresr, e m e i s tin g o f two sec tio n s of garden hose
mounted on a wooden f * * a e , was te s te d , fh e in p e rtm e e o f exactly
th e proper submergence is engfeasiaed*
Muysken, 4* Beretosateg vest het awfetlg e f fe c t van de v i j s e l . De IngoEieur*
47* W f T - f l. 1932*
A discu ssio n of th e IH&teh screw in c lu d in g a graphical method of
d eterm in in g th e .©ftjfcsiiy* M«©fa attention is g iven to 1fee vario u s
sources of lo s s in the Butch screw end their probable magnitude*
Some o f the losses a p p ly to th# closed screw, hut the bulk of the
w a te r leakage and energy loss#® mm act present is th e closed screw.
fh e le w In te rn a tio n a l E n cyclo p aed ic, f *® f * Dodd Mead end Co* lew York.
1930#
th is is a suaaftry of th e construction and operation of both
th© closed screw «id th e Dutch screw.
B ellm an , !■* f, fh e principle ©f th« A rehlnedean screw la shem ieal e n g i­
n e e rin g * Ifepublisbod ?h* 1>* fh e e ie * Library, Iowa State College,
Ames, Iowa. 1938*
A study of the characteris tle s o f th e Arehiswdeaa screw la
detail* Th® tru e nature of the ”siphon e f f e c t * is diseussed,
two simple methods are developed to o w r e e w It*
Several approximate
netheds of c a lc u la tin g th# theoretical o a p a e ity are p re s e a te d , and
the methods la th© literature m m reviewed.* A. amber of specific
r e la tio n s between the s is # o f the screw part# are presented*
An application o f tli# Arehlaaedsftn seres? to lift water a s h o rt
distance and d is tr ib u te It over a number of spiral fins in contact
with the a i r is described* fhe device was designed, built, m i tested
f o r w a te r cooling and oxygen a b s o rp tio n character isties.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•1?2Saydme# Parfee T *
las&ean
A
Is the
bottoss
(To B e a tty , T?» J . ) A w a te r h o is t in c lu d in g m A re fe iacrew* U* S. P a te n t 1,085,MS * February S, If1 4 ,
description of several innovations including * spiral slot
eor* of a closed screw, a. set of
valve gates at the
of m m h tube of the screw, and flights ©f peculiar shape-,
Swindis, .1, Q k m le & t works pasplag,
pf* S4**§, Bens Brethers, ltd,
London, I f f t ,
.A d e s c rip tio n of both type® of Arcbiaeieaa screws (the closed
screw and th e Dutch screw}* I t is sail to be used ©a some e le e t r o ly tie
c e lls ,
Tylvmd, I* Qm v®Li«egl«i oiler
ydtoovxsa* Isgeniorea 11*550-2,
' 1932 •
fhe lltor*t»ro is reviewed, end th# eafwriMSBtal results of ses®
observers ere sited, A method for the graphical eslctilati®a of the
theoretical capacity of the Dutch screw is developed, fh e Dutch
screw e*» be expected to have a voltneeirie efficiency of 90 par cent
and as ever«*ll efficiency of 60 per cert,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•ITS*
s.,
1*
u
t
m
m
m
c
i t s
d
tew a* John. J a fo ia s tio n m th e .-east o f © fe ra tla g & formd d r a f t
c o o lin g toarer. P riv a te eorasugticatlesu A®#®, lo rn # 184G*
I* A$$^b*uaa# S.* B* €©14 process water ©oftentag, %j»ri#se®s witt the
J¥#eipitttters* Ir> 4 . », Sagr, Chen* SfiiYS-iSI* 1940*
S.
Badger* W* L* end linCal** H* 1** U#*wafc» of ©he&lcal eagd nearing*
leSrwBiil Book C©*# few ¥©fte*. lff»*
4*' Butler, S* Modern j»®pisf and hydraulic* M achinery* pf* 828* 388*
C h arles Sriffia and C©«* l t d * * 'fh ila d e lffe iA * I f 15*
8*
C agle* B» 1 * m4 C a g le , 1« L *
JaspSag taaeh iB *.
tl* S * la te n t We*
i,i9o,2ii. dtt% 4, me*
8#
f*
Colyer, P* Ptasp» and fstefiag jsaefelnery* pp. 8#»3?*
%*a, 1©®4©»* liif*.
1* aad P. S*
4. G. A m ercury compressor evolved fro®, th e Archimedean screw
pmp* B e fr ite r a t in g te g ln e e rla g * ISa 1 6 6 -1 6 2 * 19-20*
S.
Depeix-r, J , G> east Dunham, 0 * W, Recent improvements in th e mercury
gas cos^ressor* Refrigerating l& jg tn e e rln r, 26*307-310. 1938.
t*
la r d in g * 6e» te n d in g * •cwafctr«TOrr«t © la e e if ie r * . B u ll® tin te > $ 9 iU
f o r i , Pa* 29S9*
10* law k ins, lehamlah* Pumps and kydraullee*
I n t e l aad Ca*» S«r York* 1883,
1 1 * lo a t h , f * L*
Tit® work of Arc used®®*
laiversity fr©a«*
"fol* 2, p» 53-84.
g * X? XXXY1XI.
Theo*
Sesferidge
1897.
12* lorck, 4 m G* .H m £ s m £ & & m » t ®ea wttervij#®!,
9 4 5 -9 8 4 . IfM*
Xnge&ieur#
31*
23* Krohnke, 1*. Sis pww* ferm elen fir d m h rn von aasaarsoknaekim *
teuieohe teasettuag, 20t5T7»9j 386-9. IS'fS*
14* Unk-Belt Co* Catalog** 6Q0,pp. flS*. Chieaga*
25* Mak-Belt Co*
Catalogs© 700,,.pf* 7 5 6 -9 6 4 .
1934*
Chicago*
If37*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
*l?4~
If* Mohl, H* I* A *tu&y #f tli© AroMaeieaa aeawwr as * p w p for ©liesieal
©agineeri&g p«rpos#», Utpabliafoed B*S* ?he#i»* library, I w « State
College, Awes, Iowa* 1936.
If* Muysken, J* lersleejjiag ,wwi hat s« t; i•* effect m
lagesieer* 4ft B* ?f«*tl* l»«t,
18* Saar International 8a@y©Xeptt®*Iia, £«$&*
1930 •
de yijeel. Be
Bodd, lead, a»d Co*, S « York*
10* lollsssa, Walter f * the principle of the Archimedean screw in ehesleal engineering, la^ahlisfeed fh»i# Thesis* library, Iowa State
College,. A®,es,. Iow a* 1838»
t0* Seyaer, Park© f* (t© Beatty, 1* J*)
Febrsary 3, 1814*
Pwif,
13, S, latent I©* 1,085,949.
El* fheroaat, ?#• t», SlArMge, 1* f* and S a i l * ® , W, 1* C h m io a l eaaly®!*
©f sater «M sewage* pp. ®«*1S* lte§r»»XfAll Book 0©,, S«w York, 19Si,
tt* fylirad, K* G» **Kdsnegl«a ©ller sastSskrisms ydesT®©*
lit 550-2, lift* '
lap*teres.,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-IT S *
x*
fhahko turn duo Beaa
Am m m m m m m
1 * % g f o r a a k la g pos®ife lo tli® dooolopooot
o f tho fffits a a tte fro jw artio ao r fl.s<t th e Arehliaodoon ao ro to r.*
low in g m m h u m toon «spe©t & l l f h m lp -to t*
ft® f o l ­
l*r* S. 3». B o lfia o ttn e f o r
suggestions ©» m t e r cooling, B*> 1 * f** t«tti f o r feoip * l t h the mt e r
c o o lin g th«ory« JSr» Sl«aa. ttiarpSqr fm
weir plat© doeiga, Sr.* H*.
w ith th o swthod o f
$®&ber for ouggoetlons m m k m r soft#nlng
p h o tic ® , and fir*. 0# B , d m m q r f o r th o oo tio ® d ir e c tio n o f th o o s tir #
y v o jo o t*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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