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AI fCA L -o.24
ARE No. 4B23
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
February 1944 as
Advance Restricted Report 4B23
DETERMINATICq OF JET-BOUNDARY CORRECTICHS TO
COWLING-FLAP-OUTLET PRESSURES BY
M ELECTRICAL ANALOGY METHOD
By S. Katzoff and Robert S. Finn
Langley Memorial Aeronautical Laboratory
Langley Field, Va.
UNIVERSITY OF FLORIDA
120 MARSTON SCIENCE LIBRARY
P.O. BOX 117011
GAINESVILLE, FL 32611-7011 USA
. NACA WARTIME REPORTS are
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aaae -J s.aaaajGtdi&wt adMtItkd ~&ksakJl&
I'ATTOI.AL ADVISrRh' CO!T'ITTEE7 FOR ATPO"A:.'TICS
DETERiF"T, ATI IO r- JjTT- O' VID"7.-)' C, -rECTInI'S -0
COWLITC--FPL/. P-Or.~TIT PC''-;SrS 3Y
AN EI,ECTRICAL-/1,:ALOCY .;-TI:CD
Py S. Katzoff and Robert S. Finn
In order to determine jet-bo..rdar,- corrections to
cor.linC--fl.ap-outlet pressures, corrections tc the ve-
locities near a rowling-flap tip ha-.,e been siudiedi ty
an electrical-anaicg:y method. 'he r'Lsenc; of ti
low-enry air leaving .the f'ap oi-enin v.s taken into
account by sn shanin~ the nacclle r or'el thac its rutr
surfa-e represented the stree-- s-.!-lace i -.' :1z tl.h flaa
Copper was found ursatiia-ctor.,' for .s:;- es electrode
material. -ood accu'.rc y 'w c obtaFined it' c}_ro:..iu. -
platef copper for tenki. electrodes .nri:I .l t ,ir:i '.:ie for
the solution ccnt..:ct.3.
An S-percent reloc.~ty j-zrriction 'as frLLnd for a
typical nacezlle in th:- LAL "'1-ro- t hli:i,-3sp.d. tunnel,
correspnrLJ.in i to a co.r::rctior, of al-'out 0.2, times free-
stream d,.ynami.c pi--su.mur at the f'. otlt. The results
agreed appro:.ir.ately, with te cc_-.ctins calculated by
Lamb's :,ethod f'or an e4C'ivair:it -sourc-e-sin. : ovird.
Ti'.' hODU'l"T iQ1
SoL:ie uncertainty has existed -:ra d- i nj l'.e "ni nitd:6
of the jet-boundary efI-ect on the ccv,'.''.r.-f =,- :-ou t
pressui'es (anr hjnc-e on the avPil'tle icolnr p j.-:'as les)' )
in tests of air-ooled enriine inf,-' l.li-'c-'s i! the
LUAL lo-foot hijh-speed tun !.l. '* e -aI. fic i. ty in
anal,'siJ c r sults ..ct oun f;':: t.i1 t h:--- i"-..r n io;pl
chiar,^c-er o" the I"'ow bu't '.1'o rCr'-, t.a:' ire'erce of the
low-an-.rgy nor.poler.ti I f'low.' orw't ,Ojf tn'- flap ope.x.nu.
In order to obtain a practical solution of tho
problem, the presence oi' the loov-en;rry-air layer nmay be
taken into account by corsiJerin; tiLe nacelle radius to
be increased by an amount equal to the dis placermeat
thickness of this layer. The potential flow about this
new body, however, although perha'-s am.nable to analysis,
is very difficult to de'rie; and the results that ;.;ilht
be calculated for a simpler body like the Rank]ne ocvid
Irefe-ence 1) were considered of questionable -nn.lica-
bility. It was therefore considered e::nedi.nt to solve
the problem in the electrical tank by use of the analogy
between the *'low of current and the potential flow of
a'r. The method consisted of measurin- ani comparing
th.e flows abnut a given nacelle morel in four tanks
(reoresentin: wind tunnels) of different size,, for the
largest of which the correction wa3 so small that it
could be adequately calculated by an aproximate method.
The present paper presents rsiulta on the jet-
boundary coz'!r.ctions and a som-'vwhat .etLailed a&scussion
of some of the techniques involved. The existing
literature on the subject is relatively unsatisfactory
in this respect.
THE-ORY ? :.3T :I
Ei ctrical analo'..- The electrical analogy arises
directly from thb simlTr'it-' of the differential equations
for the irrntational "lcw of air -.:nd the differential
equations for the flow- of ?lcctric current in a uniform
conducting nediu.i. S3th equations are LanDlcian:
*2! = 0
where $ and E ere Ute velocic: potential and tlhe
electric potential, respectively. It follows tnat, for
similar boundaries and boundary conditions, the velocity
of fluid flow is c.nalogous to the electric current in
both ;agnitude and direction, or inas;much as with
uniform conductivity of the radium the current is pro-
rortional to the voltage gradient, local velocity is
directly analogous to local voltage gradient. The
boundary conditions for tnr'sE t-sts are merely (1) the
flow is uniform and narallul to the axis at larr:c dis-
tances upstream ard duvrnat.eam frcr' the bodri, and
(2) there is no velocity cor:ponent normal to the body
or t.he tunnel wall. For the elcctric al tank, the first
condition is satisfied ty using a tank of sufficient
len gth, with electrod-s completl.-I. caveri.wg the ends of
the Lank and at right enrtius to tl,e .1Lk -a-is. The
second condition is satisfied by-: using i.isuleting material
for the body and for t~e tar.k walls.
Theory of model-nacelle descin.- "he flow of cooling
air through an alr-cooued crilin: can-ot b ~:i1.:ua-ted by -
what night appear as an obvious ronelo."y the floor' of
electric c-urrent through a high-:-i-esis :nrce membrai.e in
the nacell: model .Such a8: inturr.a! r'.sistar.,ce couldl d
result only in a flow as shorvn in fi-urer- I(a, 4UitC
ur.like the true flov, i'ig. 1(b)), b ezcat.se a disccrtinuity
in total. resPsurc, such-1. es pxist: at th,': ,1,:.- of +he
coclins;-air layer, cannot b' re.pres'entCed' in th- e ec-
trical tank'. The mAdl was therefoc- ext..niCd to a
continHation of the flap (fl7. 2) in o.- ;r tlat th- flow
of c'-rrent Pbouc this region nil.t r-cipir -t th- io1w of
the external air in the nei;_bor od of ti. i exlaio b.t.
Tn order that the flov; n'-ar i-:3 c'cl f;itranc? .nirXht
be sii.;ulated, a nLssa.-c vs.s provio.ed alcng th.e ..iodel a::is
of such area that the current flow.inl into the entrance
corresponded to the ..o'lin-ir flc.. The net cross-
sectional arer oC the ..ozlJ' at -'v,.r.' st tlion tahut
corres.ponds to the cross-sectioni, ar': of the engine
nacelle plus the disptl:cement ar'a- of its zurronding
lol::-everg-: air; tLht i.", th.: a.morut by which ths outMr
streCR.i !tine are displaced outv.ara as a r.eS3ut of the
reduced velccities in the inner l:res.
.ecsuse of the jet-bouna&ry effects on the amount
of in-ern9'l fowr a.nd on ext.rnsl press.u-es, -he ctcsizn
of tChe model shoualcl otrcab'l, not h- e::rctly the -are tor
all four tarnk:s. Tna,nu.ch as no i.eens of d ttcrmini.n:-
thes;: veriaticns nwrs a;rv ilable 3and ? ter t :.'~*.'21 "l..-'t a
20-p.n cent blocckir--. -i' the T.ntt i--''2 pn.rag; r .- '
a 0.5 ; rcnt icr '- -e in e--tc-rnr l prr..:. nt. :.t : tar
wav rlot fu..'- h:'r r o" tCrei.
For best rupresantatiloi of the external flow, the
model should not taper to zcro crcss section but should
continue indefinitely do.vntz-eta.,l iti a c.'nse-scutioEal
area equal to che displacement area of the weke:
':he -~ i'D
A"" displacemiint area of waK:.e
D nacelle drag
9o free-stream dynamic pressa.re
The rcer nross section o'f th.e nnodel 'as accordiingly made
large cnou.-h. to cor-ecpcid, by -his eutatior, to the
laru-' dra- coefficient ;-e:.-.sured for flap-oLen conditions.
The 1er.-tii of the model, hovene., was for pnir-.?c1l
pur'O-'-e orly four r'imes Iu diar.et. Altouth. the
n:odfl w ;E. tr:c.ewhat too short t o re*cr:.ent cffactively a
n.od-l of infinite lniiCth, tie crr-or ti.vrolv.id vas :,sti-ated
to be s e.a11.
fo-i- fior ocmputirg -it-bo'urary cor.',-ction.- The
sucti.-n in the L'ip opnci: is 3asRFsuL- to ce determined
by the v...lccity of t-he flow ov-r th 2flap tip, according
to thc eqiLt ion
P -o 1 -V2)
P o 2
p loca I sta-ic rst-Lc pr"''
p local statIc r.rC--Sl'O
frc 3-ctrcuirl airsp ed
V local airspo'3d
P pressure coef'.cieint
and the jet-boundary e.' ct on ext pr s Jr is accord-
ingly a-sunmc to d'.Penrl only on tlhe je'-bo'.undary .'ffect
on tn. velocities ir this rei.::on.
As has alread- been noUcd, ch}e local velocity corre-
sponds to the lomal vDitae -r.aii-.t, ::nc the ratio V/"
corresiocnds to tnh rat-io of r'e 'r otare crad-.ent along
the m l in retio., cf tie fl- ti tl: tc the voltage
gradient in the "free st e':...'" shc... of the .nodel. Froln
comiparisons uf the V/Jo 0 atics i_-s ,_,.if-n in thi- dif-
ftrent tanh's, the ,iet-'cnbuxrd':*.l'y coa-'e-cti-ns in the srraller
tanks are found relative to u-: zorreztion in- the largEst
tarin which cn ',e obtai.Ined ac')r-:.tely bj y a cripl calcu-
.PFARTUS AI'D -;'.':RO S3
Tanks.- Four semicylindrical ts.n.ks; 'er? used, all
about 30 inches Innr, with dial.et..r of r.. inches,
. Inche-, 11 ircn-:s, nnd 1 i i u ..Es, res.ec lively. The
tanks were made of cell',loil sheet. curved to fit into
heavPy "w.ooden fcrm~'. and s.ealari to-rr her .jth acetone.
A sketch of che 5-in'c tan1] is s.-Auni in. figure 5.
r'a-elle model.- Te n.a-;le rdel ffij. 2), 5 inches
in diameter, was cut fPom" a i6,lcarce cylinder and given
several coats of spar varnish. TLs size, in proportion
to the 6-in h tank, coi'-rsponde,-d to a t,,rical nacelle In
the Li'!-,L 16-fcot nir:h-speed tunnel. In order to measure
the potentials near- the flap opening :.;. s.nall CoTntaCts
!narl.e of flattened ;c. 'j, plac1- nru-: wir.L .ere uro lt
through the nurfase, about 0.-. i ,, apart, aP.or-
imeridian,. i7xin,-. tIe contacts on the ,,1':;el wa7
is mu-.'uc rcre .ccu ..' POr thE prf eTent i'.' .- '
u ir. ...- -vable : I contact. 'I- I:: cl t s
wort"-. J .C..-!.c i o leads which vj-c L.-.: '.2 ,:t
thiLcO-l. i a s.n:-.L] .L : tubeI i:to w"i.ch :b c ::r -.lied with
paraffin to insur) that no notion or tn: ext .ral i3ads could
be imparted to tho contacts. The model '.ss susp3ndled from
a triangular board that rested on top of the tank; three
leveling screws were used to adjust thi height and
inclination of the nacclls model bo chat it vould be
exactly hqlf immersed in th- tan_.
Electrical circuit.- The circuit, which is essen-
tially a Theetstune b7irdge, is .shown in figure I. Whien
the bridge is balanc-d, as indicatedd hy silerce in the
headphones, the voltacg at the contact is given by the
voltage at contest vol a.e at left electrode F1
VoltaGe bct,'een ele-iro-:es P1 + R2
All voltage diffcrencos between pc.irs oi adjacent contacts
are thus found r<.]ati.e to the voltL.ge betw,:en the end
variatle ncpac.tPnf-e across on ocf 'he resistance
arm s VnP introduced to balance the str-y circuit and
solution capacitances. In order to avoid *-xcessive
diel!ctric losses, only miia and air condansers were used.
.lt.hou,hb ahsclutely i.rential for j btting a reading, the
capac-t&nce vas at no time large en.ou;h to affdzt the
impedance of its circuit, ti'.at i., to make inieccurate the
use of the simple r"sistance ratio in the receding
'he bridge w.s fed b- a 5-watt power oscillator,
operated for most of the ttsts at 100C cycles. The
lhadn'icne' v'ere, icr hich sensitivity, selected to have
a high impedance (20,000 ohms) co::parable with the
i1-pedsnce of the circuit. The tV.o 10,000-ohm resistance
boxes were cClibreted to 0.1 ohm.
.lectrodes.- Previous workers (for example, see
references 2, 3, pnd LL) with the r.Tethod of electrical
vnalogy have used electrodes of roppe', brass, or alumi-
num. Pew difficulties in the use of these metals have
been reported, a.thourh the nEcespity fcr frequent
polishing of the electrodes and for the use of acid in
the solution har ben not.;d. In the present study,
sc;oe atte.nots .vere ma,.e to use cnpper for the end elec-
trodes and lor the contact '-:ires; however, the readings
were found to drift at large and irregular rates and the
copper surfaces quickly lost th-ir polish. Satisfactory
results were obtained with chroslur.-plated copper sheets
for the end clectrodas and platinu--r: wires for the con-
tacts. Even with these mneLals, so.e slow drift was
almost always observed, but the potentials o' the
platinum contacts always drifted up or dcun together:
the cause of the drift was therefore probably ls.Iwher;,
occasioned either by chemical action at the 'nd L-lc-
trodes or b- temocrature or concentration variations.
'"lith regard to electrode mi erial, it is of interest
to note that copper was lonr aro c5 sz2arded for measure-
ments of the conductivity of soliution-. Platini'.ed
platinum is used almost exclusivelJ. for such measurements,
althouLgh smooth platinum hqa bee. usei succersfully for
solutions of low conductivi ty and the l.es noble metals,
silver and nickel, have been founr reasonably satisfactory
for less precise work.
Distance standerd.- As a prirnrry distance stc-ndard
for the determination of the free-stresui potential gra-
dient in the solution, the ir:n'trur.,ent !ic',rn in figure 5
was used. It has a platiuniim con act attaclied to a
sliding arm which can be moved precise .distances of
1 inch and 2 inches along the tanl:, 'cy ..esns of carefully
ground spacers. A more convenient secondary standard,
calibrated against the pri.-,ary standard,was made of a
pair of platinum contacts _lL.pendc.re frc.m the arms of an
inverted glass U (fig. 6).
The potential cr.dient as det -rmincd with these
standards was nearly 1 percent le.s than the ratio of
the potential difference bts.veen the end electrodes to
the distinct between the end electrodes. The difference
was tentatively ascribed to the '-hnown cendency of the end
electrodes to act as series crpacitances, wherein polar-
ization sets up a counter.voltage analogous to that set
up by a charged condenser. An effort was.s niade to
eliminate the capacitance effect. t using higher fre-
quencies, since such an effect should decrease with tne
inverse sq-)are of the frequency; however, the gradient
was fo.u-nd to rise almost li:early v.i.th freIquency, with
a total gradient increar.e of 0.6 percen-t in the range
from 1000 cycles tc 5000 cycles (the highest frequency
that was distinctly audible).
Series inductances were also tried (fiC. 7), of such
magnitude that the effective electrode capacitances could
be balanced (that is, a minn.mar gradient could he found)
with a frequency in the neighborhood of 1000 cycles.
Inasmuch as the inductances had appreciable resistances
relative to the tank resistance, a direct solution or the
circuit shov.n is not possible; the potentials could be
calculated, however, Ly sirtultaneous solution of the
equations of balance with and without an auxiliary resist-
ance in the circuit. Two diffcrsnt values (500 chmns and
1000 ohms) of this auxiliary resistance were tried and
both gave the sara result. Thi s result, however, was
identical with that originally measured at 1000 cycles.
Since the effective clecUrode capaci`anrce is thus appar-
ently not clearly defined or at least is associated with
other effects that could not be iden-tified, no further
effort was made to establish the gradient in terms of
the total applied voltage and the distance between elec-
trodes, and the gradient determined with the sliding arm
was taken as correct.
Electrolyte.- Solutions containing about O.OC5 to
0.010 percent sodium chloride in distilled vatcr were
used s electrolyte in the tanks. ':nch smaller concen-
trations still permitted sharp readings but -were avoided
because of the relotlvely large: local concentration
variations that might result from, the solutIonlof traces
of conducting matter frov, the vernish or fro:r the air.
Muchn 1Err.r concentrations were also avoided in order to
mi:iimize p.olarization at the electrodes. Tao water was
not used because it was found to precipitate considerable
amounts of material on standing. Local variations of
temperature, -which could produce large local variations
in resistance, were r.:nimized 'y- covering the tanks,
keeping them ir. a thermally insulated wooden box, and
stirring the solutions frequently. Vhen the drift was
large or v-hen stirring caused appreciable changes in the
readings, the readings were discErd3d.
Test procedure.- The tank was filled with solution
to sli-ritlvy elow the level of the diameter (allowing
for the displacement volume of the model) and then care-
fully leveled until the potential gradient as determined
with the Ftandrrd was uniform. elong the length of the
tank. Thme model was thcn lowered into the solution and
its height and level carefully adjusted until it was just
half immersed. The adjustment was facilitated by means
of marks on the model showing the pcsitioa of the. hori-
zontal mleridian. Care wa3 also taken to center the
SMeasuremnents of the potentials at the six contacts
were made in order and repeated ir rrver-se order. The
set of readings was rupest:d several rLines. Tne free-
stream gradient was measured, with tlhl rrodel in place,
at a point some distance in front cf the model. The
value of the free-strieam gradient was considerably less
than Lhat measured with the model removed because of the
increased resistance oi' tin passzae around the model.
The field of the model itself caused a negligible cor-
rection to this free-stream -radient.
The unifor.niLty of the gradient along .th tank was
checked after removal of the model.
Precision.- mhe sen.sitiitty of the brd-dge wi? very
hilrh: the resistance boxes cnuld r-enerally ee sot to
0.1 ohm, corresponding to about 0.05 percent of the
potential d'ifercnce between adjacent pairs of contacts
on the nodel. The accuracy of a gi /en set of readings,
however, is considerable 1 le',s th,!n th? secs:"itivity of
the bridge, cs indicated by th act that ing!'ependent
tests (involving rept~.ftion nf t'he entire procedure)
could give results differing by ;-,s uch as 0.5 percent;
and irreculerities of the s;ame orc"ir ap;e.ar'd in the
wall corrections deri,.ed fro... the pote6:tial difference
measured between the five d.,if .'-tit palrs of adjacent
Inasmuch as the wall effect is obtained by comparing
the potential differences measured in the largest tank
with the potential differences measured in each of the
other tenks and since few independent sets of readings
were taken, the results might contain twice the inac-
curacy of each set. If a further error of perhaps
0.1 percent is allowed in the esc:mation of Lhe wall
effect in the largest tank, a total error of about
1 percent appears to be possible in the correction de-
rived for each pair of adjacent contacLt. That the
errors will tend to be additive is, however, unlikely;
and the average of the corr'etioius for the five different
pairs of contacts, will, in any case, nave considerably
better than 1 percent accuracy.
Actual gradlents on the molel are known cnly within
2 to 3 percent because the distance between the model
contacts could not bs reesu-te or, in 1'fct, 'denuil1led
to within O.CO5 inch. The wall correction is determined
only from the ratios no the crailPrts nr.c is th3refore
not affected by inec'.sieles in the distances between the
RESULTS ANTD DISCrUSION
-::peri,.ier.tal velocity rorrsctic:.- Curves of the
jet-boundary correction to the vlcecitics in the neigh-
borhood of the flap, found b'y co..aperine th}, potential
dIffe ,-nces L~.twrur adjpcenc pairs of contaLts mineasured
in the different tanit::, aro zhc.vn in fli-Ure The
average jet-boundry-coirectlon curve is s Lovnr in
fi-ure 9. The lowest point of test cur'ves- that is,
the corr:ction fo- the largest tank wE.s zomiputed
theoretically by the -nethotd indicated in the follozinr
orotarison .ilth thcor- tical correction.- la;nb
(rlfe-nr.ce 1) sho.,ed now to ccmDotce the flow about a
:anr.-i... ovol.d in & cyl'ndr i al tanl.. T':h.e r methods
wre ut dj ct.: ro-.'ic.ce tiic correction for th-e Ilrrfgst tank,
and salo to cconoarc the exp-;ri-r3ntal r-sults :',ith those
thet co",ld ,pe been p-Ldictcf for an ovcid of roughly
the s;'ir dtl:.!iiions. 'l-he lurv it, u'inal aistribution of
crcss-scctionr.l Rees for th. rac-ile .nodel ir ctho-n in
figure "10, togethLr wi-th th-l Cdstribution for the assigned
equivalent ovoid, vhil.i hied thie ana.-se mnoximur cross
section, a or..ewhat greater -:olumn-', and C s-)rewhat
sMaller length. (An ovoid \ ith LUh sa-me maxinmujn cross
usctili anid l?.en.ih vouald have had an e4ceEsire voluere
and a coln;pror.,isE of this ty,)e was considered mcst rea-
sonable.) The computationas \era i..ade for point B on
the ovrnd, the longitudinal distance of wvhicn from the
upstream fozus is 0.17 tim-s t.h3 .istaince bjti-een foci,
or 0G.5 times th.; ri6xirmurm diA;,ete. L'h results have
been 'ilotted togeether -ith t'e e-:k)rirental results in
fiLur r The agreement is \.ithi.n practical accuracy
ovTer t'r.t entire rar e. Thu aCr.eent, howevAer, depended
to sos! e,.tent on the location of point P. If the point
hau be-j ch.,*.:n at the r.;J-j, of ~LIc ovoid instead of
nfe-r the cnd, the- corr'ctiorn for che smallest tank would
have been 32 percent instead of 21; percent, or one-third
higher; for the larger tank:s, however, the relative
difference would have been somewhat less.
Application.- According to equation (1), the cor-
rection to the pressure coefficient follows from
1 Ptunnel (V/V o)2tnr.el
free air (V o) free air
For example, where for a typical nacelle in the 16-foot
tunnel (velocity correction = 1.U0) a pressure coefficient
of -0.75 is observed, the corrected pressure coefficient
is -0.50, as given by the equation
1 '-0.7) = (l.o8)2
1 Pfree air
The pressure coefficients for the model are shown
in figure 11 for the two smallest tanks and for the free-
air condition. For the free-air condition, the suction
indicated for the region of the flap tip seems about
C OF.LUSI OUS
Jet-boundary corrections to cowlinf-flap-outlet
pressures have been studied by an electrical-analcgy
methoc', and the corrections fcund avys teen presented
as a function of the ratio of .wind-tunnel diameter to
effective nacelle diameter. The correction in the
L".AL 16-foot high-specd tunnel for a typical 5-foot nacelle
with 12-inch-chord flaps extended 00 is about 0.25 times
the free-streain dyna.nic pressure. C.-:oparison of the
results with theoretical values for a source-sink ovoid
in a circular tunnel showed approxi.aatc agreement.
It was found that accuracy in the electrical tank
requires that only the noo2er metals be used for the
electrodes. Wire contacts for prcbi:na tn' solution
potentials should be of platinum.
Langley Ms4morial Aeronautical Lqtoratory,
National Advisory Committee for aeronautics,
Langley Field, Va.
1. Lamb, H.: On the Effect of the Walls of an Oxperimen-
tal Tank on tne P.esis*ance of a Icdel. R.& M. 1 c.
C O10, Iritish A.F.C., 1926.
2. Itylor, C-. I., and Sharran, C. F.: A Mechanical Method
for Solving Problems of Flow. in Com-re3seible Fluids.
3. ai I. Io. 1195, Britibh A .C., 1929.
3. Malavard, Lucien: ; tule de auelqucs problems techniques
relevant de la tLeoric dos ailec. ApPlication a
leur solution de la mIthade rb'o llctrioue. Pub. No.
153, Put.. Sci. e:t Tech. du Ministure de l'air (Paris),
4. Fc:-rari, Carlo: Le -nalogie elcttriche ncll'acrclinamica.
Lz.b. ALro. F.. Scuola Ing. "orin3. Ccnf. Fis. e Mat.,
May 15', 1934.
NACA Fig. 1
(a) Current flow
(b) Air flo7
Figure 1.- Constrast between flow of air ani flow of
electric currei.t at a cvowl flap.
NACA cot oc
Figure 2 -- ace/@ roomP/, show'in posft/ons of p/fhun i
gure 3 kech of 8-inh ank
Figure 3. Sketch of 8-inch tank
F iqs 4,7
R, ecaeO /-eJlr dance
ba.xe -, o-/ooo o/mr.
C, vor/b/le copoctfance
--- 0 -0.00/ 5 fr? fd
phr aheadphone efector
osc., audio power
1, A~'wk eec/ro^eos
Figff, 4.- 3mA wy ep e .i//J
P, /, 0ooo ah/r
S, o,, /,douc/or o,6out
r ^ /reeue1ry of os//arfor
odufased o/, moz mU
currenf /fow //i ,'~an .
r--------- --------- -
/".ure 7- C'rcif /'or e/rnmna'/no of error's odwe 7o ,abr?,,A,
NACA Fiq5 5,6
^ \ \\ -
/ \^i \ \\
( (M)^ 1
--~--~-*--j-- _-i 7 7
i I 9 i
-~ '- ~--- ---- -t--i
) 1.00 -
12 3 4 5 6I
(a \ 1
.. I i I I -- ,-
--1 \- iLi-
^ *[:i~ia- --*- --r- --- -t-- t+--- r- -.----
1.00. .. -. ---
r---- ---. --, -~-;- r ,-
..... _. ..... -- __.i t L"... _.._ .._. _. .
1 2 3 4 5 S
Effective uacc]la di"n.eter
(a) Contacts 1 and 2.
Figure 8.- Wall effect on mean velocity between adjacent pairs of contacts.
NACA Fig. pl
1.20 I 1
.... 4 -
01.12 ------ .--
.. -- --.- .-- --- -----
S [I --4 -
1.00. -- ____ -1
I I I
i ^1.2- --. --1 --. --- -.--.- ....-- +------
1 2 3 1
T Inrnel' d..an t er
Effective nacell diameterr
(b) Contacts 2 and 3.
Figure 8.- Continued.
r 0 .
( i.ooj- ;
(c) Contacts 3 and. 4.
ir r' RA .- ronti-uep
effective nacelle diameter
1.24 4 -
I ~ I
t- t -5 ;
(d) Ctacts 4 and ---.
(d) Ccntacts 4 and 5.
_I i I
3 4 5 6
Effective nacelle diameter
Figure 8.- Continued.
NACA Fig. Se
I I _i ,
,- I I i
I I I I
Li I I I i
1.08 -- -- -- _.
1 \ 4 5 6
m V 1 I '.
Tunnel I I Ia
I. -i-I- .M ...---.. i I---
(e) Contacts 5 and 6.
Sig- r 8--- -.. .. __.Conclud
1.01--- -- ._Tu- --nre- l dia.eter
lg.e 8- Conclide,.
|| BIgure 8.- Concludei.
p1.24---- _- I------ ---
E pei rentall
-4---- _._ ----_
1.20-. ... .--
---- --- T-ncl !.iar..etcr I __.----- -
SI- .~ ffect ive
I na !l'e
So i ,
4-', I I I I ,
I i I .
i- -- ------ ----- -- j
> r -- --L --- -L-_-- L- -. _.
S I,,, --T -.. c irelical correction '
S, for Gf: rd
'L, !.,' -". ... .-.. : .... ...- -' '
I [ __l _I '
4 -i- ---- l ..- t t ^---
I I, i
1.04 -i .
1 2 3 -I 5 I
S "-. na1 ". [a a. I -E
Figure 9.- Mean wall effect on velocities in region of co.l-flap tip, and.
correEponni.ng theoretical correction for point B of the ovoid
of figure 10.
ITACA Fig. 10
1 --4---- I
-- 1 -,- --- --
IT. I / i
KI2- -r -
*u/ b' i l I I ^ s
i / l' I I o
I. --;L------------..---I -l---+-- t
'- I i
I ,7 -- T--. .-. ---- ----l------ --d 0- -
'_ __|C I | I 4f, J
S-. L, .- i-- C 0 +.'
I -"_T i __ ... ~'," ~ I I,' 1
I i t 1/ ; i T 0-'
T.-- 4. L!-
I L I I "" C H
/ I i .' I I t'rI .
-I- ---- -. *r 4 -T
-- ---- t ..... _" f-- -. ...__ '
S' r- -
I i ___L _._ ,_4 "- C
I' I i t .
~-r--- *---- ,r-
l-t ': .pi ic. z; ? L -
; I ,,: uO-
.. .. .. +.. 0 h
UNIVERSITY OF FLORIDA
120 MARSTON SCIENCE LIBRARY
P.O BOX 117011
G,)INESVILLE, FL 32611-7011 USA
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