Comparison of Measured aud Predicted Flows through Conical Supersonic Nozz]es, with Emphasis OU the Transonic Region

Size: px
Start display at page:

Download "Comparison of Measured aud Predicted Flows through Conical Supersonic Nozz]es, with Emphasis OU the Transonic Region"

Transcription

1 AAA JOUHXAL YOL. 3, NO. 9 Cmparisn f Measured aud Predicted Flws thrugh Cnical Supersnic Nzz]es, with Emphasis OU the Transnic Regin L. l. BACK, * P. F..\1Assn;u, t A!,;D H. L. GERt Jet Pr1Julsin Labratry, Callfrnia nstitute f Technlgy, Pa.sadena, Cal?f. ~'" ulldcr"la,"1 hcuc' C'"ilihril.n n"w,; hrugh,;11pc.'"" 11i. 10Z:t.!C8,~-:.!a~ç,J.)!.c"s~lrc,; 1~,"-h.s.«.111~'r;~1 luzzl.,,, with ci~ulur-arc thrnat..!,,,"illg "iftc'cllt rati"s "f hrat 'a,lius ~curvalurc t tlu"ual radills rc/rth, cir'cular-arc nr (:uical cnvcrgcnl ~cctins, und cnical (li\"t~l'gcul ~ccti()lls. 'rhcse Hcasur~_~lc~.,;,~,, ~,d(~\"i.!:..l~iil.2~~j)alill ~Jnpc!a_lu"c!'i "f 5: u.ll11500h ali"...a sla":latill pl'cs~urc rallgc f"01l1,t _psia. Thc nw lu'ugh tlh~ L.all~()nic.cgin ~:--a~-r;-;~l(1 t dcp;-u.1 ( s~cntjally 011 lcal (~-;:-(igu"'r~n, i.c., u li-e rali rei r,h; t,.-di JlCl~i()lla 1 iscllllpic fl()\~ prc(1 ict íns al!rc(~d wi th lhe da ta ili tlds rcgill ru' lhe ""z~.lc,; wilh re/r'h = 2.0, hllt C'Cillll"e'lualc f",' thc lzzle willr re/r.h = By pari:.;nn, lhe ~ilnph~ une-dilllcn~innal i!'õelllrpic fl\," H'(~dicti()11 was as rlluch as l5'l hig:h in lhe thral rcgil1 (0--;'une ~u~zh~; i;; lhe cnical sectin:-:.. dc\"ialil1s f a slnallcr Jua,::nitutl-;; ~'e f,,"d. Tr" efrcel:~ culillg a,"1 varialill in lhe "H,,"1a"y-layc,' hickllc,;,; a lhe Jlzzlc inlct,,'crc in\"cstigatetl.. as,,'cre diftt~ CJlCl :-Õ ill pr(~:-<~ll'(~ r(~acling::" \,"ith taps f \"~lj'i()us sizes. SO.1C,;cpal'alin ""'SS''''.laa,,,.,, presellled 10 "llow lhe en"'d f wall,~ling. Olhc,' fiw fealures lrat indical. 11", exlcll f clc,-iatins frlll llc-di.l1ellsillal nw include fiw cu"flieiclls, t h, ",,1 ra ius, a 11.1lca ""'';,,nllxe~ t is hpetl hal 11'sc 1'0111pari,;n" he C" ll,'asu"clllcnb alie! p. ~e!i.lills will he u,;cful 111"tue!yill!; 10Z~.lCnws wilh lhe ae!tlilillal eujl.,xily f ehcll1ieal"eact iolls. l' tncncla t li t c a = ~pced f sund a* = spced f sund a the snie endilin A = lcal nzzle crs~-sect ínal,11'1':1 Ath = nzzle-thrat an'a CJ = nw ce!\ieienl d = statie-pressure lap diameter ]) = nzzle-inlet di:unet er F = a xial t hmsl = lzzle appr:1ch sect ln leng;th 7i! = mass flw rate.l[ = :\laeh nnmber p = w,11sla ie pressure 7'0 = ambienl pressure 7'. = separat in pressure 1" ~agnal in pressure r = nzzle radius rth = 10zzle-thrat radius re = nuzzle-t hrat radius f eurvat ure rj = nzzle-inlet radius f curv,1t ure R = nzzk~inlet radius T = stag:nal in lemperalure Tv = walllemperature axial dislance frm nzzle inlet 11 = vdeity empnent in z direc'l in ]' = lw veleity at wall 'Y =,;pecifie-heat mli ~ = veleity bundary-\ay('r thicknl's,; at n07.zle inlcl ~. = di~plaeen1('nt thickness 'e = nzzle eolltractin-area rat i 'E = lzzle expansin-area v = kinematic viscsily mli ~ p = distance = densil \. defined in Eq. (ti) T = wall shear sl ress Sub. cripts e = enditin at freestream edge f bundary ln)'er i = enditin at nzz]e inlet teeeíved September 8, 1964; revi,;in reccived 1lay i, 196;). This papel' pre:;ents the results f ne pha~e f researeh carried ut at the Jet. Prpulsin Lnbratry, Califrnia nstitute f Tcehnlgy, under Cntraet N. NAS i-oo, spnsred by NAS.'\.. Scnir R~earch Engineer. t lescarch Grllp Supervisr" r-el1lber AAA. i lesearch Engineer; nw graduate stutlent a. the Universit)' f Clrad. 8 = cndit in a flw separat in t slag:nat ín ('ndit in 1 = ne-din1pnsinal flw value. nlrductin FLO\YS thru;!:h suppr.-nic nzzles are af intprest in design and develapmenl and in basic researeh.!t~ th.q.al~pli('d _fi('~l~ nazzles a..!.:." u=:ed in rcb~t engine~ amc in measurin~ fiw 111t('~ wherea.- in research they are used J1acceleratin de\'ices and in tlll' study f fiw phennu'na sueh as nnrquilibrium ceet.-. This experimental i\l\'rstigatin was initíatcd t gain a bcttcr understandin;!: f t'quilihrium fio\\"" thrugh nzzles which app('ars t be basic in studying the addilinal dects asseiated with ehemieal real'lins. Data are prescnled thrllgh tlh' subsnie, transnie, anel supersnic fiw r('gins f a number f cnical nzzlcs. Emphasis is placeel un tl)(' thrat regin. whcre the fiw is transnie" rcvius i\l\"pstil'alins f g3.sfiws thrugh ('nical nzzles h[i\~~h2.~)~ elc\"iatins frq!!! ºn.2,:dimensinal i~ntr.ql)ie fiq.\\~ as indicatcel b\' mea,;urcd wall static pr('ssures. Th('sc de\"íatins result frm radial \'Pleity ciúpneills ('aused by llp taper and eurvature f thc nzzlc.' f;imilar de\'iatins havc hepn bscn'('d \\"hcre m(,3.surements \n're madl' in the elivrrgl'nt re~in f enieal nzzlcs2'-5 and where a few measurements wcrc made in hl' enieal (,tl\"('rgent reg;in.6 Lcal \'cleity ml'a:,uremenh; in the thrat rc~in h[1\'c il~eatl'd Ln this papcr, the tw-dimcnsinality mca:,ured wall,;tatie!. tllc)l\\"j prcssul'(,'; are presenteei fr enieal nzzles f varius dimensins t ahw in eletail thse regins where the fiw is tw-dimensinal, and thus wh('re the sim pie ne-elimcnsinal fiw prcdietin fails.1 Thc cnieal nzzles invcstigated have 30 and 45 half-ang!es f.cn"crgenee, 15 half-angles f di\'ergcnec, eircular-arc cntranee and thrat seetins, and expansin-area mtis \lp t 6.6. The mtis f thrat radius f Cun"aturc t thrat radi\ls wcre 2.0 and The eftect f inlet cnfiguratin was invcstigatcd in ther nzzlcs with thc col\'erg;cnt scctins fnncd by circular ares. Operating cnditins spanned stagnatií1 prcssures frm 45 t~ 250 psia and stagnatin tcmperaturcs frm 530 t 20000R, \\'ith data reprtcd at 5~0 and 1500 R. The ~J~bi~~t p~~ \\~~ ~)11spheric. ~t the l\\'cr stagnatín.. 1'r\

2 ~ -....,._~----~---- SEPTE~[BEH 1965 l\leasuhed AND PHEDCTED FLO\VS THHOUGH CONCAL SUPEHf:OXC NOZZLES Hi07 temperature f 5300R, colnprc..."seelair was useel, anel lhe nzzles were uncled, 'fhe higher stagnatin temperatures were btained by heating cmprcs.sed air by the embustin f methanl. 'fhe prducts f cmbustin \\'ere then llixed 1õübtam Ulllfrmity bcfre entering lhe nzzles, and at these higher temperatures, the nzzle walls \\'ere cled. :\ t the highcst stagnatin teml2q[aturc,_thcjqtal..hcat~~r frm ~s tolhe nzzle \\'aljraiiles than 10/0.f the ttal cnergy f the gas a. the lzzle in]e.t s that the fi\\' \\'as learly adiabatic illall ca:~cs. -The prelu<:ts f ('mbustin euld bc' treate;1 apprxinately às air, sinccthn1iass fl\\'-raie rab f methãnõl t air \\'as small, 'e.~., a H, the mle<:ttlar weight anel speeific-heat mti were 28.6 b/mle anc~ respectively, fr the prelucts f cmhustlon cmpared with 29.0 b/mle anel 1.35 fr air. :\b, <::dcu!ated temperatures f the~rducts f ('mbu~tin, with til<' assumptin f cmplete euple<:hcmical \1C:lsuremenb reactins, eles<.:ribcelin were withinse<:. the 11,J a~ura<:y uf lwrm Bunelary-ayer thicknesses at the nzzle inlet were varied rq!n_:ilidut 5 t 45Mn11Cm1Ctl'ã(1ilb t inl'estigate bun(c: ary-!at'r J.\i;jp1lCeml'nt effects. Thl' e1tect f \\'all staticpressure lap size n the readings \\'as als il1\'e~tigateel. At the 100'er stagnatin prcssures, lhe nzzlcs \\'ere \'erexpandl'el, and the as50ciated separatin pressures are pn'sc'nteel bth fr ht-fl\\' pcratin with elcd walls anri fr eldfi\\' pc'ratin. Other fcatun'~ i the flw are induclecl in term~ uf de\'iatins frm n('-elimen~inal is('ntrpie flu\'. Fr \'cr-all nzzle perfnnan<:e, flw <:dfieic'nts and thmst rati,.. are sh\\'1, Lcal del'iatiuns in the l\1as:; fiux at the edge f the bundary layer <:alt-ulat<:d frl\1 the \1casured \\'all static pressures are inducled, a,,,;i~ the snic line lcatin. [n the transnie fiw reg,in, 'arius t\\'-dimensinal isentrpie flw preclirtins are cmpareci \\ ith the elata t indi('ate the aelcquaey f thl'se theries. divergent regins anei mst f tlh' cnvergent reg;in is less than~ Only in the nzzle-inlet regin at the lwest stagnatlon pressures, \\'here the elifference between t he static anel stagnatil1 pressure is small, is the estimateel erl2.!:. 2!.. 5% significant; this errr wuld be less at higher stagnatlon pre&,urcsj fnsielerably!argcr clifterenccs than the previusly mentinecl % thru~h l\1st f the 110zzle are fund \\'itllciifjerentsizccl taps, as cliscll.~d in.ce. V. 11"r ht-flw pemtin \\'ith clecl walls, wall temperatures \~C dctermineel frm thenncuupips embeclflecl in the wall f the nzzle anel frm calrimetric wall lh'at fiux measurements \\'ith the nuzzl<] T. St a t ic- Prcssl r'c Dis t r-ihll t iol";; :\[casured static-t-stagnatin-pre~sme mti~ are SO\\"1l in Fig. 1 fr the luzzlc','c'r a range f ~ta~natin pre~surcs fram 45 t ).10 psia at a,'ta~laliul temperat.ure 01' 1500!t, \\"ith <:led \\'alb. TH' pper limit uf LiO psia \\'as dictated by manmeter limitatills at thc' time the tests \\"ere maclc. Frm bundar~'-a,\'('r t ra ver~es, the ra ti f inlet bunclar '-la\'c'r thi<:knes,; t lozzle-inlet radm \\"as estimatcd at abul 5 'R..."0.2,1. The pre";';li'(' rati..; are ncarly in\'llriant \\'ith sta~latin pre:"sui'(' ('x('ept in the fi\\" separatin regill, \\'here lhe rise in ~tati(' prc'ssme i~ <:allsed by \'ercxpalldccl nuzzlc!)('ratin' n the thraat rcgin, there i;; sme data ~pread, bul it ~('s nt appear t vary systc'ma tically \\'i th stagna tin prc..;sure. Cnsiclerablc de\'iatins fum the predi<:tin fr ne-dimcn~inal (1 d) i:"entrupic fi\\' ('Y = 1.40), :::h\\"1[1:-; <:ln'f~a, an~ apparent in the transllic rc'gin; in particular. t hc' measured pn's:"urcs are as mu<:h as abllt 30% lid\\' the pi'('dietin jllst d\\"nstream f the thruat. DC'viatins f a smaller magnitude are bsel'\'able in the irtlet and <:nic'al euj\'ergent sc<:tin, 11. lnst r'lll1cn ta Ín Xcar,dJere the lan~eney data are f sjightl~, the circular-are abve the l d thruat fi\\' and predidin1 ('nicar',.,.. clivergent sedin, lhe measurcd pres:::mc ratis <:hangc slpe ~lp fl\\' and lstrumentatlon dlagr:\l!~ f the sys~elll t abruptly and <:rss ver the l-ri fi\\' predidin further rl\\'n-,~'\lch the nzzlcs \\'ere atta('h~d :' 5h\\'n Hl'f. 1..Stagna- ;;tream. ~ 1-d isentrpic fi\\" predictin \\'ith \'ariable spet\on prl's~ure,l"as lleasur~d lst upstre:11~1 he a ) )r~~<:h <:ifieheat \\"as ab made ancl fund t be at mst 2% ah\'e the ~, t lc engtl: f wlmh ('uld )e adjusted t speclhed predictin sh\\'n fr 'Y = This small elifferen<:e indivalues. ghanges m lel:~th \\'crc, ~n:lde t \'llr\' the nzzle- cated the predictin \\'ith 'Y = AO t be adec uate fr COTinlet bo,undal'\'-lan'r tll!~kncss. 1hese turbulent bund,alt- parisn purp~es if the cntire nzzle fi\\' regin! is cn~irlcrectj ~a\'er 1111<:kn~~sE'~ \\'ere estllnatccl. frum measurements de~e~'lbed Fr sub~equent <:umpari~ns in the thrat regin, 'Y rliffer~ m Ref... lhe appra<:h S~,( tlon \\'as cle~1 :11, the lughcr little frm thc stagnatin <:nditin v:tlue userl. stagnatlon t.cmpl'rature f ~voh. Dt~gnatlOn temper. ature Anther -d fi;,' vrcdictin referred t in the liter:lture is l'as dc'tpl'l1uned by a\'pra.gl.ng the n':\(hng~ f \1,'0 sll!~'lded that fr <:nical suurce fi\\' in the divergent regin. 'fhe therlllcuplps p!a<:ed 0,20 m. up,..;trc~ln f the nzzle 1:let1 prcdicted \\'all slati<:-pn's:"ure distributin fr isentrpi<: fi\\' le5(' t,\" thermcuplc's, 10<:ated 1 m, frm t he C~!1-~tj!!.1~ ('Y = <:n..;t)is./ _ \\'cre spaced 180 apart cir<:lljnf('l'pntially and genl'r:dly rcad " " ~ \\'ithil ~(/Q f C~.C~1ther. The air m...;s \" "tl' \\'a~ meas- l!... = { _ 'Y--=-! -1 2 [-.ig~/s)4 _ J} ~/h-l) ured wa~ u~ccl \\'th t aliwasure nfic(" aliei the fr masst.he fi\\' lot-tlo\\' ral<' f<'st~, ll1cthanul. a rtmeter The / Pb 2. b (P/pb)2h. () aecuraey f the' ttal ma5s fi\\' rate is estill1atpd t be 1.%8: The sub~('l'ipt b denutes a pint aln!!; lhe cni('al \\'all \\'here at stagnatin prcssures aoõve aõüt 100 -psi:l. At l\\'cr the indicated variables are kn\\'n, anel s is thc radial disstagnatln prcssurcs, the rcadinj!;s are le5s a('curale. tance frm the suree. lf the experimental prcs~lre and Fr the fllwing nzzles [the Fi". ), thse <:rrcspnding.:\1a('h null1ber at the circular-arc-thrat cnical shwn in F!ll~ and the 45 _] 5 (fig..jd]' t le chall1eters tangen<:~' pint are useel, Eq. () is sh\\'n in Fig, by curve f the \\'all static-pressure taps \\'ere O. 20, and b t prediet substantially l\\'cr static pressures in the <:nical in., respcctively1 and the ratis 01 hle depth-t-dianthter sectin than t.hse btained experimentally. Althugh better \\'ere abut 8, 4, and essentially infinity, respectively. The agreement <:ulc! be btaincd if the predictin l'ere initiatcd hles \\'ere as sharp-eeigec! as thpy culd be made by drilling dwnstreall1 f the tangency, the cmparisn nevertheless and thcn smthing the burrs \\'ith emery elth. The axial indicates that the aclual fiw differs frm cnical sollrce fiw lcatin f cach tap was knwn t in., and thetaps \\'cre in the first part f the enieal scct.in. 'spacec! <:ircumferentially ãiidãxially alng eaeh nzzle ldata were als btained bth at a lwer stagnatin temwall. 'fhe static prcssures were lleasurcd either \\'ith mer- p~ature f 5300R uncled walls and with n appraeh eur)' manmeters r, at the hwher )ressures \\'itll ~ length such that at the nzz mjet 51 R ~ These data, gãges, which had O,25-psia markec! increm~. The ac- t ug 1 nt shwn, indi<:ated that the effect f \\'all cling,. cumey f the readiilgs S chctatedliytllcdífference )et\\'een ~dtered the measured pressure rat.i negligib!,l excel~t in th~ the statie anel stagnatin prcssures and thus depends n lca- fiw-separatin regin, where, at the same st.agnatin pres- Lin in the nzzle and n the stagnatin pressure, 'fhe esti- sure, the separatlon pint mved dwnstream with wall mated errr in static pressul~thrughut the thrat and clingj 'fhe dependence f separatin pressure n \Vali

3 ... : : (f) O NOZ ;:) (f) a: a.. 1,0 ~ ẇ..j 1.5 O a: w O , O O 3.0 BACK, l\asser, AND GER + AAA JOURNAL Ec=7.90 EE= 2.66 'é =1.800 in. -~ GAS FLO TANGENCY z= 0.71 in. _----L --L-- ---ct li =15000R' ' Tw COOLED ALLS'jf=OA- 0.64; ô l.l R ~ 0.25, O = 3.60 TEST P' psia t:: <J O V' \ O ,6 TANGENCY TANGENCY in. z = _ r-l-..+-t=--~ --~ z = in. Z = in. LJ Z~~R5~;Tin.l!.1 _ ", a-one-omensonal SENTROPC FLO - (Y= 1.40) b-sentropc CONCAL SOURCE FLO (Y=1.40), EO. () c-hall d-sauer (REF 10) e- OSATTSCH ANO ROTHSTEN (REF (REF. 9), EO. (2)'TO-OMENSONAL 13), EO.(3) SENTROPC FLO (y= 1.35) b AXAL DSTANCE z, in. Fig. 1 Static-t-staguali()l1-pl'(,~~ll'c rati:-i all1~ lhe nzzl{. cling is discusscd in Sec n. [i'he effcet f inlet, bundarylarer thickness n the measurec!'!->ressure ratlo \\"as nt (liscerlll ) e. Thus these' iuvestigatins revea e a negligil)[c liõüiídarv- aver displacement effect, which was als agreemeut with preclictins f the clisplacement thickness ó* frm the turbulent bunclary-layer analysis.ij ln cnueetin with the preclietiu, it shulcl be mentinecl that ó* became negative upstream f the thrat as a result f the embined e!tect,.: f wall cling and fi\\" acceleratin. Preclicted values f ó are sh\vn in Fig. 12 f Ref. 1J [j' iuvestigate the effect f inlct cnfi uratin measnred pressure ratis are shwn r' 2 fr nzzles f different cntractin-area ratis but havmg the same thrat raclius thrat radius f curvature, and half-angle f divergenc3 The cnvergent sectins were fnned by circular arcs f equi11 radii f curvature. Fr cmparisn purpses,c he cld-fi\\' data shwn are average values fr eaeh nzzle ver the range sh\yn) f stagnatin are dlscussed 'pressure~ l!l indicated1 Sec v:' ehrugh S~pamted the fiw thrat data (nt and divergent regins, the measured, Rre.-ss.l!!:.e _'::!!:ll.0~~~ tiallv inde )cnelent f inlct cnfi"uratiun anel de cnel nh' n the lcal nzzle cntur. The ma~nitllelcs f the deviatins rm - lsentrplc fi\\' curve a) are similar t thse funel \\"ith the nzzle (Fi~. 1), which has the same rati f thrat raelius f curvature t thrat raeliw; (rjrtl. = 2.0) an half-angle f elivergencc as the llzz1cs sh\\'n in Fig. 2. The cffcct f thrat cnfiguratin is sh\\"n by cmparing Fig. 3 t Fig.. n Fi". 3 measureel pressure ratis fr the nzzle are sh;\\'n' fr a stagnatin-pressure range frm 45 t 250 psia and a stagnatin tempcrature f 1'500 R. lbecause f the smallcr thrat radius f curvature t thrat ra~ls f 0.625, as cmpareel t 2.0 fr the llzzle, there are larger deviatins frm the pressure rati fr' -d isentrpic fiw m the transnic regin. Thcse amunt t as m\lch as 45% just el\\'nstream f the thrat' ln the cnical cnver~ent sectin, there are als lárger <re'viatins frm l-d fi 11' than with the nzzle because f the larger 45 half-angle f cnvergence. ln additin, at the higher expansin-area mtis f the 45 _15 nzzle, the data nce mre crss ver and becme less than the -d fiw pre-

4 SEPTE;\1BEH fl6.~ :'EASURED AND PHEDCTED FLOS THHOUGH CONCAL f'uperso:\'c NOZZLES li) 1.0 ::;) 15 <! cr...j N z L2 Ls 'i = 1.55 in. (CENTER AT NOZZLE EXT te' : r. /h ' n. NLET), fé ' -- 1,h= 'c' 4'02- ç, ~ 0.7 C;.- - Q 0.6 <! cr w cr ::;) li) li) 0.4 w cr Cl r- r, ~520R. UNCOOLED ALLS NOZZLE p/.psia NUMBER (; RANGE OF TESTS.l... c AVERAGED O 1.64 O t--- r -- -] j -\ L 1-0- ONE -DMENSONAL SENTROPC FLO (r' 140) c - HALL (REF. 9), EQ (2). TO-DMENSONAL SENTROPC FLON ( r' 1.35) ,- -r - ---< -j tj. 402 ~ J L AXAL DSTANCE FROM THROAT, in. Fig.:! Static-t-~tagnatin-H'c~sllrc. ali~ "ilh \'~u'iull':';' ll7.j.lc-illlf"t (~()nligunlti()us. dictin. ith the nzzle, nly ht-fl\\' eledwall d:üa \\'ere btained, and a larger ufjstream length (l/d = 8.4) \\'as u~cd such that /R = 0. i5. -AltilOUgh n (Tã!:1 were btaincd with a thinner inlet. bundary-layer thickness, bth experimental bservalins with the nzzle and predictins indicate that the mcasurcd pressure ratis wuld be alt.ered negligibly. V. Tw-Dimcnsinal Flw PrcdictiH; Exact slutins f the tw-dimensinal (2-d) isentr )icflw cqllatlons are '.i~~y~existen_t Jr_ 0\\' rc!!:ime~ thrughollt a SllperSOllC nzzle. :\pprximate sllltin~ cnsist Clther af calculatmg the fiw field by numerical 01' graphical techniqucs 01' f btaining analytical slutins in particular fiw re~ins. Since, as cxpccted, geviatins frm l-d flw are larp,est near the thrat...1h.e transnic regin is f pmnary cncem. Als, a slutin in t:his rep,iõii -S needed ~ ~~ ~()lutlon by the methd-f-charact~ristie.:~_jl.llie ~persnic regin. n thc transnic re in, Hall9 btained a slutin f r he velcity field fr isent.'oplc. irr tatinal fiw (' - COl~ Ly a series expansin f the vclcity cmpnents lu mverse pwers f r./r'h. The first three terms fr the velcity empnents in the series slutin were calculated and appear in thc reference. Frm these, the wall stlltic-t-stagnatinpressure rati can be calculated: p/p, = - [(' - 1)/(1' + 1)]ir:}'Y/h'-) (2) where V is thc lcal velcity V at the wall, nndimensinalized with respect t the speed f sund at the snic cnditin a*. ~'he predictin frm Eq. (2) is shwn in...!'2!l.!...bycurve f, ll1chagrcci' well with the mcasured pressure distributins in the thrat \'icinit~1 n thc regins that extend circular-arc-thrat colllcal tangencics, the requirement t the Lhat thc 'lelcity at the wall be parallel t Lhe wall is nt exact1y satisfied as a (;n~eqllencc f the slutin methd; this undubtedly leads t the inferir predictin near these tangencles. l!he crrespndellce f the predictin frm Eq. (2) with the data is cqually gd fr the nzzles with \'arius inlet cnfig\tl'atin~. as shwn in Fi/!. 2 by cur\'c c. t shuld be nted tha t lall's predictin depends nly n thrat cn figuijtin tinj 1'he thrugh mcasuredthe rati pressure rcir'hratis and nt in n the inlet thrat cnfigura rcgill shwn in Fig. 2 display this same trend. 11'01' lhe.t5-15 nzzle (r./r'h = 0.625), the pf,niptiu...ísllt applimble since the series slutin divenres fr r.jr'h <. lnstead, Fil!:. 3 shws as cun'e d lhe Sauer prealctiõi1'which, as Hall has pinted ut, is the first-term apprximatin in his series slutin. This uredictin is cnsiderably belw the data L1Jis predictin fr the nzzlg) n Fig. 1 (curve d), indicates the imprvement upstream f the thrat aftrdcd by the lall slutin, curve c, in which three tenns are uscd. Hwever, at the thrat and dwnstream f it, there is little difterence between the first and third apprximatins. t wuld be f interest t cmpare the data with predictins frm the irrtatinal methd f charaetcristics in the supersnic regin; hovever, predictins by Darwell and Badhaml1 and Migdal and Landis12 fr cnical nzzles with circular-arc lhrats reveal fiw cnditins near lhe nz~je

5 1610 BACK, ~[ASSEH, AND GER AAA JOUHNAL c: () ::> O ~ ! N 1.0 O Z 'í = in. Z=~: LT':GENCY Z = in. ri TA~GENCY. TLGé -~! :JZ n. CONTOUR TANGENCY c': 9.76 E : 6.63!Er:" - rhroat z = in. r'h = in. : z : in. <::>..~ º ~ 0.6 :::;: r () () r Tw r; : Ô e R '" : 8.4 TEST O 343 O 342 V V 348 O 351 Pt. psic O O c - ONE -DMENSONAL SENTROPC FLO (y = 1.40) ~~~ V O e-osattsch AND ROTHSTEN FLO (y = 1.35) d - SAUER (REF. 13), (REF. EQ 10) (3) ) TO- DMENSONAL SENTROPlé. O g~~ ~J, ~ 10 O i=t 6! 1 16T AXAL DSTANCE z, in. Fig.3 Static-tn-1-õtagnatiun-pre:-.surc 'ati~ alu#! lhe 'l5-5 J1zzlc. axis that \\'uld ]cad t shek fnnatin, :ld ensequently inyalidate the irrtatinal a~sumptin. Predieted shek frmatin ecurs where ~ach lines l'i~inatin~ just d\\'nstrcam f the crcular are and cnical t:lgeney appraeh the nzz!e axls. Dar\\'ell anel Dadham dlscuss the predietin in elet:ul \\'ith respect t the aceuraey f the numerieal slutin and its initiatin, using either Hall's9 r Sauer'::;l transnic s!utin. As indieated in Fig. 1, fr the nzzle with r.lrtl. = 2.0, either f these slutins shuld pryide a gd apprximatin t the actua! fiw in the regin f interest. t shuld be nted that bundary-ayel' displaeement effects, nt aeeunted fr in these predictins, d infiuenee the nzzle freestream fiw bundary t sme extent; this ean aher the predicted fi\\' field. hether r nt shek frma..tilln.. actually ceurs ª..ng.J.hc_llzzle axls ean nl..be decided by expenmental bscry-atill. Rather than \\'all static-pressure measurements, either ttal pressure-prhe traverses alng the axis f enieal nzzles r sme means f yisual bservatin in a transparent nzzle with a sufficiently lng divergence sectin wuld be required. Anther apprximate slutin valid thrughut the nzzle, prviding that wall curvature effeets are nt large, is the predictin by O~watitseh anel Hthstein.13 \l"hcre L p, = [ 1 _ ~ ') _ ( Jl -- O)2(r)2J'r/(Y-) a, 1/1 The subseript 1 dentes averagc quantities fr 1-d iscntrpie fiw, in \vhich "/ = cnst Fr caleulatin purpses, it is cnvenicnt t use the relatin (/ul)(duddz) = (2/r) X [(drldz)/(m,2-1)]. ln the predictin that applies fr a cnstant,,/, the veleity distributin is cmputed frm the lcal enfiguratin f the wall. The requirement that the fiuid veleity at the \\'all be parallel t the wall is nt éxactly satisfied because f the way in whieh the slutin \\'as btained. The predictin frm Eq. (3) is sh\\'n in Fig. 1 as curve e t be in else agreement with the Hall predictin and,

6 :-;EPTE:'BEH!)(i.~ :'EASlíHED A:\D PHED[CTED FLO\\'S THHOt:GH COXCAL SUPEHSO:\C XOZZLES 1611 thu~, thl' data in the thrat vieinit~ f the nzzle. At the cireular-are-thrat cnieal tangeneies, the predietin is disrntinuus bccause f d'lr/dz2; these disentinuities are indirau-d by vertical dashed lines. ' Near the tangencies, the slutin becmes mre apprmâmate, since the restrictins n the magniiude f ihe nzzle radius and its derivativl's implied in the analysis are nt satisfird. Thr nzzle cntur deviatrs even further frm the rcstrietil1s impsed by this anal~'sis; h\\'evpr, fr cmparisn, this predictin is sh\\'n in Fig, :3 as C\1l'VCc in a narr\\' part f tl1l' thrat rcgin. The ratll('r sharp decrease in static pl'essure is prl'dicted, but tl(' pl'edietin is bel\\' the data. V. Static-Pn~,,;slll'e Tal' Sizc {j'11p pl'l'sencl' f a sta til'-pressurc hule ('auses sme fi\\' dt:::turbah'p, lhi('h altl'rs thl' ml'as\1l'l'd statie pressure fram the tnlp ndlll'. Fr shal'p-edj.!:l'd hles, dl'l'per ihan abut 2 diam, lleasllrt d statie pressurl's in f()''; \\'ith negli/!'ible prcssul'(',!:radil'nts han 1)('1'11 fund t incl'case \\'ith hle sizc; it is bdic\'l'd hat the slllall hles rl'ad 1l'arl'l' thr true static P'C';SU'l.. Othpr 'Te,'ts, sllch as sli),(ht hurrs and the prl's'1<'1'f fo'( ij.(npal'licll's, hal'c' 1)('1'11fOlllld t alter the rcadinj.(s a,; \\'1'11. Fr nzzle /Ju\\', in additill t the prcs";\'e J.(l'adil'l! indul'cd in the flll' h~' thl' Pl'p'C](" f the hle, the '-"tl'mal pn,s,;un' J.(radient is superilllp'ed in lhe fll\' directin, The fi\\' elisturbanc(' is thus expl'cted t incl'l'ase \\'ith hle sizl' )('causc a larger prcss\ll'e drp exist,; a(''oss til(' hle than "!1<'nthp fr('('stl'pam fi\\' is nt acccleralin!!j T innstigate the 'ftpct f hle sizl' n thl' stalic-pl'essul'' 'l'adings, the 2,51-1 nzzle sh\\'n in Fi!!, 2 \'as il1strumentl'd \'ith 0,010- anel O,040-in,-diam ta) Jair,.;. As llh'ntin{'d ljefrp, t Je 10 'S \\'ere as sharp-cd)!:ed as they culd be madl' hy 'nh\uthin!-( with cmer~' ('10th any sllrfacl' burl's lha! \'l're prdu(,l'd hy drilling:, The rati f hle dcpth t eliametl'r \\'as abut :3, ~tati('-pressul'e elistributin~ wl're btaitinf 0\', 1' a rang,e 01' :'tagnalin pre"s\lj'es frm 4;) t 170 psia, \'ith air :l a stag,natin tl'll\pcraturl' 01' 520 1\ (unell'd \':lls), '1'\\'0 01' thl'~1' clistributins arp sho\\'1 in Fi}!;, 4. T ali\\' a dirpet poll\parisn f t]1(' diftcrences in the re;;'f. illgs. thr 10\\'1'1' par f Fi)!:..t :lis ~hws the percentage dilterence be!\\'el'n the 0,010- and O,040-in,-diam tal' reading,.; at lcatins \\'hl''(' t]wse t\l'o taps rerl' axially \\'ithin in, 01'e:1<'hthpl'. This is the limit t \'hieh the axiallcatin 01' t}w taps is kno\'1. :\s S('l'n in Fi)!:.,, thl' pressure elifferenel' bet\l'l'l'n the smallc:'t and lar;;est tal' '('aelings varies sy~tell\atie:dly thrug,h thl' nzzle; ':nelll\ differences (pllls r minus) thai \'lll,[ be assciatcd with reading ace\ll'aey are nt pviclent. The smallest tap has the 10\\'1'1' rl'adin)!:, as lul:ó been Obsc'l'\'ed in fi\l'" with neg,ligib}e acerler:ltin. fthe pereentag:(' (lifference in the tap reading,s is a ma-"ill\ull\ m t l' transol1lc reglon. \\' lere l' pressurc grarlient S largest. '1 he clifterence S 1i:i'r(]101lscernible in 111e nzz}e-inlet regin \\'here the freestreall\ \'Clci ty is l\\' anel in the fi\\'-separatin regin fr t!1<' l\\'-st.agnatinprcssure tcst \\'hl're the reversc fl\l' velcity is re!atively 10\~ The O,OO3-in. uncert:.líni\' in the axial elistancc bet\\'een hé ~lnd-.õ=i'o-in,--jiã~n- tap pairs \\'llld alie' the re': centage difterences sh\\'n 1l l' 19. :tõf'o, 1 at m:ót. - The trends f ihe difl'ci:ei'icp."sh\\'n fr the t\\' tests were typieal f thse funel at intennediate stagnatin pressures f 75, 100, aud 125 psia, and dllplieate tesis at sme f the pressures inelicated the data t be reprdueible. ln a system in \\'hich pressure gradients ean exceed thsc alng the nzzle, JaiviuH folln differences f the sl1me magnitude as thse shwn 1l Fig. 4 fr tap diameters ranging frm 0,0016 t iu. by measuring the pressure distributins alng a fiat plate u which a liquid jet impinged. 1n that investigatin, a limiting value f the tap size was fund fr \\'hieh n further ehange in the measured pressure distributin \\'as bserved;~ O,004-in,-diam tap read the same as the 0.OO6-in,-diam tap.j \\ '\ O. /Q/6 w ~ t:, 0.8 ~ 0,7 f= 0.6 <J: a:: 0,5 w wg: ~ 0, '~ 1'1 ~ TEST 103 J [;1 0.8 r,=534 R,.~ i'i l- ~- 13bB TAP d DA ~j n 0,7 11=170,3 pso ~ 0.4 r '03 i '" 0019, 02' 01 ~ 0,----,.. 8r 'Q TEST 100 ~ Ti =550R,_L_-, PO 45.1 psi i j! f) r; Fig. l Statie-t-~tagllatic)-)l es~\l t~ ratis alllg' ti " 2..~ ",,;11. di'!'l',',,"1 siz,~d J"'"'''''''' lap", 25 ~~ 1 j J t}46j. - -!'J r; ti <'>} 1 THROAT º 61 TEST p. psi J X ,1 8 "'" 2 - /j j., ~Q.. Q ~Q ~ "O v_, ' Q.: AXAL DSTANCE z, in, T imli('ate the mag:nitwll' ()f the diftprcnces bet\l'een the tap rl'ading;s in antllc'r \ ay, rderpncl' is made t an estimatr 01' tlw stat ie-pl'( sslll'(' tal' 1'1'1'01', H,\' elimensinal allalysis fr li 10\\'-spel'(1, 'ssl'nti:dl,\' eollstant-prperty tmbulent bundar~' layer \\'ith nl'.l.dig;ible fi\\' aeeekrati0ll, Li\"es('y ( t al.15 and thers give the cltr,),p fr dl'<'p hles: - D.p.1p. 'T = - (r/*) T \'here d* = r(t/p)/2/., ri is the tap diameter, anel T is the \\'all shear slress, _\eerding t experimental measmemenh by jjvcsey et a. and llll'rs. D.p/T inpreasl's mnlnically \\'ilh d* t'abut 3 at d* ~ DOO,lhe limit at \\'hich mea:;mements have been ma,jp. Hy cmparisn, in the thrat rcgin fr the highl'st slagnatin-pres:óure test, \':dul's f (p, PO),'T are a" large as 40: tl1<' errt'spnding nllue 01'r* based n the O,040-in,-diam lal' is abut ü200, Fr hl' lwe.sl stagnatin-pressnre "st, lhe pn'clicted \'alue in the thrat rl'gin i,,,:lcs:;, (PO - PO) r ~ 10, as i.s t he crrespnding \'alue d* ~ 1900, ln these estimates, the \l'all.shear stress \\'as predictl'd frm the analysis f Hef. 8. Cnfrtunalely,.since the true statie \U'PSSUl'eis nl kn\l'n, ne can nly enclude fl'l11the data sho\\'1 in Fig..t tha~ static-pressul'e distributin.s sh\l'n in Figs. 1-3 arepr "'G71bly;lightly-hig;her-than the tru~ -- \'1. Separalill P"essul'cs 1}"r verexpanded uzzle p<,ratin, the ralis f separatin re rth = 2,. 'fhere \\'1'1'1'100 few pressure taps in the divergent t ambient~ressul'e regin f the.t5 -\5 are sh\\'n nzzle in fr 1~'lJr a l11eaningful nzzlesrepre.senta tin. The data are sh\\'n by thc barred verticallines. hc that have ' ujp_er bar is the tap reading upstream f the sepanítior pmt; lhe l\\'er b:j.j'\\'uld be ihat at the succeeding tap if separatin haa nt ccurred and was determined frm higher stag,natin-pressure tests. Thus, the actual value lies between the values shwn, Ehe?vaeh number at separatin was ealculat d fr isentrpic fiw (y = 1.4) based n the average ambient separatin jjressure frpressure1 th!:_hõ\.fi\l' The lests mtis with f separatin-t clq.e ~Us [shaded symbls) are generally abut 5 t 10%-')cl~ cld-fiw values (pen symbls). These l\\'er values at the same stagnati?n pressure crrespnd t a releatill f the

7 161~ BACK, :\Af'f'ER, AXD GrEH A1AA JOURKAL <>..~ º 065 ~ 060!;:; a: UJ 050 º a.. '"UJ ZUJ iê :J 045 ::<... Z UJ a:... cr NOZZLE. 30-SO FG 30-SO O 30-SO O 2 S- 1 ) O 164 _ FG 2 1;,R SOO} COOlED ALLS < &. < OS8 520 UNCOOLED S20 S30} ALLSTi "t + L 7} 36 O a R ~02S ~005 ~010 Fr the nzzle, the pl'edictin frm Eq. (,O is ,_ in fair agreernent with the exp<,rimental values. This crrespnence is expceted frm thr elsc agrcement f prediete and measured statie prcssurps in the thl'at regin. H\\'ever, fr the nzzlc, the experimental values exeeed the predietin frm El(. (4), in \\'hi('h nl~' the first term in lhe braekels is rctained. As menline befre, the lall slutin di"erge;,; fr r,/ru. < 1. f nl., the first te~ in the brackets is inc!udeel, tlll' pn'dietin is iuenti('af \'ith that f either Saucr10 01' Os\\'atit;:ch and Hth;:tein.13 Thus, tjhe l\\'er!)redic!l'd values ~f.tll(' ~h\' tlll' ll1aelequae~' 01 PXlst~ J(J\. cpfli('ient P'('(ll('tln5 fr furtla:r nzz]ps \\'ith r" ru. -:.) \'111. Thl'lst Batiu,.; SEPARATlON MACH NUMBER M, St"H..atil1 tu alu"ielll-pl"'~~urt nll'ill~ lzzlt,,,,,,. n.ti~ f,' ~epamtin pint d\\"nstream 'ith wall elin).!:, as ms mentined in Sel'.][1. This indieatl'~ t!!at wall (;Q.Q.li!!g..l'1G- imprtant in the interaetiõi11)rt\\"cen the shck \\"ave and bunelary layer ~dlll'h ):-esulh in fi\\" separatiçm frm tlh' -nzzle \\"al1. :\hlberg l't :11.'6 ab fuund the same tn'nd. Fr ur data, it is nt c!car \\"hetlll'r tlh'l\\"er srparatiun pressures are due nly t l\"flll cling, sinl'e, \"ith hut fiw and cled walls, the bund:u'~'-la~'l'r-thiekness Reynlds numbl'rs ai the separatin pint estimated frm the analysis f Hef. S wcre abut ne-half f th"e fr l']d fi\\" at thr same stagnatin pressure and bundary-byer thickne"" at the nzzh' 'inlet. n this regar.!. the data shu\l'n in Fig. 5 fr the nzzle 'ilh ht fi11" and COOll'd walls d nnt n'veal :ly delinite trcnd bet\\"l)en thc results with relati\"cly thin bundar}' a~'ers (ó/ R ~ 0.05) at thl' nzzle inlel :wd thosl' \\"ith thiekl'r layers (ó/r ~ 0.25). Hwcvcr, it is diffil'ult t determine lhether there is an~' depenenl'e n lhe bunelary-laycrthickncss Hl'}'nlds numbcr, wing t the sl'attcr f thc rcsults at the hig:hest separatin :\al'h nlllnbers (la:'t fur :,hadeel pinb), \\"hich l'rrc"pnd t sl'paratin near the nzzle-exit plane. The data in Fig. 5 cxtpnel n'r rathpr 101\" rati;; f :'tagnatin-t-ambient pressurl' ]JPcause f thp relatin'ly small expansin-arca ratis. "'1l'n these data arl' cnmpared \\"ith thers bt:rineel with un('h'd \\"a1b. s\l(,h a., tl1l' :l('('umulated results f Arens and :-;piegll'j' (Rl'f. 17. Fig. 2), the ht-flo\' data \\"ith a l'led wall aj"('fund t lic bl'o\' thnse J"('sult;;. V. Fl',- CefTicicn t~ Ld tz;1 Fi~. O.Lemparisns bet\\'cen mcasu'ed ma;:s fi\\" ratl' at a sta~natin temperatul'e f 1500 H (cled walls) and eolhputed values fr l-ri iscntrpil' fi\\' (' = 1.35) are sh\\'n ill terms f the fi\\' l'eflil'ipnt Cd = li1/,i,. At the 101\"('1' sta!; natin pressures, there is apprccl:1) e Sl'atter in the value::;,)=: Sme f the scatter is undubtedh' due t errl's in the mass fl\\'-rate measurem!:nts. ~nhe ';lp;her stagnatin p~, the scatter is]ess,-and fr bth nzzles, the fi\\' ee(fjcient i::; apprximately bel\\'cen 0.98 and LQ. Sinl'e the fi\\' thrugb. lhe transnic l~or1 detellnines ti1c mass f_~'j'ate th[ugh the nzzle, Fig. O als cntains the Hall predictin! - - T elparly illu~tratr the d""iatius, lh~ nzzle.~ ar!:. a;;"1ll)).!:..!.l t dischar~ int~ ae ('.!!.!.UH) and tlh' thrust rati,; are sh\\'n fr hypthetil':1 expansin-area rati~ frm a ":llh' nf t that f thc slatie-pn'ssure tap lcatin neare~t the nzzle pxil. C'H' terns in the thm,' ('XH pssin.l:c.llj'~j thl' ' n tlll' nzzje-inl('( arca 01' dtel'tin' l'hamber ellll wall :1d tlll' integratl u \\'all pl'e:'sure distributin resulting in tl\' axial fl'<'p n the nzzle sidc \\'all. The "hape 01' the thrustrati ('un'e is depp)h!ellt n dl\'th'r the 'al pn'"sure is le,.;s 01'!-!:reatcr than the -d fl\\' ":lup :\d n the ma~nitude f thr dittej"('''.as shll'n in Fig". 1 and :~. :-;h\\'n fr l'mparisn is the ften C/uteu ('urre('till faclr ~( + cso) ú.ll noll:lxial exi t fw fr i'qni!:a! L1Qzz!':J Thmst ra tios tr clei flo\' \\'õü1(l ije thp sanh' a" th"e shulm in Fig. 7. hased n thp data nh'ntined in Sec \:. Snie Line t'able cnt.ain:< a l'mparisn at a stagnatin telllperatul'c f 15000R (cled \\'alls) f pr~lil'tcd and ex~~'imqlt:ll 1.calín f thc intersectin f the.'unic lille \\'ith the edge f the bundalt la' pr. The cxppllnh'nt:11 "aluc::; ('õrrc;;pnd t the pilrt at-;;i~h the :-ach num!jpr btained frm the mcasured ;;tatíc-pressure distributins fr isl'ntrpie fi\\' (' = 1.35) ;;: :( 0ge Li ~. zuj 096 UJ 102 LL u '20 LL.. O'J.~,-,"... ;=...J ge T, "5000R, COOLED ALLS NOZZLE ~ 30- S' ~ ' ~045 E11 f~ r_nozzle 4S-15' FLO SEPARA TON N NOZZLE CJ = 1111 '~l= _ (' + )(~') r, T 90 _ 81' ('t') r, '% ] "( (r'hy r, -... ] (4)~ Fig. 6 STAGNATlON PRESSURE P,. psi Flw ccllicicnts. '( r,;, é )',TERM EO(4) ONLY / e

8 SEPTE~mER 1965 ~EASURED AND PREDlCTED FLOS THROUGH CONCAL SUPEHSOi\"C XOZZLES? 16~ Tahlc 1 Cnlpllrisn f prcdicted nnd cxpcrinlcntlll. nic linc il11cr"cctil1 with edgc f holl.ulary layt~r at T, = { (cled wall. ) Nzzle ') 4;' _lfi (tlr'h )xv. 0.lrrO O.:H Ulr'h), ms equal t unit~'j Une predietin fr iscntrpic flw S frm l'ither Saucr10 01' O,;watitsch and Rthstcin :13 ~/r'h = b + 1):2]'/~(r'>.'r,)1/~ () x LL ::;; < (f) '<. a: :::" (f)::'" <1-06. ~ '<. 0.9 i= 98 05U ~!(~---- ~. r'~d~~ t 6~ "--"" b --.:-~V-&~ 01 '--p-..., ,"-- li '1500R, -' 10! D COOLED ALLS ' NOZZLE 1 CONVERGENT-'-DVERGE';;:;:-Ti ' --r NOZZLE AREA RATOA/A,~ Fig. 11 Lcal t llc-tlilll('l"illal 11a",", fllx "ati,", alllg lhe tlzzlcs (vahll:s \\'c.'e dctc.",ui,u c fnuu a.vel'ugetl 1'/1'1."ati,.. sltwn in Fig~. alui :3). ~ \\'l('n' ~ is the axial distan\;.l:u :-:trcam f til!' "l'mctric thr at Thl' t H'r Sl'nhpic flll' 1)1'C(ctln :; rm!-a s analysis.9 Fr the 300-lli nzzh', thl' predidin frm Eq. () -!;i\'c,; a \"alue lar;.:!'!" than thal mea,;lrcd fr thc \lpstrl':un distance \O the snic li/h', \'ith hettl'r agrl'clllenl aftrdcd by /[all's prediclin. lall's a!lal~'si:; is!lt applicahll' t the 45-1.,) nzzll', "incp r,ir', < 1: b\' usin~ Eq. (), thc predi<.:teu elistan('l' i:-: 1110n' than tll"ic{,-tll!' ('xperll11ent:lll~:- deducecl \'alu!'. -'1 1l' ('lcl-t!j\' ('xp(,1"nh7õiãi 'alue:; \"(Jl1d 1)(' tfi(',;aml' as hsp indiea ted in Tahl(', haspd 0(1 the data mcntloned in S('e. 1li,.'as,; Flu,'\: Hatis Fr th(' eall'ulatin f hul\(lar~'-la~'l'r fi\\" and hl':\t ransfpr 10 nzzlc \"alls, tlh' l(wal ma~s fiux ~p!'), at thc l'd~p f the hund:l'~' aye~' i~ lh'pdl'(1. rny assul11inl-!; isl'nt rpit' flu\\' (1' = ].,1), tlus leal ma,;s '7rux \\"a:-: eall'ulalt d frm thp mcasun'd stalic-pr('~"ure distrihutins and is sh\\"n nnrlinh'nsinalized hy the ]-d isplltrpic fi\\" 'aluc in Fi~, 8. Thru~h mst f lhe nzzh', lhe leal mass tlux is c:;s than H' lurhulenl -d \'alu~\\"hieh hundary-ayerimplips flo's, lwer ) \\"all a: heat (p \"),',5. flux% 'fll!' sinccmas:; fr flux dp\'iatin amoll11t~ t ah\lt 20/c in tl!' inlet rel-\in and just dwnstrcam f tht thrat fr the _1.') '15 nzz!(': \\"ilh the :30-15 nzzh', til(' dl'\"ialins an' ks:;. The maximum \'alue~ f lhe mas:; flux (p \'), ceu~usl up,;tream f the thrat at hciiltl'r;('i'!ion ôf the -;Qjlic!ine ~'ith til!' edg;e 01 f]lltoull(lar~' ":iycr. l1 is in thi,; reginth;ll ilcat-tran,;fcr measlii'('ml'nls indieat(' til(' maximum hl'at fiux t lhe \\"all,l.6.1~ COJlclusin;; "'all static-pj"l,,:,;ure nll'a:-;uremenb hal"l' heen presenteei fr air flwing hru;.:h cnical nzzh's \\"ith circular-ar<' ' ~ 0.98 "- Q >- < a: >- V ::> a: :x: > ~ ' T, '1500'R, COOLEDALLS NOZZLE 30-15' ~ ~ ' ~ 0.45 thrat.-. ('ll1parisolls ha\"l' 1)('1'11 l1:ldl' with prl'di(,tins. Tl!' rl'sults indieate til!' fll\'inl-!;. ) 111 th(' thrat J"l'gin, w}wrl' lhe flw is ransllie, t\l'odill1l'l:-:illal isclltrpie flml' predidills an' ill elsl' agrl'l'l1ellt with lhc.laia fr tlh' 10ZZ!('S wilh a rati f thmal radill_ f (~llrya'"n' t hral radills r, 'rtl, = 2.0, hllt inadl'qllale fr the lzzll' \'ith r,ir'l> = 0.ti25, j)l'\'iatins as :trge a,; 30 and 450/;. frum thl' sim 111' lll,-dimpll-l:d isplltrpi(~ fl\\' pn'( wtlol \\"l'n' follllel ill tlll' lhrat rpgill fr thl' lzzlcwith r, 'r'h = 2.0 :llld O.G2.,), n'sp('cti\"['~', 2)rnlatic-pr~~l1paSlln'('lt,,- ill t 111' 1hn~l' alld dil'crgl'ltilf't'illill" uf lzzll';-' \ ith thl' :-:allh' r, 'Tt, :11r! half-alll-(]' 01' dinrgcnce l'n' f0'd t be es:;l'ltially illd('h'ld('!.!1 ~ari()ls illlpl l'nfi~ura tins, :» :'111:111('1'de\'i:ffills in statil' pn'sslln' frm (H!e-dillll'lsinal fi 11' \"('re folllld ill thp enil"al sel"lins, 111 til!' enyprgl'll"c rpgill, the l1agllitlld(' illl"l"ea.-l's \'ith l"lll'l'rg('('e alll-!-c, \\"hpre:ls ill hc din'rgl'lt'e rl'gin, this efteet was 10t im esti;.:atl'd,;ill('p ali til!' lzzles tl'sted h:ltl a 1,') h:llf-all.!:dl' f di~'gell("p. 4)tFr lllderl'xp:lnded peratill, ~rl's,;urc.jn!:.l~lt:. nll'nt;~werp in';l'lsiti\"e t lhe cltl'("ts f btlll"ll'd :llld 1111 t'll'd mlls alld tu lzz!' illlpl bolllldary-:t~''r thicknl';;~ t 0.45 f tia' nuzz!p-illlet radill.-. Thus. hundalt-layer eftect:; l're follnd t he negligible, 5) 'rps:;un:f(.;itfíng,; depend U tap size, wilh signific:llt dittej"l'lce;, folllld })('tween a!ld O.O-O-in.-diam hles. The smalle:-:t tap rl'ads thc 100n~r prc,;surc, which i,; belic\'ce 6) Fr~yerl'xpallded nzzll' peratin, thc separatiun pint t 1110\"['( hc~arerd\\"n~trc:lln the truc statie wlth prc~sure~ wall cling fr lests at lhe s:lme stagnalin H'es;;ure, s that lhe mlis 01',;eparatin-lalllhient pre:;slrl' fr thc ht-fll' tc,;ts \\"ith cled walls l'ere gcnel:ajly í) S-las;, abut fi\\' 5rate 10 10% and thrust ]wlw.elepenel the cld-fll\" n the\":llues,l tw-(funl'nsillality'ór thp fi\\" hrugh th(~ trallsnic regiul, with boulld:jr' laycr cttpct,; rp!:itin'l\" l1imprlallt fr lhe lzzle:,; im'l',;tig:~tcd that ha~pã~siõll-:ii'ca ratis t 6.G.J S) n the tran;:oc rcgin. lcal ma,_s fiuxes at lhe ed~c f lhe holllldary la~'er dedllced froll thp static-pres:;ure nll'asurcml'nls deyiale less frm nl'-dimcnsillal fi\\" \'alup,; than d the statie pressure,;. n the ('nn~rl-!;l'nce sl'clill, the magnitudes f these rll'\'iatins are abut the same as thc~' are in til(' lransnic reg.in and depellel 011 thc ctl\'crgence angl('. Hefcl'ClCCS ~\ -... 'Back, L. 11., ~[assier, 1'. F., :m Cier, 11. L., "Cnvective heat transfer in a en\'ergent-divergent nz7.le," ntern. J.!leat '" ~ ias:; Tran:,fer 7,,,)4D-.'j68 ( D(4). ""! Scheler, K. an 13ierlein, J. A., "Sme experimcnts n fi\\" :,eparatin in rcket n07.7.le:,," A!{S J. 23, 28-3:2, 40 ( 1!);,;n, Fra7.er, R. P., Eisenklam, 1'., and \Vilkie, D., "nvestigatin f super:<nic fiw separat in in n07.zle:,," J. :\[eeh. Eng. Sei., Campbel, C. K and Farley, J. "., "Perfrl1lance f several Fig. 7 Vnriatin NOZZLEEXPANSON-AREARATOA/A, f t1u'18t ru1i with cxpnn8in-urea.. ~267-:27!)(J959). 'nical cnvergent-divergent rcket-type exhau:'l n07.zle:,," rati (curves wcrc b1ail1cd frm avcraged 1'11" ra1is NASA Ti\" D-467 (Septel1lber 1!/(0). ~ shwn in Fig8. and 3). Arens, :\1. and Spiegler, E., "Separate fi\\" 111 verex-

9 ',BACK,.\L\SSEH, AND GEn AAA JOUnXAL panded nzzle~ at l\\' pres~ure mtis," Bul. He~. Cuneil bmel " ;\[igdal, D. alld Lalldi:;, F., "Characteri~ties f cnic!\l superllc,45-;j5(1962). 7' 6 Frtini, A. alld Ehlers, R. C., "Cmpari:;n f experimental '-... ~ '- snic u Oswatit~eh, lzzles," AHS K. alld J. 32, Hthsteill, 18!JS-!JO \V., (1962). "F\\' paltem in a cnt predicted heat tranhfer in a bell-~haped lzzle with upstrcam verging-divcrgillg nzzle," NACA T;\-12\.,) (Mareh 194\1). fiw disturbances," NASA TN D-1743 (August 19(3). 11 Jaivin, G. 1., "EfTect f hle size n prcssure mcasurements 7 Stantin, T. E., "The variatill f velcity in the neighbr- made with a fiat-plate dyllall1ic-head prhe," Jet Prpubin hd f the thrat f a colstrictill in a wind challnel," British Lab. Tt ;~2-617, Pa.. adena, Calif. (June \.\ H(4). Acrnautical Hesearch Cullcil H & :\ (lu30). " Live~ey, J. 1.., Jacbll,./. D., and Suthem, C..., "The _ 8 Ellitt, D. G., Bartz, D. R., and Silve', S., "Calculatin f static: hle errr prblem," :\ircraft Elg. XXXV, (lu62). ~urbulent bundary-layer grwth alld heat transfer in axi~~ymmet ric lzzles," Jet PrjJul:;ill Lab. T{ 3:!-3S7, Pasl\dena, 16 Ahlberg,.1. L, lamiltll, S., ;\igd,d, D., and Xilsn, E. X., i'truncated jjerfe"1 lzzle~ in pt ;llul1lzzle desigll," :\ ns.. Calif. (Fcbruary 15, 106;{). 31, 614-6:!O (1!J(1). v Hall, , "Transnic flw in -dill1en~i(jllalalld axially- 17 Arells, ;\1. alld Spiegler, E., "Sh(H'k-indlleed hund'll'~' symmetric nzzles," Quart. J. ;\ech.. -\ppl. ;\lath. XV, 487- layer ~cparatill ill \,cj'('xpahh'd ('(Jni.,,1 exhau~t nzzle<'.')(js ( U(2). A AA./. 1, :;7S-5,-'; 1 ( 1!G:j). ~ 10 Saucr, n., "(;pncral ('hara, t!'ri~ti( ~ f the tlw thruugh ' Kl()z~i, J../., ".-\11 illvbtig:atillf hpat tr:ll~fpr thrll~h 1111' nzzlcs at ncar eritiml ~pecd~," NAC:\ '1';\[ (./UC 1047). turbulcllt b<hl1ldary layer in ali axiall~' "Yll1etri(', ('Oll\'er~ellt- ') li Darwel, l. ;\1. alld bdhalll, l., "Shck frmatill in diverg:el1t lzzle,",\erdyl1ami(' Lab., ()hi" :-,tate Ul1i\. T.\-S c()l1icall1()zzlp~," A[A:\.., 1!1:~2-1\);!4(ln6:!). (.uly l!);js).

1.3. The Mean Temperature Difference

1.3. The Mean Temperature Difference 1.3. The Mean Temperature Difference 1.3.1. The Lgarithmic Mean Temperature Difference 1. Basic Assumptins. In the previus sectin, we bserved that the design equatin culd be slved much easier if we culd

More information

NASA. Comparison of Predicted and Experimental External Heat Transfer Around a Film Cooled Cylinder in Crossflow. NASA Technical Memorandum 83017

NASA. Comparison of Predicted and Experimental External Heat Transfer Around a Film Cooled Cylinder in Crossflow. NASA Technical Memorandum 83017 NASA Technical Memrandum 83017 Cmparisn f Predicted and Experimental External Heat Transfer Arund a Film Cled Cylinder in Crssflw Francis S. Stepka and Raymnd E. Gaugler Lewis Research Center Cleveland,

More information

CE113 Structural Laboratory Reinforced Concrete Beam Assignment #3 Reinforced Concrete Beam Pretest Predictions

CE113 Structural Laboratory Reinforced Concrete Beam Assignment #3 Reinforced Concrete Beam Pretest Predictions CE113 Structural Labratry Reinfrced Cncrete Beam Assignment #3 Reinfrced Cncrete Beam Pretest Predictins Assignment #3 is an individual assignment t be submitted in draft frm the week f the cncrete cylinder

More information

1.- L a m e j o r o p c ió n e s c l o na r e l d i s co ( s e e x p li c a r á d es p u é s ).

1.- L a m e j o r o p c ió n e s c l o na r e l d i s co ( s e e x p li c a r á d es p u é s ). PROCEDIMIENTO DE RECUPERACION Y COPIAS DE SEGURIDAD DEL CORTAFUEGOS LINUX P ar a p od e r re c u p e ra r nu e s t r o c o rt a f u e go s an t e un d es a s t r e ( r ot u r a d e l di s c o o d e l a

More information

THE UNEARNED NO CLAIM BONUS. C. P. WELTEN Amsterdam

THE UNEARNED NO CLAIM BONUS. C. P. WELTEN Amsterdam THE UNEARNED NO CLAIM BONUS C. P. WELTEN Amsterdam I. The claims experience f a mtrcar insurance is assumed t give sme indicatin abut the risk (basic claim frequency) f that insurance. The experience rating

More information

Student Academic Learning Services Page 1 of 7. Statistics: The Null and Alternate Hypotheses. A Student Academic Learning Services Guide

Student Academic Learning Services Page 1 of 7. Statistics: The Null and Alternate Hypotheses. A Student Academic Learning Services Guide Student Academic Learning Services Page 1 f 7 Statistics: The Null and Alternate Hyptheses A Student Academic Learning Services Guide www.durhamcllege.ca/sals Student Services Building (SSB), Rm 204 This

More information

Combination of beams. Chapter 12 Treatment Planning Combination of Beams. Opposing pairs of beams. Opposing pairs of beams. Opposing pairs of beams

Combination of beams. Chapter 12 Treatment Planning Combination of Beams. Opposing pairs of beams. Opposing pairs of beams. Opposing pairs of beams Chapter 12 Treatment Planning Cmbinatin f Beams Radiatin Dsimetry I Text: H.E Jhns and J.R. Cunningham, The physics f radilgy, 4 th ed. http://www.utled.edu/med/depts/radther Cmbinatin f beams Achieve

More information

Morningstar Document Research

Morningstar Document Research Morningstar Document Research FORM8-K EMC INSURANCE GROUP INC - EMCI Filed: May 11, 2016 (period: May 11, 2016) Report of unscheduled material events or corporate changes. The information contained herein

More information

Times Table Activities: Multiplication

Times Table Activities: Multiplication Tny Attwd, 2012 Times Table Activities: Multiplicatin Times tables can be taught t many children simply as a cncept that is there with n explanatin as t hw r why it is there. And mst children will find

More information

Experiment 1: Freezing Point Depression

Experiment 1: Freezing Point Depression Experiment 1: Freezing Pint Depressin Purpse: The purpse f this lab is t experimentally determine the freezing pint f tw slutins and cmpare the effect f slute type and cncentratin fr each slutin. Intrductin:

More information

Effect of inclined heat transfer rate on thermosyphon heat pipe under sound wave

Effect of inclined heat transfer rate on thermosyphon heat pipe under sound wave As. J. Energy Env. 2009, 10(04), 214-220 Asian Jurnal n Energy and Envirnment ISSN 1513-4121 Available nline at www.asian-energy-jurnal.inf Research Article Effect f inclined heat transfer rate n thermsyphn

More information

Retirement Planning Options Annuities

Retirement Planning Options Annuities Retirement Planning Optins Annuities Everyne wants a glden retirement. But saving fr retirement is n easy task. The baby bmer generatin is graying. Mre and mre peple are appraching retirement age. With

More information

Disk Redundancy (RAID)

Disk Redundancy (RAID) A Primer fr Business Dvana s Primers fr Business series are a set f shrt papers r guides intended fr business decisin makers, wh feel they are being bmbarded with terms and want t understand a cmplex tpic.

More information

Conduction in the Cylindrical Geometry

Conduction in the Cylindrical Geometry Cnductin in the Cylindrical Gemetry R. Shankar Subramanian Department f Chemical and Bimlecular Engineering Clarksn University Chemical engineers encunter cnductin in the cylindrical gemetry when they

More information

Special Tax Notice Regarding 403(b) (TSA) Distributions

Special Tax Notice Regarding 403(b) (TSA) Distributions Special Tax Ntice Regarding 403(b) (TSA) Distributins P.O. Bx 7893 Madisn, WI 53707-7893 1-800-279-4030 Fax: (608) 237-2529 The IRS requires us t prvide yu with a cpy f the Explanatin f Direct Rllver,

More information

B a rn e y W a r f. U r b a n S tu d ie s, V o l. 3 2, N o. 2, 1 9 9 5 3 6 1 ±3 7 8

B a rn e y W a r f. U r b a n S tu d ie s, V o l. 3 2, N o. 2, 1 9 9 5 3 6 1 ±3 7 8 U r b a n S tu d ie s, V o l. 3 2, N o. 2, 1 9 9 5 3 6 1 ±3 7 8 T e le c o m m u n ic a t io n s a n d th e C h a n g in g G e o g r a p h ie s o f K n o w le d g e T r a n s m is s io n in th e L a te

More information

Resource 2.3.1 Installing Videoconference Systems

Resource 2.3.1 Installing Videoconference Systems ICT Vlume 2.3.1 Installing Videcnference Systems Page 1 Deakin eslutins (Infrmatin Technlgy Services Divisin) Audi Visual and Netwrks Unit ICT Vlume 2.3 Videcnferencing Standards Resurce 2.3.1 Installing

More information

Operational Amplifier Circuits Comparators and Positive Feedback

Operational Amplifier Circuits Comparators and Positive Feedback Operatinal Amplifier Circuits Cmparatrs and Psitive Feedback Cmparatrs: Open Lp Cnfiguratin The basic cmparatr circuit is an p-amp arranged in the pen-lp cnfiguratin as shwn n the circuit f Figure. The

More information

Watlington and Chalgrove GP Practice - Patient Satisfaction Survey 2011

Watlington and Chalgrove GP Practice - Patient Satisfaction Survey 2011 Watlingtn and Chalgrve GP - Patient Satisfactin Survey 2011 Backgrund During ne week in Nvember last year patients attending either the Chalgrve r the Watlingtn surgeries were asked t cmplete a survey

More information

Distribution of Globular Clusters and Young Star Groups on the Sky. x x x

Distribution of Globular Clusters and Young Star Groups on the Sky. x x x PENN STATE ASTRONOMY LABORATORY è 11 THE STRUCTURE OF THE MILKY WAY GALAXY I. Objective In this lab, yu will learn that we live in the Milky Way Galay. Our slar system and all the stars yu can see with

More information

i n g S e c u r it y 3 1B# ; u r w e b a p p li c a tio n s f r o m ha c ke r s w ith t his å ] í d : L : g u id e Scanned by CamScanner

i n g S e c u r it y 3 1B# ; u r w e b a p p li c a tio n s f r o m ha c ke r s w ith t his å ] í d : L : g u id e Scanned by CamScanner í d : r ' " B o m m 1 E x p e r i e n c e L : i i n g S e c u r it y. 1-1B# ; u r w e b a p p li c a tio n s f r o m ha c ke r s w ith t his g u id e å ] - ew i c h P e t e r M u la e n PACKT ' TAÞ$Æo

More information

New York University Computer Science Department Courant Institute of Mathematical Sciences

New York University Computer Science Department Courant Institute of Mathematical Sciences New Yrk University Cmputer Science Department Curant Institute f Mathematical Sciences Curse Title: Data Cmmunicatin & Netwrks Curse Number:CSCI-GA.2662-00 Instructr: Jean-Claude Franchitti Sessin: 2 Assignment

More information

Calibration of Oxygen Bomb Calorimeters

Calibration of Oxygen Bomb Calorimeters Calibratin f Oxygen Bmb Calrimeters Bulletin N.101 Prcedures fr standardizatin f Parr xygen bmb calrimeters. Energy Equivalent The calibratin f an xygen bmb calrimeter has traditinally been called the

More information

!"#$%&'()%"*#%*+,-./-*+01.2(.*3+456789*!"#$%&"'()'*+,-."/01&2#."'3424,'

!#$%&'()%*#%*+,-./-*+01.2(.*3+456789*!#$%&'()'*+,-./01&2#.'3424,' "#$()"*#*+,-./-*+01.2(.*3+456789* "#$"()*+,-."/012#."3424, Dr. Peter T. Gallagher Astrphysics Research Grup Trinity Cllege Dublin :2";,

More information

EM EA. D is trib u te d D e n ia l O f S e rv ic e

EM EA. D is trib u te d D e n ia l O f S e rv ic e EM EA S e c u rity D e p lo y m e n t F o ru m D e n ia l o f S e rv ic e U p d a te P e te r P ro v a rt C o n s u ltin g S E p p ro v a rt@ c is c o.c o m 1 A g e n d a T h re a t U p d a te IO S Es

More information

Motor Calculations. Calculating Mechanical Power Requirements Torque - Speed Curves Numerical Calculation Sample Calculation Thermal Calculations

Motor Calculations. Calculating Mechanical Power Requirements Torque - Speed Curves Numerical Calculation Sample Calculation Thermal Calculations Mtr Calculatins Calculating Mechanical Pwer Requirements Trque - Speed Curves Numerical Calculatin Sample Calculatin Thermal Calculatins Calculating Mechanical Pwer Requirements Physically, pwer is defined

More information

Electric Circuits II. More about Mutual Inductance. Lecture #22

Electric Circuits II. More about Mutual Inductance. Lecture #22 EE 05 Dr. A. Ziduri Electric Circuits II Mre abut Mutual Inductance Lecture # - - EE 05 Dr. A. Ziduri The material t be cvered in this lecture is as fllws: Mutual Inductance in Terms f Self Inductance

More information

In this chapter, you will learn to use net present value analysis in cost and price analysis.

In this chapter, you will learn to use net present value analysis in cost and price analysis. 9.0 - Chapter Intrductin In this chapter, yu will learn t use net present value analysis in cst and price analysis. Time Value f Mney. The time value f mney is prbably the single mst imprtant cncept in

More information

How do I evaluate the quality of my wireless connection?

How do I evaluate the quality of my wireless connection? Hw d I evaluate the quality f my wireless cnnectin? Enterprise Cmputing & Service Management A number f factrs can affect the quality f wireless cnnectins at UCB. These include signal strength, pssible

More information

SCO TT G LEA SO N D EM O Z G EB R E-

SCO TT G LEA SO N D EM O Z G EB R E- SCO TT G LEA SO N D EM O Z G EB R E- EG Z IA B H ER e d it o r s N ) LICA TIO N S A N D M ETH O D S t DVD N CLUDED C o n t e n Ls Pr e fa c e x v G l o b a l N a v i g a t i o n Sa t e llit e S y s t e

More information

WINDOW REPLACEMENT Survey

WINDOW REPLACEMENT Survey WINDOW REPLACEMENT Prperty wners and develpers undertaking rehabilitatin prjects fr bth Tax Act Certificatin and Sectin 106 Cmpliance are encuraged t repair and retain existing histric windws. Hwever,

More information

OP 8: Building Energy Consumption

OP 8: Building Energy Consumption OP 8: Building Energy Cnsumptin 6 pints available A. Credit Ratinale This credit recgnizes institutins that have reduced their building energy usage. B. Criteria Part 1 Institutin has reduced its ttal

More information

In Australia, compulsory third party insurance (CTP) covers

In Australia, compulsory third party insurance (CTP) covers COMPULSORY THIRD PARTY INSURANCE: METHODS OF MAKING EXPLICIT ALLOWANCE FOR INFLATION B. J. BRUTON and J. R. CUMPSTON Australia SUMMARY An inflatin index is essential when cnstructing claim payment mdels

More information

«С e n tra l- A s ia n E le c tric - P o w e r C o rp o ra tio n», JS C

«С e n tra l- A s ia n E le c tric - P o w e r C o rp o ra tio n», JS C J o in t - s t o c k c o m p C E N T R A L - A S IA N E L E C T R IC P O W a n y E R C O R P O R A T IO N I n t e r n a l A u d i t P O L IC Y o f J o in t - S t o c k C o m p a n y C E N T R A L - A S

More information

R o t h IRAs : How They W o r k and How to Use Them

R o t h IRAs : How They W o r k and How to Use Them R t h IRAs : Hw They W r k and Hw t Use Them Rth IRAs differ frm ther tax-favred retirement plans, including ther IRAs (called "traditinal IRAs"), in that they prmise cmplete tax exemptin n distributin.

More information

Ready to upgrade the Turbo on your Diesel?

Ready to upgrade the Turbo on your Diesel? Ready t upgrade the Turb n yur Diesel? Tday s diesel engines represent the state f the art in technlgy with high pwer density, excellent drivability, and gd fuel ecnmy. Frtunately fr the diesel enthusiast,

More information

NPS ARCHIVE 1968 JOHNSON, L.

NPS ARCHIVE 1968 JOHNSON, L. NPS ARCIVE 1968 JNSN, L. EXPERIENTAL INVESTIGATIN F TURBULENT JET ATTACENT T A CNVEX WALL by Larry Dean Jhnsn i:rvterev CA 93943-5101 UNITED STATES NAVAL PSTGRADUATE SCL TESIS EXPERIENTAL INVESTIGATIN

More information

Volatility and Revenue Forecast Errors

Volatility and Revenue Forecast Errors Vlatility and Revenue Frecast Errrs Vlatility and Revenue Frecast Errrs Last mnth, the Pew Center n the States tgether with the Rckefeller lnstitute f Gvernment issued a reprt n trends in revenue frecasting,

More information

Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeoff

Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeoff Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeff Reading: Chapter 2 Stats 202: Data Mining and Analysis Lester Mackey September 23, 2015 (Slide credits: Sergi Bacallad) 1 / 24 Annuncements

More information

Solar Geometry P L A N E O F S U N

Solar Geometry P L A N E O F S U N 1 Slar Gemetry The Earth s daily rtatin abut the axis thrugh its tw celestial ples (Nrth and Suth) is perpendicular t the equatr, but it is nt perpendicular t the plane f the Earth s rbit. In fact, the

More information

Electrochemical cells

Electrochemical cells Electrchemical cells In this chapter, we turn ur attentin t electrn transfer reactins. T identify an electrn transfer reactins, we must assign xidatin states review rules in Chapter 3. e.g. Zn(s) Cu(NO

More information

EXPERIMENT 12 THE RC SERIES CIRCUIT

EXPERIMENT 12 THE RC SERIES CIRCUIT 260 12-1 I. THEORY EXPERIMENT 12 THE SERIES CIUIT In this experiment we will charge and discharge a capacitr thrugh a resistr, and measure the vltage acrss the capacitr as a functin f time. The purpse

More information

How to put together a Workforce Development Fund (WDF) claim 2015/16

How to put together a Workforce Development Fund (WDF) claim 2015/16 Index Page 2 Hw t put tgether a Wrkfrce Develpment Fund (WDF) claim 2015/16 Intrductin What eligibility criteria d my establishment/s need t meet? Natinal Minimum Data Set fr Scial Care (NMDS-SC) and WDF

More information

C o a t i a n P u b l i c D e b tm a n a g e m e n t a n d C h a l l e n g e s o f M a k e t D e v e l o p m e n t Z a g e bo 8 t h A p i l 2 0 1 1 h t t pdd w w wp i j fp h D p u b l i c2 d e b td S t

More information

Victims Compensation Claim Status of All Pending Claims and Claims Decided Within the Last Three Years

Victims Compensation Claim Status of All Pending Claims and Claims Decided Within the Last Three Years Claim#:021914-174 Initials: J.T. Last4SSN: 6996 DOB: 5/3/1970 Crime Date: 4/30/2013 Status: Claim is currently under review. Decision expected within 7 days Claim#:041715-334 Initials: M.S. Last4SSN: 2957

More information

Data Warehouse Scope Recommendations

Data Warehouse Scope Recommendations Rensselaer Data Warehuse Prject http://www.rpi.edu/datawarehuse Financial Analysis Scpe and Data Audits This dcument describes the scpe f the Financial Analysis data mart scheduled fr delivery in July

More information

1 of 5 P28 Lab #5 Summer 2004 Stanford Physics Dept. Ballistic Pendulum Gregory S. Romine

1 of 5 P28 Lab #5 Summer 2004 Stanford Physics Dept. Ballistic Pendulum Gregory S. Romine 1 f 5 P8 Lab #5 Summer 004 Experiment 5 Ballistic Pendulum In this experiment yu will aain be examinin a system that cnserves bth mmentum and enery. The ballistic pendulum is a device ften fund at well

More information

Lecture 3: 09.14.05 The first law of thermodynamics

Lecture 3: 09.14.05 The first law of thermodynamics 3.012 Fundamentals f Materials Science Fall 2005 Lecture 3: 09.14.05 The first law f thermdynamics Tday: LAST TIME...2 WORK AND HEAT CHANGE THE INTERNAL ENERGY OF A SYSTEM...3 The first law: cnservatin

More information

The Gibbs Free Energy and Cell Voltage

The Gibbs Free Energy and Cell Voltage The Gibbs Free Energy and Cell Vltage When an amunt f charge, Q, mves thrugh a ptential difference, E w = - Q E b/c wrk dne by the system E > 0 fr galvanic (vltaic) cells Recall, G = H TS = E + PV TS Fr

More information

I\4anila ALL LIFE INSURANCE COMPANIES AND MUTUAL BENEFIT ASSOCIATIONS DOING BUSINESS IN THE PHILIPPINES

I\4anila ALL LIFE INSURANCE COMPANIES AND MUTUAL BENEFIT ASSOCIATIONS DOING BUSINESS IN THE PHILIPPINES Republic f the Philippines Department f Finance INSURANCE COMMISSION l07l United Natins Avenue I\4anila Circular N. 201442-A Date Octber 30,2014 CIRCULAR LETTER TO ALL LIFE INSURANCE COMPANIES AND MUTUAL

More information

Unemployment, Gold, Money and Forecasts of Inflation

Unemployment, Gold, Money and Forecasts of Inflation Carnegie Melln University Research Shwcase @ CMU Tepper Schl f Business 3-1996 Unemplyment, Gld, Mney and Frecasts f Inflatin Allan H. Meltzer Carnegie Melln University, am05@andrew.cmu.edu Fllw this and

More information

CSE 231 Fall 2015 Computer Project #4

CSE 231 Fall 2015 Computer Project #4 CSE 231 Fall 2015 Cmputer Prject #4 Assignment Overview This assignment fcuses n the design, implementatin and testing f a Pythn prgram that uses character strings fr data decmpressin. It is wrth 45 pints

More information

Patient Participation Report

Patient Participation Report Patient Participatin Reprt In 2011, Westngrve Partnership decided t establish a PPG (Patient Participatin Grup) that wuld allw us t engage with ur patients, receive feedback frm them and ensure that they

More information

Calculating Pump Head How to calculate the Pump Head for Open and Closed Systems. 6/27/2012 Vemco, Inc.

Calculating Pump Head How to calculate the Pump Head for Open and Closed Systems. 6/27/2012 Vemco, Inc. Hw t calculate the Pump fr Open and Clsed Systems 6/27/2012 Vemc, Inc. Befre we can discuss pumpp head, we must understand the difference between an pen hydrnic system and a clsed hydrnic system. It is

More information

/* ------------------------------------------------------------------------------------

/* ------------------------------------------------------------------------------------ Pr o g r a m v a r e fo r tr a fik k b e r e g n in g e r b a s e r t p å b a s is k u r v e m e to d e n n M a tr ix * x M a tr ix E s ta lp h a B e ta ; n M a tr ix * z M a tr ix ; g e n M a tr ix X

More information

How much life insurance do I need? Wrong question!

How much life insurance do I need? Wrong question! Hw much life insurance d I need? Wrng questin! We are ften asked this questin r sme variatin f it. We believe it is NOT the right questin t ask. What yu REALLY need is mney, cash. S the questin shuld be

More information

Statistical Analysis (1-way ANOVA)

Statistical Analysis (1-way ANOVA) Statistical Analysis (1-way ANOVA) Cntents at a glance I. Definitin and Applicatins...2 II. Befre Perfrming 1-way ANOVA - A Checklist...2 III. Overview f the Statistical Analysis (1-way tests) windw...3

More information

Custom Portlets. an unbiased review of the greatest Practice CS feature ever. Andrew V. Gamet

Custom Portlets. an unbiased review of the greatest Practice CS feature ever. Andrew V. Gamet Custm Prtlets an unbiased review f the greatest Practice CS feature ever Andrew V. Gamet Descriptin In Practice CS, the firm can use any f the fur dashbards t quickly display relative infrmatin. The Firm,

More information

INTERMEDIATE CAD FILE MANAGEMENT

INTERMEDIATE CAD FILE MANAGEMENT INTERMEDIATE CAD FILE MANAGEMENT Intrductin File mismanagement is the dwnfall f many brilliant individuals. If yu are wise, yu wn't be ne f the peple wh meet disaster due t pr file management. Cmputers

More information

System Business Continuity Classification

System Business Continuity Classification Business Cntinuity Prcedures Business Impact Analysis (BIA) System Recvery Prcedures (SRP) System Business Cntinuity Classificatin Cre Infrastructure Criticality Levels Critical High Medium Lw Required

More information

GED MATH STUDY GUIDE. Last revision July 15, 2011

GED MATH STUDY GUIDE. Last revision July 15, 2011 GED MATH STUDY GUIDE Last revisin July 15, 2011 General Instructins If a student demnstrates that he r she is knwledgeable n a certain lessn r subject, yu can have them d every ther prblem instead f every

More information

Fixed vs. Variable Interest Rates

Fixed vs. Variable Interest Rates Fixed vs. Variable Interest Rates Understanding the Advantages and Disadvantages f Each Rate Type When shpping fr financial prducts, there are a lt f factrs t cnsider. Much has changed in the financial

More information

How to Avoid Moisture Damage to Walls from Condensation

How to Avoid Moisture Damage to Walls from Condensation Hw t Avid Misture Damage t Walls frm Cndensatin Backgrund Infrmatin Exterir building walls are barriers between the atmspheric cnditins n the utside and the atmspheric cnditins n the inside. Certainly

More information

T c k D E GR EN S. R a p p o r t M o d u le Aa n g e m a a k t o p 19 /09 /2007 o m 09 :29 u u r BJB 06 013-0009 0 M /V. ja a r.

T c k D E GR EN S. R a p p o r t M o d u le Aa n g e m a a k t o p 19 /09 /2007 o m 09 :29 u u r BJB 06 013-0009 0 M /V. ja a r. D a t a b a n k m r in g R a p p o r t M Aa n g e m a a k t o p 19 /09 /2007 o m 09 :29 u u r I d e n t if ic a t ie v a n d e m S e c t o r BJB V o lg n r. 06 013-0009 0 V o o r z ie n in g N ie u w la

More information

FTE is defined as an employee who is employed on average at least 30 hours of service per week.

FTE is defined as an employee who is employed on average at least 30 hours of service per week. On March 23, 2010, President Barack Obama signed int law cmprehensive health care refrm legislatin, the Patient Prtectin and Affrdable Care Act (H.R. 3590) passed in the Senate. The Health Care and Educatin

More information

Chapter - 3. Cable Connections

Chapter - 3. Cable Connections Chapter - 3 Cable Cnnectins One bradband alternative is thrugh cable TV, where yur Internet cnnectin is delivered t yur hme thrugh yur televisin cable. Many cable prviders wn't qute yu an exact speed,

More information

Using PayPal Website Payments Pro UK with ProductCart

Using PayPal Website Payments Pro UK with ProductCart Using PayPal Website Payments Pr UK with PrductCart Overview... 2 Abut PayPal Website Payments Pr & Express Checkut... 2 What is Website Payments Pr?... 2 Website Payments Pr and Website Payments Standard...

More information

H ig h L e v e l O v e r v iew. S te p h a n M a rt in. S e n io r S y s te m A rc h i te ct

H ig h L e v e l O v e r v iew. S te p h a n M a rt in. S e n io r S y s te m A rc h i te ct H ig h L e v e l O v e r v iew S te p h a n M a rt in S e n io r S y s te m A rc h i te ct OPEN XCHANGE Architecture Overview A ge nda D es ig n G o als A rc h i te ct u re O ve rv i ew S c a l a b ili

More information

Reliability Comparison Study. HP Inkjet Print Cartridges vs. Refilled Brands. Cartridge Reliability Print Quality

Reliability Comparison Study. HP Inkjet Print Cartridges vs. Refilled Brands. Cartridge Reliability Print Quality Reliability Cmparisn Study HP Inkjet Print Cartridges vs. Refilled Brands Cartridge Reliability Print Quality September 2005 Fr distributin in Eurpe, Middle East, and Africa 5401 Tech Circle Mrpark, CA

More information

Collaboration in Public H e alth be tw e e n U niv e rs ity of H e id e lbe rg and U niv e rs ity of D ar e s S alaam How t h e c oop e r a t i on e m e r g e d Informal c ont ac t s from e arly 1 9

More information

manual Page 1 / 5 effects in an easy good LED strips can be Selection guide applications. 1) Selection (indoors, outdoors) desired number of LEDs

manual Page 1 / 5 effects in an easy good LED strips can be Selection guide applications. 1) Selection (indoors, outdoors) desired number of LEDs Technical instructin Intrductin LED strips are a new generatin f innvative lighting prducts that allw creating spectacular effects in an easy way. LED strips have ther advantages like small dimensins,

More information

Licensing Windows Server 2012 for use with virtualization technologies

Licensing Windows Server 2012 for use with virtualization technologies Vlume Licensing brief Licensing Windws Server 2012 fr use with virtualizatin technlgies (VMware ESX/ESXi, Micrsft System Center 2012 Virtual Machine Manager, and Parallels Virtuzz) Table f Cntents This

More information

What Does Specialty Own Occupation Really Mean?

What Does Specialty Own Occupation Really Mean? What Des Specialty Own Occupatin Really Mean? Plicy definitins are cnfusing, nt nly t cnsumers but als t many f the insurance prfessinals wh sell them. Belw we will try t prvide an understandable explanatin

More information

efusion Table of Contents

efusion Table of Contents efusin Cst Centers, Partner Funding, VAT/GST and ERP Link Table f Cntents Cst Centers... 2 Admin Setup... 2 Cst Center Step in Create Prgram... 2 Allcatin Types... 3 Assciate Payments with Cst Centers...

More information

Class 23 Doppler Effect

Class 23 Doppler Effect Cla 23 Dppler Effect What determine hw lud we hear f the und prduced by a urce? In what way de the ditance f the urce frm u affect it apparent ludne? Belw i a imulatin f the und wave emitted frm a pint

More information

2. Before we answer the question, here are four important terms relating to redox reactions and galvanic cells.

2. Before we answer the question, here are four important terms relating to redox reactions and galvanic cells. CHAPTER SEVENTEEN ELECTROCHEMISTRY Fr Review 1. Electrchemistry is the study f the interchange f chemical and electrical energy. A redx (xidatin-reductin) reactin is a reactin in which ne r mre electrns

More information

IFRS Discussion Group

IFRS Discussion Group IFRS Discussin Grup Reprt n the Public Meeting February 26, 2014 The IFRS Discussin Grup is a discussin frum nly. The Grup s purpse is t assist the Accunting Standards Bard (AcSB) regarding issues arising

More information

Fahrenheit & Celcius. Working with. Temperature Scales

Fahrenheit & Celcius. Working with. Temperature Scales BRSP - 13 Page 1 Wrking with Fahrenheit & Celcius Temperature Scales Walking quickly frm the parking lt tward the terminal, I felt s warm I had t remve my jacket. The airprt thermmeter read 28 degrees.

More information

I n la n d N a v ig a t io n a co n t r ib u t io n t o eco n o m y su st a i n a b i l i t y

I n la n d N a v ig a t io n a co n t r ib u t io n t o eco n o m y su st a i n a b i l i t y I n la n d N a v ig a t io n a co n t r ib u t io n t o eco n o m y su st a i n a b i l i t y and KB rl iak s iol mi a, hme t a ro cp hm a5 a 2k p0r0o 9f i,e ls hv oa nr t ds eu rmv oedye l o nf dae cr

More information

Magnetism II Lab Title - 1

Magnetism II Lab Title - 1 ** Disclaimer: This lab write-up is nt t be cpied, in whle r in part, unless a prper reference is made as t the surce. (It is strngly recmmended that yu use this dcument nly t generate ideas, r as a reference

More information

OPERATING EFFICIENCY OF A NON-MEMBRANE GROUND HEAT AND MASS EXCHANGER AFTER 15 YEARS OF OPERATION

OPERATING EFFICIENCY OF A NON-MEMBRANE GROUND HEAT AND MASS EXCHANGER AFTER 15 YEARS OF OPERATION TECHNICAL SCIENCES Abbrev.: Techn. Sc., N 11, Y 008 DOI 10.478/v-008-001-0 OPERATING EFFICIENCY OF A NON-MEMBRANE GROUND HEAT AND MASS EXCHANGER AFTER 15 YEARS OF OPERATION Institute f Agricultural Engineering

More information

Trends and Considerations in Currency Recycle Devices. What is a Currency Recycle Device? November 2003

Trends and Considerations in Currency Recycle Devices. What is a Currency Recycle Device? November 2003 Trends and Cnsideratins in Currency Recycle Devices Nvember 2003 This white paper prvides basic backgrund n currency recycle devices as cmpared t the cmbined features f a currency acceptr device and a

More information

Gauss Law. AP Physics C

Gauss Law. AP Physics C Gauss Law AP Physics C lectric Flux A Let's start be defining an area n the surface f an bject. The magnitude is A and the directin is directed perpendicular t the area like a frce nrmal. Flux ( r FLOW)

More information

CSAT Account Management

CSAT Account Management CSAT Accunt Management User Guide March 2011 Versin 2.1 U.S. Department f Hmeland Security 1 CSAT Accunt Management User Guide Table f Cntents 1. Overview... 1 1.1 CSAT User Rles... 1 1.2 When t Update

More information

3 Fluid flow in porous media

3 Fluid flow in porous media Fluid flw in prus media In Chapter we cnsidered hw t represent a particle size distributin by, where pssible, a single term that is representatie f all the particle sizes. This term may then be used fr

More information

Hardware components. Typical connections and data flow. Student 3 page 1: Low Merit

Hardware components. Typical connections and data flow. Student 3 page 1: Low Merit Student 3 page 1: Lw Merit Hardware cmpnents Extensin cards Descriptin, Hw purpse determines cnnectins Extensin cards extend the capacity f the mtherbard by allwing a circuit bard r card t cnnect t it

More information

System Business Continuity Classification

System Business Continuity Classification System Business Cntinuity Classificatin Business Cntinuity Prcedures Infrmatin System Cntingency Plan (ISCP) Business Impact Analysis (BIA) System Recvery Prcedures (SRP) Cre Infrastructure Criticality

More information

A n d r e w S P o m e r a n tz, M D

A n d r e w S P o m e r a n tz, M D T e le h e a lth in V A : B r in g in g h e a lth c a r e to th e u n d e r s e r v e d in c lin ic a n d h o m e A n d r e w S P o m e r a n tz, M D N a tio n a l M e n ta l H e a lth D ir e c to r f

More information

4370.4 REV-1. cash flows from operating activities, cash flows from investing activities, and cash flows from financing activities.

4370.4 REV-1. cash flows from operating activities, cash flows from investing activities, and cash flows from financing activities. CHAPTER 5 STATEMENT OF CASH FLOWS IN DETAIL 5-1 Cash is the lifebld f any nging cncern. Cash is INTRODUCTION the fuel that keeps the business aflat. As was stated in Chapter 2, the Balance Sheet and the

More information

Gain vs. Proportional Band

Gain vs. Proportional Band Gain vs. Prprtinal Band The end result f the analysis f a typial lp tuning predure, whether pen lp r lsed lp, is a set f parameters with whih t adjust the ntrller. One f these parameters is ntrller gain.

More information

Information Guide Booklet. Home Loans

Information Guide Booklet. Home Loans Infrmatin Guide Bklet Hme Lans This Infrmatin Guide bklet prvides yu with general infrmatin nly. It will als help yu t better understand any recmmendatins we have made fr yu. Infrmatin Guide Hme Lans January

More information

The ad hoc reporting feature provides a user the ability to generate reports on many of the data items contained in the categories.

The ad hoc reporting feature provides a user the ability to generate reports on many of the data items contained in the categories. 11 This chapter includes infrmatin regarding custmized reprts that users can create using data entered int the CA prgram, including: Explanatin f Accessing List Screen Creating a New Ad Hc Reprt Running

More information

Market Velocity and Forces

Market Velocity and Forces Market Velcity and Frces SUPPORT DOCUMENT NASDAQ Market Velcity and Frces is a market sentiment indicatr measuring the pre-trade rder activity in the NASDAQ Stck Market trading system. It indicates the

More information

w ith In fla m m a to r y B o w e l D ise a se. G a s tro in te s tin a l C lin ic, 2-8 -2, K a s h iw a z a, A g e o C ity, S a ita m a 3 6 2 -

w ith In fla m m a to r y B o w e l D ise a se. G a s tro in te s tin a l C lin ic, 2-8 -2, K a s h iw a z a, A g e o C ity, S a ita m a 3 6 2 - E ffic a c y o f S e le c tiv e M y e lo id L in e a g e L e u c o c y te D e p le tio n in P y o d e r m a G a n g re n o su m a n d P so r ia sis A sso c ia te d w ith In fla m m a to r y B o w e l D

More information

S m o k e a l a r m s s a v e l i v e s!

S m o k e a l a r m s s a v e l i v e s! Dcument type: Practice Nte Title: Dmestic smke alarms Dcument number: AC2209 Versin: 3 1. Legislative requirements As f April 2003, Building Cde clause F7 Emergency Warning Systems requires that smke alarms

More information

Writing a Compare/Contrast Essay

Writing a Compare/Contrast Essay Writing a Cmpare/Cntrast Essay As always, the instructr and the assignment sheet prvide the definitive expectatins and requirements fr any essay. Here is sme general infrmatin abut the rganizatin fr this

More information

Introduction to Fractions and Mixed Numbers

Introduction to Fractions and Mixed Numbers Name Date Intrductin t Fractins and Mixed Numbers Please read the Learn prtin f this lessn while cmpleting this handut. The parts f a fractin are (shwn belw): 5 8 Fractins are used t indicate f a whle.

More information

Design for securability Applying engineering principles to the design of security architectures

Design for securability Applying engineering principles to the design of security architectures Design fr securability Applying engineering principles t the design f security architectures Amund Hunstad Phne number: + 46 13 37 81 18 Fax: + 46 13 37 85 50 Email: amund@fi.se Jnas Hallberg Phne number:

More information

B rn m e d s rlig e b e h o v... 3 k o n o m i... 6. S s k e n d e tils k u d o g k o n o m is k frip la d s... 7 F o r ld re b e ta lin g...

B rn m e d s rlig e b e h o v... 3 k o n o m i... 6. S s k e n d e tils k u d o g k o n o m is k frip la d s... 7 F o r ld re b e ta lin g... V e lf rd s s e k re ta ria te t S a g s n r. 1 4 3 4 1 5 B re v id. 9 9 3 9 7 4 R e f. S O T H D ir. tlf. 4 6 3 1 4 0 0 9 s o fie t@ ro s k ild e.d k G o d k e n d e ls e s k rite rie r fo r p riv a tin

More information

Phi Kappa Sigma International Fraternity Insurance Billing Methodology

Phi Kappa Sigma International Fraternity Insurance Billing Methodology Phi Kappa Sigma Internatinal Fraternity Insurance Billing Methdlgy The Phi Kappa Sigma Internatinal Fraternity Executive Bard implres each chapter t thrughly review the attached methdlgy and plan nw t

More information