Boundary Lyer Theory

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586 XIX. Throretical aaotin~ptiona for the calculation of turhdcnt flow8 A. 1lrl.z [4] gave n very Iuctd derivation of eqn. (19.18). In latcr times von J
I lorv t,hr c:onst~;~,~~(, of in t.c:gr;rt.iotl, C, ~nnst I)c tlet~crtninctl from the condit,ion at the wnll :~ntl sc~vcs t.o fit, t.lw t.url)tilrnt vrlocity clistrib~~t~ion to Llrat in tl~c laminar sub- Iaycr. Ilo\vc.vcr, c:vc:n wil,I~out tlvt.nrrnining C it is possible to tlcdr~cc from eqn. (19.27) :L I;l\v an:~logotts t,o t.I~:ll in cqt~. (19.21). 111 spite of t,hc f;lc:t tkrt cqn. (19.27) is v:llid only in the ~~cighI)o~~rhootl or tlto w;~ll, I)(Y:RIIRG of the ass~~~nptiot~ thati t -- const., we shall at,t,rrnpt t.o ~tsc it, for thc whole rrgion, i. I?. up to 11 = h. Since at y =: h we Irnvc u -7 u,,,,,. wc ol)t,:~in 7',,,ar - 7 11 I h u,,,, = "*O In li -t C , - -- In - ; (y = disb:~nrc from wall) "*o K Y , I , his 1111iv(:rs;11 vcl~(~i(.~~-(l~fc(;l, I:LW tlrw 1.0 I'rnndt,l is shown plotlet1 ;ls c:urvc (I) in ITig. ,1!).2. In t.11~ prc?c:c:tling argument we sr~cccetlccl in deriving a urrivcrsal vclocityclist.ril,~tt.io~~ I:lw from I'r:~n(It.I's law of friction in cornplcbc analogy wit,h that in o(111. (1!).21), whic:h was olll.:linctl from von IChrrn~in's si~nilarit~y rrrlc. The only clifferent:(: is in t.l~c: form of t.llc: functions of y/h wl~ich'appear on the right-had side of cqns. (1!).21) : L I I ~ (1!).28) rrspc.cl,ivrly. on rcflcxidn this will not appear incomprchc?nsil,lc, if wc: f.altc intm nccount the tlifkmncc in t*hc assumption concerning the sl~r:~ring st.rcss. Vorl 1C:'Lrrn;in nssnmctl a linear slrcaring-stress distrib~ttion, bltc: mixing Icngt,l~ bring 1 - u'lu". On t h other hand, Prantltl assumed a constant. sl~cnriitg st,ross and 1 - ?I. l'igurc 19.2 cor~tair~s a comparison hetwccn t.hcsr: two I:rws. A I~rt.l~c:r cornprison with cxpcrirncnt is clcfcrrcd to Chap. XX. It* may be worth 11ot.ing in pnssing Il~nt, it. is possil,l(: lo ol)l.:li~l 1.I1v sin~l,l,: I.(~SIII(. l.l~:it. 1 .- x ?I front tl~c vclocit,y-tlrfi:c:t. I:LW (I!).27), t.ogot.lwr wil.11 vot~ I tlisc:~~ssrd in gr(~~t.vr (I(~l,i~il in 1 . l SII(YYT- ~ (ling clrnpt.cr, give a value of x -- 0.4. 11'110 scc:on(l co~rst,:~nt,. 0, tl(,l)c*~ltls 011 t,11(, n:ttarc of t,hc wd1 snrf:icc; rdov:l~~t, n~~rncrirnl v:rlnc,s will IN! givrn in (%:I;). XS.
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McGRAW-I4ILL SERIES IN MECHANICAL E
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vi Contents CIIAPTEII V. Exnct ~olu
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Y Contents A " I XI X 'I'lirorrt.ir
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xvi I'orcworcI Thc result was t.11~
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From Author's Preface to the First
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the aid of thorctical considcmtioti
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even in fluitls wit,lt vcry srnall
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10 I. Or~llinr of lluicl rnot,ion w
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The vclwil y IL at some point i11 t
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Fig. 1.6. Firld of flow of oil nho~
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22 I. Outliric of fluid motion with
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2 (i TI. O~~tlittr of Imun~lnry-lsy
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Fie. 2.511 Fig. 2 .5~ Fig. 2.5b Fig
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S - point orscpnrnt.ion T'ig. 2.12.
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3 8 \ Y?\ If. 011tli11e of boundary
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42 11. 011tli11e of Iw~~ntlnry-Inyr
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[:j2a] I?o~cilhrntl, I,.: Thr forn~
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50 111. l)crivnt,ion of thc cquntio
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Fig. 3.3. Tmcd clintor1,ion of flui
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of flltitl is strcsscd in thrcc nlu
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1:i~ 3.8. Qltnsintzt.ia cotnprrssio
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66 111. 1)wivntion of the eqnntions
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CHAPTER I V General properties of t
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74 TV. Gencrol proprtic~ of tho Nov
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Ilcre v, c, :tntl k tlrnol,c 1.I1t:
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conclil.ion (4.14) plays n part wl~
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86 V. 1':xact solul ions of tlir N:
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90 V. ICxnct sol~ttion~ of tho Nnvi
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94 V. Exnct sohltiono ol' tho Nnvic
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Table 5.1. Functions occrtrring in
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11. Flow taenr n rotnting disk. A f
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106 V. JCxact solutions of the Navi
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cnu bo npplirtl nt mont, nn fnr RS
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114 VI. Vcry slow motion where r2 =
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1 I8 VT. Very slow motion r. 'l'l~o
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122 VI. Very rrlow motion ext.endcd
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126 VT. \'cry slow rnot.ion Part B.
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130 VII. Boundnry-layor cquntionzl
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'1. Skin friction \VlIat1 t.11~ I)o
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138 VII. no~~ndnry-layer cqnntions
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142 VII. Hor~nclnry-lnyrr rq~~ntii~
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146 VII. I~o~~ntlnr~ Inyrr cq~~ntio
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CIIAFTER VIII Gencral propertiee of
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164 VIII. Ccnernl propertic8 of Lhe
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158 VIII. General ppropcrtics of th
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VIII. General propertien of the bou
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'I'his c.quat,ion Lmnsforms into t1
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170 TX. 1Sxact uolutions of t.ho st
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174 TX. Exnct ~olut,ionu of tho sto
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178 IX, Exact solutions of tlrc ste
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and t,llc? clnsh now clet~otos tlil
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1 86 10 0.8 0.6 0.4 0.2 0 -0.2 -0.4
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ccnt,rred nt, (m -1- 1, n). 1'110 t
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194 IX. Jqxnct eolutions of thc stc
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O~l:cr ehnpw: Second-order cITcetls
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202 X. Approximate rncl.hoda for st
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206 X. Approxitnnte rnct.l~otls for
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210 X. Approximate mcthod~ for shad
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214 X. Approximato mothotls for sha
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218 X. Approximntn met,hods for shn
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222 X. Approximate methods for stea
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220 XI. Axinlly symniobricnl nnd th
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230 XI. Axinlly symmctricnl and thr
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23.1- XI. Axially uynimet.rira1 nnc
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the two wries expnnsicws for sin (%
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242 XI. Axially nymmct.riral and tl
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in cross-flow, tlrprntls only on lh
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250 XI. Axinlly nyrnmet,rirnl nntl
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XI. Axinlly ~,vn~n~et.rir;~l nnrl I
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258 XI. AxhIly syn~rnrtrirnl nncl t
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. . lit 1 h1:lgt.r. '1.: 'l'l~idc I
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206 XIT. l'l~rr~nnl bo1111r11iry ln
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270 XIT. 'I'l~rrtnal boundary layer
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can I)r rct.ni~rrvl in inrotnl~rrss
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if wc: pillf - - 'I1, - (A7'),. 11,
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Rotntirig rli~k: (:II:I~I. V, in pn
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286 X11. 'IY~rrrr~al bo~~ndnry laye
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290 XlI. Tl~rrnmal boundary layers
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with 0,' -. () at, r] - 0 and 0, =
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2!)H XI[. Thcrn~al bor~nrlnry Inyrr
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302 XJI. Therninl boundary layers i
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306 XII. Tllcrrnal hor~ndary layers
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310 XJI. 'I'hcrmnl boundnry layers
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314 X11. Thermal boundary laycrs in
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318 XIT. Tl~crnial bonndnry layers
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322 XII. Tl~or~nnl I)onndnry lnyers
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326 X l I. 'l'l~crn~nl hounrlnry ln
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330 X[[1. lmninar bor~ndnry lnyers
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334 XIIT. Lnrninnr 1)oundary laycra
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338 XI I I. Im~linnr I>orirtclt~ry
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342 XI11. Tmninnr Imlndary layeru i
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346 XI 11. T,ntninar I~or~nrjary hy
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350 XIII. 1,mninnr honnclxry lnycrn
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354 XI 11. 1,nminnr h~nrlnry 1:ryrm
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Fig.. l3.16. In 13.18. lain~innr ho
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a Intninn.r l)out~rlary I:~.ycr, bu
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1 I Itc vnriolts c4Twl.s ol'sl~oclt
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370 XIIJ. I~tminar boundary layers
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\'all I)rirst., 15.11..: 'l'hr prol
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CIIAPTER XIV Boundary-layer control
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5. J'rrvrntion of trauaitinn by the
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frorii th; 1c;ulitig rxlge! (l3l:wi
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390 XIV. Ilo~~n~lnry-lnycr contml F
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. - v, (x) =cons/ Fig. 14.14. 1,ant
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invc?st.igai.ctl. In this msc too,
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402 XIV. Dounclery-layer control 1.
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Ni\('A 'rM !I74 (1!)41). 1861 Sinli
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110 XV. Non-~teldy bortndnry layers
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414 XV. Non-st.cncly hour~tlnry Iny
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418 XV. Non-slmrly l~orrnclnry Inyr
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422 XV. Non-st,cndy hoixnd~ry Inycr
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420 XV. Non-nl,mdy Fig. 15.58 Fig.
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XV. Non-utcncly boouclary lnyers wh
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434 XV. Non-stcxcly boundary layers
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438 XV. Non-atcndy boundnry inyer~
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442 XV. Norl-st,aady boundary Isycr
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440 XV. Non-st,rndy ho~~nclnry laye
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450 XVI. Origin of tnrhulence I pyi
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XVT. Origin of turbulcncc I n. Some
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458 XVI. Origin of turbulence I b.
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462 XVI. Origin of tnrb~rlmcc 1 num
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466 XVi. Origin of t.r~rhr~lrncc 1
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470 XVI. Origin of h~rlwlcnce T I R
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474 XVI. Origin of l,t~rl~~tlct~rr
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478 XVI. Origin of I.rtrb~tlmcr 1 t
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482 XVT. Origin of tmbulcncc I c. E
Page 254 and 255: 486 XVI. Origin of k~rbulenre I 148
Page 256 and 257: 490 XVII. Origin ol t,urbulencc 11
Page 258 and 259: 404 XVII. Oriein of tnrbnlencc TI F
Page 260 and 261: 498 XVII. Origin of turbnlmco II t,
Page 262 and 263: Tlw tlisl.nr~cc Iwt,wccn the point,
Page 264 and 265: c. Efict of ~urtintl on trnt~nition
Page 266 and 267: 510 XVl I. Origin of Idmlrnro I I '
Page 268 and 269: 514 , XVII. Origin of turbulence 11
Page 270 and 271: 518 XVI I. Origin of turhr~lcncc 11
Page 272 and 273: on the bnsis of t.hc tl~corct,ical
Page 274 and 275: 626 XVII. Origin oI t.11r011lonco I
Page 276 and 277: 630 XVII. Origin ot t.~~rhr~lrncc J
Page 278 and 279: XVII. Origin of t.urh~~lencc TI 7 !
Page 280 and 281: 638 XVII. Origin of t~~~rbnlc~~rr I
Page 282 and 283: \vi(,l~ a (-ylit~(lw envcrv(1 wiI.1
Page 284 and 285: 646 XVII. Origin of turbulence TI F
Page 286 and 287: 550 X\'ll. Origin of t,11rh111rnrc
Page 288 and 289: 554 XVII. Origin of t,rlrbuloncc TI
Page 290 and 291: 558 XVITI. Fundamentals of tr~rbule
Page 292 and 293: 562 XVlI1. R~nclnmont.nIu of tur1)u
Page 294 and 295: The corrrlnt,ion co~ffiricnt~ y~ ra
Page 296 and 297: 670 XV111. I'nntlntnrt~t~nlrr of tt
Page 298 and 299: 574 XVIII. 1'undnnient.alu of tnrl~
Page 300 and 301: CHAPTER XIX Theoretical assumptions
Page 302 and 303: 682 XIX. Thcoroticnl wsltmptionu fo
Page 306 and 307: 5l)O XIX. Tl~rorrt,icnl nmumptions
Page 308 and 309: 594 XIX. 'rheoreticnl nssornptions
Page 310 and 311: 698 XX. 'I'~~rl~ulrnt flow f,lrro~~
Page 312 and 313: 602 XX. T~rrbulcnt flow thro~tgh pi
Page 314 and 315: 606 XX. 'l't~rhl~lc~rit flow thro~~
Page 316: GI0 XX. Turbulent flow throngh pip
Page 319 and 320: Icror~~ ()I(, phj.sic*:~l ~)oint. o
Page 321 and 322: 620 XX. Tnrbnlcnt flow tlvough pipe
Page 323 and 324: dimensions Fig. 20.26. 1tc.sist.anc
Page 325 and 326: 628 XX. T~lrbnlmt flow through pipe
Page 327 and 328: 632 XX. Turhulcnt flow through pipc
Page 329 and 330: 636 XXI. Td~nlcnt houndnry layers a
Page 331 and 332: 610 XXI. Ttrrbulent bor~ndnry layer
Page 333 and 334: 644 XXI. Turbulent boundary laycrs
Page 335 and 336: 048 XXI. Turbulent boundary layers
Page 337 and 338: 652 XXI. Turt)~~lcnt houndnry layer
Page 339 and 340: 656 XXI. Turbulent boundnry layers
Page 341 and 342: 660 XX I. Tl~rhlent bo~~ndary layer
Page 343 and 344: 664 XXI. Turbulent boundary layers
Page 345 and 346: CHAPTER XXII The incompreesible tur
Page 347 and 348: 672 XXll. 'l'llc incon~prcssiblc tu
Page 349 and 350: 070 XXII. Tlic incompreaaibto lnrl)
Page 351 and 352: FRO XXII. Tho incornprcs~iblo turbu
Page 353 and 354: 684 XXII. 'Yhc incon~prcssible Lnrb
Page 355 and 356:
688 XXJI. The incon~prcssible t,urb
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002 XXI1. Tho inro~nprc~sil~lo tt~r
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is prol)nt~t,iot~nl to the rnclius.
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lf$8] Mucsm:tnn, 11.: Z~~snrntncnhn
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70-t XX I1 I. 'Ihrbulcnt bonrwlnry
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708 XXIII. Turbulent bonndnry Iaycr
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712 XXI 11. 'I'~~rl~~~lemt bo~~ntln
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716 XXIII. 'I'urbr~lcnt bor~ntlnry
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720 XXIII. Turbulent boundary layer
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724 XXlll. 'rur1)ulcnt boundnry Iny
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[04] Smith, P.D.: An integral predi
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732 XXIV. Frcc trtrbt~lent flows; j
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700 XXIV. Prrc tr~rb~tlent flowa; j
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Neglecting u12, we obtain XXIV. Prc
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744 XXIV. lhc L~trl)ulcnt Ilow~; jo
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748 XXIV. Free turbulent flowa; jet
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762 XXIV. Frcc td)ulcnt flows; jcta
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756 XXIV. Prrc torbulent flows; jet
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760 XXV. DotcrminnLion of profilo d
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764 XXV. I)ot.crtninntiotl of profi
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768 XXV. Determination of profile d
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XXV. 1)obrlninalion of proRlo drag
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776 XXV. 1)ctormination of profile
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A. Reviews organized in serial publ
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784 Bibliography Sherman, I?. S., I
Page 405 and 406:
Clementa, lt.R., and Mad, D.J.: The
Page 407 and 408:
792 Bihliography 13ird, R.R., Slewn
Page 409 and 410:
Oswatitach, I
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H:I:IR, 11. 776, 777 Ilnnsr. 1). 62
Page 413 and 414:
Scl~crb:trl,l~, I
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805 811bjrct lntlrx 209, 354, 385,
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812 Snhjcct lntlcx - vorl.irrs 526,
Page 419:
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