Boundary Lyer Theory

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474 XVI. Origin of l,t~rl~~tlct~rr 1 1%. (:. vnn dcr llrRge Zijnen 1411 and M. Tlanscn. 'i'hcsc mcasurernents led to the rc.sult. t.11nt. t,hn crit,ic:d Jbynoltls numhcr was cont,ainccl in the rangc Soon nfi.cr, 1 I. 1,. I)rytlcn I 16. 171 and his c:ollaltornt~ors nndertook I& vcry t,horougl~ s.nd r,aroli~l inves(.ig~t.iorl of this l,ypc of flow. I)tlring the course of tht:sc invcst,igat,ions rxt,cnsivc? t1at.a. OII t,ho volorit.y clistrihl~l.ior~ were cnrcfullg plotted wit,l~ the aid of Imt-wire a.ncn~omrt.crs in t.rrrns of spncc roortlinntcs n.nd timc. Ilowc~nr, t,llc: srlcct.ivc an~plilication of (lisI.urImnc(~s ~~r(dicI.r(l Ity the theory could not yet Itr det.cct,cd. At nl~o~rt the same time, cxpcri~ncr~t~s cn.rrict1 out n.t Goct~tingcn on a Ilnb pinto ill a w:rtcr chnnncl yicltletl a qunlit,at.ivc confirmation of tho t,hrory of stahilit,y. 'i'l~e plrot~ogr:rphs in Fig. 16.15 clcpict n t,urbrilent region which originated from n tlist.nrl)nncc of long wavelcr~gth. 'J.'ho similnrit,y between these pl~otogmphs mtl the !.l~corct,ic;~.l pxl,tcr~~ of nt.ream1inrs of a neutral clistt~rltnnce shown in I'ig. 16.14 is irrcfttta,I~lc. 111 tiiswsing (,r:~nsit.ion it is necessary to introduce one very important pnrarnrt,rr which rncn.surcs t h "tlcgrcc of dislmrl~nncc" in the external stream. Ik im- ~tort:t,nc-r wn.s lirsl, rccogniscd whrn mrnsttrctnc~lts of t,ho dmg of sphrres were per- (i)rnwI it1 tIi(lr.rcnt, win11 h~nnrl~. 111 this (:onnexion it/ was discov~rcd that the critical Ilrynoltls nrrml)or of a sphcrc, that is that valuc bf the Reynolds number which rorrcspontls to the abrnpt, t1t:crrasc in tllc dm.g cocflicierrt sl~own in Pig. 1.5, depends vtq rna.rl~r:tIly "11 t.11~ sl,rcngt.h of tho tlisturltnnccs in t,l~c free stream. This can bc ~~~cnsttrrtl clt~nt~t,il,at,ivoly with tho aid of 1.110 time-averngc of [.he oscillxl,it~g, tur- Intlrnt, vrlocilirs :\s thry occur, for exn.nlplr, I)~hin(l a S~~IY>II (see nlw Scc. XVlll f). d. Compnrimn of tho theory of stnhility with cxlwri~ncnt, where rJ, denotes the mean velocity of thc flow. Tn gcnernl, nt n c:rrta;hir~ cIist,at~t.c. from the screrms or Itoncyeombe, tho torbeloncc in a wid tu1111el boco~~~es iwtropic, i. e. one for which tho mean oscillations in thc three components arc cqttal: - - ,'I2 = "'2 = p. 111 this cnsc it is suficicnt to rwtrict oncsclf to thc o~cillnt~iorl u' irl tJ~c dircat,iorl of flow, and to put T = ~/Z/U,. Fig. I(i.15. Flow along a flnt plnta; tt~rbu- Ience originating from n disturbmcc of long wavelength after I,. Prnndtl [A81 The photngraplw wcrc Inken with thc aid ors alnw molion-plcbro eamcrh, which lravrllcd on s lrollcy nlong will1 the flow; con~cqurnlly, lhc camara In trsincd on the nnnlc group or vorllcrs nil tbc time. Tho flow la made vinihlc by uprinkling alumlnirtm dust on Lhe wafcr rn1rCar.e 478
476 XVI. Ori~in of turhulrnce 1 (1. Comparison of the throry of stal~ility nith rspcrinlr~~t. 477 . . . ' Fig. 16.17. Oscillogra~n of the a'-rotn- (37 2.23 --.-----..A"ponent of fluctualions caused by Lr181\ ranclorn ("11:1t,t1ral") dislr~rl)nnccs in $ 152 2+8 *- , -- the Intninar bor~ndary hyrr on n flat plate in a stream of air. Mcasvrementa on t.mnsition from htniriar to L~trbrt- S % 8 I . 2.74 D I . - . . . . . . . . 1)uritig t h cxpcritncnt-s wit,Il urti/iri~rl (~;.v/~II./J,III(.c.G :I t II~II IIIVI,:II st,~ril~ t.\ I ISII(IIII~ ovvr :L wi(lt,li ol'nl)out, 30 ctn, 045 mm I,ltivlc :t~ttl 2.5 nlm tlwl) W:IS ~~l:lcnl :I(. :I tlisl;111t.(. of 0.16- nlm fronl l,ltc wall nntl wn.9 cxcit.c.tl I)y :I tn:~gnc.lic: lic.l(l in(l~~c-vtl wiI.11 IIIV :~i(l of an alt.crnat,it~g crtrrrnt.. 111 this wnjr it, \\.:IS possil)lc: 1.0 in(l~tw L\vo-(litt~(~t~siot~:~l
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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
Page 198 and 199: \'all I)rirst., 15.11..: 'l'hr prol
Page 200 and 201: CIIAPTER XIV Boundary-layer control
Page 202 and 203: 5. J'rrvrntion of trauaitinn by the
Page 204 and 205: frorii th; 1c;ulitig rxlge! (l3l:wi
Page 206 and 207: 390 XIV. Ilo~~n~lnry-lnycr contml F
Page 208 and 209: . - v, (x) =cons/ Fig. 14.14. 1,ant
Page 210 and 211: invc?st.igai.ctl. In this msc too,
Page 212 and 213: 402 XIV. Dounclery-layer control 1.
Page 214 and 215: Ni\('A 'rM !I74 (1!)41). 1861 Sinli
Page 216 and 217: 110 XV. Non-~teldy bortndnry layers
Page 218 and 219: 414 XV. Non-st.cncly hour~tlnry Iny
Page 220 and 221: 418 XV. Non-slmrly l~orrnclnry Inyr
Page 222 and 223: 422 XV. Non-st,cndy hoixnd~ry Inycr
Page 224 and 225: 420 XV. Non-nl,mdy Fig. 15.58 Fig.
Page 226 and 227: XV. Non-utcncly boouclary lnyers wh
Page 228 and 229: 434 XV. Non-stcxcly boundary layers
Page 230 and 231: 438 XV. Non-atcndy boundnry inyer~
Page 232 and 233: 442 XV. Norl-st,aady boundary Isycr
Page 234 and 235: 440 XV. Non-st,rndy ho~~nclnry laye
Page 236 and 237: 450 XVI. Origin of tnrhulence I pyi
Page 238 and 239: XVT. Origin of turbulcncc I n. Some
Page 240 and 241: 458 XVI. Origin of turbulence I b.
Page 242 and 243: 462 XVI. Origin of tnrb~rlmcc 1 num
Page 244 and 245: 466 XVi. Origin of t.r~rhr~lrncc 1
Page 246 and 247: 470 XVI. Origin of h~rlwlcnce T I R
Page 250 and 251: 478 XVI. Origin of I.rtrb~tlmcr 1 t
Page 252 and 253: 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
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574 XVIII. 1'undnnient.alu of tnrl~
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CHAPTER XIX Theoretical assumptions
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682 XIX. Thcoroticnl wsltmptionu fo
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586 XIX. Throretical aaotin~ptiona
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5l)O XIX. Tl~rorrt,icnl nmumptions
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594 XIX. 'rheoreticnl nssornptions
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698 XX. 'I'~~rl~ulrnt flow f,lrro~~
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602 XX. T~rrbulcnt flow thro~tgh pi
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606 XX. 'l't~rhl~lc~rit flow thro~~
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GI0 XX. Turbulent flow throngh pip
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Icror~~ ()I(, phj.sic*:~l ~)oint. o
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620 XX. Tnrbnlcnt flow tlvough pipe
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dimensions Fig. 20.26. 1tc.sist.anc
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628 XX. T~lrbnlmt flow through pipe
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632 XX. Turhulcnt flow through pipc
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636 XXI. Td~nlcnt houndnry layers a
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610 XXI. Ttrrbulent bor~ndnry layer
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644 XXI. Turbulent boundary laycrs
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048 XXI. Turbulent boundary layers
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652 XXI. Turt)~~lcnt houndnry layer
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656 XXI. Turbulent boundnry layers
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660 XX I. Tl~rhlent bo~~ndary layer
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664 XXI. Turbulent boundary layers
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CHAPTER XXII The incompreesible tur
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672 XXll. 'l'llc incon~prcssiblc tu
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070 XXII. Tlic incompreaaibto lnrl)
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FRO XXII. Tho incornprcs~iblo turbu
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684 XXII. 'Yhc incon~prcssible Lnrb
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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
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Clementa, lt.R., and Mad, D.J.: The
Page 407 and 408:
792 Bihliography 13ird, R.R., Slewn
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Oswatitach, I
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H:I:IR, 11. 776, 777 Ilnnsr. 1). 62
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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,
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List of most commonly used synibola
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