Boundary Lyer Theory

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210 X. Approximate mcthod~ for shady rqi~etions which is connortctl with thc momentum thickness in thc samc way as t.lle first shape factor, A, was connected with t,hc boundary-layer t,hickness, 0, in cqn. (10.21). Tn atltlit,ion wc sldl put = %" v ' (10.28) so that It is wrn from crjns. (10.21), (10.27) nntl (10.24) that (.hc slmpc fa.ctors ,,I anti li satisfy Lhe universal relation for thc saltc of brcvity, mtl suI)st,ituti~lg, I< ant1 Z from eqns. (10.27) and (10.28) rcspecl,ively, togothor wil,l~ fl (K) ard /,(I() from eqns. (10.31) and (10.32), we obtain, furthcr, from Lhr momcntum cqu:~t,io~l (10.20) togcthcr with a2 6,'/v = 4 ~IX/tlx, thc rrl;~t,iotl 2 /2(1
212 X. Approximntr 11iet11odg for stc~rly cquntions 'bhlr 10.2. 1211xili:iry fr~nrtio~in for the npproximntr rnlr~~letiorl of lnlliitier boundary I:~yera, b. The npproxitnste mct,hod clue to 'rh. von Kbrmhn nntl I
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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
Page 66 and 67: cnu bo npplirtl nt mont, nn fnr RS
Page 68 and 69: 114 VI. Vcry slow motion where r2 =
Page 70 and 71: 1 I8 VT. Very slow motion r. 'l'l~o
Page 72 and 73: 122 VI. Very rrlow motion ext.endcd
Page 74 and 75: 126 VT. \'cry slow rnot.ion Part B.
Page 76 and 77: 130 VII. Boundnry-layor cquntionzl
Page 78 and 79: '1. Skin friction \VlIat1 t.11~ I)o
Page 80 and 81: 138 VII. no~~ndnry-layer cqnntions
Page 82 and 83: 142 VII. Hor~nclnry-lnyrr rq~~ntii~
Page 84 and 85: 146 VII. I~o~~ntlnr~ Inyrr cq~~ntio
Page 86 and 87: CIIAFTER VIII Gencral propertiee of
Page 88 and 89: 164 VIII. Ccnernl propertic8 of Lhe
Page 90 and 91: 158 VIII. General ppropcrtics of th
Page 92 and 93: VIII. General propertien of the bou
Page 94 and 95: 'I'his c.quat,ion Lmnsforms into t1
Page 96 and 97: 170 TX. 1Sxact uolutions of t.ho st
Page 98 and 99: 174 TX. Exnct ~olut,ionu of tho sto
Page 100 and 101: 178 IX, Exact solutions of tlrc ste
Page 102 and 103: and t,llc? clnsh now clet~otos tlil
Page 104 and 105: 1 86 10 0.8 0.6 0.4 0.2 0 -0.2 -0.4
Page 106 and 107: ccnt,rred nt, (m -1- 1, n). 1'110 t
Page 108 and 109: 194 IX. Jqxnct eolutions of thc stc
Page 110 and 111: O~l:cr ehnpw: Second-order cITcetls
Page 112 and 113: 202 X. Approximate rncl.hoda for st
Page 114 and 115: 206 X. Approxitnnte rnct.l~otls for
Page 118 and 119: 214 X. Approximato mothotls for sha
Page 120 and 121: 218 X. Approximntn met,hods for shn
Page 122 and 123: 222 X. Approximate methods for stea
Page 124 and 125: 220 XI. Axinlly symniobricnl nnd th
Page 126 and 127: 230 XI. Axinlly symmctricnl and thr
Page 128 and 129: 23.1- XI. Axially uynimet.rira1 nnc
Page 130 and 131: the two wries expnnsicws for sin (%
Page 132 and 133: 242 XI. Axially nymmct.riral and tl
Page 134 and 135: in cross-flow, tlrprntls only on lh
Page 136 and 137: 250 XI. Axinlly nyrnmet,rirnl nntl
Page 138 and 139: XI. Axinlly ~,vn~n~et.rir;~l nnrl I
Page 140 and 141: 258 XI. AxhIly syn~rnrtrirnl nncl t
Page 142 and 143: . . lit 1 h1:lgt.r. '1.: 'l'l~idc I
Page 144 and 145: 206 XIT. l'l~rr~nnl bo1111r11iry ln
Page 146 and 147: 270 XIT. 'I'l~rrtnal boundary layer
Page 148 and 149: can I)r rct.ni~rrvl in inrotnl~rrss
Page 150 and 151: if wc: pillf - - 'I1, - (A7'),. 11,
Page 152 and 153: Rotntirig rli~k: (:II:I~I. V, in pn
Page 154 and 155: 286 X11. 'IY~rrrr~al bo~~ndnry laye
Page 156 and 157: 290 XlI. Tl~rrnmal boundary layers
Page 158 and 159: with 0,' -. () at, r] - 0 and 0, =
Page 160 and 161: 2!)H XI[. Thcrn~al bor~nrlnry Inyrr
Page 162 and 163: 302 XJI. Therninl boundary layers i
Page 164 and 165: 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
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486 XVI. Origin of k~rbulenre I 148
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490 XVII. Origin ol t,urbulencc 11
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404 XVII. Oriein of tnrbnlencc TI F
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498 XVII. Origin of turbnlmco II t,
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Tlw tlisl.nr~cc Iwt,wccn the point,
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c. Efict of ~urtintl on trnt~nition
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510 XVl I. Origin of Idmlrnro I I '
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514 , XVII. Origin of turbulence 11
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518 XVI I. Origin of turhr~lcncc 11
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on the bnsis of t.hc tl~corct,ical
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626 XVII. Origin oI t.11r011lonco I
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630 XVII. Origin ot t.~~rhr~lrncc J
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XVII. Origin of t.urh~~lencc TI 7 !
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638 XVII. Origin of t~~~rbnlc~~rr I
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\vi(,l~ a (-ylit~(lw envcrv(1 wiI.1
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646 XVII. Origin of turbulence TI F
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550 X\'ll. Origin of t,11rh111rnrc
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554 XVII. Origin of t,rlrbuloncc TI
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558 XVITI. Fundamentals of tr~rbule
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562 XVlI1. R~nclnmont.nIu of tur1)u
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The corrrlnt,ion co~ffiricnt~ y~ ra
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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
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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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