Boundary Lyer Theory

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326 X l I. 'l'l~crn~nl hounrlnry lnycrs in Inniinnr flow (12131 Spnrrow, 1C.M.. and (:re g, J L Ijent, trnnsfer from n rot,nting disk to fluids of any PrandlI nutnbcr. .J. Hd, l'ronskr 8i, i49-251 (l!)s!,). (1301 Sparrow, K.M., and Gregg, J.L.: Mnsa t,rnnrrfer, flow, and hent tmnsfer nhout. n rotnting disk. .I. Hoat. 'l'rnnsier 82, 21)4-302 (IOOO). [131] Squire. 11. 11.: Scct.iori of: Modern I~cvtrloptnmt~ in Fluids Dy~~nn~ics (S. C:old~tein, ctl.), Oxford, 11, li23- (727 (l!)RR). 11921 Squire. 11. I{.: Ilrnt Lrnnsfrr cnlr~ilat~ior~ for ncrofoils. AIEC ItM 1986 (1942). (133) Squire, 11.11.: Notc. on the effect of variable wall ten~pcratr~re on Imnt trn~iefer. ARC lthl 2753 (1!)53). [I341 Stewnrt., W. 15., niicl Proher, It.: Hcnt. trnnsfcr and dirnnion in wedge flows with rapid liinnn trnndcr. InL. J. llcnt, 'I'rniisfer
328 X I1 1. J,nn~i~~nr bo~~ntl:~ry Inyrrs in comprcusihle flow or1)itnl velocity of a satellite of w, = 8 lzmlsec, the temperature rise even in a real gas is still of t,l~c order of 10,000 tlcg C. Tho mngc of Mach numbers M, 1 6, in which thrrc cxisl, Inrgo cIiKcrrnncs bctwcon tho bchavionr of a real as opposed to a perfect ,gas, is givrn t.Itt: tmme of hypersoltic flow. 'l'llc occtlrrence of chemical reactions (ioniznl.io~l, tlissocint.ion) wl~ich sc:t in behind a shock wave or in t.he Imundary layer OII :I. solitl Imly ill :I Itypt?rsonic sl.rt::~m by virt,no of tho cxistcncc: ol:t high f,c:tnj)c:r:~.t,trrc, c.otwitlcr;tl)ly c.otnldic:xtcs t,llc I.;~slr of annlyzing t,ho flow. For this reason, wc sl~i~ll rt,s(.rit:t, our consitlcrat.ions to that range of Mach numbers in which tho fluid can still 1)c :~ssl~mctl t.o obry 1.11~ perfect-gas law; ir~ air, this corrcspontls to a range of M.,, -r: 6. In motlcrn t~itncs ni11(:11 nttcnt.ion has I)ccn giver: t,o tllcstntly of l)onntJary- Inyrr Ilows at hyprrsonic vclocit.irs ant1 in 1,hc presence of c1iemic;tl reactions. For drtails, tllc rrntlrr is rcfcrrctl to t.he hole by 1%'. 11. J)ormnce [20]. Fig. 13. I. Tcmpcrnt,uro rise in air in ternis ol thc flight velocit.y, w,, and t,lle Mach w,Rm/secJ n~~nil~cr, M,. 'Vhc curve Iabcllcd "l)erI'ect gas" mas calculst~d wit.11 the nit1 of eqns. (13.1) nntl (13.2). Thc velocity 111s = 7.0 km/sec in that of nn nrtificinl satellite in orbit,, and lo,< = 11.2 km/scc roprcsenh the e-9cnpc ve~ocit~y of n satalIite from I 0 ~ 6 I2 I 8 I 24 I 36 I 42 , the earth ~ Him Even in I.llc mngc of snpcrsonic Mach numbers ( M, < 6 in air), the t,cmperature rise irt thr gascww stream is high enough to force us to talrc int,o a.ccount the effect of t,cmpcrehrc: on the proportics of tJllc gas, in particular, on ils viscosity. The lrinematic viscosit,y of most gases, and of air wnong Lhem, incrcascs cor~sitlcrably as the t.ernl)craturc is incronsctl. In t,llc caso of air, as sltown I)y E. R. van Driest [30], it is possible to use an interpoI:~t.ion fbrmuln l):~.sctl on I). M. Sntdlcrland's theory of viscosi1,y. This can be written wllrrc /I,, clcnotcs the viscosity at the reference Lrnjperaturc To, and Sl is a constant whit:l~ for air assumes the value S1=llOK. ' l'ltc lm?twli~tg rel:~t.ion I)ct~weon tlle viscosiby /I of air and the temperature, T, is scerl plottd a.s curve (I) in Fig. 13.2. Sinco t,hc relation (13.3) is still too complicated, it is c:nst.omnry l,o npproxirn:~.l,c i(( in thcorc~t.icnl calculat.ions by tho simpler power law where 1,llc constant h sc3rvcs to nchicve a better apl)rosim:tl,ion 1.0 thc more cx:~c% Sut,hrrIn.nd formt~la (13.3) in 1.h~ nciglll)onrl~ootl of a tlcsirotl l,rt~ll)c~r:l.l.lr~~c r:111p (cf. Scc. XIlTtl). Fig. 13.2. The dynamic vis- coaity, 11, of air in tcr~ns of the temperaturc T Curvc(1) ?dras~~rc~ncnls and inler- pnlalion forlaula (13.3) hased on Sntherlnntl's rquntlnn. Ourvcn (2). (3). rind (4) pow~r lacs. cqn. (13.0, wit11 difirnnt values of thc exponent ro
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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
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
Page 166 and 167: 310 XJI. 'I'hcrmnl boundnry layers
Page 168 and 169: 314 X11. Thermal boundary laycrs in
Page 170 and 171: 318 XIT. Tl~crnial bonndnry layers
Page 172 and 173: 322 XII. Tl~or~nnl I)onndnry lnyers
Page 176 and 177: 330 X[[1. lmninar bor~ndnry lnyers
Page 178 and 179: 334 XIIT. Lnrninnr 1)oundary laycra
Page 180 and 181: 338 XI I I. Im~linnr I>orirtclt~ry
Page 182 and 183: 342 XI11. Tmninnr Imlndary layeru i
Page 184 and 185: 346 XI 11. T,ntninar I~or~nrjary hy
Page 186 and 187: 350 XIII. 1,mninnr honnclxry lnycrn
Page 188 and 189: 354 XI 11. 1,nminnr h~nrlnry 1:ryrm
Page 190 and 191: Fig.. l3.16. In 13.18. lain~innr ho
Page 192 and 193: a Intninn.r l)out~rlary I:~.ycr, bu
Page 194 and 195: 1 I Itc vnriolts c4Twl.s ol'sl~oclt
Page 196 and 197: 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
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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
Page 391 and 392:
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,
Page 419:
List of most commonly used synibola
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Boundary Lyer Theory

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