Boundary Lyer Theory

the two wries expnnsicws for sin (%In) in eqns. (11.37) antl (1 1.38), we det,ermille t,he
cocfficicnt~s of cqn. (1 1.3) as follows
Tlie resulting vclocit,y dist.rit)rtt,ions for various val~rcs of the n.nglc $ nre seen
in IGg. 11.7; for t,l~eso graphs t,hc vclonity ?L has been con~prlted up to t,l~e term 27.
Tho vclocitfy profiles for > 90° exhil)it a point of inflexion bcrausc they are associated
with the rnnge of prcssnrc incrcnsc:.
In connexion wit,h t,hc prot~lcrn at hand, we can repeat our previous rernarlrs
concerning the gcnrral pract.icahilitay of applying n Blasit~s series. 'J'l~c cnlc~rlnt.iol~ of
the fundnment,al cocffiaicnt.~ beyond t,lrc t,t:t.rn r7 involves an unaccept>able arnogrnt
of con~put,ntion, md furt,hertnorc, the calculation of slender bodics rcqr~ires consid~rd)ly
more t,c:rms. All t.11is pr~t.s n very severe 1irnit.ntinn on this method. For frrrther
resnlts concerning spl~cres, r~fercnce sl10111d b0 rna.tle t,o the succcctling section.
Trnusverse curvnlure. We hnvc! statrd rcprnlcdly t.llxt the rqunt,ion of nlotion (11.27n)
of an nsinlly syn~tnrt,ric: flow 11ns t.hc snrnc for111 as tliat for t.110 t,wo-di~~~r:~~~io~~:iI mse o~ily 011
condition t,lr:d bl~c l)oun~lnr,y-ln.ytrr tl~irknms is cvcrywl~r!rc much stnnllcr t11nn 1 . l rntli~w ~ of tl~o
conl.our of tlir I~ody (R< r). '('his contlilion is nol. ~ ~hi~fi~d in t.11~ case of n long but thin cylintlcr
or, for thnt ~nnttm, in t.he c:m of nny long and slcnder hly of rcvolul~ion. 'I'l~c bor~nrlnry Inycr
on surlt R I)otly grow (IOWII~L~P~III and iLq I,~I~~II~I~ss ~ C ~ J I Icornp&nl)lc I C ~ wit11 tl~c rrltli~~s cvc~lt.unlly.
'l'ltis I~rings intn rvi~lw~co tho rsnc:nl.i:~ll.v I.l~rco-tli~~~c~lnio~~nl nntnro r)f ISllo I)o~~~ltl:lry Inyrr
on n I)otly of rovolr~I.ion \rrl~iedl rrs111I8 from t h con~~~:rrnt,ivcly large cr~rvnb~rrc of (he surfnro
ol tho body in tho transvrrsc direction.
R,. A. Srhnn ~ntl R. Jk)ntl [95] t,rmt,rtl I.lir mso of n nlcntlcr rylinrlcr, of rnrli~m r, -- a = ronst,
plnccd in a nrriforrn axial stIrc:t~n. . 1l1c . RRIIIO J)~OI)ICIII was st~~dird Oy 11. 11. Kelly [Go] ~ h o
introtlncetl ccrtain nnn~cricnl rorrrrtions. M. D. G1:iurrt nnd M. J. LigI~Lhill [41] ol~tninrrl
~0111Lionq hy tl~c npplication of J'ohlliausrn's approxl~nnta n~cthod (scc See. Xlh) antl of nn
cwyt~ipt~ntic ueries axpnn~ion. Tho flow dong the generators of o cylinder of arbitrary cross-srction
anr, worked out hy .J. C. Caoko [IR] wllo employed a Blnsius seriw nn well ns I'ol~lhnusen'n npproxitnnle
procedure.
The nlnrc gc~~crnl msc of n con~prmsil,lr, nsinlly syn~n~rI.ric I~o~tnclnry I;~yar on ;I I~ody
of rcvolr~tio~~ whosc ronto~~r is a f~lnction or t.l~c lonp,ilr~rlit~nl c:oortlinnlc, a:, ill ~~wlir:~l:ar,
tlm cnsos of n circulnr cylintlrr nntl n spllcrc, wcro sl.otliccl by It. I". I'robstcin nnrl I). 1Slliot. [RR].
I1 turnrtl ont t,l~nt thc trnnsvcrsc curvnturc has the S~IIIO cni\ct on RIICII Ilo~s wit11 n. prcssurc
grnelicnl 11s n ~II~I~I~~IIII:I~~~~~,
fiivonr:ibIo prrssttrt! gn~dirnt. As 11 r~wtlt,, 1110 sl~wring dr~w is
inrrtvwrcl C I I sc:l~rrrnl,ion
~ is tlclayctl.
b. Apprnxirnnte solutin~~s for nxially crytnmc~ric bo~a~~tlnry lnycrs