Boundary Lyer Theory

418 XV. Non-slmrly l~orrnclnry Inyrr~
I5 x a 111 1) 1 t- . Ci~c~tltrr r!/litctla~
I'or tJto rircwlar cylintlcr of ratlitis 11 in n strcntn of vrlocity I/,, we obtth:
as swtt from rrp. (15.45). 'l'llc tlist.nnco covrrctl uut,il sapration begins is R, = 1, I/,,
st, t.Ir:~t,
b. Bo~lnclnry-lnyrr forinntion nhrr inipnlnivc dart of niotio~~
Inserting tho vnlucn from cqns. (15.47) intorrp. (I5.46), wr find that I.l~c tin~r cln11s~tl IIIII~I t,lie
onset of ucpnrntion is
I'ig. 15.2. I)int,:~nce 8
t.ravrrsccl by rlliptic cylinelrr
r~nt.il thc: onset elf
scpnrntion in t.hc vnuo
of i~npnlsivc? :~.ctdt.r:~t,ion
fro111 red,
4
y, = 0 for Px < ---
3 '
For k = I cqn. (16.48) t,r~~nnfortn~ inlo cqn. (16.4f;) for 1110 cirex11:ir e:yIit~tlvr. Ibgit~t~i~~g with
tlh vnlr~o the ti~nn L, for tho onsct of sc[)nrnl.ion clccrcn~as will1 i~~e:rc::tninl: k -7 h/w. IIII~I 1.11~.
position of tho point of nepnrntion move8 Crom the end of &xis rx f,ow~lrtls LIic cntl of nxia b. 111
the limit D/n -+ m, i.e. br a plate at right angles to tlw tlirrc~fion of motion, wc 11:tvr I ,
and !I, - 11. Iirnce the onsct of srparation is i~n~nctlint*? for t.Itc c.:~st: of n fl:lt pl:lfn ~wrpc*ntlit.~~inT
10 t.hr rlirrction of rnot,ioti, n.ntl it tnkes plrmc nt ths ctlgc.