Boundary Lyer Theory

142 VII. Hor~nclnry-lnyrr rq~~ntii~t~s for t\vo-di~i~rr~nio~l~~l Ilow; I)o~~nilr~r,y Inyrr on n plelo
Fig. 7.9. Vclocity rlist.ril)~~lion in tho Inn~i~inr hounrlnry lnyrr on n IlnL plntr nt, xrrn i~~rirlrncr.
nn ~ncasr~rcd by Nikr~rndso [20]
I:ij!. 7.10. Lord rocffiricnt
nf 6Izi11 frirtion 011 a flnt,
])l:iln at ZPITJ iriridr~lco in
0.001
i~~con~prcssi blo fln\v, dclcrminc~l
from tlirocl. tncnnnrc-
0 0005
twnt of shearing strcss by 0.0067
O hd~recl skm fiiclioon measurement
fmm velonfy profile
D/recl skin frctlin measuremen/, x - 28 6 cm
0 t r ,x-56cm
- ! I l l l l l l l I 1 I
,.
I ltc laminar law of friclion on :L flat phtc was also subjectctl to careful expcrirncntal
verification. The local shearing stress at the wall can be determined
intiirecthj from the slope of the velocit,y profilc at the wall together with eqn. (7.31).
In rccrnt t,imcs IT. W. Liepmann and S. Dhawan [18] measured the shearing stdress
tlirocI.ly from the forco acting on a small porl,ion of t,ho plnto which wns nrrnngctl
so t,l~at it could move slightly with respccl to the main plate. The results of tl~eir
wry careful measurements arc seen reprotluccd in Fig. 7.10, which shows a plot
of the local coefficient of skin friction cf' -- to/k Q 1Jm2, against, thc R.cynolds
number R, = 11, z/v. In the range of R, = 2 x 10"o 6 x 10"both laminar and
t,urbrrlcnt, flows arc possible. It can be sccn that direct and indircct mcas~~rcmcrtt~s
nrc in cxcrllont agrrorncnt, with each ol,l~or. Mcns~~rcrnonl,~ in tho lnn~innr rnnga give
a strilcing (!o11fit311:kt,io11 of 1Hwius's oqn. (7.X) frm~ which cff .?: 04Wi/d~~. 111
the turl~r~lcnf~ range there is al~o goo(1 ngrecmcnl with I'rntdt.1'~ thcorctif:nl forrnr~l:~
which will bc deduced in Chap. XXI, cqn. (21.12).
r 7
Jllc conlplctc ngrccmcnt bctflwcen t~hrorcticnl and expcrin~cntd rcsr~lt.~ wlliol~
cxist,s for the velocity distribut.ion nncl t,hc shcnring stxcss in a 1aniinn.r honndn.ry
lnyer on s flat plate at zero incidence that, has hcen hrougl~t inta evidcncr in Figs.
7.9 antl 7.10 for the rmge R, > lo5 nnequivocally dcmonstratcs thc valitlity of t,he
bountlnry-ln.yer n.pproximntions from the physicnl point, of vicw. TII spit.(! t,I~is,