Boundary Lyer Theory

698 XX. 'I'~~rl~ulrnt flow f,lrro~~gl~ pipen
Fig. 20.1. Vrictionxl rc:sistsancc in a ntl~ootl~ pipe
R- y
v I I I 5 . 1 o r 1c1-1i1i11c Cor ln~~~i~trr flow: curvr (21 rrwn cqn. (20.5). afkr DI%qi.il~s (51 Tor
I'ig. 20.2. Vnlocil,y diu-
I.ril~t~t.ion ill utnootli
pip for varying Rey
nolds number, after
Nikr~rsdao 1451
whnrc tllc oxponcnt n. varies slightly with t.hc Itcynolcls number. Y'hc plots in IGg. 20.3
show that thc assumption of a simplc: l/n-th-power law agrees wcll with rxpwimcnt,
.zs the gmplls of (u/(J)" againsl y/R, fall on straight lir~cs, wlicn n sr~i(,:~.l~It: cl~oicc:
for n has l~orn madc. Thc valuc of t.hc cxponcnt 7s is n = 6 at. tl~c lowost, ltcynoltls
number R = 4 x 10R; it increases to n = 7 at R = 100 x 10%nnd 1.0 71. = 10 at,
thc liighcst hyrloltls numhr, R -- 3240 X ICYR, nttn.inotl in this invcstig:~t.iorr.
found that
Fig. 20.3. Velocity distribution in arn0ot.h pipes. Vcrificat.ion of tho ruurumption in eqn. (20.6)