Boundary Lyer Theory

638 XVII. Origin of t~~~rbnlc~~rr II
As the Ilright k is incrc:rsctl, the position of Lhe point of tjrarisit1ion ztr moves closer
to tllc ronghncss clcn~cnt, which nlcnns tht tlic curves in Fig. 17.41 arc trnversctl
froni left to right. The expcritncnl,nl points begin to tlcvint,e from this curve upwnrds
as soon ns the point of tmnsit.ion has rcncl~ctl tho rougllness element, i. e. when x,, -. x,.
Thy t.hnn lie nlorig tho fnrnily of stmight lines which contain r,/k as a parameter
and is given by
Pig. 17.41. 'I'l~r rri1,ic:nl Ikynolcln nulnbrr for lntninnr Im~~~clnry Iayrr nn o fitnc:Lion of t,l~r rnlio
of t~riglil, k nfn~npl~nr~n elcincwL 14, tlltr dioplnrcntcnl, I I~icknracr of I lw I)onnclnry l~~ycr nl. Ihe poniI.ion
of f.lir rongl~nms rlrtncnt,, dl,. for single, t\vo-~Ii~~~r.~~siotid ro~~gliness rle~nc~~it,s in inron~prr~~~iI)I~
fl0\\.
Tlw ~w:~~t~rrtn~~nIs
wv ~:~li~C:~vl~~rlly inlrr~~~~lnl~~d 1,s rqn (17.28)
t
.-
[I*
it is nlso RIIOWII in Fig. 17.41. According t,n Jnp:tncse ~nonsuremcnls [237), the
l~ypcrbole-like branch of the curves in Fig. 17.41 possesses 11nivers:~l vnlitlity,
both for flows with cliKcrent, weak pressure gmtlicnt,~, nnd with different inlensitics
of turbulence. Increased turhnlence eauscs merely an enrlicr deviation of the cnrve to
the left,, in the direction of the tnrb~rlc~~cc-tlepet~(let~t crit,ionl IEeynoltls nuinbcr of
,
IIRVC Itvl I