Boundary Lyer Theory

660 XX I. Tl~rhlent bo~~ndary layers at zero pressure gradient
For mall Reynolds numbers R, < loR eqns. (21.42) and (21.43) give practically
the snmc results, whereas at larger Reynolds numbers eqn. (21.43) gives somewhat
greater values. We are, thus, jr~stified in retaining the simpler equation (21.42)
because there is noclanger of finding values of k,,,, which are too high. Equation (21.42)
stdes that the admissible height of roughnes.9 elements is independel~t of the length of
the plate; it is tlt+rminctl sololy by tt~r velocity and by tho ItincmaLic viscosity in
:~ccortlancc: with thc contlitior~
(21.44)
It follows that t,he absolutc values of admissible roughness for a modcl and its
original arc equal if tile velocity and kinematic viscosity arc the samc in both cmes.
Vor long botlios this may lead to extremely small admissible roughnesses as compared,
with t,hcir linear dimensions, see Table 21.3.
Fig. 21.10. Atln~issible roug11ne.w
k,dm for rough platcs at zero inci-
dence, and aircrnft wings from
cqn. (21.44)
For ~xnct'icnl applicntions iL is still more convenierlt to relate the admissible
valuo of ronghncss directly to the Icngth of the plntc, 1, or more generally, to the
length, I, of t h I)otly undcr consiclcration, (c. g. length of ship's hull, wing chord,
blntlo chortl in t~rrl)inrs or rol.ary cornprcssors), I)ccnr~se this lcatls to a more graphic: