Boundary Lyer Theory

654 XXT. l'url~ulmt I~o~~ntlnry lnyrr~ at zero pressure gradient
causes the coefficient of skin friction to increase only if the Reynolds number ex-
ceeds a certain value, in complete similnrit,y with pipe flow (see See. XXId).
In the romplot,cly rough rcginic it is possible to make use of the following
interpolation forrnnlnc for t h oorffirirnts of skin friction in terms of relative rough-
ness :
2.87 1- 1.58 lng -"
(21.37)
ks
which are vnlid for 102 < Ilk, c~ lofi.
In order to use these clingrams for roughr~esa other than the sand roughness
assumetl hero, it. is necessary to tlctcrmine t hr equivalrnt send roughness as explained
in Src. XXg.
In the cslrulat.ion of t.ltc tlrag on ships it, is important to consider plates with
vcry small roughness (painted mctd plntcs) as well as smooth plates covered with
single protuheranccs, srrch as rivet, heads, wrltlctl seams, joints, etc. F. Schultz-
Grunow [62] carried out a large numl)cr of rncns~~rements on such surfaces in the
open cl~annd of the Tt~stitut~e in Gont,i.ingcn mcntioncd in See. XXg Atlditionnl
comprchcnsivc data on ronghncsscs occuring in shiphilding can also IIC fountl in
several papers hy G. I