lot 



IIY^Ro^>v\.\^fI^.s i\ snip df.sicx 



^'■r. 7 1.0 



(c) VS\. l'.t;Ui, \ul. 11. Tal.lf '.1, |). Ill, fur- 

 ship lengths of 10 through 500 ft 



(ti) Polliinl, J., and DiKlcbout, A., "Tii(''orif du 

 Nnvirc," 1892, \'ol. Ill, pp. 374-375, using essen- 

 tially the dimensional formula given previously 

 hut with different symbols and metric units, for 

 ship lengths of 5 through 120 in, 10. 1 through 

 31)3.7 ft. 



(9) Taylor, for 20-ft jilanks in fresh water at OS 

 dog F, 



(a) C = 0.03117?:"'" 



An alternative form is 



(b) lir = 0.00907 .sr' "' for 60 deg F, fresh 

 water, and a 20-ft friction plane. 



(10) I^p and Troost [SNAME, Nortii. Cidif. 

 Sect., 29 Feb 1952; see SNAME Member's Bull., 

 Jun 1953, pp. 18-22] 



^ = ,..[(f.)v/^]..... 



= log. (It) + I log. C, + KC" 



or Cfo = O.133(log,off„ + 0.724 - log.o -4)-' = 

 where the subscript combination "FD" signifies 

 friction drag. 



(11) G. Hughes' "2-diml" formula is Cp = 

 1.328«:°' + 0.014/2;''-"* [7th ICSII, 1954, 

 SSPA Rep. 34, 1955, p. 76, Eq. (2)]. 



(12) Telfer, Lackenby, and others, 



C, = a + bR~', so that for /2„ = «> , Cy = a 



Here, the lower-case subscript of the Reynolds- 

 number symbol is not to be confused with the 

 exponent n. A table of the specific friction co- 

 efficient Cf for "smooth paint surfaces," derived 

 from the I^ackcnby formula Cy = 0.0000 -f- 

 0.0791/?:"" for the Froude-Kempf data, is given 

 by G. S. Baker, over a range of /?, from 1 to 75 

 million (IN A, Apr 1952, p. 02|. 



(13) Blasius, for laminar flow on a flat, smooth 

 plate, 



C, = 1.32H/1';" ' 



(14) For a completely rough surface of length /> 

 and an equivalent sjind-roughnesa height of Kg , 

 as given by L. .\. Haier, 



Cr = [l.89-f l.f.2(log,„^'jJ " 



45.9 Specific Friction Coefficients for the 

 Schoenherr or ATTC 1Q47 Meanline. Tables 

 l.j.c anil 4.j.d are small illustrative sections of a 

 group of larger tables, mentioned in Sec. 45.7, 

 calculate<l in the 1940's by the Experimental 

 Towing Tank of the Stevens Institute of Tech- 

 noloK.v and published in August 1948 as SX.\ME 

 Technienl and Research Bulletin 1-2. These 

 tables give values of the .specific friction resistance 

 (■(H'dicient (V as determined by the .\'1"T'C 1947 

 (Schoenherr) meanline, ]'>|s. (5.xiva) or (5.xivb) 

 and the formulas of item (1) of Sec. 45.8, for fully 

 developed turbulent flow on a flat, smooth plate. 

 The range of the argument /?„ for entering the 

 complete set of tables is suflTieient to cover both 

 model and ship regions. The entries in Tables 

 45. c and 45.d are modificHi so that all /?„ values 

 are in terms of millions [5th ICSTS, Lontlon, 

 1948, p. 112, item 4, top of page]. 



The meth(xl of picking Cy values by inspection 

 and using them for Hy calculations is illustrated 

 in Sec. 45.22. 



45.10 Laminar Sublayer Thicknesses in Tur- 

 bulent Flow. S<jme quantitative knowledge of 

 the thickness 5/, of the laminar sublayer next to 

 a solid boundary is of interest in a study of rough- 

 ness efTects, to determine whether the.se are 

 essentially viscous or primarilj' pressure phe- 

 nomena. It has been found [Rouse, IL, EMF, 

 1940, p. 194; Baines, W. D., "A Literature Survey 

 of Boundar^'-Layer Development on Smooth and 

 Hout^h Surfaces at Zero Pressure Gradient," 

 IIIIR, 1951, p. 25] that the thickness 5,, of the 

 laminar sublayer in turbulent flow over a rough 

 surface can be expres.sed by 



di. = (a coeflicient) 



(a coeincicnt) 



4 



(r..vi) 



r. 



where values of the coeflicient vary from about 

 11.0 to 12.0, and [/, = Vto/p is the shear 

 velocity. Using the larger cocfTicient, a number of 

 5;. values calculated for a wide range of li, are 

 Ijlotted in Fig. 45. F. It is to be noted that the 

 5,. values increase slowly milh Icnyth for a given 

 speed, hut they decrease rapidly with speed for a 

 given length. The reasons for this are discussed 

 presently. 



It is interesting to note that the permi.ssible 

 average ronghne.s.s height A' v. for a livdroilyn.'im- 



