102 



IlM)R()l)^ \ wiKs i\ siiir i)isi(,\ 



Sec. ■f5.S 



TAlU.i: l-Vli-SAMIIK I UlIK OK A-, AMI Cy Kill TlIK ATH ' I'.MT Mkasune IN THE SHIP UANGK 



This t«l>le is ndnptoti from ihe upixr portioD of the tiiblo on page 12 of SNAMIC Technical and Research Bulletin 1-2, 

 published in Aug 104S. The listings of R, in the extreme left-hand column arc in terms of (10*) or millions. Those in all 

 other columns arc Cjr(10>). 



the pumping; of the cinulatiiifi water can be In this and similar furmula.?, a.s /?, 

 derived. 



45.8 List of Principal Friction-Resistance For- 

 mulas for a Flat, Smooth Plate in Turbulent Flow. 

 For convenient reference, there are ILsted here- 

 under all friction formulations, including that 

 for the ATTC 1947 (Schoenhcrr) moanline, which 

 have been used by physicists and naval architects 

 for analysis or calculation purposes for the past 

 eight decades or more: 



',C, 



0. 



(2) (a) For the local specific friction drag co 

 efhcient Ci,y or the shearing-stress coefficient C, , 

 K. E. Schoenhcrr gives [MIT Hydrodyn. Synip., 

 111.31, p. lO'.i] 



t'/.C — 



0.279 + Cf 



(1) ATTC 1947 [PNA, 1939, Vol. II, p. 82; 

 SNAME Res. and Tech. Bull. 1-2, Aug 1948, p. 3] 



(C,)-»» = 4.132 log.o {R.Cr) 

 Alternative forms are 



(b) Another expression derived by L. Land- 

 weber from the ATTC 1947 formulation is [STG, 

 19.'):.', p. 1.S7; S.XAMi:, VXiW, p. 17) 



C, = 



0.310 



log; (2/e,) -I- 2 log. (2/e,) 



(a) 

 (b) 



(c) 



o.242(c;'' ») = log.o (/e.c,) 



(r,)"' = 



0.242 



log.o (JRnC,) 



' Liog,o(/e.c,)J 



= 0.0585(log,„ {R,Cr)Y* 



where lis is tiic Reynolds number based upnn the 

 inoinentum thickness O(theta). 



(3) Schultz-Gninow [XA('.\ r<Tli. .Memo 98G, 

 Sep 1941) 



(a) 



Cy = O.I'J7(log„, /i*, - 0.407)" 



For all praclic.'il |)ur|)oses this rather cunibersonio 

 formula may be re|)lai'e(i by 



