°L-X ( 



C R = C T - C Ft (R L _ Xq ) — 



and 



x £- x o _ 

 C F t ( R x C -x )— F =/3 



c n { W "T + AC 



(12) 



(13) 



where j3 = ( R x p _ x /R L )/(S xp _ x /S). Also, using flat-plate theory, we can write for the flo\ 

 over the area S v 



L £- x o 



( R0 xg-x o ) _ 2 R xC-x C F t (R x C -x ^ 



combining Equations (13) and (14) we get 



\ 0x e- x o, 



T r l 



S x C 1 



C F g(S xe )— +AC TJ I 



(14) 



(15) 



The empirical relation used to evaluate the turbulent frictional drag is the Schoenherr 

 flat-plate formulation 11 



C F log 10 (R x C F ) = 0.242 



(16) 



where R x is a Reynolds number based on the length of the plate. Using Equations (16) and 

 (14) and changing to the present notation, we can write 



N/C Ft (Rx g -x o )log 10 ^(%_ Xq 



Substitution for C F in Equation (14) yields 



R Xo = R xc -34.151 (%_ x J t l 



0.24: 



' x £- x oJ t 



(17) 



(18) 



To obtain x Q , Equation (15) is solved iteratively, after initially setting (3= 1.0 to obtain 



Rq . Then x can be obtained directly from Equation (18). The value of C F „ (S x „) in 



xg - x x x 



Equation (15) is obtained using laminar boundary-layer theory for axisymmetric bodies. 



Schoenherr, K.E., "Resistance of Flat Plates Moving through a Fluid, " Transactions of Society of Naval 

 Architects and Marine Engineers, Vol. 40 (1932). 



14 



