24 



frj^'" 4 -'^ \ 



where m and ^^ are constants, [72] becomes 



which is a first-order differential equation in r^d of the Bernoulli type. For H constant, [75] 

 gives for interval of integration x^ to a;, 



- l+m r,/""* J_ 



[76] 

 "1 



<Ke)l"" = ^/(r^^);^- . (1.^) Co^'" J ' '.^^'" ^'' 



where 



is (l + m) (« + 2) [77] 



Lyon found that H = 1.4 gave good agreement between the experimental and calculated 



drags. ^^ Since ( t^/ pf ^)q in Equation [73] gives almost a straight line on a log-log plot 



as shown in Figure 6, a power law approximation proves a close fit. For 10^ < /?« < 10^, a 



least-squares fit of [73] gives 



OT =0.1686 



[78] 



^Q =0.006361 

 A more convenient nondimensional form of [76] is 



ii)Mr" = (o: mr ^ ^ r i^r i^r -i) 



2 2 11 L (j/^) 



[79] 



BOUNDARY LAYER NEAR THE TAIL 



It is apparent that the previous assumption S « r^ is no longer valid towards the after 

 end of the body where the radius r goes to zero at the tail and the boundary layer progres- 

 sively thickens. Consequently the general form of the momentum equation [61] has to be em- 

 ployed; for constant h, it may be integrated to the form 





where the subscript g refers to the initial point of integration and the subscript e to the tail 

 of the body. 



Experimental evidence 2"^ indicates that t —^ + ^^ -£. / ardy in the right- 



"^ pf/^ pV^ dx Jq 



hand side of Equation [80] is substantially linear with respect to x along the after end, and 



drops to zero at the tail. Consequently 



