1-0 



V° 2 = 0-768 



0-5 



WEDGE J3 2 =5° Q g =0-695 (EXAd) 



CONE £ 3 = |< Q 3 =0-397 (BY SIMILITUDE) 



05 



10 



Figure 11. Comparison of velocity distributions over 5 wedge and 14 cone. 



angle /3 2 ) and a cone (semi-angle /? 3 ) be expanded as power series then, the velocity 

 near the tip of the wedge was 



dw 



a Z"- 1 where n = x/(x - 0*) (2) 



dz 



whereas for a cone the velocity was of the form 



r" _1 P'„(cos 



sm 



(3) 



where n must here satisfy the condition P' n ( — cos /? 3 ) — 0. The exponents of the 

 first terms of the two series for the velocity distributions can be made the same by 

 means of (2) and (3), which define an "angular transformation" and the coefficients 

 of the leading terms become the same if the uniform stream ratio q x o/q x3 is defined 

 by 



— = | P n {— cos/3 3 ) 



#003 



(4) 



By means (2), (3) and (4) conditions near the apex can be made similar in plane 

 and axi-symmetric flow; Armstrong further shows that the conditions near the rim are 

 the same for the two and three dimensional cases. Fig. 1 1 illustrates the similarity 

 obtained between a 5 deg. wedge and a 14 deg. cone. 



Fig. 12 gives a comparison between drag coefficients of cones calculated by 



226 



