A' = 2 77pc2fy2 sin 2 a + p hV U cos (r? + a ). 



[79f] 



Flow without circulation past a Joukowski airfoil of a certain shape is shown in 

 Figure 125. For another profile, there is shown in Figure 126 first, the flow without circula- 

 tion, then the flow due to the circulation alone, and finally the resultant flow due to the super- 

 position of the two; the circulation has been chosen so as to make the resultant velocity finite 

 at the trailing edge. 



The trailing edge can be rounded off by allowing the initial circle to enclose both of 

 the singular points {- c, 0). A Joukowski profile constructed by R.H. Smith^^^ with /3 = 0, 

 a/c = 1.35, h/c = 0.135 is shown by the heavy curve with two rounded ends in Figure 127. 

 Streamlines for the flow without circulation past this contour are shown in Figure 128. 



The extended contour with a pointed end in Figure 127 represents the profile of U.S. 

 Navy strut No. 2. It can be reproduced without visible error, using the niethod of Section 56, 

 by assuming 5 line sources and 8 line sinks of suitable strength properly disposed along the 

 axis. Figure 127 shows also the calculated distributions of pressure over both theoretical 

 profiles in comparison with the observed distribution over strut No. 2 in an air stream; the 

 flow is from right to left. 



(See Reference 1, Article 70; Reference 2, Sections 7.20, 7.30, 7.31, 7.32, 7.40, 

 7.50.) 



Figure 125 — Flow without circulation past a Joukowski airfoil. A and B 

 indicate stagnation lines. 



187 



