^p^^k^u {e - 1) (1 - ^') 



1-^1 



1 , c+i 



— In 



2 C- 1 



Hence q =0, and, if a prime denotes values as given by Equations [137a ', b ']. 



[137h'] 



H^H 



'-U, 





> <!„-<- ^c 



1 - 



.2 2 



[137i ',]']. 



on the X-axis and in the y2-plane q = |m| and u = u' - U. 



On the ellipsoid itself, where t," = (^ = l/e, i/i = 0, so that this is a stream surface. 

 Also, q>-=0,q=\q \ and 



?l^ 



1 - 



/•2 1 \ /2 2 



1/2 



^'ffl^ / a^-. 



1 - e"- \a^ - e^ x^ 



1/2 



[137k'] 



since x = a^. As i^ -♦ ~, e -» 0, e^ g -> 3/2, and g -♦- (3/2) U yja^ - x /a, as for a sphere. 

 As 1^ -♦ 1, e -» 1, gf, -♦ 1 - e^ and q -► - f/; the ellipse has then become a cylinder. 



Some of the streamlines, for e = 0.866, g = 0.466, are shown in Figure 230; they are 

 selected to be equally spaced at infinity. The excess of pressure above that in the stream, 



Figure 230 - Streamlines for flow past a prolate spheroid in the direction of its major axis. 

 The pressure is shown along the axis, over the spheroid and outward along a minor 

 axis. The foci are shown by dots. See Section 137, Case 2. 



351 



