Thus the flow becomes that of a dipole of moment e^ g^ a^ U /i located at the center of the 

 ellipsoid. If e is small, the coefficient e^ g^/2> becomes 1/2, as for a sphere; see Section 127. 

 The velocity components are §' = and 



^r^i 





1/2 



e-i 



— In 



L-\ 



--9,U 



1 - 



1/2 



e 



1 4 + 1 



— < In -^ 1 



2 C-l 



On the a;-axis, y.-~l, \x\ - k^, q = \u\ and 



[137a'] 



[137b'] 



±q^^g,U 



k \x\ 1 |a;l + A 



1/2 



on the equatorial or yg-plane /i = 0, ©'= A; (C - 1) > ? = 1^1 and 



[137c'] 



1 \/S^T^ + -t 



on the equatorial circumference of the ellipsoid itself (^ = ^ = 1/e and 



/I 1 + e \ 



M=tf =_r?t/ — In el. 



V ^1 \ 2 1 - e / 



[137d'] 



[137e'] 



A few streamlines for equidistant values of ip are shown in Figure 229. Here 

 a/b = 2, e = 0.866, g^ = 0.466. 



The kinetic energy of the fluid, as found by substituting (^, //, co for A, /x, v in 

 Equation [136h], using Equations [137i<, 1, m] and [137v], k = ae, 6^ = a^ (1 - e^), 

 / ^ /i^ c?fi = 2/3, / ^'^ ^oj =277, and setting 4 = ^g = 1/e, is 



r = - npab^U^ 

 3 



e^^i 



1 - e^ 



[137f'] 



Case 2. Flow Past a Prolate Spheroid Parallel to the Axis of Symmetry, Let the fluid 

 at infinity flow at velocity U toward /j = - 1. Adding, from Equations [119a, b], Ux to ^ and 

 U'(S^/2 to i// as given by Equations [137v,w], to represent the superposed uniform flow. 



cf) = kUfi 



,1 C+ 1 



[137g'] 



350 



