The volume of fluid flowing per second through the opening is, using Equation [l39g] 



for u, 



- 2n j Uiodoj - 2n cA. 

 



[I39i] 



Some lines of flow for equidistant values of ip are shown in Figure 239. By adding a 

 uniform flow parallel to the plane, more general cases can be treated. 

 (See Reference 1, Article 108.) 



Figure 239 — Symmetrical streamlines for flow through 

 a circular aperture in an infinite plane wall. 



140. ROTATING ELLIPSOIDAL SHELL 



Consider the fluid inside a shell whose surface is the ellipsoid 



2 2 2 



f{x, y, z) - — + — + 1=0. 



a2 §2 ^2 



[140a] 



The direction cosines of the normal at any point of the surface are, from Equations [136b, c, d], 



I = 2k — , m = 2k , n ^ 2k 



a^ h^ c2 



371 



