also 



1 dcf, 

 a dO 



2 c: A 



{a + r f - c^ 



sin 6, 



[134g] 



and the particle speed is g = \q/)\. 



In Figure 223 streamlines are drawn which leave the source in the same plane in 

 directions 22.5 deg apart, and eventually become parallel to these same directions, which 

 are also indicated in the figure. (See Reference 1, Article 96; Reference 2, Section 15.40.) 



Figure 223 — Streamlines due to a point source at c^ near a sphere. See Section 134. 



135. BOUNDARY CONDITIONS IN ROTATION 



The general boundary condition, that the fluid and the boundary must have a common 

 component of velocity normal to the boundary, can be put into a useful special form when the 

 boundary is rotating as a rigid body. 



Let the boundary rotate at angular velocity w^ about the 3-axis. Then any point on it 

 located at (x, y, z) is moving parallel to the a;y-plane with a linear velocity tj, {x'^ + y^) ; 

 and, by similar triangles, as illustrated in Figure 224, its x and y components of velocity are 



[y = - oj y, F = w^ ar, ly = 



338 



