Figure 214 - Streamlines due to a moving 



sphere momentarily concentric with a 



surrounding stationary spherical 



shell. See Section 129. 



The kinetic energy of the fluid is, from [17c], in which 9^ = on the shell and r = a 

 on the sphere, 



1 r 1 h^ + <2a^ 



T =— p \ (j> qdS =—77 p 



2 J ' 3 ^,3.^3 



[129e] 



The integration extends only over the sphere, where r = a, dS = 2n-a^ sin 9 dd. 



All of these formulas hold momentarily only, as the center of the moving sphere passes 

 the center of the shell. (See Reference 1, Article 93.) 



130. SPHERE AND A WALL; TWO SPHERES 



The flow caused by a small sphere moving in the presence of a rigid wall can be 

 found to the first order of approximation by elementary methods. Let a be the radius of the 

 sphere and x the distance of its center C from the wall; let it be moving at speed f/ in a 

 direction inclined at an angle a to a line OCT drawn perpendicularly away from the wall, as 

 shown in Figure 215. Using the method of successive approximation, let three flows be 

 superposed, as follows: 



Figure 215 - Diagram for a small sphere 

 near a wall. See Section 130. 



323 



