-41- 



287 



Appendix II» The Velocity Potential for a Pulsating 

 Sphere Moving Perpendicularly to a Wall » 



1» Statement of the problem * 



An Ideal incorrrpresslble fluid Is bounded by a plane 

 infinite rigid wall^ and has a pulsating and moving sphere 

 imn,ersed in it. It is required to find the velocity poten- 

 tial describing the (Irrotational) flow, and to obtain the 

 kinetic energy of the liquid. The case of a moving sphere 

 is classical and can be found in the standard books on Hydro- 

 dynamics. The pulsating sphere, however, does not seem to 

 be generally known and has certain features of interest. 

 The treatment here follows [5]» 



Let A be the radius of the sphere at any time T, 

 and B the distance of its center from the rigid wall. The 

 velocity potential 4' describing the flow of the liquid 

 satisfies the potential equation 



77 



<^ = 



■K- The method used here can also be applied to a spherical 

 wall. 



