356 



Section IV 

 The Electrostatic Problem 



In Section III fimctlons ^, , <p^ and <p were Intro- 

 duced into the energy equation to take account of the 

 presence of free and rigid surfaces. However, the re- 

 sults obtained depended only on the function (p^ . This 

 function (p.. can be evalioated, to a first approximation, 

 by finding the kinetic energy of water motion due to a 

 fixed expanding bubble. Consider the velocity potential 

 for a fixed expanding bubble, assumed spherical, located 

 at a distance H beneath the surface in water whose depth 

 is D feet. If we take spherical coordinates, R, 9, Y 



® 



with pole at the center of the bubble, the problem can be 

 formulated mathematically as follows : 



Find a potential function $(R,0) such that 



(4.1) 

 (4.2) 

 (4.3) 



QR 



= A on the sphere, 



§-0 



on bottom, 

 $ = on surface. 



