266 



-20- 



The potential function "t" for the flow of the 

 surrounding water has been constructed in equ:ition (2.1). 

 The pressure in the water can be obtained from Bernoulli's 

 equation as follows; 



(2.24) Z^l(^ad^)2- (|±-B. If-) =0, 



where P is the excess over hydrostatic pressure, Z = R cos 9, 

 and the term B' -^5- appears because of the moving coordinate 

 system. A substitution of (2.1) in (2.24) yields 



P f A A» ) ' 1 



(2.25) -= ^ g ' ' + terms in higher powers of ^ . 



For points in water not too near the bubble, the first term 

 on the right hand side of (2.25) is dominant and the other 

 terms may be dropped. Introducing non-dimensional variables, 

 we obtain 



(2.26) p = Lf (a?a):^2P^^ L(^2.j., 



The pressure in the water, therefore, depends essentially 



on the quantity (a a)* • 



2 

 The fori!iula (2.18) for (a i)* can be given an inter- 

 esting interpretation. The last term — -,g/A represents 

 the (non-dimensional) pressure of the gas inside the bubble, 

 and (2.26) then shows that the pressure at any point in the 

 water is composed of two parts: the internal pressure of the 

 gas, and the dynamic pressure due to the motion of the water. 

 This is more clearly seen if equations (2.26), (2.18) are re- 

 written in terms of the original dimensional variables. The 



