336 



(1.2) C = L(2gZy3)'^/2. 



Note that the unit of velocity Is proportional to the 

 square root of Z , for 



(1.3) L/C = (2gZo/3)^/2. 



Parameters in the Bubble Motion 



If the pressure and volume of a tinit mass of the gas 

 formed by the explosive are connected by the adiabatic 

 relation: 



(1.4) PV*^ = K, 



then the internal energy of the bubble when expressed in 

 non-dimensional terms will depend upon a parameter k 

 which is defined as follows: 



(1.5) k = K(E/M)"*^(pgZQ)"^~V(Y - 1). 



Since y - 1 is very close to zero, the value of k will 

 hardly change when Z varies slightly. In most cases, 

 therefore, we shall be able to treat k as constant inde- 

 pendent of Z-. 



The effects of free surface, gravity and bottom are 

 expressed with the help of a function ^J, . V/e put 



(1.6) p^= -[f (x) + log 2]/(H + B) 



= -^(x)/H 



