434 



(i) Conynrs Hi-rriiuj's formulie in non-d imtns ional form. 



(2) Formulat given in the ri.-port "The Behaviour of an Underwater Explosion Bubble." 



The values of the integrals given in Table 1 were obtained from the numerical integration 

 of Taylor's equations for the motion of an explosion bubble in the absence of all surfaces. It 

 has be^n assumed that the perturbing efft^ct of the presence of the surface on the radius^time 

 curve of the bubble is snail during the time when the Bubble is large and the two integrals are 

 growing. 



It will oe seen that Conyers Herring's formula for a 5 dt is considerably in error, and 

 an alternative formula viz., O.37 x 10"-' a z obtained empirically, is put forward in the Table 

 which gives reasonable ayrt'ement. Inserting this approximation, .ind the one given in the last 

 line of the Table, in equ>)tion (8) now yields 



2<i> 



3 11/^ 

 a z 6 



m 



(R.H.S. Non-dimensional) (9) 



To take the approxirrat ion one stage further the value of the rise due to gravity obtained, 

 may be inserted. The equation given was 



Rise due to gravity h = i42 (Non-dimensional) (lO) 



^o'6 



Hence the displaceiicnt s of the bubble towards the surface in non-dimensional units 



3 X 



(Non-dimensional) (ll) 



But a^-'z^ is very nearly independent of c, i.e. independent of charge weight and also of 

 z^ (depth). Replacing it by an average value giving the best fit over the whole range, (ll) 

 Becomes finally. 



Non-dimensional displacement 



tow.'irds origin of x co-ordinates = - O.37 2^ 



in first period ° * 



J at 



(Nonwiimonsional) 

 (12) 



