342 



MOTION OF THE GAS SPHERE 



shown by the data of Fig. 8.19, in which the periods for 0.55 pound 

 charges of tetryl fired at various depths in approximately 24 feet of 

 water (2) are plotted against d + 33. Also plotted for comparison is 

 the period-depth relation T(sec.) = 4..53W''' {d + 33)-^/'' obtained for 

 charges fired in deep water. 



The most accurate calculation of periods when both surface and 

 bottom must be considered is the result of Friedman (37) given by Eq. 

 (8.61), which for the present purpose may be written 



(8.68) T{d + 33)5/« = QMl{rQWy^' 1 + 



^.Ml{rQWyi^F{x)' 

 hoid + 33)1/3 



200 



175 



150 



125 



100 



5 10 15 



DEPTH (ft) 



Fig. 8.19 First and second periods of bubble pulsations for 0.66 pound loose 

 tetryl charges fired in 24 feet of water. 



20 



where W is the charge weight in pounds, and F{x) is the function of dis- 

 tances d and ho from the surface and bottom defined by Eq. (8.60). 

 The argument x is defined by the ratio {d — ho)/{d + ho), and F{x) takes 

 on the limiting values — ^ near the surface, + 1 near the bottom, ^^ and 

 zero for a charge fired at a distance equal to 3^3 of the depth of water 



^2 The divergence of the function F{x) for d « ho makes its use less convenient 

 than that of the function F'{x) = — ( 1 + x) F{x) in terms of which the period is 

 given by 



0.561 inQWyi' r, 0.341 (nQWy' F'(x)n 



T = 



(d + 33)' 



d{d + 33)5/6 



Values of F'{x) as a function of x nvc, as follows 



X 



F'{x) 



-1.0 

 1.00 



■0.8 

 0.998 



0.6 

 0.985 



0.5 

 0.970 



0.4 -0.3 -0.2 

 0.946 0.911 0.861 



■0.1 

 0.791 



