185 



DIGEST 



This paper summarizes, and in the Appendix derives the main formu- 

 las concerned with the radial expansion and compression of spherical gas- 

 filled cavities in water. The principal needs for these formulas are twofold, 

 in connection with the pulsating motion of the gas globe resulting from an 

 underwater explosion, and in connection with the behavior of bubbles of gas 

 suspended in the water when subjected to changes in external pressure. 



A sphere of gas in water under hydrostatic pressure, not subject to 

 the action of gravity, is capable of oscillating radially with preservation 

 of its spherical form. The period of oscillation at small amplitude is 



r„ = 



124 Kp7 



[2b] 



when To is in seconds and iJ^ in inches. As the amplitude Increases the pul- 

 sation is slower, and the variation within moderate limits is shown in Figure 

 1 . At large amplitudes the formula becomes 



l■0 ^ 2.0 217 v^ 



0.8 



R„i„ , 



7^ [4b] 



Rmo./Ro 



Figure 1 - Curves referring to Undamped 

 Oscillations of a Bubble or Globe 

 of Gas under Water 



So is the radius when the gas pressure equals the 

 hytirostatic pressure, ffmax ^^ the maxiuium radius, 

 ^min is the minimum radius, T„ is the period of 

 very small oscillations, T is the period of oscil- 

 lation having given value of Rrn^x/^o- The curves 

 are drawn for y = ^3, but y makes little difference. 



The pulsation of the 

 cavity may be described as a cyc- 

 lic variation of R/R„, and ex- 

 amples of this are given in Figure 

 2. 'These show the main features 

 of the motion, including the in- 

 crease of intensity of the pres- 

 sure peak and the lengthening of 

 the period at greater amplitudes. 

 The values of R„i„/Ro at differ- 

 ent values of R^^^/Rq are shown 

 also In Figure 1 . 



The pressure in the wa- 

 ter is equal to that in the gas at 

 the boundary between them, to the 

 static pressure p^ at a great dis- 



tance, and at intermediate positions is affected by the flow as shown in 

 Equation [7b], page 6; its peak value is given by the formula 



= Po 



^[fe)' -']*'. 



This digest is a condensation of the text of the report, containing a description of all essential 

 features and giving the principal results. It is prepared and included for the benefit of those who 

 cannot spare the time to read the whole report. 



