517 
= ih S 
observed value in the present investigation viz. Q.6 x 107" second, 
S. Butterworth” has more recently examined this question theoretically by a different process and 
also finds that the time of rise of pressure as affected by the presence of charge case and surrounding 
water is of the order 0.5 x 1077 second, 
After the charge-case has burst, the bubble of high pressure gas will rapidly expand with 
consequent fall of pressure. In the present investigation we are not concerned with the expansion of the 
bubble after a time of the order of .001 second, when it rises to the surface and expends its remaining 
pressure in throwing masses of water into the air in the form of a spray and plumes. 
From such general considerations it is to be anticipated that the pressure pulse passing through 
the water at a point some distance from the charge will have a short, but finite, time of rise to a maximum 
value followed by a more gradual fall of pressure to zero again at a rate determined by the expansion of 
the gas bubble. A glance at typical explosion records at once reveals these Shige scl oe assis time 
of rise being usually of the order of 10 ~ second whilst the time of fall, of the order of 10” secom, 
Gepends on the size of the charge. in what follows we shall deal in more detail with the principal 
characteristics of the records. It is our purpose also to determine as far as possible how nearly the 
recorded p/t curve represents the actual pressure-time variations taking place at that point in the water 
in which the p.e. gauge is situated, 
(1) Time of Rise and Maximum Pressure, 
In the original paper follows a detailed discussion of (a) the effect of the charge case, and 
(b) the effect of the finite size of the piezo electric gauge and the weight of the charge. 
(2) Rate of Fall of pressure. Variation with Weight of Charge. 
The question.of expansion, with consequent fall of pressure of the gas bubble has been dealt with 
mathematically # by Professor H. Lamb the deductions being in general agreement with the experimental 
results now obtained. Considerations of the rate of growth of the gas bubble indicate that the rate of 
fall of pressure is inversely proportional to the radius of the charge, i.e., to the cube root of the 
weight of the charge. 
Measurements of the time ‘t' in which P. 27 falls to 0.25 of its initial value (taken from records of 
charges varying in weight from 2&4 to 1000 lbs.) indicate that this deduction is experimentally verified. 
The results of observations are plotted in Figure 23 where it is seen that 
log = 0.32 Wort & wr? 
i.e. Bae wo yr? x 
bt 
which relation within experimental limits, indicates that the rate of fall of pressure varies inversely 
as the linear dimensions of the charge. Taking m, as the rate of rise of pressure and m, as the rate of 
fall, the following are approximate mean experimental values of the ratio m,/m, for 24, 18%, 100 and 1000 Ibs. 
charges, viz. 2, 4, 7 and 16 respectively. These values were employed to calcuate the correction to the 
Hilliar maximum pressure gauge G.F, It will be seen that the ratios vary approximately as the cube root 
of the weight of the charge. 
(2) irae serie 
: S. Butterworth. See Appendix 8. 
4 Phil. Mag. January 1923, H. Lamb. 
* Note - This result is obtained by assuming an exponential fatl of pressure, The form of 
the pressure is more accurately expressed by the difference between two exponential 
functions but the slight change in 5P/8t involved f fom P = 1 to P = 25 between the above 
expression and the more accurate one is negligible. 
