232 



Experiments under vacuum . 



Though experiments under a vacuum do not represent any possible full-scale explosion in open water, 

 they are of interest for two reasons :- 



(1) v«ith a given value of the non-dimensional parameter z*,,*. the effect of the free surface on the 

 motion of the bubble is as small as it can be, so that comparison with the formulae of Report A 

 is as justifiable as it can be; 



(2) The instability of the free surface, which occurs when It is accelerated downwards under the 

 action of external pressure, is absent. 



Before the revolving drum camera h;d been constructed, a number cf single photographs were taken 

 of the bubbles produced by sparks in oil using a o.u/u. F. condensEr charged to UOOO volts. These photographs 

 were timed to cccur at times t = 5, 10. 15, 20 .... up to 12O mi 11 iseconds after the initiating spark. 

 Figure u shows the bubble at t = 0.025 seconds. It will be seen that it is a very smooth and perfect sphere. 

 It remains spherical during its expansion, but during its contraction its vertical dimension decreases more 

 rapidly than its transverse diameter so that it becomes flattened. This flattening is more pronounced on 

 the under side than the upper side. Figure 5 shows the bubblr at t = 0.05 seconds. The flattening is here 

 very opparent. 



AS the bubble decreases in diameter tho flattening becomes more and more accentuated, till the 

 underside becomes concave and the bubble assumes the shape of a mushroom. Figure 6 shows the bubble at 

 t = 0,08 seconds. This is somewhere near the minimum size at the end of the first period of pulsation. 



Figure 7 shows the radius, a, and the rise, 2 - z, of the centre uf the bubble at times up tu 80 



milliseconds after Its formation. To compare these with calculations based on tho assumption that the bubble 



remains spherical, it is necessiry to assume a value for the energy, M, which the spark gives to the oil. 



It will be seen that, in Figure 7, if a smooth curve is drawn through the points representing the radius of 



the bubble its maximum value, a „, will be about 3.7 cm., and since the total depth z of the liquid from 

 max -^ 



the level where the pressure is zero is 6.05 cm., a-^y/Z-, = 3.7/6,05 = 0.61. 



In C-imrie's calculated curves in Report A for c = 0, i.e , with no gns inside the bubble, it will be 



found that a /z = 0.63 for z' = 1.0, 0.25 for z' = 2.0, n. m for z' - 3.0 and 0.098 for 2' = U.O. 



rriciX L 00 o 



It appears therefore that the bubbles represented in Figure 7 correspond very closely with the condition 

 z' = 1.0. when z" = 1.0, the scale-length, l, is the same as the depth z of the explosion below the 

 level of zero pressure, so that L = 6.05 cm. This corresponds with energy w = g/x" = i.i5 x 10 ergs, when 

 p = C.875 9m./cm. ^ 



The non-dimensional time scale t* in which the calculations are expressed is related to the true time 

 scale t by the relation t = f /{L/g) = 0.0786 t' seconds, when L = 6.05 cm. Multiplying the ordinates of 

 Comrie's curve for z* - l.O by 6.05, and the abscissae by 0.0786, the calculated relationships between a, 

 (z - z) and t are found. These have been plotted in Figure 7. It will be seen that, until the top of the 

 bubble is very near the free surface, its observed radius and rise are close to what was calculated 

 theoretically. 



Experiments under surface pressure of 6.5 cm. of oil . 



The depth of the spark was 6.05 cm. so that experiments in which the surface pressure was that due 

 to 6.5 cm. of oil are equivalent to explosions at a depth of (33 x 6.05)/6.5 = 30. 8 feet in open water. 



z"q = z /L where 

 scale length defl 



Zg = p//3g. P is the pressure at the level of the explosion and L is the 

 ned By the equation (3) of Report A, namely L = (w/gp)* 



