_ 5 - 135 



similar to that of 2200 lb. exploding at 103 feet. Similarly a 1 oz. charge exploding at a depth 

 of 10.0 - u.O = 6.0 feet Oelow the surface would be similar to a 300 lb, charge at 50 feet if the 

 atmospheric pressure above the 1 oz. charge weru reduced to 4.0 feet of water, 



Condi tions when the bubble rs nea r tts point of greatest contractio n. 



The approxiiTBt ion in which G(a) is neglected in comparison with W does not give useful 

 results near the point of minimum radius. To investigate phenomena which depend on conditions 

 near this point it is necessary to use (5) instead of (lU). The calculation must then refer to 

 one charge and one depth only, though it is still convenient to use tne non-dimensional form (5), 

 As an example a charge of 1.65 ID. exploded at depth of 20 feet is chosen, because in an experiment 

 made under these conditions effects were produced which might be attributed to the effect of gravity. 

 In this case the value of L is tUS cm. or in. 6 feet, and z' = ^iii^{^° = 3.62, aiid f = l.UTt 

 when t is expressed in seconds. 



For convenience in calculation (ll) may be exoressed in terms of a' and L by the formula 



^ = 0.0177 L°-" a'-°-" 

 and when L = "15 cm., this gives 



(19) 



(20) 



Figure 2 shows the radius and depth of tne centre at time t after the explosion. In the 

 experiment above a box containing an air-backed plate was placed at a depth of 6 feet, 14 feet 

 above the charge. This is shown in Figure 2, 



Effect of vertical motion on maximum pressure . 



When the effect of compressibility and of vertical motion is neglected the maximum pressure 

 in the bubble occurs when G(a) = W and from (ll) this will be found to correspond with 



-!^ = (I.ISS)"" = 0.51 



and 



p = 1.308 X lo' (0.51)^-" = 5.63 X 10^ = 563 atmos. (2l) 



t*hen M = 4.65 lb. = 2100 gm. 



a^ = ^75Y = 4130 so that a = 16.0 cm. 



and a' = 1^ = 0.036 (22) 



It will be set-n that the effect of the vertical motion is to prevent the high pressure 

 associated with this very small radius from being formed. Thus in Figure 2 the minimum radius 

 will be seen to be a' = 0.120, which is 3.3 times as great as that which would occur in the absence 

 of gravity. The pressure corresponding with a = (O.liO) (445) = 53.4 cm. is only 5.0 atmos., so 

 that this effect on gravity is to reduce the maximum pressure in this case in the ratio 100:1. 



The amount of energy radiated in the form of a compressibility wave during the period of 

 greatest compression depends on the p^^,, the greatest pressure. Conyers Herring and Willis have 

 developed formulae giving for the proportion of W which is radiated the formula 



/p , 



F = Fraction radiated = A / -~^ / c (23) 



where A depends only ony and c is tlie velocity of sound in water. For y = 1.25, A = 1.87, so 

 that (23) would give as the fraction radiated 



