137 



Pressure at fixed point vertically above art expLo sion. 



In some experiments carrieO out recently, in which a rectangular air-baci<ed steel plate 

 0.173 inches thick anfl 6 feet x * feet sides was used, it was found that a charge of «.65 lb. 

 fired at a distance of 14 feet vertically below the plate (which was then horiiontal) produced a 

 displacement whose maximum value was 4.35 inches. A similar plate held verticaUy was dished so 

 that the maximum displacement was only 1.15 inches when the charge was fired at the same distance 

 (l« feet) but in the same horizontal plane as the plate. This very large difference cannot be 

 accounted for Oy considerations based on the pressure waves which have been measured by piezo- 

 electric gauges, for no great differences have been detected in the pressure waves at points over a 

 sphere centred on the explosive. 



It was to account for these experimental results that the present investigation was made 

 and the values of charge weight and depth used were taken to corr9Spond with those of the experiment. 

 The expression (30) for calculating pressure contains some quantities which were not needed in 

 calculating the radius and vertical velocity of the bubble. The accelerations "a" and U' have to 

 be calculated. This was done graphically, plotting the values of 4' and U' against t". The 

 Initial (non-dimensional) height of the plate above the charge was 0.97 (i.e. lU feet/u). At each 

 value of t' valuts of a', S", ¥', U', U' cino r' (= 0.97 - =') wer-e tabulated for a range of vslues near 

 the time when the bubble was reaching its minimum diameter (i.e. :it t' = 0.U08). 



Setting these in the expression (30) the following values were calculated:- 



These values are shown graphically in Figure 3. 



Comparison uith pressure during the early staats of the expansion of 

 the bubbl e . 



The maximum pressure In the pressure wave is known from piezo gauge measurements. A 

 empirical expression representing approximately by results of these pressure measurements is 



p^ = 4.6 X 10' M'-"/r 

 n = 7 .; V ,n« u-1/3 



(31) 



pp being expressed in dynes/sq.cm. , M mass in gm. of T.N.T., r distance in cm. from the charge. 



For a Charge of 4.65 lb. n = 5.86 x 10^ seconds and p^^ = 138.5 x 10* = ye atmos. at a distance 



r = 14 feet = 426 cm. This pressure Is very isuch larger than the maximum pressure calculated for 



the later pressure rise illustrated In Figure 3, but its' duration Is so small that It Is difficult 



to show it in a diagram of the scale of Figure 3. The attempt Is made, however, on the left hand 



side of the figure. The pressure falls to 10 atmos. In time given by -5.8 x lO^t 10 _ .,, 



e - jjg - .072, 



I.e. in time 0.5 milliseconds. If this exponential fall In pressure were continued It would fall 

 to ^ of an atmosphere in a little over a millisecond. In fact this does not happen, the pressure 



