118 -12- 



For comoarison with the amount of energy used up in stretchiny the plate, the mean enerjy of the 



pressure wave per unit volume of the material of the plate has been calculated. This Is t^ = 



(l/tabt) [e J , , and the values of I . are tabulated in column 14 of Table 2. Comparing these 



vrplale wp _ !»•»• 



with the corresponding figures of column 8 for mean energy used in stretching the plate, it is 



seen that in It of the 19 cases analysed more energy was given to the plate than thers was in the 



part of the original pressure wave whicn fell on the plate. The ratio "p^^^p 1= O'^e" '" column 15. 



Though some error is likely in estimating both w and I It does not seen possible that it could 



give rise to values of W /I as much in excess of 1.0 as many of those tabulated in column 15. 



Possible errors in ^^. 



Errors in »( might arise from three causes. 



(1) The yield point of the mild steel might be different from 20 tons/square inch. Since 

 w is proportional to th£ yield stress the figures for '•-''^^p could only be reduced by assuming 

 a yield stress lower than JO tons/square inch. This is a very unlikely explanation of such 

 large values as those given in column 15. 



(2) The type of dishing is not quite the same as that assumed In calculating w , The values 

 of h /z are in almost all c*ses greater than 2.06, the value corresponding with the distortion 

 of a soap film by uniform pressure. Since the latter is the distortion corresponding with the 

 minimum work for a given value of z, any error oue to this cause would lead to an underestimate 

 of W and a more accurate analysis of distortion would therefore give rise to an increase in the 

 figures in columns 8 and 15. 



(3) The plate might not be held sufficiently firmly at the edges to justify the use of the 

 fixed edge condition. Errors due to this cause would give rise to a decrease In the figures of 

 columns 6 and 15. It does not seem likely that any ■^ery considerable error could arise from 

 this cause. 



Erro rs in E . 



Apart from the question whether some energy might not be drawn by diffraction from the 

 part of the Shockwave outside the plate, (and this is likely to be small for reasons already given) 

 the energy in the Shockwave may be less than that given by (58). Errors of this kind, however, 

 cannot be large because the figures in (58) are derived directly from piezo-gauge measurements 

 which are remarkably consistent. In this connection it is worth noticing that the energy of the 

 flow round the bubble is, according to (58) and (59), 



(1.85 + 1.21) X 10^° = 3.06 x 10^° ergs/gm. of T.N.T. 



Expressed in calories this is 730 calories/gm. Penney has calculated that about 30» of the 

 available energy is nested in irreversible heating of the water near the bubble by the very 

 intense Shockwave. 



The energy which T.N.T. is capable of giving up by adiabatic ex|»nsion of the products of 

 detonation is, according to Robertson(9), 926 calories/gm. HJones' theoretical calculation makes 

 it 980 calorles/gm. Both these values are greater than 880 calories/gm. which is the figure taken 

 by Conyers Herring. Taking Jones' value the wastage, according to fenney, is 305 of 980 = 29« 

 calories, so that the total work done by the explosive is 730 + Z9H = 1C2« calories.. This is 'H 

 greater than Jones' calculations. It will be seen, therefore, that any appreciable increase In 

 the estimated energy of the pressure wave would be inconsistent with the known thermo-chemical data 

 of the energy available on combustion of T.N.T. 



Comments on results given in Table 2 . 



It is shown that only a fraction of the energy which is communicated to the plate is due 

 to the pressure in the pressure wave before this pressure falls to zero. The empirical hypothesis 

 that the whole of the energy of the wave striking the plate is given up to it would enable a more 

 accurate prediction of damage in the cases analysed to be nade than the assumption that no further 

 energy is given to the plate after the pressure on It falls to zero. Even this hypothesis, however, 

 underestimates the energy which the water gives to the plate in most cases. It seems necessary 



to ..... 



