11. 



117 



(2) The pressure due to the pressure wave may rise again after falling to zero, either 



Dy cavitation in the water some way away from the surface of the plate (an effect which would 

 allow the water between the cavitation zone and the plate to move forward and exert a pressure 

 on the plate as it is decelerated by the stresses in the plate) or by drops shooting forward 

 towards the plate after It has parted from fhe water at the instant of zero pressure. 



(3) The long continued pressure due to the expansion cf the bubble or pressure effects 

 accompanying its first ra-canpressi.-.n. 



It is not, in general, possible to distinguish between these alternatives, using only the 

 measurements of the dishing of the plates. On the other hand (2) may be dismissed as inadequate 

 in cases where the energy used in distorting the plate is considerably greater than the whole 

 energy of the part of the pressure wave which falls on the plate. For this reason this energy 

 has been calculated. 



Total energy of pressure wave falling on the filate .. 



To calculate the total energy which falls on the plate it is necessary to find an 

 expression for the solid angle o) subtended at the charge position by the plate. Integration 

 gives the I'ormula 



t tan 



■,/JT7T^ 



(55) 



when the charge Is situated on the normal through the mid-point of the plate» The total energy 

 of the pressure wave is 



(56) 



E« = ■» 77 (^ p cu^ + ^ pu) r^jt 



and at some distance from the centre, i.e. when the extent of tne disturbance along a radius Is 

 small compared with the radius, p = p cu so that the total energy is 



pVdt 



(57) 



Assuming that the pressure may be represented by the expression p = p e " and that p and n 

 have the values given in (52) 



2v_ (U.6 X 10^ 

 p c 1 7.5 X lO' 



M = 1.21 X lo'" M ergs 



(58) 



This may be compared with the amount of Kinetic energy which is left behind in the kinetic wave(8) 

 surrounding the bubble, namely 



W = 1.85 X 10'° M 

 The total energy falling on the plate is, therefore, from (55) 

 0) I , 



[ t ] 



plate 



w _ 



U 7T 



(/xTr~^T?' 



(59) 



(«) 



Using a = 35 inches, b ■= 23 inches, some values of - tan"' 

 Table 3. ^ 



i/xrr?T^ 



are given 



TABLE 3. 



For 



