260 



(a) Calculation of expression ( C). 



We require the quantity 



Po^' 



integrated, at the Taylor cavitation time, between x = 0, 



and X » X , where x is the distance at which (t - |) vanishes at t = &,, I.e. the co-ordinate 

 of C at this time. 



X is determined by the equal ion:- 



2 e °^ e" tt5 = (1 ta) f~ ^ e"<^ 



(U) 



Using the expression for (^ obtaine'ft 'rem equations (2) ■and (u). Performing the above 



integration, and using the above equation for x , we obtain for E the value:- 



PC L (1 + a) L{l*a)J ' J 



2& 

 1^ 



The total available energy is thus eqitil to E + E^j + E^, which gives us:- 

 ivailable energy 



2 ^}e (l+a) "^ 



Pa '^ «rt^) 



(l») 



(15) 



This agrees with the results given by Fox and Rollo but differs slightly from that used by Kirkwood 

 which is equivalent to:- 



Available energy = 



^0^ 



(a * i) 



2a 



(1«) 



stained by adding together Ej and E , but neglecting E 



The total energy that falls on unit area of plate is given by integrating the energy in the 

 incident wave. It is simply:- 



Total energy = 



oje 



2Po= 



{") 



Thus, the ratios of total energy to energy initially given to plate as kinetic energy, and 

 to energy converted into kinetic energy of cavitated water or spray, can be expressed as functions 

 of the single quantity a. The relevant information is given in Table 1. 



TABLE 1. 



Available damaging energy, as a fraction of the total 

 energy, according tn vcrio us assumttio ns. 



We are interested principally In the region of small a, and it is just here that we get 

 the biggest gap between the Taylor energy, and the total available energy. The extra energy Is in 

 the form of kinetic energy of the cavitated water. When this water collides with the plate and a 



layer 



