27 215 



and for y = 4/3. 



The maximum pressure, occurring at the Instant at which R = R^ and the water 

 comes to rest, is, If y = 4/5, 



.... = p. ^ [(|-)' - >] + p. ("ol 



If R^/Rq is small, only the terms in {Rg/R^)* need be kept. Then, 

 approximately, for y = 4/3, 



An examination of Equation [39a] shows that for any R< R^/^, which implies 

 that iZj < Rg/2 also, the error in Equations [42] and [45] is not over 7 per 

 cent. 



The effective impulse, j{p - Pf))dt, may be found by direct inte- 

 gration, but it is most easily found by using Equation [9] on page 46 of TMB 

 Report 480 (4) 



fip-Po)dt = ^4(/?^^) - \pfv^dt 



where R and v replace r^ and u in the original. If tj, the instant of min- 

 imum radius, is taken as the lower limit, at which dR/dt = 0, /i{R^ dR/dt) be- 

 comes simply the value of R^dR/dt at the upper limit t. Hence, from Equations 

 [28] and [5Tb] 



'i 



or, using Equation [29] and eliminating p by means of Equation [54a], 



