12 2 



The kinetic energy of the plate is ^tt a cTt v and the equation of energy givus 



3 TT 



pa * en 



(23) 



the first term corresponOing to the energy of the inflowing water and the second to that of the plate. 

 In terras of the applied momentun 



1.851 r fl/p { 1 + 1.178 '2 } 



(2») 



The ratio - — — gives the relative proportion of energy or momentum residing in the plate and 



associates] water r^spict ively. 



Thus in the case of steel for which ^ = 7.7 if t = 0.5 inch a = 2 feet this ratio Is 

 0,189 so that of the whole energy comnunicated by the blow only 16* resides in the material of the 

 plate. 



If we tal<e the form v 





I + 



the plate momentum is 



^ 2 



dx = - 77 a crt V 



while the plate energy is 



7 ? 7 



ax = - 77 a' crt v„ 



These give in place of (l3) 



1 = I 7^ pa.^oi 



^ = - ^M I^ '^ ^ 5 -^ 



2 (25) 



and in plaCi; of (lu) 



I = 1.868 



2, 1 + 1.266?! 



£S 



ra 



P (1 + 1.205 'g)2 



pa 



(26) 



The formula corresponding to (26) for the motion 



. 6 x^ , 1 x" 



,2^ 1 + 1.311 ^ 



P (1+1.068^)2 



pa 



and for mot ion 



(27) 



I = 2.181 is. 



2 1 + 1.1*95 'ii 



P (1*1.074^)2 



(28) 



If we take what is probably an extreme case viz:- ^ = 1 equations (24), (26), (27), (28), 

 fij- =■ 0.850, 0.870, 1.022, 1.265 respectively. 



give 



These 



