4 



in which 





225 



1225 



Thus If we take a form intermediate between those dealt with in Sections (2) and (3) vi^:- 

 1 + ij I we find 



. = -ill pa v„ 

 75 V7 ° 



E = 12i pa? V 

 105 ° 



(i3) 



or on eliminating the central velocity v 



1.868 r ilp 



(W) 



The form 



(15) 



(16) 



£ = 1.891 r a/p 



(17) 



Finally the form 



which is such thit v and 



ax 



at x 



a Jives 



(18) 



-5iL na V , E = 0.21015 pa^ v„^ 

 525 7T ° ^0 



(19) 



2.181 r a/p 



(20) 



A comparison of equations (9), (lU), (17), (20) shows that the form assumed By the plate under 

 the a&lion of a blow of jiven momentum is not of jreat consequence in regard to the energy of the 

 inflowing water after the blow and we ney therefore taKe for this energy 



E = 2 r a/p 



(21) 



The formula assumes the plate so light that its own momentum ond kinetic energy are negligible in 

 comparison with the momentum and kinetic energy of the associated water. 



We now proceed to determine the effect of the mass of the plate. 



Kodi fi cation du c_ to m e rtj a of plate . 



Let the plate nave aensitycr and thickness t. Then assuming first piston motion the momentum 



of the plate iSTr a crtv so that equation (8) must be replaced by 



I = -^^ pa + crt 

 3 n 



(22) 



The 



