The whole reaction force over the plate is 

 a 



2TT 



^ p d f = « p C(, a^ I aj^ 



x^" * ' a„tti)<U 



(7) 



Calling the integral in (7) I,, we have 

 I. = I M^" * ' <#n ^^ ^ 



*nM 



2n + 3 



2n + 3 



2n + 3 ^ J, 



-ll 



2n + 3 *i 



L 



2n + 3 



M^"*' K<U 



/^ K<1U 



Since ^ = -K/M^"^ 



To Jotermine thi- definite integrals we have the reduction formula 



while 



(2n+ 1)^ 



^ KC^ = I 



fj"* ^ Kc(u = 1 + (2n)^ 



,u'" - ' K(^ 



(8) 



(9) 



(10) 



Using (9) and (10) to evaluate (e) we obtain 



I = i , I 



lu 



31" 



. 1. 



1606 



" 3 ■' 45 ■ ' 1575 ^ 11025 

 so that the whole reaction force opposing depression is 



(11) 



° I 3 46 ^ 11025 * 



In the case of a sudden blow of momentum I per unit area 



(12) 



77 a I 



F dt 



if the plate is very light, so that 



, . i p V a 1 . » a. * 111 

 77 ° [3 »5 ^ 1575 



1606 

 11025 



(13) 



Energy of foL lowing wate r. 



The velocity v of any element is assisted by the pressure p so that the work done by the 

 ra ^a 



water on the plate is 2 tt f p vd f or the work doni,- on the water by the plate is - 2 77 ^ pv d ^, 



The 



