and since, 



/27rd\ _ sinh (27rd/L) 

 y L y ~ cosh (27rd/L) ' 



therefore, 



■nH cosh [27r(z+d)/L] (inx 27rt\ 



U = — -— ; COS I — I . 



T sinh (27rd/L) \ L T / 

 ************************************* 



************** EXAMPLE PROBLEM ************** 



GIVEN : A wave in a depth of d = 40 feet, height of H = 10 feet, and a 

 period of T = 10 seconds. The corresponding deepwater wave height is 

 Hq = 10.45 feet. 



FIND : 



(a) The horizontal and vertical displacement of a water particle from 

 its mean position when z = 0, and when z = - d. 



(b) The maximum water particle displacement at a depth d = 25 feet when 

 the wave is in infinitely deep water. 



(c) For the deepwater conditions of (b) above, show that the particle 

 displacements are small relative to the wave height when z = - Lo/2. 



SOLUTION : 



(a) L^ = 5.12 T^ = 5.12(10)^ = 512 feet , 



d 40 



0.0781 . 



Lc 512 



From Appendix C, Table C-1 



sinh ( — 1= 0.8394 , 



1 /27rd\ 

 tanh I 1= 0.6430 . 



When z = 0, Equation 2-22 reduces to 



H 1 



A = 



2 tanh(27rd/L) ' 

 2-20 



