************** EXAMPLE PROBLEM 4**************** 



GIVEN ; A wave in a depth d = 12 meters (39.4 feet), height H = 3 meters (9.8 

 feet), and a period T = 10 seconds. The corresponding deepwater wave height 

 is Hq = 3.13 meters (10.27 feet). 



FIND: 



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

 mean positon when z = 0, and when z = -d. 



(b) The maximum water particle displacement at an elevation z = 7.5 meters 

 (-24.6 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 = -L /2. 



SOLUTION ; 



(a) Ljj = 1.56t2 = 1.56(10)2 = 156 m (512 ft) 



d 12 



L 156 

 o 

 From Appendix C, Table C-1 



= 0.0769 



/2Trd\ 

 sinh I 1 = 0.8306 



tanh (—1 = 0.6389 



When z = 0, equation (2-22) reduces to 



A. 5 1 



2 tanh(2TTd/L) 

 and equation (2-23) reduces to 



Thus, 



H 



B = - 



2 



B = - = - = 1.5 m (4.92 ft) 

 2 2 



When z = - d. 



and, B = 0. 



H 3 



A = -— = = 1.81 m (5.92 ft) 



2 slnh(2iTd/L) 2(0.8306) 



2-20 



