Entering Table C-2 again, it is found that when 



When 



z = 1?^ 2 = 2.48 feet 

 27r(z + d) 



cosh 



cosh 



47r(z + d) 



= cosh [27r(0.1124)] = 1.260. 



= cosh [47r(0.1 124)] = 2.175 



z = T?^ 2 = ~ 1-52 feet , 



cosh 



cosh 



27r(z + d) 



47r(z + d) 



cosh [27r(0.0924)] = 1.174 



cosh [47r(0.0924)] = 1.753 



Thus, the value of u at a crest and trough respectively according 

 to second-order theory is 



4 1.260 3 / 47r\^ 2.175 



u^2 = :; (32.2) (0.0418) — — - + - -— (23.9) -^^ = 3.6 ft/sec , 

 ''''' 2 1.2040 4 \200) 0.202 



4 1.174 



u,y = (32.2) (0.0418) — 



''2 1. 



3 / 47r\2 1.753 



+ -— (23 9) 



2040 4 \200/ ■ 0.202 



2.0 ft/ 



sec 



(c) To find the horizontal distance that a particle moves during one 

 wave period at z = 0, Equation 2-55 can be written as: 



U(z) = 



AX(z) _ /ttH ^ C cosh [47r(z + d)/L] 

 T ~ \ L 2 sinh^ (27rd/L) 



where AX(z) is the net horizontal distance traveled by a water 

 particle, z feet below the surface, during one wave period. 



2-45 



