u = - (9.8)(0.1385) — ; 0.700 m/s (2.29 ft/s) 



c,l 2 1.2040 



^t.l 



^ (9.8)(0.1385) \[IIIq = -0.660 m/s (2.17 ft/s) 



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



z = ri(, 2 = 0.602 m (2.48 ft) 

 2Tr(z + d) 



When 



cosh 



cosh 



4Tr(z + d) 



= cosh[2ir(0.1100)] = 1.249 



= cosh[4ir(0.1100)] = 2.118 



cosh 



cosh 



z = Ht 2 = -0.398 m (1.52 ft) 

 2ti(z + d) 



4tt(z + d) 



= cosh[2Tr(0.0934)] = 1.177 



= cosh[4Tr(0.0934)] = 1.772 



Thus, the value of u at a crest and trough according to second-order 

 theory is 



1 



1.249 3 U 



2.118 



u = — (9.8)(0.1385) +-|-^l (7.22) 



c,2 2 1.2040 4 l60i 0.202 



= 0.718 m/s (2.36 ft/s) 



1.177 3 U 



t,2 



(9.8)(0.1385) „^,„ , ,,„ 



2 1.2040 4 \60 



+ T br (7.22) 



1.772 

 0.202 



= - 0.553 m/s (1.75 ft/s) 



(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) /ith\2 C cosh[4ir(z + d)/L] 



L/ 2 sinh2(2Trd/L) 



2-42 



