hence , 



L = ^ ,o»r = 81.7 m (268 ft) 

 0.1835 



Evaluation of the constant terms in equations (2-13) to (2-16) gives 

 HgT 1 5.5 (9.8)(8) 1 



2L cosh(2ird/L) 2 (81.7) 1.742 



Hgii 1 5.5 (9.8)(3.1416) 1 



= 1.515 



L cosh(2Trd/L) 81.7 1.742 



Substitution into equation (2-13) gives 



= 1.190 



pTfdS - 5) 1 

 L 81.7 J 



u = 1.515 cosh — -— [cos 60°] = 1.515 [cosh(0.7691) ] (0.500) 



From Table C-1 find 



Therefore, 



u = 1.515 (1.3106) (0.500) = 0.99 m/s (3.26 ft/s) 



w = 1.515 (0.8472) (0.866) = 1.11 m/s (3.65 ft/s) 



a^ = 1.190 (1.3106) (0.866) = 1.35 m/s^ (4.43 ft/s^) 



a^ = -1.190 (0.8472) (0.500) = -0.50 m/s^ (1.65 ft/s^) 



Figure 2-3, a sketch of the local fluid motion, indicates that the fluid 

 under the crest moves in the direction of wave propagation and returns dur- 

 ing passage of the trough. Linear theory does not predict any mass trans- 

 port; hence, the sketch shows only an oscillatory fluid motion. 



e. Water Particle Displacements. Another important aspect of linear wave 

 mechanics deals with the displacement of individual water particles within the 

 wave. Water particles generally move in elliptical paths in shallow or tran- 

 sitional water and in circular paths in deep water. If the mean particle 

 position is considered to be at the center of the ellipse or circle, then ver- 

 tical particle displacement with respect to the mean position cannot exceed 

 one-half the wave height. Thus, since the wave height is assumed to be 

 small, the displacement of any fluid particle from its mean position is small. 



2-15 



