By Equation 2-1 



L 

 T 



512 

 T 



For d = 10 feet 



512 

 C = — = 51.2 ft/sec. 



Z; ~ 512 



0.0195. 



Entering Table C-1 with d/L^ it is found that. 



hence 



10 



0.05692 



- = 0.05692. 

 L 



. r I . . , , , 1 d l\ 



= 176 reet [transitional depth, since — < — <—), 



\ Ad i-f A j 



c = 



176 

 10 



= 17.6 ft/sec. 



2.234 Local Fluid Velocities and Accelerations . In wave force studies, 

 it is often desirable to know the local fluid velocities and accelerations 

 for various values of z and t during the passage of a wave. The 

 horizontal component u, and the vertical component w, of the local 

 fluid velocity are given by; 



u = 



H gT cosh[27r(z + d)/L] 



2 L 



w = — 



cosh (27rd/L) 



H gT sinh[27r(z + d)/L] 

 2 L cosh (27rd/L) 



cos 



sin 



(2-13) 



(2-14) 



These equations express the local fluid velocity components any distance 

 (z + d) above the bottom. The velocities are harmonic in both x and t. 

 For a given value of the phase angle 6 = (2irx/L - 2iTt/T) , the hyperbolic 

 functions, aosh and sinhy as functions of z result in an approximate 

 exponential decay of the magnitude of velocity components with increasing 

 distance below the free surface. The maximum positive horizontal velocity 



2-12 



