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



d 



= 0.05641 

 L 



hence , 



3 / 1 d n 



L = = 53.2 m (174 ft) transitional depth, since — < — < — 



0.05641 I 25 L 2, 



L 53 2 



C = - = — = 5.32 m/s (17.4 ft/s) 



T 10 



An approximate value of L can also be found by using equation (2-4b) 



gT2 / ^ /4tt2 d' 



L^ /tanh — s 



2Tr V \t2 g 



which can be written in terms of L as 



therefore. 



L «== 156 Vtanh(0.1208) 



L %156 Vo.1202 = 54.1 m (177.5 ft) 



which compares with L = 53.3 meters obtained using Table C-1. The error in 

 this case is 1.5 percent. Note that Plate C-1 could also have been used to 

 determine d/L. 



*************************************** 



d. 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 the following equations (with X and t as defined in Figure 2-2) : 



H gT cosh[2iT(z + d)/L] /zirx 2Trt\ 



u = — — -— cos (2-13) 



2 L cosh(2iid/L) \ L T / 



H gT sinh[2Tr(z + d)/L] /2Trx 27rt\ 



w = — — : sin (2-14) 



2 L cosh(2Tid/L) \ L T 



2-12 



