where 



u = velocity, 



D = pile diameter, 



V = kinematic viscosity (approximately 1.0 x 10"^ ft.^/sec. for 

 sea water.) 



Results of steady state experiments are indicated by dashed lines. 

 (Achenbach, 1968.) Taking these results, three ranges of Rg exist: 



(1) Subcritical; Rg < 1 x 10^ where Cp is relatively constant 

 (-1.2), 



(2) Transitional; 1 x 10^ < Rg < 4 x 10^ where C^ varies, and 



(3) Supercritical; Rg > 4 x 10^; where C^ is relatively 

 constant (*0.6 - 0.7). 



Thus, depending on the value of the Reynolds number, the results of 

 steady state experiments show that the value of C/j may change by 

 about a factor of 2, 



The steady-flow curves shown in Figure 7-58 show that the values of 

 Rg defining the transitional region vary from investigator to investi- 

 gator. Generally, the value of Rg at which the transition occurs de- 

 pends on the roughness of the pile and the ambient level of turbulence 

 in the fluid. A rougher pile will experience the transition at a smaller 

 Rg. In the subcritical region, the degree of roughness has an insignifi- 

 cant influence on the value of C^. However, in the supercritical region, 

 the value of C^ increases with increasing surface roughness. The varia- 

 tion of Cj-) with surface roughness is given in Table 7-2. 



The preceding discussion was based on experimental results obtained 

 under steady, unidirectional flow conditions. To apply these results to 

 the unsteady oscillatory flow conditions associated with waves, it is 

 necessary to define a Reynolds number for the wave motion. As Equation 

 7-16 shows, the fluid velocity varies with time and with position along 

 the pile. In principle, an instantaneous value of the Reynolds number 

 could be calculated, and the corresponding value of C^; used. However 

 the accuracy with which C^j is determined hardly justifies such an 

 elaborate procedure. 



Keulegan and Carpenter (1956), in a laboratory study of forces on a 

 cylindrical pile in oscillatory flow, found that over most of a wave 

 cycle the value of the drag coefficient remained about constant. Since 

 the maximum value of the drag force occurs when the velocity is a maximum. 



it seems justified to use the maximum value of the velocity 



when 



7-102 



