n 



(1) Factors influencing D . The variation of drag coefficient C^ 

 with Reynolds number R for steady flow conditions is shown in Figure 

 7-85. The Reynolds number is defined by 



R =-^ (7-45) 



e V 



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 R exist: 



(1) Subcritical : R^ < 1 x 10 where C-q is relatively 

 constant (« = 1.2) . 



(2) Transitional: 1x10 <R<4xlO where C„ varies. 

 — e D 



(3) Supercritical : R^ > 4 x 10 where Cp 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^ may change by about a factor 

 of 2. 



The steady-flow curves shown in Figure 7-85 show that the values of Rg 

 defining the transitional region vary from investigator to investigator. 

 Generally, the value of K„ at which the transition occurs depends 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 insignificant influence on 

 the value of Cr, . However, in the supercritical region, the value of Cp 

 increases with increasing surface roughness. The variation of Cn with 

 surface roughness is given in Table 7-4. 



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 (7-23) 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 Cr, used. However the accuracy with which 

 Cr, 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 



7-138 



