From Figure 7-85, C^j = 0.89 which is less than the value of C^ = 1.2 

 used in the force calculation. Consequently, the force calculation gave a 

 high force estimate. 



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



2 

 Hallerraeier (1976) found that when the parameter u /gD is approximately 



equal to 1.0 , the coefficient of drag Cj^ may significantly increase because 



of surface effects. Where this is the case, a detailed analysis of forces 



should be performed, preferably including physical modeling. 



r 

 (2). Factors Influencing M . MacCamy and Fuchs (1954) found by 



theory that for small ratios of pile diameter to wavelength, 



% = 2.0 (7-52) 



This is identical to the result obtained for a cylinder in accelerated flow of 

 an ideal or nonviscous fluid (Lamb, 1932). The theoretical prediction of 

 Cw can only be considered an estimate of this coefficient. The effect of a 

 real viscous fluid, which accounted for the term involving Ctj in equation 

 (7-48), will drastically alter the flow pattern around the cylinder and 

 invalidate the analysis leading to C^ = 2.0 . The factors influencing Cr, 

 also influence the value of C^ . 



No quantitative dependence of Cw on Reynolds number has been 

 established, although Bretschneider (1957) indicated a decrease in Cj^ with 

 Increasing R . However for the range of Reynolds numbers (R < 3 x 10 ) 

 covered by Keulegan and Carpenter (1956), the value of the parameter A/D 

 plays an important role in determining C^ . For A/D < 1 they found 

 C„ =s 2.0 . Since for small values of A/D the flow pattern probably 

 deviates only slightly from the pattern assumed in the theoretical develop- 

 ment, the result of % = 2.0 seems reasonable. A similar result was obtained 

 by Jen (1968) who found C^ ^ 2.0 from experiments when A/D < 0.4. For 

 larger A/D values that are closer to actual design conditions, Keulegan and 

 Carpenter found (a) a minimum C„ ^ 0.8 for A/D " 2.5 and (b) that Cj^ 

 increased from 1.5 to 2.5 for 6 < A/D < 20 . 



Just as for C^j , Keulegan and Carpenter showed that C^, was nearly 

 constant over a large part of the wave period, therefore supporting the 

 initial assumption of constant Cy and Cr, . 



Table 7-5 presents values of Cw reported by various investigators. The 

 importance of considering which wave theory was employed when determining 

 C^ from field experiments is equally important when dealing with Cw . 



Based on the information in Table 7-5, the following choice of Cw is 

 recommended for use in conjunction with Figures 7-71 and 7-72: 



,5 



C, = 2.0 when R < 2.5 x 10" 



M e 



R 

 e 5 



C =2.5 when 2.5 x 10 < R < 5 



5 X 10 



C,, = 1.5 when R > 5 x 10^ 

 M e 



X 10 > 



(7-53) 



7-144 



