cf) and k were also related to the parameter Uj^^g^^clear/v for constant 

 values of clear/Dia, although the scale effect was worse for these rela- 

 tionships. (\) and k showed very good correlation with the Keulegan- 

 Carpenter parameter, u T/Dia, although these relationships were the 

 same for a constant absolute clearance, rather than a constant relative 

 clearance. Correlation between (J) and k and the Reynolds number was 

 poor. 



10. Because a scale effect was evident in the above relationships, 

 several of the dimensionless parameters were combined to form new 

 dimensionless parameters that contained all of the important variables 

 (clear, Dia, Uj^^x' ^^^ ^^ • ^^ attempt was made to find a single param- 

 eter that was related to either (j) or k for all wave and pipeline condi- 

 tions tested in this investigation. 



Both (j) and k showed very good correlation with the parameter 

 (clear/u T) (Dia/u T) . These relationships were valid for all pipe 

 diameters ,'T30ttom clearances, orientation angles, and wave conditions 

 tested. 



In addition, the relative clearance was combined with both (}) and 

 k to form the quantities cj) (clear/Dia) and k(clear/Dia3 , both of which 

 exhibited very good correlation with more of the dimensionless combina- 

 tions than either <}) or k alone, k (clear/Dia) was best correlated with 

 (clear/u^^j^T) (clear/Dia) . (j) (clear/Dia) was also correlated with this 

 p arameter, b ut exhibited better correlation with the parameter 

 /Dia/un,axT (^ear/u^^^T) (clear/Dia) . 



11. C^, CL(l-k), and CL(k) were correlated with the same parameter 

 as (() and k, (clear/Ujjj^^^T) (Dia/u T) . However, these correlations were 

 not as good as the previous correlations between the coefficients of 

 lift and k or (}>. 



12. For a pipeline that is not parallel to the wave crests, the 

 lift forces are apparently due only to the components of the horizontal 

 water particle velocities perpendicular to the axis of the pipeline. 

 Using this convention, consistent values of the coefficient of lift, 

 Cl, are obtained for all angles of orientation. In addition, the rela- 

 tionships between the lift force parameters Cl, (j), and k, as well as 

 relationships between these parameters and various dimensionless param- 

 eters defining the wave and pipeline conditions, are identical for all 

 angles of orientation. 



13. The maximum lift force (FL(l-k) or FL(k), whichever is greater) 

 exhibited good correlation with the Reynolds number, (Uj^j^j^-Dia/v) . This 

 relationship did not hold for the maximum positive lift (FL(l-k)) or 

 the maximum negative lift (FL(k)) alone, but only for the largest of 

 these two forces in any situation. The relationship was the same for 

 all diameters over the range of conditions tested. 



120 



