Both (p (clear/Dia) and k (clear/Dia) are correlate d with the dimen- 

 sionless combinations (clear/Uj^^^ T) (clear/Dia) and /Dia/u^g^^ T 

 (clear/u, T) (clear/Dia) . However, k (clear/Dia) appears to be better 

 correlated with the first parameter, while (}) (clear/Dia) shows better 

 correlation with the second parameter. 



It is clear that for values of the dimensionless parameters lower 

 than those shown on the plots, both (j) (clear/Dia) and k (clear/Dia) 

 will remain at a value of zero. This would correspond to situations 

 where the clearance was minimal relative to the horizontal velocities, 

 wave periods, and horizontal excursions of the water particles. Thus, 

 both k and <p would be expected to equal zero and 0°, respectively, and 

 the relative clearance would either equal or approach zero. 



Large values of the dimensionless parameters correspond to situa- 

 tions where the clearance is large relative to the horizontal veloci- 

 ties, wave periods, and horizontal excursions of the water particles. 

 For these cases, k and (j) will remain at maximum values of 1 and 90°, 

 respectively, while the relative clearance, (clear/Dia), will increase 

 with increasing values of the dimensionless parameters. But as the 

 relative clearance is increased beyond this point, the lift forces will 

 decrease to zero, so extension of the plotted relationships to much 

 larger values of the dimensionless parameters is of little value. 



6 . Relationships Between the Coefficients of Lift and Parameters 

 Defining the Wave and Pipeline Conditions . 



The coefficient of lift, C^, the effective positive coefficient of 

 lift, CL(l-k), the effective negative coefficient of lift, CL(k), and 

 the maximiom effective coefficient of lift (maximum of Cj^(l-k) or CL(k)) 

 were plotted against various combinations of the dimensionless param- 

 eters. The parameter, (clear/iij^^^ T) (Dia/u^iaxT) , which previously 

 gave the best correlations with $ and k also demonstrated the best cor- 

 relation with C^, CL(l-k), and CL(k). However, these relationships 

 exhibited more scatter than the previously discussed interrelationships 

 between the coefficients of lift and the parameters, k and ({>, so it is 

 suggested that the previously discussed relationships be used for design 

 purposes . 



7. Relationships Between the Lift Forces and Parameters Defining the 

 Wave and Pipeline Conditions . 



As with the coefficient of lift, the total lift force (Ft = 

 1/2 Cr p A Ujjj^^^) can be partitioned into the maximum positive lift, 

 Fl(I-k), and the maximum negative lift, Fj^(k) (Fig. 6). These three 

 forces, as well as the maximum lift force (maximum of either Ft (1-k) or 

 FL(k)) were plotted against various combinations of the dimensionless 

 parameters. Only one relationship exhibited good correlations for the 

 data from all three diameters plotted together. Tliis was the Reynolds 

 number, u^^-^-Dia/v, versus the maximum lift force (either FL(l-k) or FL(k) 

 whichever is greater) (Fig. 63) . 



109 



