I£ such data were included in the plots of C, versus k and (jj, values 

 of Ct ranging from to the maximum values shown in Figures 40 and 41 

 would be present in the vicinity of k = 1 and ()) = 90° in the respective 

 plots. TiTe same applies to the plots of C, (k) versus k and (}). 



These trends were observed in the data taken for the largest bottom 

 clearances (1 and 2 inches) . However, since these lift forces were so 

 small, a significant amount of error could be introduced into the cal- 

 culated values of Cj^, cj), and k because of the presence of eddy-induced 

 forces, as discussed above. Therefore, these data were omitted from 

 the plotted relationships, since errors in cj) or k corresponding to low 

 values of Cj^ would produce considerable scatter, obscuring the valid 

 relationships shown. 



4. Relationships Between (f) and k and Parameters Defining the Wave and 

 Pipeline Conditions . 



To use the above relationships between Cj^, ^, and k to determine 

 the wave-induced lift forces acting on a pipeline, either (J) or k must 

 be known. Thus, a value of one of these parameters must be determined 

 from relationships of (f) or k with the wave conditions and pipeline con- 

 figuration. 



The lift force phenomenon is a fionction of the following variables: 



Ca) Pipeline configuration 



(1) Diameter 



(2) Clearance 



(3) Orientation angle 



(b) Fluid properties 



(1) Density 



(2) Viscosity 



(c) Wave-induced flow conditions 



(1) Maximum horizontal water particle velocity perpendicular 

 to the pipeline axis 



(2) Wave period, which represents the duration of the flow in 

 one direction 



(3) Length of the horizontal excursions of the water particles 

 perpendicular to the pipeline axis [this quantity is di- 

 rectly proportional to the product of the above two param- 

 eters) 



Assuming that only water with a limited range of temperature is being 

 dealt with, the fluid properties will be ignored for the present. The 

 orientation angle of the pipeline can be handled as discussed above, 

 considering only the components of the horizontal fluid motions 



89 



