cycle, with maximum downward forces occurring under the crests and 

 troughs of the passing waves. These two cases represent the extreme 

 conditions bounding the lift force phenomena. At any intermediate 

 clearance between these limiting cases, both positive and negative 

 lift forces will occur at different parts of the wave cycle, and the 

 positions of the maximum upward and downward lift forces will not 

 coincide with the positions of maximum horizontal velocities in the 

 wave cycle. 



In order to use this lift force model, values of the parameters, 

 Cl, (j), and k, must be determined for the given set of wave and pipe- 

 line conditions. A model investigation was carried out to determine 

 relationships between these parameters and various dimensionless param- 

 eters defining the wave and pipeline conditions. 



6. A direct relationship was found between the lift force 

 parameters, cf) and k. Relationships were also found between the 

 coefficient of lift, Cj^, and both <^ and k. In addition, C^ can be 

 partitioned into the positive effective coefficient of lift, C^ (1-k), 

 and the effective negative coefficient of lift, Cj^(k) . Both of these 

 parameters are also related to both (j) and k. The correlation is better 

 with k than (}) for the relationships involving C^, CL(l-k), and CL(k). 



All of these relationships were the same for all pipe diameters, 

 bottom clearances, and wave conditions tested. 



7. The average value of C^ at k = and cj) = 0° (which corresponds 

 to a pipeline in contact with the bottom with no clearance) is 4.5. 

 This is the same as the potential flow solution for the lift force on 

 a circular cylinder against a plane wall subject to a steady, inviscid 

 flow parallel to the wall. 



8. Maximum values of Cl occur at k = 1/2 and (}) = 30°, where 

 Cl = 9. In the interval from k = to 1/2 and (() = 0° to 30°, the 

 effective positive coefficient of lift CLCl-k) remains at approximately 

 4.5, while the effective negative coefficient of lift Cj (k) increases 

 from to 4.5. In the interval from k = 1/2 to 1 and (J) = 30° to 90°, 

 CL(I-k) decreases to 0, while CL(k) increases to reach a maximum of 

 about 6 or 7 at k = 0.75 and cj) = 45°, and then decreases to a maximum of 

 4.5 at k = I and cj) = 90°. 



9. Using the above relationships between Cl, <i>, and k, if either 

 ([) or k is known, the remaining two parameters can be determined. 

 Therefore, an attempt was made to find relationships between (J) and k 

 and various dimensionless parameters defining the wave and pipeline 

 conditions . 



The best correlation was found in the relationships between (p and 

 k and the parameter clear/u^^^T for constant values of the relative 

 clearance, clear/Dia. However, comparison of the data corresponding to 

 the different pipe diameters indicates a slight scale effect is present. 



119 



