There appears to be a better correlation between k and the parameters 

 involving Cr (Cr , CjCl-k), and CL(k)l than between the analogous relation- 

 ships using (j), so the former relationships should be used. Also, in com- 

 paring the plots of CL(l-k] versus k (Fig. 42) and C^Ck) versus k (Fig. 44), 

 the scatter appears minimal in the plot with C^Ck) for the interval of k 

 between and 1/2. For the interval of k between 1/2 and 1, the scatter 

 is much less on tlie plot between CL(l-k) and k. Therefore, it is suggested 

 that when determining a value of C^ for a given value of k, the plot of 

 CL(k) versus k be used for values of k less than 1/2 (except for k close 

 to 0), and the plot of CL(l-k) versus k be used for values of k greater 

 than 1/2 (except for k close to 1) (see Fig. 46). For k close to 0, it 

 can be assumed that Cj^ = 4.5. tiowever, for k ~ 1, the value of Cl can 

 vary from about 4.5 to zero, since as the clearance is increased from the 

 point where (}) = 90° and k = 1, both cf) and k remain at their maximum values 

 of 90° and 1, respectively, while the lift effect diminishes to zero. 



Vi/lien the above relationships between (p, k, C^, CL(l-k), and Cj^(k) are 

 plotted for only the 4-inch-diameter pipe model, the scatter is reduced. 

 Although the data for all three diameters completely overlap (showing the 

 same relationships hold for all diameters), the amount of scatter increases 

 with the smaller diameter models. This is because the data extend to 

 liigher relative clearances (clearance-diameter) for the smaller diameter 

 models than the corresponding data for the 4-inch-diameter model, since all 

 models were tested at the same actual clearances. 



Since the lift effect diminishes at high values of the relative 

 clearance, the lift forces on the smaller diameter models at the largest 

 bottom clearances were very small in many cases. This is especially true 

 for the smaller waves and higher orientation angles, where the horizontal 

 velocities perpendicular to the pipeline were very low. In such cases, 

 the lift forces were often insignificant, so the values of C^, <t> , and k 

 calculated from the least squares analysis were not as accurate. 



In addition, as the lift forces decrease with high relative clearances, 

 eddy-induced forces may approach the magnitude of the lift forces, thus 

 introducing further error in the calculated values of C^, (j), and k. 



The lift forces were generally significant for all clearances tested 

 using the 4-inch-diameter pipe section, and since the measured forces were 

 larger, the experimental error involved in measuring them was less than 

 for the smaller diameter models. 



Because of this, the data taken for very large bottom clearances were 

 not included in the plotted relationships. For higher clearances, values 

 of k and c}) equal to 1 and 90°, respectively, would be expected, since the 

 choking phenomenon would not occur throughout the vave cycle. However, 

 as the clearance is increased, the lift effect diminishes, resulting in 

 decreasing values of the coefficient of lift. 



87 



