The slight amount of scatter in these plots in the vicinity of k = 

 1 and (}) = 90° is due to the error in calculated values of (p and k for 

 the largest bottom clearances where the lift effect was small (as dis- 

 cussed above) . 



Larger values of' the dimensionless combination, (clear/iL T) 

 (Dia/u^ T) , than given in the plots would correspond to larger bottom 

 clearances and pipe diameters relative to the maximum velocities, wave 

 periods, and water particle excursions. For these conditions, the 

 values of k and <p would remain at 1 and 90°, respectively, while the 

 lift effect would eventually diminish to zero with increasing values of 

 this parameter. These trends are evident in the data taken at the 

 largest bottom clearances (1 and 2 inches), although these data were 

 not included in the above plots. 



Similarly, lower values of the dimensionless parameter than given 

 in the plots would correspond to higher maximum velocities, wave peri- 

 ods, and water particle excursions relative to the smallest bottom 

 clearances and pipe diameters. So for lower values of this parameter, 

 both k and ({) should remain at their defined minimum values of and 0°, 

 respectively, corresponding to lift forces acting in the upward direc- 

 tion only, with very little or no flow possible under the pipe section. 



Although (}) was defined as varying from 0° to 90° only, negative 

 values of i^ are exhibited in the data for the lowest values of the 

 dimensionless parameters plotted. However, since most of these data 

 points correspond to the smallest diameter pipeline model tested (2 

 inches), this could be partly due to experimental error, since the measured 

 forces were smallest for the smallest model. Also, part of this dis- 

 crepancy could be due to the difficulty of accurately defining the peak 

 of the wave crest in the experimental wave records. This point was 

 arbitrarily defined as the midpoint of the zero crossings on either 

 side of the wave crest in the digitized data records. However, in some 

 cases, the waves were not perfectly symmetrical, so the maximum eleva- 

 tion of the water surface did not coincide exactly with the midpoint of 

 the zero crossings. This was especially true of the largest waves with 

 the longest periods, which in the plotted relationships would correspond 

 to the minimum values of the dimensionless parameters (at the lowest 

 bottom clearance tested). Thus, the actual kinematics under these waves 

 would be slightly out of phase with the calculated kinematics, resulting 

 in an error in the calculated value of cj). However, this source of error 

 should be the same for the large-diameter models as for the smallest models. 



5 . Relationships Between ({) (clear/Dia) and k (clear/Dia) and Parameters 

 Defining the Wave and Pipeline Conditions . 



Many other useful relationships were found by multiplying cj) and k 

 by the relative clearance, (clear/Dia), and plotting these dimensionless 

 products versus various dimensionless parameters defining the wave and 

 pipe conditions. Figures 59 to 62 are examples, although several other 

 parameters also showed good correlation with <p (clear/Dia) and k (clear/ 

 Dia). 



104 



