(J) and k were also correlated with the Keulegan-Carpenter parameter, 

 %iax T/Dia. However, these relationships were not the same when the 

 data corresponding to a given relative clearance were compared for dif- 

 ferent pipe diameters. The relationships were the same for a given 

 absolute clearance, rather than a relative clearance (clear/Dia) . These 

 relationships are shown in Figures 53 and 54 for the combined data from 

 all three pipe diameters. 



The parameter, Uj^a.x <^-l®^^/^j demonstrated correlation with both cfi 

 and k, but these relationships also exhibited a scale effect, such that 

 the relationships for a given relative clearance were not the same when 

 comparing the data for different pipe diameters. Figures 55 and 56 are 

 examples of these relationships for the 4-inch-diameter pipeline. 



Correlation between the Reynolds number, Uj^^x Dia/v, and the param- 

 eters, (j) and k, was not good, especially when comparing the data for 

 the different pipe diameters. 



Since none of the above dimensionless parameters alone could be 

 used to determine a value of cj) or k for any given pipe diameter, clear- 

 ance, and wave condition due to the presence of scale effects, several- 

 of the parameters were combined in various ways to form different dimen- 

 sionless parameters containing all four of the important variables 

 [clear, Dia, u^g^^, and T) . An attempt was made to find a single param- 

 eter containing all of the important variables that was well correlated 

 with (}) or k for all wave conditions, pipeline sizes, and configurations. 



Several relationships were found that exhibited good correlation for 

 all the wave and pipeline conditions tested. However, since this is a 

 model study and, therefore, limited to lower values of the Keulegan- 

 Carpenter parameter and Reynolds number than prototype design situations 

 in the ocean, caution should be used in extrapolating these results. 



The dimensionless combination, (clear/Uj^^^^ T) (Dia/Uj^j^^T) , demon- 

 strated the best correlation with both cj) and k for all conditions 

 tested. These relationships are given in Figures 57 and 58. Since both 

 k and <^ define the point at which choking occurs in the wave cycle, it 

 appears that the choking phenomenon is directly dependent on the water 

 particle excursions relative to both the pipe diameter, (l^ia/^jjioy T) , 

 and the bottom clearance, (clear/ Uj^^^^ T) . 



Although the parameter, (clear/u^ T) , is equivalent to the ratio 

 of the bottom clearance to the horizontal excursion of the water parti- 

 cles (differing only by the constant 1/tt) , the quantity (u^^x ^^ should 

 not be thought of only as defining the length of the water particle 

 excursions. Both variables, u^jj^-j^. and T, are independently important in 

 defining the choking phenomenon. The larger u^^ax' ^^® sooner the chok- 

 ing conditions will develop in the wave cycle for a given clearance and 

 pipe diameter. Similarly, since the wave period, T, defines the duration 

 of the horizontal flow in one direction, the larger the wave period, the 

 sooner choking will develop relative to the temporal length of the wave 

 cycle. 



97 



