(b) the part defining the magnitude of the negative lift, ClCR) . The 

 quantities, CL(l-k) and CL(k) , can be referred to as the effective posi- 

 tive coefficient of lift and the effective negative coefficient of lift, 

 respectively. Since Cl = 9.0 for k = 1/2, both CL(l-k) and C^Ck) are 

 equal to 4.5 at this point. This means that the lift forces can reach 

 the same maximum magnitude in both the upward and downward directions as 

 are attained in the upward direction only for the same pipe in contact 

 with the bottom (where C^Cl-k) = 4.5, but C^Ck) = 0). 



The effective positive and negative coefficients of lift are plotted 

 versus both (j) and k in Figures 42 to 45. Again, the correlations are 

 much better with k than with (j). The average value of C^Cl-k) drops only 

 slightly between k = and k = 1/2, but for values of k greater than 1/2, 

 the effective positive coefficient of lift drops rapidly to a value of 

 when k = 1 . 



The average value of CL(k) increases with k until it reaches a maximum 

 value of about 6.0 when k = 0.75, and then decreases to about 4.S when k = 1. 

 Individual maximum values of CL(k) attain values slightly greater than 7.0 

 in the vicinity of k = 0.75. But even the average maximum value of 6.0 for 

 the effective negative coefficient of lift indicates that the downward 

 lift forces may attain maximum values 33 percent greater than the maximum 

 possible lift forces acting in the upward direction. Maximum values of 

 Cj (k) corresponds to a value of (f) of about 45°, which is half way through 

 the phase shift cycle. 



The potential flow theory gives a value of C^ = 4.495 for zero bottom 

 clearance, with a discontinuous jump to very high negative values of Cl 

 for a very small clearance (Yamamoto, Nath, and Slotta, 1973) . In the 

 potential flow solution, the value of Cj depends only on the relative 

 clearance; i.e., the ratio clearance-diameter. The coefficient of lift is 

 negative whenever the pipe is not in contact with the bottom, and its 

 magnitude decreases as the relative clearance is increased. 



Although the potential flow solution appears to work reasonably well 

 when a pipeline is touching the bottom, this approach does not work when 

 there is a small clearance. This is because viscous effects are very 

 important for the flow through the narrow bottom clearance constriction. 

 The choking phenomenon limits the maximum flow velocities and corresponding 

 pressure drops on the bottom side of the pipeline, thereby limiting the 

 maximum possible downward lift forces. 



Tlie results of this investigation indicate that the effective negative 

 coefficient of lift, Cf^(k) , can attain a maximum value of only 7.0. This is 

 much less than the values of C^ suggested for small relative clearances by 

 potential flow theory. The coefficient of lift is obviously not a simple 

 function of relative clearance, since for a given clearance and diameter, 

 both the lift effect and the coefficient of lift will vary with the wave- 

 induced flow conditions. For the smallest relative clearances, the positive 

 lift forces were larger than the negative lift forces, especially where 

 the horizontal water particle velocities and excursions were high. 



