Maximum negative lift (per unit length) 

 - FlCI^) = - J Cl P a Umax' (k) 



= - ^ (8.3)(2)(8)(1.84)2 (0.67) 



= - 150.6 pounds per foot 



(c) Since <j) = 45°, the positive lift forces are maximum at 0° + 45° = 

 45° and 180° + 45° = 225° in the wave cycle, and the negative lift 

 forces are maximum at 90° + 45° = 135° and 270° + 45° = 315° in 

 the wave cycle. 



(d) At e = 120° 

 Fl = ^ Ct P a u_^' [cos^ (120° - 45°) - 0.67] 



2 ^L M n ^max 



(8.3) (2) (8) (1.84)2 [cos^ (120° - 45°) - 0.67] 

 135.6 pounds per foot 



Again, it should be stressed that the relationships involving the 

 lift force parameters, Cl, c^), and k, were determined from model studies 

 conducted at much lower values of the Keulegan-Carpenter parameter and 

 Reynolds number than those encountered in full-scale situations in the 

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

 to prototype designs. 



Further studies using a larger scale facility are necessary to 

 evaluate the importance of scale effects in these relationships, to 

 determine their limitations, and possibly to extend or modify them so 

 they are valid for any scale. 



IV. CONCLUSIONS 



1. The traditional steady- flow lift force model, expressed as 



Ft = 1/2 Cl p A u^, is not a suitable model for the description of wave- 

 induced lift forces. This model assumes that the lift force acts in 

 one direction only (upward or downward) throughout the entire wave 

 cycle. 



2. For pipelines located at a small clearance above the bottom, 

 a viscous choking effect limits the maximum velocities through the 

 constriction formed by the bottom clearance. Correspondingly, the 

 pressure drop on the bottom side of the pipe section is also limited. 



In contrast, the flow velocities and corresponding pressure drop 

 over the top side of the pipeline are not limited. As the choking 

 effect develops and the flow becomes restricted through the bottom 



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