several of the parameters. Figure 65 shows the relationship for Cm 

 versus clear/u^^^T. 



10. Relationships Involving the Horizontal Coefficient of Drag . 



The horizontal coefficient of drag was plotted against several 

 dimensionless parameters, but no useful relationships were found. This 

 was expected since the horizontal drag forces in this investigation were 

 much smaller than the inertial forces, due to the limited horizontal 

 excursions of the water particles relative to the diameter of the pipe- 

 line. 



11 . Example Problems . 



GIVEN: A design wave with height, H = 10 feet and period, T = 10 seconds 

 acts on a pipeline with a diameter, Dia = 8 feet in a water 

 depth, d = 80 feet. The pipeline is oriented at an angle of 

 30° with respect to the wave crests. Section A of the pipeline 

 is in contact with the bottom; section B spans the bottom at a 

 clearance, clear = 6 inches. 



FIND : For both sections A and B, find 



(a) the values of the lift force parameters (C^, (}>, and k); 



(b) the maximum positive and negative lift forces; 



(c) the positions of these maximum lift forces in the wave 

 cycle; and 



(d) the lift force at 9 = 120° in the wave cycle. 



SOLUTION: 



Lo = f~ = 5.12 (10)2 ^ 5^2 feet 

 d _ 80 _ n icf,9 



Using tables, ^ = 0.1885, so L = f^ = 424 feet 



0.1885 



. , 2TTd , .„, 

 smh — j— = 1.481 



z = distance from bottom to center of pipe 

 sections . 



113 



