This relationship shows that for any pipe diameter, orientation angle, 

 or bottom clearance, the maximum lift force increases with the Reynolds 

 number in a regular manner, at least over the range of the data in this 

 investigation. The maximum lift force may occur in either the upward or 

 downward direction, depending on the magnitude of the bottom clearance 

 relative to the wave conditions and pipe size. This relationship does 

 not hold for the maximum upward lift or maximum downward lift alone, but 

 only for the largest of these two forces in any given situation. 



8. Relationships Involving the Vertical Coefficients of Mass and Drag 

 and the Vertical Inertial and Drag Forces . 



Both the vertical coefficient of mass and the vertical inertial 

 forces were plotted against several dimensionless parameters defining 

 the wave and pipeline conditions, but no useful relationships were 

 found. This is not surprising when considering that the vertical iner- 

 tial forces are relatively small, and thus subject to error from the 

 transverse eddy-induced forces which were not accounted for in the 

 least squares analysis. 



No attempt was made to plot relationships involving the vertical drag 

 forces or drag coefficients, since these forces were negligible. 



9 . Relationships Between the Horizontal Coefficient of Mass and 

 Parameters Describing the Wave and Pipeline Conditions . 



A limited number of horizontal force data were taken using the 4-inch- 

 diameter two-dimensional model. Values of C^^ and Cp were calculated 

 from the least squares analysis, and an attempt was made to relate these 

 coefficients to various dimensionless parameters describing the wave and 

 pipeline conditions. 



Figure 64 shows the horizontal coefficient of mass plotted versus the 

 relative clearance, clear/Dia, together with the potential flow solution 

 for a circular cylinder in the vicinity of a plane wall subject to a 

 uniform flow with constant acceleration (Grace, 1974) . The data follow 

 the potential flow solution reasonably well, although for a given rela- 

 tive clearance, there appears to be some variation in the value of Cp^j 

 with varying wave conditions. Also, the wave force data give slightly 

 higher values of the coefficient of mass for the highest bottom clearances 

 tested. Although the experimental data are limited, they indicate that 

 the potential flow solution may be very useful in determining a value for 

 the horizontal coefficient of mass, at least for wave conditions where the 

 inertial forces predominate over the drag forces. 



However, since there was some variation in the values of Cw for 

 different wave conditions for the same relative clearance, an attempt 

 was made to determine relationships between the horizontal coefficient 

 of mass and the various dimensionless parameters defining the wave and 

 pipeline conditions. Reasonably good correlations were found between 



III 



