perpendicular to the pipeline axis. Since the length of the horizontal 

 water particle excursions is directly proportional to the product of 

 the wave period and the maximum horizontal water particle velocity, only 

 four independent variables are left: diameter, clearance, horizontal 

 water particle velocity, and wave period. Thus, any single parameter 

 used to relate Cj^, (j), or k to the wave and pipeline conditions must 

 include these four variables. This constraint is necessary if the rela- 

 tionship is expected to be valid for general application under any set 

 of wave and pipeline conditions. 



The four variables can be arranged into several dimensionless param- 

 eters. The important parameters should include the following: 



(1) relative clearance, clear/Dia 



where clear = bottom clearance 

 Dia = pipe diameter 



(2) Keulegan-Carpenter parameter, u T/Dia 



^ ^ max 



where T = wave period 



u = component of maximum horizontal water particle 

 velocity perpendicular to the pipeline axis 



(3) clear/u T 



max 



NOTE. --Not all of these parameters are necessary to describe the system 

 since some are redundant, but some may be more useful than others. 



Since viscosity is an important variable involved in the choking 

 phenomenon, the Reynolds number, Ujj^^^ Dia/v, and a Reynolds number for 

 the clearance, u^^^^^ clear/v, are also important parameters (where V = 

 kinematic viscosity) . 



The dimensionless parameters, clear/Ujjj^-j^^ T, u^^^ T/Dia, u^g^-^ clear/v, 

 and u^ax Dia/v, were plotted versus the lift force parameters, Ct, cj), k, 

 Cl(I-k), and Cj^(k), for constant values of the relative clearance, 

 clear/Dia. The correlation was not good with the parameters involving 

 the coefficient of lift (C^, C^Cl-k), and CL(k)). However, good cor- 

 relation was found between several of the dimensionless parameters and 

 the quantities c]) and k. 



The parameter, clear/u^ T, exhibited the best correlation with 

 both 9 and k for each relative clearance, although there was some varia- 

 tion in these relationships for the data corresponding to the different 

 pipe diameters (see Figs. 47 to 52). Although the differences are not 

 large, the data do indicate the presence. of a scale effect in these 

 relationships . 



90 



