in which the "particle Reynolds number" R^ is given by 



R - iiili. 



"^d " ^r ' C553 



and the "critical Reynolds number" R is given by 



OL. 



377 ., .2 



Q 



R^ = |i Cl-n) n ^ . 0.17 ^ , C56) 



as discussed in Appendix A. With a and 3 chosen to correspond to the 

 mean values of the ranges indicated in equation (53) , the value of the 

 critical Reynolds number is expected to be of the order 70. Thus, for 

 small values of Rj, i.e., R(i 1_ IOj the flow and the resistance are 

 purely laminar;for large values of R^^, as will be the case for most 

 prototype conditions, i.e., R, >_ 1,000, the flow will be turbulent in 

 nature. 



Rather than using equation (50) directly with the empirical 

 formulas suggested by equations (51) and (52) it is illustrative to 

 take the relationship for f as given by equation (54) and treating R^, 

 depending upon the solution through its dependence on |u|, as a known 

 quantity. Introducing |u| from equation (37) leads to an implicit 

 expression for f. 



^-^TI/^*(l^fe^^^^-lJ (57, 



do 



which may also be interpreted as an implicit formula for the factor 

 X = k Jif/ (2n) . This formula clearly reveals the possible scale effects 

 associated with hydraulic modeling of porous structures to be an increase 

 in the value of f, since R^ would be lower in the model than in the 

 prototype if a Froude model criterion is used. 



With the empirical formulas for the hydraulic properties of a 

 porous medium given, a completely explicit procedure for determining 

 the transmission and reflection characteristics of a rectangular 

 crib-style breakwater has been developed. 



30 



