3. Comparison with Experimental Results . 



a. Empirical Formulas for Flow Resistance of a Porous Medium. The 

 procedure developed in Section 11.2 for the prediction of transmission 

 and reflection coefficients of porous breakwaters involves the use of 

 empirical relationships for the hydraulic properties of a porous medium. 

 Thus, only if these empirical relationships may be applied with confid- 

 ence can the procedure itself be regarded as accurate. 



For steady flow the Dupuit-Forchheimer resistance law reads 



- It = 7- (<^ + BU)U , (58) 



in which H is the piezometric head. 



In permeameter tests it is customary to measure the head loss, AH, 

 over a distance, Lp^, for various values of the discharge velocity U. 

 Rearranging equation (58) in a manner similar to that introduced in 

 Section II. 2 this may be written 



H n d 



in which R^ and R^, are given by equations (55) and (56), respectively 

 and 6 has been introduced according to equation (52). Realizing that 

 the porosity, n, of the porous material tested may vary it is convenient 

 to introduce a reference porosity, n , and to write equation (58) in 

 the form 



. J ... 1-n , 1-n „ R 

 „* gd AH , r. ,n .3 . r ,, 8 c. ,^„^ 



^f = ^2 L- f-r^^ ^JT^ = ^0 — 3 ^^ " 37 rT^ f^O^ 



U H r n d 



r 



* 

 From experiments the value of C£ may be evaluated and plotted 

 against Rj = Ud/v. The results obtained by Sollitt and Cross (1972, 

 Tables F-1 through F-6) are presented in this manner in Figure 4 with 

 the grain diameter, d, being chosen as the median diameter of the 

 gravel tested and taking n^ = 0.46 as the reference porosity. The data 

 exhibit a remarkably low degree of scatter and are well represented by 

 the relationship suggested by equation (59) with Pq = 2.7 and R^, = 170. 

 For comparison, the curve corresponding to g^ = 2.7 and R^, = 70, which 

 correspond to the mean values of the ranges suggested by Engelund's 

 (1953) analysis, equation (53) is shown. Although inferior to the curve 

 corresponding to R,, = 170, this curve provides a fair representation of 

 the data. 



