Engelund (1953) reviewed a number of empirical formulas for the 

 hydraulic properties of porous media consisting of sand. He recommended 

 the following empirical relationships: 



Cl-n)^ 



^ (A-87) 



d 



and 



^i , (A-88) 



in which d is the grain size of the porous material ^ v is the kinematic 

 viscosity of the pore fluid, and Kq and Bq si's constants whose values 

 have been found to vary within the range, 



780 < a < 1,500 or greater 

 o ' ^ 



1.8<6 < 3.6 or greater . (A-89) 



The coefficient ct, which depends on the fluid viscosity, is expressing 

 the Darcy-type resistance associated with laminar flow of the pore fluid. 

 The flow resistance associated with the coefficient B is the velocity 

 square-type normally associated with turbulent flow. From equation CA-86) 

 it is seen that we may take 



f = ■=— - 6U (1 + -^ -^TT-) , (A-90) 



3tt CO o 8 SU 







in anticipation of the domination of turbulent resistance in prototype 

 flow of water through breakwaters. Written in this form the degree to 

 which laminar resistance affects the results is given by 



ct 

 3tt a 377 ^, ^ 2 , V . ,. „,. 



-8 BIT = -^ f^-"^ " - ^dir^ ' f^-91^ 







where equations (A-87) and (A-88) have been introduced. This expression 

 may be written as: 



3-n- g _ _ 

 8 BU " R 



(A-92) 



121 



