refined by Abou-Seida (1965) and then by Madsen and Grant (1976) to develop an 

 empirical relationship for prediction of bed-load transport: 



r w = 12.5 U„) 3 (22) 



where Y M and X^ are dimensionless variables defined by 



v - 4b 



w d„ 



(23) 



and 



Xh -_ 1/2 f r £ f™ (24) 



For the above , 



q b = bed-load transport rate per unit width, ft 3 /sec/ft 



p = fluid density, lb m /ft 3 



d g = grain diameter, usually expressed at mean or median, ft 



u crit = orbital near bottom critical horizontal velocity, ft/sec 



to = sediment fall velocity, ft/sec 



sg = specific gravity of sediment 



f w = friction factor for wave motion 



Swart (1974) expressed the friction factor for wave motion under turbulent 

 conditions as 



0.194 



(25) 



r" w = exp|5.213l— £j -5.977 



where a is the wave amplitude and d e is the equivalent effective bottom 

 roughness , given by 



d e = d g fox flat, well- smoothed beds (26) 



d g = 2.5 d g for disturbed, unsmoothed beds (27) 



d s = 25 (n T ) 2 /l r for rippled beds (28) 



wnere 



d g = median grain diameter, ft 

 n r = ripple height, ft 

 l r = ripple length, ft 



18 



