sediment transport per unit width of channel: 



q b = (lll,000/d ff 3/4 ) S 1/2 (72/1. 5) 3 C/ 3 (15) 



For the above , 



q b = bed- load sediment transport per unit width of channel, ft 3 /s/ft 



S = channel slope 



n = Manning's roughness coefficient 



U = average water velocity, ft/sec 

 Rouse (1938) also used the duBoys method to obtain another expression for bed- 

 load transport, using only easily available quantities: 



10 Y . Y 2 g 1/2 (A u 3) ^ .... 



(Y fl -Y) 2 d g 



where h u is the depth of uniform flow. This equation also has the shortcoming 

 that it is based primarily on laboratory flume tests with no field validation. 



12. Schoklitsch analysis . The Schoklitsch method for determining bed- 

 load transport uses a hydraulic discharge relation to evaluate the amount of 

 sediment that may be moving within a given channel section. Laboratory 

 observations to determine the discharge conditions for incipient sediment 

 motion were related to actual prototype bed- load measurements and the 

 following relationship for q cr , critical discharge (volume of fluid flow 

 required for initiation of sediment transport) was obtained: 



q cr = 2.717 ( Ys /Y -D 5/3 dj< 2 S>"> (17) 



This value for critical discharge then is related to the bed- load discharge, 

 q b , in ft 3 /sec per ft, and hydraulic discharge q, in ft 3 /sec per ft, by 



q b = 2500 5 3/2 (q-q„) (18) 



when d is in feet. Equation 17, and other slight variations of it, has been 

 used extensively in Europe. 



13. Einstein analysis . Einstein's (1950) analysis utilizes statistical 

 methods to account for the instantaneous fluctuations in velocity that occur 

 during turbulent flow. Einstein's work resulted in a formula that 

 incorporated statistical reasoning to relate the rate of bed-load transport to 

 properties of the grain and flow. His relationships were based on the premise 

 that the probability that any single particle, moving at a given time, is 

 related to its fall velocity, size, specific weight, and hydraulics of the 

 flow. This was carried one step further to assess probability of scour or 

 erosion. Einstein felt that the likelihood of erosion is related to the 

 amount of time that instantaneous lift exceeds the weight of the particles 

 being acted upon in the channel section. Einstein's equations for bed-load 



16 



