66 einstein-johnson. SEDIMENT TRANSPORT [Ch. 3 



In an existing channel the sediment function may be determined ex- 

 perimentally. Instruments have been devised to measure that part 

 of the bed-material load which moves along the bed as bed load or 

 surface creep (Iowa University, 1940b) ; normal suspended-load sam- 

 pling instruments and procedures (Iowa University, 1940a, 1948) may 

 be used to measure that part of the bed material which moves sus- 

 pended in the upper layers of the stream cross section. The total rate 

 of these relatively large particles has been found to be actually a 

 well-defined function of the discharge (Einstein, 1947), and this rela- 

 tionship may well be used to predict future or past bed-material 

 motion in this same channel if the flow rates are known. 



Whenever a reach of channel which has a sediment function, and 

 which is usually called an alluvial reach, shows a low or zero rate 

 of deposition or scour, the sediment function may be interpreted over 

 a given length of time to determine the total or average bed-sediment 

 supply of the watershed above. Basically, the sediment supply is 

 naturally the primary factor determining the behavior of the stream, 

 and in the course of centuries the stream channel has been built up 

 by sediment deposits until it has finally become able to move the bed 

 sediment at the rate of supply. The rate of transportation of load, 

 therefore, may be used as an indicator of the sediment supply. 



If the different types of bed sediment move in a given channel at 

 rates which are a well-defined function of the discharge, it must be 

 possible to determine this relationship analytically. Attempts in this 

 direction date back to the last century, when the first bed-load equa- 

 tions were developed by DuBoys (1879). A bed-load equation, in 

 contrast to what is termed a bed-load function herein, is a local rela- 

 tionship between the rate of sediment motion per unit of width and 

 unit of time and the local bed and flow conditions. In such instances 

 the bed usually is described by an average or representative grain 

 size. The flow in any vertical section, both the average and the ve- 

 locity distribution, is defined basically by the local shear stress and 

 by the total water depth. In the usual cases of bed-material load, 

 where most of the load moves near the bottom, the flow velocities may 

 be derived from the local shear stress alone. 



All the early bed-load formulas, and most of those that are used 

 today, describe the flow by its shear stress only. In some of these 

 formulas one or two coefficients have been introduced which may 

 change in value somewhat for different depths and sediment sizes 

 (Vanoni, 1947). Recent attempts to eliminate the necessity of using 

 these variable coefficients have led to an interpretation whereby the 

 bed-load equation is used only to express the motion of bed material 



