reduced, the difference between Z and Z' decreased and finally when 
Z assumed values less than unity, which is normally the case, the dif- 
ference between Z and Z'! was small enough such that use of equation 
(29) allows accurate results. The relationship between Z andi Ze ass 
shown in Figure 28 (Einstein and Chien, 1954). 
2. Similarities Between Oscillating and Unidirectional Flow. 
The similarities between oscillating flow and unidirectional flow 
with low shear velocities are pronounced. It was found that the concen- 
tration distribution in oscillating flow (from equation 9) could be ex- 
pressed by: 
€/€, = exp(MY) , (31) 
where M was found in Section II to be (from equation 13): 
M= -V,/E , (32) 
E is the sediment exchange coefficient. The coefficient, M, which 
defines the rate at which the concentration decays with elevation, behaves 
in a manner similar to Z of the unidirectional flow theory. In oscillat- 
ing flow, as in unidirectional flow, the value of M fitting the experi- 
mental results was different than the value which would be predicted from 
equation (32), assuming E independent of V,. Figure 15 and Table 3 
show that for the four concentration distribution curves obtained when 
V, was increased from 0.035 to 0.0626 foot per second, the absolute value 
of M increased, as an average, by the factor 1.19. When V, was in- 
creased from 0.035 to 0.0498 foot per second, the absolute value of M 
increased, as an average, by 1.13. If the exchange coefficient, E, of 
equation (32) were a function of the flow hydraulics only and independent 
of the sediment-settling velocity, then the average increase in the abso- 
lute value of M would have been 0.0626/0.035 (= 1.8) and 0.0498/0.035 
(= 1.42), respectively. Therefore, it can be concluded that the sediment 
exchange coefficient, E, is a function of both Ve) sand) Up; vandathac 
M, for a constant flow velocity, is not directly proportional to Vg. 
This conclusion agrees with Einstein and Chien (1954) that in unidirec- 
tional flow for high values of settling velocity relative to the flow 
shear velocity the sediment exchange coefficient cannot be accurately 
approximated by the momentum exchange coefficient. 
The difference between the sediment and momentum exchange coefficients 
depends on the relative magnitudes of the sediment-settling velocity and 
the turbulence intensity. If the sediment-settling velocity is small 
compared to the turbulence intensity, the two coefficients are approxi- 
mately equal; when Vz = 0, the two coefficients are identical. As V, 
becomes relatively larger, the difference between the two coefficients 
increases. In unidirectional flow the turbulence intensity is usually 
very large compared to V, and the theory is accurate under most situa- 
tions. Unfortunately, this is usually not the case in oscillating flow. 
66 
