Use Equation 4.19:
3/2
3/2
D 90
1/ 6
Q
qB = 1.606 3.306 b
y o S f - 0.627 Dm
Q
n
b
From Equation 4.21:
2/3
19.6 .06 3 / 2
1 -
nb = (.04) 1 +
= 0.038
200 .04
From Equation 4.23:
Qb
1
= 0.84
=
1.5
Q
19.6 0.06
1+
200 0.038
3/2
3/2
2.81/ 6
qB = 1.606 3.306 (0.84)
0.038 (9.8) (.0005) - 0.627 (2.01)
qB = 1.89 ton / day / ft
Q S = 1.89 x 200 = 378 tons / day
4.13.4 Problem 3 Application of the Einstein Method to Calculate
Total Bed-Material Discharge
A test reach, representative of the Big Sand Creek near Greenwood, Mississippi was used
by Einstein (1950) as an illustrative example for applying his bed-load function. His
numerical example is reproduced here. For simplicity, the effects due to bank friction are
neglected. The reader can refer to the original example for the construction of the
representative cross section and the consideration of bank friction. The characteristics of the
channel cross-section follow.
The channel slope was determined to be S = 0.00105. The relations of the cross-sectional
area, hydraulic radius and wetted perimeter versus stage for the representative cross section
are given in Figure 4.19. For this wide and shallow channel, the wetted perimeter is
assumed to equal the surface width. The averaged values of the four bed-material samples
are given in Table 4.7, and the grain size distribution is presented in Figure 4.20. Note that
of these composite samples, 95.8% of the bed material falls between 0.589 and 0.147 mm,
which is divided into four fractions. The sediment transport calculations will be made for
individual size fractions with selected representative grain sizes equal to the geometric mean
grain diameter of each fraction.
The kinematic water viscosity ν is 1.06 x 10-5 ft2/sec, and the specific gravity of the sediment
is 2.65.
4.44
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