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

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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