Sediment Transport Concepts - Sediment Transport in Irrigation Canals: A New Approach - page 151

In which the subscripts i and j represent:

=

i i* x

=

j j* t

where:
Q s =

sediment discharge (m 3 /s)

p = porosity

B = bottom width (m)

x = distance step (m)

z = bottom level above datum (m)

t = time step (m)

α = parameter used for stability and accuracy of the numerical scheme.

The stability of the scheme is given by (Vreugdenhil, 1989):

σ 2 ≤ α ≤ 1 (5.141)

Accuracy of this scheme is increased if (Vreugdenhil, 1989):

σ 2 α ≈ + 0 . 01 (5.142)

In which σ is the Courant number:

NV Q s /Q
1

t
x

σ = (5.143)

Fr 2

−

where:
N = exponent of the velocity in the sediment transport equations

discharge (m 3 /s)

Q =

sediment discharge (m 3 /s) Q s =

V = mean velocity (m/s)

t = time interval (s)

x = distance (m)

=

Fr Froude number

Figure 5.33 shows a schematization of the deposition or entrain-
ment computation at the bottom of the canal and Figure 5.34 shows the
calculation of the changes in the bottom level according to the modified
Lax method.

5.4.2 Sediment movement

Under the conditions that the incoming sediment load into an irrigation
canal with uniform flow is equal to the equilibrium transport capacity of
the canal and there is no entrainment of any sediment from the bottom,