Sediment Transport Concepts - Sediment Transport in Irrigation Canals: A New Approach - page 133

The sediment transport per unit width can be approximated by the power
law, where the coefficients M and N are supposed to be locally constant
(de Vries, 1987):

MV N

q s = (5.92)

Differentiation of the sediment transport equation with respect to V
results in:

d q s
d V =

MNV N − 1 (5.93)

This gives:

d q s
d V

V
q s

=

N (5.94)

where:
q s = sediment transport capacity per unit width (m 3 /s · m)

V = mean velocity (m/s)

M , N coefficient/exponent depending on the water flow and

sediment characteristics.
For some predictors the value of N can be directly derived from the
equation.
For Engelund and Hansen (1967) N follows from:

=

0 . 05 V 5

q s = (5.95)

( s − 1) 2 g 0 . 5 d 50 C 3

which gives N 5.

According to Klaassen (1995), the equation for N can be used for
more complex sediment predictors such as Ackers and White (1973),
van Rijn (1984a, 1984b) and Brownlie (1981b).
The Ackers and White predictor given by (see Annex A) is:

=

G gr Vd 35 V
u ∗

n

q s = (5.96)

Differentiating and comparing the results with the equation for N gives
the following relation for N (de Vries, 1985):

m F gr
( F gr −

N = 1 + (5.97)

A )