Methods to Predict the Friction Factor - Sediment Transport in Irrigation Canals: A New Approach - page 243

Table B.3. u ∗ k s / v parameter for ripples.

D 50 (mm) 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

u ∗ (cr) k s / v 499 899 1450 2037 2650 3286 3782 4590 5445 6344

10000

1000

Rough regime

100

Transition regime

10

Smooth regime

1

Plain bed
Bed form

0.1 0.0

0.10 0.20 0.30 0.40 0.50

Figure B.1. Hydraulic regimes
in irrigation canals.

Mean diameter d 50 (mm)

For regimes with smooth and transitional flows, the de Chézy coef-
ficient is a function of the flow condition only and follows from the
equations given by van Rijn (1993):

18 log 12 h
3 . 3 u ∗

C = Smooth flow regime (B.16)

18 log

12 h
k s +

C = Transition flow regime (B.17)

3 . 3 u ∗

18 log 12 h
k s

C = Rough flow regime (B.18)

where:
C de Chézy coefficient (m 1 / 2 /s)

=

h = water depth (m)

kinematic viscosity (m 2 /s)

ν =

u ∗ = shear velocity (m/s)

k s =

total equivalent roughness (m)
A good approximation of the de Chézy coefficient for canals with
ripples is obtained by replacing the total equivalent height by the height
related to the bed form k s (equation B.15) and can be represented by:

h
200 d 50

C = 18 log (B.19)