Methods to Predict the Friction Factor - Sediment Transport in Irrigation Canals: A New Approach - page 242

Another bed form in the lower regime (Fr < 0.8) is the dunes. The
shape of the dunes is similar to the shape of ripples, but their length and
height are greater than those of ripples are. Relationships for dune length
and dune height have been based on flume and field data and are given by
van Rijn (1994):

0 . 11 d 50
h

0 . 3

d
h =

e − 0 . 5 T )(25

(1 − − T ) (B.12)

λ d = 7 . 3 h (B.13)

where:
T = excess bed-shear stress parameter

λ d = dune length (m)

d = dune height (m)

d 50 = median diameter (m)

water depth (m)
The greatest influence of k s (equivalent height related to the grain) on
the total value of the equivalent roughness height k s will occur for those
bed forms that have the smallest equivalent height related to the bed form.
The smallest height occurs for ripples and the influence of the height k s
on the total equivalent roughness height k s for the specific conditions of
irrigation canals is approximately 1.5-2%.

h =

k s
k s +

4 . 5 d 50
4 . 5 d 50 +

k s =

20 γ s r r

λ r ≈

2% - ripples occurrence (B.14)

For other bed forms the influence of the grains on the total roughness
will be smaller than for ripples (smaller than 2%). For that reason and
because the grain roughness is constant during changes of the bed form
size, the grain roughness can be neglected. Hence, the equivalent height
related to the bed form is recommended and for ripples the total equivalent
roughness can be computed as:

k s = k s = 20 ∗ 1 ∗ 0 . 1 ∗ 100 ∗ d 50 = 200 d 50 (B.15)

Minimum values of the parameter u ∗ k s / v for ripples in irrigation
canals follow from:
• k s = 200 d 50 ;

• critical Shield shear velocity u ∗ cr .

For those canals the values of the parameter u ∗ k s / v are shown in
Table B.3. Once the sediment on the bottom of an irrigation canal comes
into motion the flow will be considered as hydraulically rough. Figure B.1
shows the types of flow regime in irrigation canals.

u ∗ =