Methods to Predict the Friction Factor - Sediment Transport in Irrigation Canals: A New Approach - page 241

Values for k s and k s follow from the equations given by van Rijn (1982):

k s = 3 d 90 to 4 . 5 d 50 (B.4)

20 γ r r r
λ r

k s

= (Ripples) (B.5)

1 . 1 γ d d 1 e − 25( d /λ d )

k s

= − (Dunes) (B.6)

where:
γ r =

ripple presence ( γ = 1 for ripples alone)

γ d = form factor ( γ d = 0.7 for field conditions)

r = ripple height ( r = 50 to 200 d 50 )

d = dune height

λ r =

ripple length ( λ r = 500 to 1000 d 50 )

λ d = dune length

The resistance due to the grain roughness is small compared to the one
caused by the geometry of the bed form. Many attempts have been made
to describe the geometry of ripples and dunes. Yalin (1985) described the
geometry of ripples generated by a subcritical flow in channels with cohe-
sionless and uniform bed material. The ripple length λ r is in the interval:

600 D ≤ λ r ≤ 2000 D (B.7)

The “largest population” of the ripple lengths can be found within the
range:

900 d 50 ≤ λ r ≤ 1000 d 50 (B.8)

A value that represents the ripple length well can be given by:

λ r = 1000 d 50 (B.9)

The ripple height can be described by Yalin (1985):

r is 50 to 200 d 50 (B.10)

where:
D

= representative grain size ( D = d 50 )

λ r = ripple length (m)

r = ripple height (m)

For practical purposes it can be assumed that for r = 100 d 50 and

λ r = 1000 d 50 :

r
λ r ≈

0 . 1 for 1 ≤ D ∗ ≤ 10 and T ≤ 3 (B.11)