The length of channel measured along the thalweg is labeled Lc. Thus, the mean slope of the
channel bed before relocation is:
∆z
S1 =
(5.23)
Lc1
and after relocation is
∆z
S2 =
(5.24)
Lc2
Sinuosity is defined as the ratio of the length of channel, Lc to the length of the valley, or
Lc
Sn =
≥1
(5.25)
Lv
Clearly,
L c1
Sn1 =
(5.26)
Lv 1
L c2
Sn2 =
(5.27)
Lv 2
but
L V1 = L V2 = L v
(5.28)
and
∆z1 ∆z2 ∆z
=
=
(5.29)
L v1
L v2
Lv
Thus,
Lc1 ∆z Lc2 ∆z
Sn1S1 =
=
= sn2S2
(5.30)
L v L c1 L v L c2
The new channel slope and channel sinuosity are inversely related. If Sn2 < Sn1 then S2 > S1.
The new channel alignment, hence Sn2, can be chosen by the designer with due consideration
given to the radii of curvature, deflection angles and tangent lengths between reversing curves.
As indicated before, consideration should also be given to prevailing average conditions in the
extended reach. The new slope S2 can be calculated from Equation 5.30, and the relationship
for meandering (Equation 5.1) should be satisfied.
5.57
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