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