Environmental Engineering Reference
In-Depth Information
with:
τ =
ρgh S
τ =
ρgh S
=
τ
ρghS
and
and
(B.31)
( ghS ) 0 . 5
( gh S ) 0 . 5
u =
and
u =
(B.32)
with
h +
h
h
=
(B.33)
Hence:
u
u
2
h
h
=
(B.34)
Expressing the shear velocity in terms of the mobility parameter θ the
equation becomes:
θ
θ =
h
h
(B.35)
It was found for the lower regime that:
θ =
0 . 4 θ 2
0 . 06
(B.36)
The mean velocity is calculated by:
2 . 5ln
h
2 d 50
V
u =
6
+
(B.37)
Combination of the equations will result in the de Chézy coefficient:
g 0 . 5 h
h
0 . 5 6
2 . 5ln h
2 . 5 d 50
C
=
+
(B.38)
where:
h
h +
h =
=
water depth (m)
τ +
τ =
effective shear stress (N/m 2 )
τ
=
u =
shear velocity (m/s)
=
θ
dimensionless mobility parameter
=
density (kg/m 3 )
ρ
V
=
mean velocity (m/s)
C
=
de Chézy coefficient (m 1 / 2 /s)
S
=
bottom slope
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