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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