Environmental Engineering Reference
In-Depth Information
The variable
∂
is the contraction coefficient, the value of
∂
varies from
0.624 to 0.648. The discharge coefficient
C
d
is a function of
h
1
/
a
and
ranges from 0.596 to 0.607 (Bos, 1989). Similarly the velocity coefficient
C
v
ranges from 1.0 to 1.2. Rajaratnam and Subramanya (1967) presented
an alternative discharge equation:
C
d
Ba
2
gh
Q
=
−
C
c
a
(4.38)
C
c
C
d
=
(4.39)
a
2
h
1
C
c
1
−
The contraction coefficient
C
e
is constant and is approximately 0.60.
Estimation of
C
d
is accurate for higher values of
h
1
/
a
; for
h
1
/a <
4, an
error of 5% might occur (Ankum, 2004).
Rajaratnam
and
Subramanya
(1967)
presented
an
equation
for
submerged flow conditions
C
d
Ba
2
gh
Q
=
(4.40)
where:
h
=
head loss (
h
1
−
h
3
) (m)
h
3
=
downstream water depth near the gate (m)
For free flow conditions the downstream water depth should be
smaller than:
1
1
h
3
<
C
e
a
2
8
F
2
−
+
(4.41)
where:
C
e
=
contraction coefficient (
≈
0.60)
F
2
=
Froude number corresponding to the downstream water depth
h
3
downstream water level above the sill (m)
For values of
a >
0
.
67
h
1
the discharge follows the equation for a
broad-crested weir (Ranga Raju, 1981).
h
3
=
1
.
7
BH
3
/
2
Q
=
(4.42)
Pressurized flow
Culverts with a submerged (pressurized) flow can be schematized as
a pipe with diameter (
D
) that gives the same hydraulic radius as the
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