Environmental Engineering Reference
In-Depth Information
vena
contracta
h
1
h
3
a
Free flow case
∆
h
h
1
h
3
h
2
a
Figure 4.10. Underflow gate
(Paudel, 2010).
Submerged flow case
The basic head-discharge equation for a submerged orifice flow is:
C
d
C
v
A
or
2
g
(
h
1
−
Q
=
h
2
)
(4.36)
where
h
1
−
the head differential over the orifice. A well designed
submerged orifice maintains a small approach velocity and
C
v
approaches
unity. For a fully contracted, submerged, rectangular orifice the discharge
coefficient
C
d
=
h
2
=
0.61 (Bos, 1989).
For a not fully contracted orifice, only a part is suppressed (bottom
only or both bottom and sides) and the discharge coefficient will be:
C
d
=
0
.
61(1
+
0
.
15
r
)
where:
r
ratio of the suppressed orifice perimeter to the total orifice
perimeter
If the water discharges freely through an orifice with bottom and
side contraction, the flow pattern equals the flow of the free outflow
underneath a vertical sluice gate and the discharge depends upon the
upstream water depth and gate opening:
=
C
d
C
v
A
or
2
g
(
y
1
−
C
d
C
v
A
or
2
g
(
y
1
−
Q
=
y
)
=
∂a
)
(4.37)
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