Environmental Engineering Reference
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Total energy line
h
1
Sharp crest
Aerated pocket
h
1
P
Figure 4.6. Sharp crested weir
(Paudel, 2010).
Total energy line
H
h
P
Figure 4.7. Short-crested weir
(Paudel, 2010).
where:
Q
=
discharge (m
3
/s)
C
d
=
discharge coefficient and is a function of
h/P
B
=
crest width (m)
h
=
water depth over the crest (m)
H
=
upstream energy head above the crest (m)
P
=
height of crest above the upstream bed (m)
Any side contraction (contracted weir) is corrected by a contraction
coefficient
C
c
. For small values of
v
0
,
C
d
becomes equal to
C
c
.An
empirical relation for C
d
was derived by Rehbock (Henderson, 1966):
0
.
08
h
P
C
d
=
0
.
611
+
(4.31)
The theory for sharp-crested weirs forms the basis for the design of
short-crested weirs (spillways) (Bos, 1989). The curvature of a short-
crested weir has significant influence on the head discharge relationship
(Bos, 1989). The head discharge equation for a short-crested weir
(Figure 4.7) with a rectangular control is similar to a sharp-crested weir.
Different spillways are in use, such as a WES spillway, ogee spillway and
cylindrical-crested weirs. In irrigation schemes they are mostly used as
escapes, drops or check structures (Bureau of Reclamation, 1987). For a
rectangular control section the head discharge equation is (Bos, 1989):
3
2
gH
3
/
2
CB
c
2
Q
=
(4.32)
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