SONU KHAN
M TECH(F)
HYDRAULICS STRUCTURES
GC 5975
14CEHM028
Weir is a Small over flow-type dam generally used to
increase the level of a river or stream and it is also used to
measure the volumetric rate of water flow.
The discharge relationship for weirs is usually expressed as
Q=
S
O
NU
KHA
O/S
Lis the length of the weir
H is the head over the weir crest
g=9.81 m/sec
2
and
Kis the coefficient of discharge
1-Based on shape
(a) Rectangular weir
(b) Nonrectangular weir
2 -Based on Crest Width
(a)Long-crested
(b)Broad-crested
(c)Narrow-crested
(d)Sharp-crested
3-Based on effect of size on nappe
(a) Suppressed weir
(b) Contracted weir
4-Based on discharge condition
(a)Free falling weir
(b)Submerged Weir:
5-based on
n
h
Ratio
(a)Weirs
(b)Sill
6-Special type of proportional weirs
(a)Linear proportional weir or Sutroweir
(b)Quadratic weir
1-Based on shape
(a) Rectangular weir
(b) Nonrectangular weir
The Rectangular weir is the most commonly used thin plate weir
Q=
L
i
s t
hel
i/L
L is the length of weir
H is the head over the weir crest
and t
his the coefficient of discharge
The head H above the crest should be measured on the upstream of the
weir at a distance of 4 to 5 times the maximum head above the crest.
Some of these formulae which are commonly used are described
(b.1) Triangular weir
Ventilation of a triangular weir is not necessary.
For measuring low discharge a triangular weir is very useful.
The nappeemerging from a triangular weir has the same shape
for all heads.
Q=
f
t
hs
H
atan
=
L
(l
w
L.r
−ℎ
m
L.r
)
l
w2l+ℎ
m
ℎ
m=
u
m
L
s
u
m=approach velocity
y=90°, C =0.5-0.47
A trapezoidal weir is a combination of a rectangular and a triangular
weir. As such the discharge over such a weir may be determined by
adding the discharge over the two different types.
Q=
L
i
s t
hel
i/L
Cipolletiproposed the following equation for discharge
over a Cipollettiweir
Q=1.86Ll
i/L
A parabolic weir is almost similar to spillway section of dam.
The weir body wall for this weir is designed as low dam. A
cistern is provided at downstream.
Q=
4
5
t
h(2 )
w/Ll
L
K is a constant of parabolic profile chosen
t
hdepends on head H and shape
Equation of profile is S
V
=
A circular sharp-crested weir is a circular control section used
for measuring flow in open channels, reservoirs, and tanks.
Q=ℵt
h0
L.r
, ℵ=7(
A
h
),t
h=f(
A
h
)
d is the diaof circle
Given by Stevens (1957)
This is the simplest device for flow measurement.
It is more suitable for large discharges.
The width of the weir is taken as the width of
the waterway.
The following equations is used:
5.1
3
2
3
2
HbgCQ
cd
The discharge coefficient C
dequals 0.89.
To design the weir, His the only unknown and can be calculated
from the equation.
If the characteristics of the weir are known, the
discharge can be evaluated from the equation.
S N Value of h/B Type of weir
1 0<(h/B)≤0.1 Long-crested
2 0.1<(h/B)≤0.4 Broad-created
3 0.4<(h/B)≤1.5to 1.9
(upper limitdepends on h/p)
Narrow-crested
4 (h/B)≥1.5 to 1.9
(Lower limit depends on h/p)
Sharp-crested
(a) Free falling weir:
A weir is said to be a free falling weir if downstream liquid level
is below the weir crest.
(b) Submerged Weir:
If the downstream liquid level is above the crest level of the
weir the nappeis submerged and the weir is classified as
submerged weir.
lis the head over weir and
P is the height of weir
Q=
S
O
KNU
)
YHA
P
Y
Type T
E
K Given By
Sill >20
1.06(1+
/
A
)
O/S
Kandaswamy
and Rouse
0-∞
6
+[
6
(
6
S+
+
+1
P
]
+.(
Swamy
Weir ≤5
0.611+0.08
d
Rehbock
If H/P≤5.0it is called Weirs and
H/P>20 it is act as Sill
+
N=1.06
+
w=14.14
+
L=8.15
+
i=15
O
=l/D
If P=0 the weir is called Zero height Weirs.(By Sherman
,1967)
The weirs, in which the discharge is proportional to head, are known as proportional
weirs.
Q∝l
(a) Linear Proportional weirs or SUTRO weir
This linear proportional weir was invented by Stout (1897) and modified
later buSutro(Pratt, 1914 ). Sutroreplaced the infinite wings of the Stout
weir by a rectangular base weir based on graphical methods. Detailed
experiment were conducted on it by Soucek, Mavis, and Howe (1936). This
modified weir, ternedthe SutroWeir, achieves a linear discharge-head
relation given by
Q=b(h+
V
)
b=wK
/V
, K=2
( )
/V
and
=0.62
b=constant
(b) Quadratic Weir
The quadratic weir with an infinite width at the water surface was
first obtained by Haszpra(1965). However, a practical weir with a
finite width designed by KeshavaMurthy (1969) achieves a
discharge-head relation given by
Equation of profile
f(x)=y=w1−
S
a
tan
(
−
a
√
((
)
Discharge Equation
Q=b(ℎ+
O
)
b=
S
√O
K=2
( )
/v
=0.62
(c) Logarithmic weir
The logarithmic weir was designed by GovindaRaoand Keshava
Murthy (1966) to achieve a discharge-head relation given by
Q=b ln(1+
5/-.
/5
)
The weir width become zero at a certain height for a given base
weir and then reaches a negative value.
Banks et al. (1968) designed a type of weirs which may be
termed exponential weirs to differentiate them from the
logarithmic weirs. The exponential weirs achieve a discharge-
head relation given by
Q=K
a/P
Two new type of weirs termed as new baseless weirs (designed
as NBW-1 and NBW-2) have been designed by LakshmanaRao
and Chandrasekaran(1970a,1971) to achieve the discharge-head
relation given by
Q(NBW-1)=Khln(1+h/T) and
Q(NBW-2)=Kℎ
w/L
ln(1+h/T)
In which T is a arbitrary dimensional parameter
Based on alignment it may be Normal weir ,Side weir and
Oblique weirs.
(a) Normal Weir:
(a) Flat-Veeweir.
Flat veeweir are suitable for measuring accurately a wide range of
flows, relatively easy to install, and are economical. Such weir are
designed by modifying slightly the Crump weir.
To estimate the regime characteristics of a river in relation to
watershed protection and flood prevention measures. A veeWeir
with a very large apex angle and with very little crest width is
installed with weir crest slightly above the channel bed. Figure
shows the details of a Large veeweir.
A labyrinth weir is a linear weir that is folded in plan-view to
increase the crest length for a given channel or spillway width.
Due to the increase in crest length, a labyrinth weir provides an
increase in discharge capacity for a given upstream driving head
relative to traditional linear weir structures. Labyrinth weirs are
particularly well suited for spillway rehabilitation where dam
safety concerns freeboard limitations, and a revised and larger
probable maximum flow have required replacement or
modification of the spillway
The Piano Key Weir (PKW) is a particular geometry of weir
associating to a labyrinth shape the use of overhangs to reduce
the basis length. The PKW could thus be directly placed on a
dam crest. Together with its important discharge capacity for
low heads, this geometric feature makes the PKW an interesting
solution for dam rehabilitation. However, its hydraulic design
remains problematic, even at a preliminary stage.