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 Total Downloads : 348
 Authors : K. K. Gupta, S. Kumar, K. Kumar
 Paper ID : IJERTV2IS120690
 Volume & Issue : Volume 02, Issue 12 (December 2013)
 Published (First Online): 17122013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Flow Characteristics of SharpCrested Triangular Planform Contracted weirs
K. K. Gupta S. Kumar K. Kumar
Associate Professor Deptt. of Civil Engg., Graphic Era University, Dehradun, India
Assistant Professor Deptt. of Civil Engg., Graphic Era University, Dehradun, India
U.G.Student Deptt. of Civil Engg.,
Graphic Era University, Dehradun, India
Abstract
Weirs are a barrier across a river to amend its flow characteristics. They have been widely used for the purpose of flow measurement and control. Weirs are usually in the form of obstructions smaller than most conventional dams, which cause water to pool behind them, while allowing water to flow steadily over their tops pose problems of submergence upstream of the weir due to large afflux required to pass the discharge downstream. Various weirs of modified plan form have been suggested in the past to enhance their discharging capacity with minimum head over the weirs and to restrict the afflux. Presented in this paper are results of the experimental study carried out to investigate the discharge characteristics of a sharpcrested contracted triangular planform weir under free flow conditions in a rectangular channel. The efficiency of the triangular planform weirs is found better than the normal weir. A discharge equation has been proposed for the given range of data and found that the proposed equation is
within 5% of the observed ones. Sensitivity of the
weir, i.e., change of discharge due to unit change in head is also carried out which indicates that the weir is more sensitive at the low head and low vertex angle.
Key words: triangular planform weir, flow
discharging capacity. Moreover, conventional weirs are also inherited with afflux and submergence of area upstream of the weir. Various weirs of modified planform like oblique weirs, diagonal weirs, Duckwill weirs, Labyrinth weirs etc. have been suggested in the past to enhance their discharging capacity with minimum head over the weirs and to restrict the afflux.
Labyrinth weirs are folded in plan view (i.e. the weir crest is not straight in planform) to provide a longer crest length compared with a normal weir having the same lateral space to increase the discharge for a given operating head. Since labyrinth weirs passes large flood at a comparatively low head, they can therefore be widely used to a particular advantage in situations where a weir is required to pass a range of discharge with a limited variation in upstream water levels and also where the width of a channel is restricted. For large reservoirs, the labyrinth weir also can be used as the overflow structure. It allows the overflow sill to be raised for the same maximum level of the water and flood, and thus, increase the storage capacity of the reservoir.
Discharge (Q) over a sharpcrested suppressed weir under free flow condition in a channel is expressed in terms of the following mathematical expression
measurement, vertex angle, discharge coefficient and open channel.
Q 2 C
3 d
3
2g LH 2
(1)

Introduction
A weir is built across a stream in order to raise level of water on the upstream side and to allow the excess water to flow over its entire length to the downstream side. It is desirable to provide more flood storage and/or larger capacity for weirs to pass the probable maximum flood safely. If the weir cannot adequately pass the updated flood, it is needed to enhance the
Where Cd = coefficient of discharge, L = crest length of the weir, g = acceleration due to gravity, H = head over the crest. The Cd depends on flow characteristics and geometry of the channel and the weir (Bagheri S, Heidarpour M., 2010).
For a sharp crested weir with end contraction, if velocity of approach is considered then equation (1) is modified as:
2
V 2
3
V 2 2
3
V 2 2
heights and higher discharges. Emiroglu et al. (2010)
Q Cd 2g L 0.1n H a H a
a
(2)
and Bilhan et al. (2010) studied the hydraulics of weir
3
2g
2g
2g
using soft computing techniques.
Where n is the numbers of end contractions,
Kumar et al. (2011, 2013) conducted an
Va
Q
BH Pis velocity of approach, B is width of
experimental study to investigate the discharging capacity of a sharpcrested suppressed triangular and
the flume and P is weir height.
Labyrinth weirs of various plan forms like trapezoidal, rectangular, triangular etc. and also a combination of these have been used in practice. This weir may be of one fold or multiple folds as per the requirement and may be sharpcrested or broad. An extensive investigation dealing with the behavior of the labyrinth weirs was performed by Taylor (1968). He presented his results in the term of a magnification ratio i.e., ratio of discharge over labyrinth weir and normal weir for the same head over the crest. Hay and Taylor (1969, 1970) tested various plan shapes in the form of labyrinth weirs and presented the results in the form of curves between the ratio of discharge over labyrinth weir (Q) to corresponding normal weir (Qn) and h/w. where, w = weir height. They found that the triangular planform weir is more efficient than the trapezoidal plan form.
Tullis et al. (1995) studied labyrinth weirs having trapezoidal plan form. They found the capacity of a labyrinth weir is a function of the total head, the effective crest length and the coefficient of discharge. The coefficient of discharge depends on weir height, total head, weir wall thickness, crest shape, vertex configuration and the angle of the side legs. Tullis et al. (2007) conducted experiments on three submerged labyrinth weirs of different geometries with halfround crest shapes. They described the submerged labyrinth weir headdischarge relationship using the dimensionless submerged head parameters and found that the relationship is independent of labyrinth weir sidewall angles.
Aeration performances of different planforms of labyrinth weirs have been studied by various investigators [Wormleaton et.al. (1998, 2000), Emiroglu et.al. (2005)] and they found that the geometry of labyrinth weirs provides increased sill length and often results in the overfall jets colliding with each other, both of which may lead to increased aeration. They found that the aeration efficiency of the labyrinth weirs generally is better than the equivalent length linear weir and it increases as the weir included angle becomes smaller and also at lower overfall drop
curved plan form weir under free flow conditions in a rectangular channel. They found that the efficiency of the triangular and curved plan form weirs was better than the normal weir. Sensitivity of the weir, i.e., change of discharge due to unit change in head was also carried out which indicated that the weir was more sensitive at the low head and low vertex angle.
Presented in this paper are results of the experimental study carried out to investigate the discharge characteristics of a sharp crested triangular planform weir with end contraction under free flow condition in a rectangular channel. It is intended that the triangular planform weir will discharge more compared to normal weir for the same head of water.

Materials and Methods

Experimental work
The experiments were conducted in a horizontal rectangular tilting flume of length 5.360 m; width 0.262m and depth 0.450 m in the hydraulics lab of Graphic Era University, Dehradun, India. Sharpcrested triangular planform weirs were fabricated of mild steel plates and were located at 5.150 m downstream from the head of the flume. Head over the crest was measured using the point gauge of accuracy Â± 0.1 mm and discharge by means of an orifice meter provided in the inlet pipe and connected to the pressure gauges. Water was guided to a sump provided at the end of the flume in the downstream of the weir to ensure free flow condition. Regulating gate and wave suppressors were provided at the upstream of the flume to control the discharge and to dissipate the surface disturbances, respectively.
The experiments were performed for weirs of vertex angle = 1800, 1500, 1350, 1200, 1050, 900, 750 and 600
and for each vertex angle for varying discharges. Fig. 1 shows the definition sketch of a sharp crested triangular planform weir with end contraction and Fig. 2 shows the layout of the experimental setup. For each run, the head over the crest of the weir was measured at about 45 times upstream of the weir using point gage to avoid the curvature effect. The ranges of the data collected in the present study are given in Table 1.
S.no
(degree)
P (m)
H (m)
Qo (m3/s)
No. of Runs
1
180
0.1043
0.0314 0.0777
0.0022 0.0091
10
2
150
0.1040
0.0362 0.0834
0.0031 0.0101
14
3
135
0.1033
0.0273 0.0812
0.0022 0.0094
13
4
120
0.1022
0.0259 0.0847
0.0022 0.0103
12
5
105
0.0992
0.0237 0.0754
0.0022 0.0094
12
6
90
0.1009
0.0224 0.0721
0.0022 0.0096
13
7
75
0.1019
0.0309 0.0690
0.0038 0.0099
12
8
60
0.0995
0.0248 0.0541
0.0031 0.0094
13
S.no
(degree)
P (m)
H (m)
Qo (m3/s)
No. of Runs
1
180
0.1043
0.0314 0.0777
0.0022 0.0091
10
2
150
0.1040
0.0362 0.0834
0.0031 0.0101
14
3
135
0.1033
0.0273 0.0812
0.0022 0.0094
13
4
120
0.1022
0.0259 0.0847
0.0022 0.0103
12
5
105
0.0992
0.0237 0.0754
0.0022 0.0094
12
6
90
0.1009
0.0224 0.0721
0.0022 0.0096
13
7
75
0.1019
0.0309 0.0690
0.0038 0.0099
12
8
60
0.0995
0.0248 0.0541
0.0031 0.0094
13
Table 1 Range of parameters
X
L/2
X
B H
P

Plan (b) Section XX
P



Analysis of Data
3.1. Data Presentation and Analysis
Data collected in the present study is analyzed to obtain the functional relationship of discharge coefficient for all tested triangular planform contracted weirs in a free flow situation in the form of Rehbocks (1929) equation. i.e.
C a b H
d P
0.262 m
(c) 3D View of the weir and the flume
Fig. 1 Definition sketch of sharp crested triangular planform contracted weir
(3)
Where a and b are the coefficients to be found using experimental data. The most general values for these coefficients are proposed by Rehbock as a = 0.611 and b = 0.075.
0 . 0 6 5 m p ip e in le t
R e g u la t in g G a te
S u m p
T ra in g u la r P la n fo rm w e ir F lo w s u p p re ss e r
X X
0 . 2 6 2 m
0 . 2 4 5 m
0 . 7 0 m
O p e ra t in g Va lv e
5 . 1 5 m 0 . 2 1 m
P L A N
0 . 4 0 m
0 . 4 5 m
P 2 P 1
0 . 6 5 m
O p e ra t in g Va lv e S E C T IO N X – X
F ig . 2 L a y o u t o f e x p e r im e n ta l s e t – u p
Variation of observed discharge with head over the crest for the triangular planform contracted weirs of different vertex angles is shown in Fig. 3. All the plots are curvilinear, cofocal with the best one being for the largest skew length, i.e. = 600. Fig. 3 clearly indicates that for the same value of H, discharge increases with the decrease of vertex angle due to increases of the crest length of the weir. For each data set, the Cd was computed using Eq. (2) for known value of discharge, head over the crest and the crest length for weirs of different vertex angles.
0.012
0.010
Qobserved (m3/s)
Qobserved (m3/s)
0.008
angle and for the vertex angle 180Â° i.e., the normal weir, the Cd increases with H/P, which satisfies the Rehbock (1929) equation for Cd.

Discharge equation for triangular planform contracted weir
Cd
=
0.537 + 0.081 (H/P)
For = 1800
R2 = 0.89
(4a)
Cd
=
0.645 – 0.075 (H/P)
For = 1500
R2 = 0.94
(4b)
Cd
=
0.706 – 0.199 (H/P)
For = 1350
R2 = 0.96
(4c)
Cd
=
0.703 – 0.222 (H/P)
For = 1200
R2 = 0.98
(4d)
Cd
=
0.768 – 0.358 (H/P)
For = 1050
R2 = 0.94
(4e)
Cd
=
0.721 – 0.310 (H/P)
For = 900
R2 = 0.98
(4f)
Cd
=
0.693 – 0.325 (H/P)
For = 750
R2 = 0.95
(4g)
Cd
=
0.592 – 0.168 (H/P)
For = 600
R2 = 0.96
(4h)
Cd
=
0.537 + 0.081 (H/P)
For = 1800
R2 = 0.89
(4a)
Cd
=
0.645 – 0.075 (H/P)
For = 1500
R2 = 0.94
(4b)
Cd
=
0.706 – 0.199 (H/P)
For = 1350
R2 = 0.96
(4c)
Cd
=
0.703 – 0.222 (H/P)
For = 1200
R2 = 0.98
(4d)
Cd
=
0.768 – 0.358 (H/P)
For = 1050
2 = 0.94
(4e)
Cd
=
0.721 – 0.310 (H/P)
For = 900
R2 = 0.98
(4f)
Cd
=
0.693 – 0.325 (H/P)
For = 750
R2 = 0.95
(4g)
Cd
=
0.592 – 0.168 (H/P)
For = 600
R2 = 0.96
(4h)
Invoking the Rehbock equation, the variation of Cd with H/P is fitted to linear equations for weirs of different vertex angles as follows:
= 1800
0.006 = 1500
= 1350
A high correlation between C
and H/P may be
0.004
0.002
0.000
= 1200
= 1050
= 900
= 750
= 600
d
noted for all the weirs. Variations of constants a and b with central angle are shown in Fig. 5. A second order polynomial has been fitted to the data for a and b as follows (angles are in radian):
0.02 0.04 0.06 0.08 0.10
H (m)
a 0.148 2 0.574 0.176, R2 0.90
(5a)
Fig. 3 Variation of Q
observed
with H for weirs of
b 0.192 2 0.644 0.239, R2 0.89
(5b)
0.70
0.65
0.60
Cdo
Cdo
0.55
0.50
0.45
0.40
different vertex angles
= 1800
= 1500
= 1350
= 1200
= 1050
= 900
= 750
= 600
1.0
0.8
0.6
0.4
a,b
a,b
0.2
0.0
0.2
a
0.4 b
0.2 0.4 0.6 0.8 1.0
H/P
Fig. 4 Variation of Cd with H/P for weirs of different
0.6
0.5 1.0 1.5
2.0
(radian)
2.5 3.0 3.5
vertex angles
Variation of Cd with H/P is shown in Fig. 4 for the weirs of different vertex angles. It can be noted that Cd decreases with an decrease of vertex angle due to interference of the falling jets for high value of H/P. However, for the low value of H/P, the interference of jets is not so severe, resulting in high Cd. The value of Cd decreases with increase in H/P for different vertex
Fig. 5 Variation of a and b with
Out of 99 data sets for triangular planform contracted weirs, 75 data sets were used to develop the relationship for coefficient of discharge. The generalized equation of Cd for the triangular planform contracted weir to be used in Eq. (2) for the computation of discharge can be written as:
d
d
C 0.148 2 0.574 0.176 0.192 2 0.644 0.239 H
P
discharges over the triangular planform contracted weir and normal weir, i.e., Q/Q is plotted with H/P in Fig.
n
(6) 7.
This equation is valid in the range 0 < H/P < 0.83 and 60 1800.

Validation of the proposed discharge equation
The remaining 24 data sets, not used in the derivation of Eq. (6), were used next to validate the proposed relationship for Cd i.e., Eq. (6). The computed discharge is compared with the corresponding observed ones in Fig. 6, which shows that the computed discharge is within Â±05% of the observed ones for the weirs of all vertex angles studied herein. For a numerical measure for error between the observed and computed values, an average percentage error term e is
The efficiency of triangular planform contracted weir is high for low central angle and decreases with increase of H/P due to interference of the jets downstream. For H/P = 0.05, the weirs of vertex angle 1500, 1350, 1200,
1050, 900, 750 and 600 are respectively 1.53, 1.88, 1.99,

, 2.47,3.14 and 2.35 times more efficient than the normal weir. However, for H/P = 1.0, the efficiency of triangular planform contracted weir is low and even for = 600, the efficiency is only 1.55 times the normal weir.
4
= 1800
= 1500
= 1350
defined as (Ghodsian M., 2003): 3
= 1200
= 1050
Q/Qn
Q/Qn
100 N Q

Q

= 900
Q
Q
N
N
2
2
e computed observed
= 750
= 600
i1
observed
(7)
The average percentage error in the computation of discharge over the weir using Eqs. (2) and (6) is found in the range 0%05% for weirs of different vertex angles.
Line of perfect agreement
Line of perfect agreement
0.010
1
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
H/P
0.009
+5% error line
+5% error line
0.008
Q calculated
Q calculated
– 5% error line
– 5% error line
0.007
0.006
0.005
0.004
Fig. 7 Variation of Q/Qn with H/P for the weirs of different vertex angles
3.5 Sensitivity analysis of the triangular planform contracted weir
Sensitivity analysis, i.e., change in discharge due to unit change in the head of water is carried out for the proposed discharge equation of the triangular planform contracted weir, which can be written as:
0.003
2
H
V 2
3
V 2 2
3
V 2 2
0.002 Q
a b
2g L 0.1n H a H a
a
0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010
Q observed
3 P
2g
2g
2g
(8)
Fig. 6 Comparison of computed discharge using Eqs.
(2) and (6) with the observed ones
3.4 Efficiency of the weir
The values of a and b can be obtained from the Eqs. (5a) and (5b) respectively. Differentiating Q with respect to H and arranging the terms, one can get
V
V
1
2 2
H a
An efficient weir passes more discharge for constant
dQ 3 Q 2g – n 2b
head and length of weir compared to the other. To
dH 2
3 3 V 2
H
V 2 2 V 2 2 L0.1n H a
3Pa b
examine the efficiency of the triangular planform
H a
a
2g
P
contracted weir for different vertex angles, ratio of
2g
2g
(9)
The larger value of dQ/dH implies higher sensitivity. Data collected in the present study was used to compute dQ/dH for different values of the vertex angles. The variation of dQ/dH with H is depicted in the Fig. 8. A perusal of Fig. 8 reveals that the discharge through triangular planform contracted weir is more sensitive to the low head. As the head increases, the sensitivity decreases due to interference of the water jet downstream of the weir crest. Further, sensitivity is higher for the low vertex angle of the triangular planform contracted weir due to large weir crest length.
0.20
Notations
B = flume width
Cd = coefficient of discharge for triangular planform contracted weir
g = acceleration due to gravity
H = head over the weir
L = crest length
n = numbers of end contractions.
P = weir height above the bed of flume
Q = discharge over triangular planform contracted Weir
Q0 = observed Discharge
Qc = computed Discharge
= 1800
0.18 = 1500
0.16 = 1350
= 1200
Qn = discharge over corresponding normal weir
Va = velocity of approach
vertex angle
dQ/dH (m2/s)
dQ/dH (m2/s)
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
= 1050
= 900
= 750
= 600
a, b = coefficients
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0.00 0.02 0.04 0.06 0.08 0.10
H (m)
Fig. 8 Sensitivity of the curved weirs as function of head


Conclusion
An experimental study was carried out to investigate the discharging capacity of a sharpcrested triangular planform contracted weir under free flow conditions in a rectangular channel. The coefficient of discharge of the triangular planform contracted weir decreases with decrease of vertex angle due to interference of falling jets for high value of H/P. However, for low values of H/P and higher values of vertex angle, the Cd is high. The computed discharge
using the proposed equation is within 05% of the
observed ones. The efficiency of the curved weir is high for low vertex angle and decreases with increase of H/P due to interference of the jets downstream. For H/P = 0.05, the weirs of vertex angle 1500, 1350, 1200,
1050, 900, 750 and 600 are respectively 1.53, 1.88, 1.99,
2.63, 2.47,3.14 and 2.35 times more efficient than the normal weir. However, for H/P = 1.0, the efficiency of triangular planform contracted weir is low for all vertex angles. Sensitivity analysis indicates that the discharge through triangular planform contracted weir is more sensitive to the low head and low vertex angles. As the head increases, the sensitivity decreases due to interference of the water jet downstream of the weir crest.
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