hydraulic performance of sharp- crested rectangular ...

International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.33 (2015) © Research India Publications; httpwww.ripublication.comijaer.htm

HYDRAULIC PERFORMANCE OF SHARPCRESTED RECTANGULAR PLANFORM CONTRACTED WEIRS S. Kumar K. K. Gupta Professor Associate Professor Deptt. of Civil Engg., Deptt. of Civil Engg., Graphic Era University, Graphic Era University, Dehradun, India Dehradun, India ([email protected]) ([email protected])

Abstract Labyrinth weir is an example to increase the discharging

N. Mishra Assistant Professor Deptt. of Civil Engg., Graphic Era University, Dehradun, India ([email protected])

capacity, increasing events of floods etc. Labyrinth weirs consists of a series of linear weirs which are folded in plan view 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.

capacity of an existing weir effectively and economically by providing longer crest length of the weir without changing the existing structure width. Hence they are well suited to the sites where larger discharges are required on a stream having restricted width and the maximum water surface elevation is limited.

Discharge (Q) over a sharp-crested suppressed normal weir under free flow condition in a channel is expressed as

The present research work mainly aims of the experimental study carried out to explore the hydraulic performance of a sharp-crested contracted rectangular planform weir under free

Q

flow conditions in a rectangular flume. The efficiency of the

2 Cd 3

2 g LH

3 2

(1)

rectangular planform weirs is found better than the conventional

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).

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 is also

For a sharp crested weir with end contraction, if velocity of approach is considered then equation (1) is modified as

carried out which indicates that the weir is more sensitive at the low head and higher L/B ratios. Keywords rectangular planform weir, flow measurement, discharge coefficient and open channel.

I.

Q

V2 2 C d 2 g L 0.1n H a 3 2g

V2 H a 2g

3 2

Va2 2g

3 2

(2)

INTRODUCTION Where

n is the numbers of end contractions, Q Va Bc H P is velocity of approach, Bc is the clear width of the flume and P is weir height.

A weir is an obstruction built across a watercourse in order to raise the water level on the upstream side and to allow the excess water to flow over its entire length to the downstream side. There is a need to enhance the discharging capacity of the existing weirs due to expanding demand of more storage

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Initially Taylor (1968) did an extensive investigation dealing with the behavior of the labyrinth weirs and 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. Following the Taylor‟s work, 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/P. They found that the triangular planform weir is more efficient than the trapezoidal plan form.

Kumar et al. (2011, 2013) conducted an experimental study to investigate the discharging capacity of a sharp-crested suppressed triangular and 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. Presented in this paper are results of the experimental study carried out to investigate the discharge characteristics of a sharp crested rectangular planform weir with end contraction under free flow condition in a rectangular channel. It is anticipated that the rectangular planform weir will discharge more compared to normal weir for the same head of water.

Tullis et al. (1995) conducted extensive experimental work on 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 half-round crest shapes. They described the submerged labyrinth weir head–discharge relationship using the dimensionless submerged head parameters and found that the relationship is independent of labyrinth weir sidewall angles.

II.

EXPERIMENTAL WORK

The experimental runs were carried out using a horizontal rectangular tilting flume of length 5.360 m; width 0.262 m and depth 0.450 m located at the hydraulics lab. of Graphic Era University, Dehradun, India. Sharp-crested rectangular 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 ± 0.1 mm. Pre calibrated orifice meter was used to measure discharge provided in the inlet pipe and connected to the pressure gauges. To ensure free flow condition, water was guided to a sump was provided at the end of the flume in the downstream of the weir. Regulating gate and wave suppressors were provided at the upstream of the flume to control the discharge and to dissipate the surface disturbances, respectively.

Ghare et al. (2008) proposed a methodology for the optimal hydraulic design of trapezoidal labyrinth weirs. Ghodsian (2009) conducted experiments on sharp, quarter round, half round and flat top crest shape weirs and using dimensional analysis, he proposed an equation for calculating discharge over labyrinth weir. Khode et al. (2012) did experimental studies on flow over seven trapezoidal labyrinth weir models. Based on regression analysis they developed an equation for discharge over the labyrinth weir. Anderson and Tullis (2012) compared the hydraulics of piano key and rectangular labyrinth weir and found that PK weir was efficient than the rectangular labyrinth weir. Recently, Crookston and Tullis (2013) did experimental studies on labyrinth weirs and based on the results of physical modeling they presented a method for the hydraulic design and analysis of labyrinth weirs.

The experiments were performed for weirs of L/B ratio = 1.000, 1.023, 1.069, 1.140, 1.245, 1.397, 1.623 and 1.976 and for each L/B ratio for varying discharges. Fig. 1 shows the definition sketch of the weir with end contraction and Fig. 2 shows the layout of the experimental set-up. For each run, the head over the crest of the weir was measured at about 4–5 times upstream of the weir using pointer gage to avoid the curvature effect. The ranges of the data collected in the present investigation are given in Table 1.

X

P X

B/3

B/3 B Bc

(a) Plan

H B/3

P

(b) Section X-X

0.262 m

(c) 3D View of the weir and the flume

Fig. 1 Definition sketch of sharp crested rectangular planform contracted weir

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International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.33 (2015) © Research India Publications; httpwww.ripublication.comijaer.htm Sump 1.50m 0.065 m pipe inlet Regulating Gate Rectangular Plan form weir Flow suppresser X

X 0.262 m

0.245 m

Operating Valve 0.70 m

0.21m

5.15 m

0.40m

PLAN

0.45 m P2

P1

0.65m

SECTION X-X

Fig. 2 Layout of the experimental set-up Table 1 Range of parameters for rectangular

functional relationship coefficient of discharge for all tested

planform contracted weirs

weirs in the form of Rehbock‟s (1929) equation. i.e.

S. no.

L/B

P (m)

H (m)

Qo (m3/s)

No. of Runs

1

1.000

0.1043

0.0314 – 0.0777

0.0022 – 0.0091

10

2

1.023

0.1071

0.0412 – 0.0825

0.0038 – 0.0099

12

3

1.069

0.1060

0.0398 – 0.0864

0.0038 – 0.0108

12

experimental data. The most general values for these

4

1.140

0.1051

0.0426 – 0.0856

0.0044 – 0.0106

12

coefficients are proposed by Rehbock as a = 0.611 and b =

5

1.245

0.1043

0.0378 – 0.0855

0.0038 – 0.0108

12

0.075.

6

1.397

0.1044

0.0324 – 0.0809

0.0031 -0.0103

12

7

1.623

0.1001

0.0342 – 0.0773

0.0038 – 0.0101

11

the rectangular planform contracted weirs of different L/B

8

1.976

0.1018

0.0291 – 0.0682

0.0038 – 0.0101

11

ratio is shown in Fig. 3. Fig. 3 clearly indicates that for the

Cd

a b

H P (3)

Where a and b are the coefficients to be found using

Variation of observed discharge with head over the crest for

same value of H, discharge increases with the increase of L/B

III. 3.1

ANALYSIS OF DATA

ratio due to increases of the crest length of the weir. For each

Data Presentation and Analysis: Data

data set, the Cd was computed using Eq. (2) for known value of discharge, head over the crest and the crest length for weirs

collected in the present study is analyzed to obtain the

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of different L/B ratio. Variation of Cd with H/P is shown in

3.1

Fig. 4 for the weirs of different L/B ratio. It can be noted that

contracted weir: As per the Rehbock equation, the variation

Cd decreases with an increase of L/B ratio due to interference

of Cd with H/P is fitted to linear equations for weirs of

of the falling jets for high value of H/P. However, for the low

different L/B ratio as follows:

value of H/P, the interference of jets is not so severe, resulting

Cd

in high Cd. The value of Cd decreases with increase in H/P for

Cd

Discharge equation for rectangular planform

= 0.537 + 0.081 (H/P)

For L/B=1.000

= 0.677 - 0.126 (H/P)

For L/B=1.023

R2 = 0.89 2

R = 0.92

(4a) (4b)

different L/B ratio and for the normal weir, the Cd increases

Cd

= 0.707 - 0.141 (H/P)

For L/B=1.069

R = 0.96

(4c)

with H/P, which satisfies the Rehbock (1929) equation for Cd.

Cd

= 0.764 - 0.211 (H/P)

For L/B=1.140

R2 = 0.95

(4d)

Cd

= 0.778 - 0.213 (H/P)

For L/B=1.245

R2 = 0.95

(4e)

Cd 0.012

= 0.814 - 0.235 (H/P)

For L/B=1.397

2

2

(4f)

2

R = 0.96

Cd

= 0.825 - 0.334 (H/P)

For L/B=1.623

R = 0.92

(4g)

Cd

= 0.870 - 0.484 (H/P)

For L/B=1.976

R2 = 0.96

(4h)

Qobserved (m3/s)

0.010

A high correlation between Cd and H/P may be noted for all the weirs. Variations of constants „a‟ and „b‟ with L/B ratio are shown in Fig. 5. A third order polynomial has been fitted to the data for „a‟ and „b‟ as follows:

0.008 L/B = 1.000 L/B = 1.023 L/B = 1.069 L/B = 1.140 L/B = 1.245 L/B = 1.397 L/B = 1.623 L/B = 1.976

0.006 0.004 0.002

a 1.56

b

L B

1.74

3

L B

7.345

L B

7.9

L B

3

2

11 .39

L B

5.01,

R2

0.89 (5a)

12 .05

L B

5.87 ,

R2

0.88 (5b)

2

0.000 0.02

0.04

0.06

0.08

0.10

1.0

H (m)

0.8

Fig. 3 Variation of Qobserved with H for weirs of different L/B ratio.

0.6

a,b

0.4 0.8

0.2 0.0 -0.2

Cdo

0.7

a b

-0.4

0.6

-0.6

L/B = 1.000 L/B = 1.023 L/B = 1.069 L/B = 1.140 L/B = 1.245 L/B = 1.397 L/B = 1.623 L/B = 1.976

0.5

0.5

0.4

0.6

H/P

0.8

1.5

2.0

2.5

L/B

Fig. 5 Variation of „a‟ and „b‟ with L/B

0.4 0.2

1.0

Out of 92 data sets, 68 data sets were used to develop the relationship for coefficient of discharge. The generalized equation of Cd for the rectangular planform contracted weir to be used in Eq. (2) for the computation of discharge can be written as:

1.0

Fig. 4 Variation of Cd with H/P for weirs of different L/B ratio.

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Cd

1.56 1.74

L B

3

L B 3

7.9

L B

2

L B

7.345 2

12 .05

3.4 Efficiency of the weir

L B

11 .39 L B

5.01

An efficient weir passes more discharge for constant head and length of weir compared to the other. To examine the efficiency of the rectangular planform contracted weir for different L/B ratio, ratio of discharges over the rectangular planform contracted weir and normal weir, i.e., Q/Qn is plotted with H/P in Fig. 7.

(6) H P

5.87

This equation is valid in the range 0 < H/P < 0.82 and 1.000 ≤ L/B ≤ 1.976.

The efficiency of rectangular planform contracted weir is high for higher L/B ratio and decreases with increase of H/P due to interference of the jets downstream. For H/P = 0.05, the weirs of L/B ratio 1.023, 1.069, 1.140, 1.245, 1.397, 1.623 and 1.976 are respectively 1.73, 1.87, 2.17, 2.16, 2.18,2.78 and 3.90 times more efficient than the normal weir. However, for H/P = 1.0, the efficiency of rectangular planform contracted weir is low.

3.3 Validation of the proposed discharge equation The remaining 24 data sets, not used in the derivation of Eq. (6), were used 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 ±05% of the observed ones for the weirs of all L/B ratio studied herein. For a numerical measure for error between the observed and computed values, an average percentage error term e is defined as (Ghodsian M., 2003):

e

100 N

N

Qcom puted Qobserved

i 1

Qobserved

4


3

(7) Q/Qn

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 L/B ratio.

2

1 0.012 Line of perfect agreement

0 0.1

0.4

0.5 0.6 H/P

0.7

0.8

0.9

1.0

er ro

rl

in e

0.3

3.5 Sensitivity analysis of the rectangular planform contracted weir

0.006

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 rectangular planform contracted weir, which can be written as:

0.004

0.002 0.002

0.2

Fig. 7 Variation of Q/Qn with H/P for the weirs of different L/B ratios.

%

0.008

-5

Q calculated

+5 %

er ro

rl in e

0.010

0.004

0.006 0.008 Q observed

0.010

0.012

Q

Fig. 6 Comparison of computed discharge using Eqs. (2) and (6) with the observed ones.

2 H a b 3 P

2 g L 0.1n H

Va2 2g

H

Va2 2g

3 2

Va2 2g

3 2

(8)

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

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International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.33 (2015) © Research India Publications; httpwww.ripublication.comijaer.htm H dQ dH

3 Q 2 H

2 a

V 2g

Va2 2g 3 2

1 2

than the normal weir. However, for H/P = 1.0, the efficiency of rectangular planform contracted weir is low for all L/B ratios. Sensitivity analysis indicates that the discharge through rectangular planform contracted weir is more sensitive to the low head and low L/B ratios. As the head increases, the sensitivity decreases due to interference of the water jet downstream of the weir crest.

(9) 2 a

V 2g

3 2

-

n L-0.1n H

2b Va2 2g

3P a b

H P

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 L/B ratio. The variation of dQ/dH with H is shown in the Fig. 8. A perusal of Fig. 8 reveals that the discharge through rectangular 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 higher L/B ratio of the rectangular planform contracted weir due to large weir crest length.

0.14

Bc = clear flume width B =contracted flume width Cd = coefficient of discharge for rectangular 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 rectangular planform contracted Weir Q0 = observed Discharge Qc = computed Discharge Qn = discharge over corresponding normal weir Va =velocity of approach a, b = coefficients


0.12 0.10 dQ/dH (m3/s/m)

NOTATIONS

0.08 0.06

REFERENCES

0.04 0.02 0.00 0.02

0.04

0.06 H (m)

0.08

1.

Anderson R.M. and Tullis B.P. (2012), comparison of piano key and rectangular labyrinth weir hydraulics, J. of Hydraulic Engg., ASCE, 138 (4): 358-361.

2.

Bagheri S, Heidarpour M. Application of free vortex theory to estimate discharge coefficient for sharpcrested weirs. Biosystems Eng 2010; 105 (3): 423–7.

3.

Crookston B.M. and Tullis B.P. (2013), hydraulic design and analysis of labyrinth weirs I: discharge relationships, J. of Irrigation and drainage engg., ASCE, 139 (5): 363-370.

4.

Ghare A.D., V.A. Mhaisalkar and P.D. Porey, 2008. An approach to optimal design of trapezoidal labyrinth weir. World applied sciences journal, 3(6): 934-938.

5.

Ghodsian M. Flow through side sluice gate. ASCE J Irrig Drain Eng 2003;129 (6): 458–62.

6.

Ghodsian M., 2009. Stage Discharge relationship for a triangular labyrinth spillway. Proc. Inst. Civ. Eng. Water Manage.,162 (3): 173-178.

7.

Khode B.V., A.R.Tembhurkar, P.D. Porey and R.N. Ingle, 2012. Experimental studies on flow over

0.10

Fig. 8 Sensitivity of the rectangular weirs as function of head

IV.

CONCLUSION

An experimental study was carried out to investigate the discharging capacity of a sharp-crested rectangular planform contracted weir under free flow conditions in a rectangular channel. The coefficient of discharge of the rectangular planform contracted weir decreases with decrease of L/B ratio due to interference of falling jets for high value of H/P. However, for low values of H/P and higher values of L/B ratio, the Cd is high. The computed discharge using the proposed equation is within 05% of the observed ones. The efficiency of the rectangular weir is high for low L/B ratio and decreases with increase of H/P due to interference of the jets downstream. For H/P = 0.05, the weirs of L/B ratio 1.023, 1.069, 1.140, 1.245, 1.397, 1.623 and 1.976are respectively 1.73, 1.87, 2.17, 2.16, 2.18,2.78 and 3.90 times more efficient

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labyrinth weir. J. of irrigation and drainage engg., ASCE, 138:548-552. 8.

Hay N, Taylor G. A computer model for the determination of the performance of labyrinth weirs. 13th Congress of IAHR, Koyoto, Japan; 1969; 361– 378.

9.

Hay N, Taylor G. Performance of labyrinth weirs. ASCE J Hyd Eng 1970; 96(11): 2337–57.

10. Kumar S., Ahmad Z. and Mansoor T (2011) “A new approach to improve the discharging capacity of sharp-crested triangular plan form weirs”. J. flow measurement and instrumentation, Elsevier 22 (2011); 175-180. 11. S. Kumar, Z. Ahmad, T. Mansoor and S.K. Himanshu (2013) “A new approach to analyze the flow over sharp-crested curved plan form weirs”. International Journal of Recent technology and Engineering, Vol.2, No.1 (March, 2013); 24 – 28. 12. Rehbock T. Discussion of precise weir measurement, In: Schoder EW, Turner KB, editors. ASCE Trans 1929; 93:1143–62. 13. Taylor G. The performance of labyrinth weir. Ph.D. thesis, University of Nottingham, Nottingham, England; 1968. 14. Tullis BP, Amanian N, Waldron D. Design of labyrinth spillways. ASCE J Hyd Eng 1995; 121 (3):247–55. 15. Tullis BP, Young JC, Chandler MA. Head-discharge relationships for submerged Labyrinth weirs. ASCE J Hyd Eng 2007; 133 (3):248–53.

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