Experimental Study of Combined Oblique Weir and … · combined flow over weir and under gate was...

VOL. 8, NO. 4, APRIL 2013 ISSN 1819-6608

ARPN Journal of Engineering and Applied Sciences

©2006-2013 Asian Research Publishing Network (ARPN). All rights reserved.

www.arpnjournals.com

306

EXPERIMENTAL STUDY OF COMBINED OBLIQUE WEIRAND GATE STRUCTURE

Shaker A. Jalil and Sarhan Abdulsatar SarhanSchool of Engineering, Faculty of Engineering and Applied Sciences, University of Duhok, Iraq

E-Mail: [email protected]

ABSTRACTFlow measurement in open channel is important to support the system management. An experimental study in a

laboratory flume is carried out to study flow over a sharp crested weir and under gate in combined structure as flowmeasurement device. Four different oblique angles to the longitudinal axis of the channel and four different heights of gateopening were used. The basic principles of statistical analysis are employed to correlate between the hydraulic andgeometric dimensionless parameters with the discharge coefficient. Different relationship models with acceptablesignificance are suggested. It was found that the major parameters effecting significantly on discharge coefficient are (h/d,α, L/d, P/d), and value of Cd range from 0.623 to 0.403, with Standard Error 0.0047. Within the limitations of the presentexperimental work two different discharge equations were predicted. The first equation Which assumed that the coefficientof discharge is the same for weir and gate with R2 of o.972, and the second which assumed that there is different percentof discharge for each weir and gate with R2 of 0.997.

Keywords: combined structure, oblique weir and gate, gate opening, coefficient of discharge.

INTRODUCTIONThe measurement of flow rates are carried on in

many practical fields. Wide range of flow measuringtechniques and instruments are introduced. U. S.Department of The Interior (1997) published a theoreticaland experimental study for water measurement devicesand their efficiency. Roger C. Baker (2000) published ahandbook for nearly all the measurement devices withtheir equations and their calibration. Weirs of varioustypes and shapes are one of the oldest structures used formeasuring the discharge of water in open channels. SaraBagheri et al. (2010) studied the curvature of nape profiletheoretically as by quadratic and cubic equations togetherwith different physical models for sharp crested weir, theyintroduced that the coefficient of discharge and simulateflow profile reasonable between them. Shesha Prakash etal. (2011) investigated the flow over inclined rectangularweir with angles 0˚ 15˚, 30˚, 45˚, 60˚, they had found thatthe discharge over the weir increases with the increase ininclination; they introduced a single head-discharge-inclination equation which can be used for any rectangularweir of any desired inclination. Gates also have been usedas a flow meter for controlling and measuring irrigationflows for many years ago. Jung-Fu Yen et al. (2001)investigated characteristics of vertical sluice gate andpredict equations for discharge coefficient anddimensionless discharge, they conclude that betteraccuracy for flow conditions can be achieved byappropriate contraction coefficient for the gate which hassignificant effects on the hydraulic characteristics of thegate, the study was for free and submerged water depth.The energy loss due the contraction of cross section wasused as flow meters by Aldabakh A. J. and Jumaa E. A.(2007), they used a portable devices as a sharp pier fixedin the middle of rectangular channel, the change in theflow profile due to the pier prism in flow was used to

create a relationship between the coefficient of dischargeand Froude number for free flow.

Bahzad and Tahseen (2005) studied thecharacteristics of free flow over normal and oblique weirswith semi circular crests, they found that the value of Cdincrease as values of head to crest height ratio increase fornormal weirs, and Cd increase as the ratio decrease foroblique weirs. Nguyen Ba Tuyen (2006) carriedexperimental study on oblique weir with angles of 0˚, 45˚and 60˚, his study shows the relation between energy lossand the discharge coefficient, he has analyzed the velocitycomponents vertically and horizontally for a reasonabledistance upstream and downstream using simulation, thenhe compared between the experimental and theoreticalinvestigation, and related the coefficient of discharge tothe geometric parameter, also Nguyen Ba Tuyen (2007)studied experimentally flow over oblique weir the analysisof his data which was collected from acoustic (ADV) andelectro-magnetic (EMF) single point velocimeters anddepth measurements, he found that the coefficient ofdischarge slightly decrease with increasing oblique angle,and increase with increasing discharge capacity .

Combining weir and gates in one structure mayreduce effect of sediments and floating materials upstreamand may affect scoring downstream. The performance ofthe combination has been studied by many researchers.Abdel-Azim, at (2001) studied the combined flow overshape rectangular weir and rectangular gateexperimentally they found empirical dimensionlessrelationship for the coefficient of discharge with threedimensionless geometric parameters they find also thatthere is no effect on flow when the opening isn’t verynarrow. Abdel-Azim et al. (2002) carried experimentalinvestigation on combined measurement device ofrectangular weir and rectangular gate, they predict nondimensional equation for the discharge through this devicefor horizontal and sloping channel, the investigation

http://www.arpnjournals.com/

mailto:[email protected]

VOL. 8, NO. 4, APRIL 2013 ISSN 1819-6608




307

conclude that the major geometric parameters effects thedischarge value are the H/d (depth of flow upstream to thegate opening) and y/d (the distance between the weir andthe gate to the gate opening). Kassem Salah El-Alfy(2005) studied experimentally the effect of streamlinescurvature on discharge coefficient due the height of theweir his investigation include of four different types ofweirs, he introduced relationships between dischargecoefficient, Cd and the relative head, H/Y for these weirs.Hayawi H. A. M. et al. (2009) investigated the coefficientof discharge for a combined hydraulic measuring device ofrectangular weir and semi-circular gate, their results showthat Cd increase as the value of head over to the diameterof gate increase. Hayawi H. A. M. et al. (2008) theirinvestigation was to find the characteristics of free flowthrough the combined triangular weir and a rectangulargate. They found that the theoretical discharge is inverselyproportional to the geometrical dimensionless parameters

and directly to distance between the bottom of the weirand the upper edge of the gate.

In this investigation the characteristics ofcombined flow over weir and under gate was studied inopen channel as a device for controlling the flow. A plateof transparent plastic was used with different anglesoblique to the flow direction together with different gateopening from the bed of the channel

THEORETICAL BACKGROUNDThe flow toward the combined structure of weir

and gate is a fall over weir and flow through the gate, thetwo discharges capacity are depending on the depth ofwater in the channel upstream of the combined structure,Figure-1 shows the definition sketch for the flow with thegeometric parameters. To compute the discharge throughcombined structure the equations of the flow over a weircan be added to the equation of the gate assuming onecoefficient of discharge (Cd) for the overall structure.

0.12

0.0020.006

P

H

h

d

m

m

m

= 0.3

m Flow Direction

Alfa

90°60°45°30°

L

W

Figure-1. Definition sketch for the investigation.

weirgateth QQQ (1)

23

23

22 hLggHdLQth (2)

Where

Qth = discharge passing over the weir and under gate (L3

/T)Qweir = discharge passing over the weir (L3 /T)Qgate = discharge passing under gate (L3 /T)H = upstream head (L) = h + P + dd= height of the gate opening (L)h= head depth of water over the weir (L)P= vertical distance between the lower edge of the weirand the upper edge of the gate opening (L)L = weir length (L)g = acceleration of gravity (L/T2)

The actual discharge of total structure can bewritten using one coefficient of discharge as follows:

2

32

3

22 hLggHdLCQ dact (3)

Where

Cd = coefficient of discharge

Based on Eq. (3) and using dimensional analysis,the following functional relationship can be obtained.

),,,,,,,,( eed WRh

P

d

L

L

h

d

P

d

h

d

HfC (4)

Where

= oblique angle from the direction of flow in degrees.

eR = Reynolds number

eW = Weber Number

The values of Reynolds number and Webernumber are not affected due to turbulent flow andneglecting surface tension. The angle can be replacedby the ratio of L/W which is the length of the weir to thechannel width.

EXPERIMENTAL WORKThe experimental investigation was carried out in

a horizontal flume of working length 5m, having a


VOL. 8, NO. 4, APRIL 2013 ISSN 1819-6608




308

rectangular cross section of 0.45m height and 0.3m width.Accurate point gauge with venier scale reading to 0.1* 10-3

m was used for measurements of flow profile headupstream at center line of flume each 5 cm. A plate of0.006 m thickness of transparent plastic was used to

construct four weir models of 0.12m height and lengthsadequate to the oblique angles. The weir was sharpened to0.002m from the upper and lower sides. Figure-2 showsphoto for the flow over and through the combinedstructure.

Figure-2. Representation of the combined structure.

The height of the gate opening was 0.02, 0.03,0.04 and 0.05m for each of the four angle, so sixteendifferent models was tested. The models were classified

into four groups depending on the value of oblique angleTable-1 shows the groups.

Table-1. Details of the model tested.

GroupModel

No.depthd (cm)

Crest lengthL (cm) L/d L/W L/P

Aα = 90º

1 2 30 15 1 2.5

2 3 30 10 1 2.5

3 4 30 7.5 1 2.5

4 5 30 6 1 2.5

Bα = 60º

5 2 34.6 17.3 1.2 2.9

6 3 34.6 11.5 1.2 2.9

7 4 34.6 8.7 1.2 2.9

8 5 34.6 6.9 1.2 2.9

Cα = 45º

9 2 42.4 21.2 1.4 3.5

10 3 42.4 14.1 1.4 3.5

11 4 42.4 10.6 1.4 3.5

12 5 42.4 8.5 1.4 3.5

Dα = 30º

13 2 60 30 2 5

14 3 60 20 2 5

15 4 60 15 2 5

16 5 60 12 2 5

RESULTS AND DISCUSSIONSThe data collected from the tests of the four angle

group and four heights of gate opening models arepresented in Figures 3 to 6. It is clear that the dischargepassing the combined structure is increases with increaseof the upstream head (H) and with increase of the gate

height opening and also the discharge increases withdecrease of the angle (α), which means a longer length ofweir and gate. The increase of the discharge capacity ofthe other geometrical parameters for certain upstreamdepth is reasonable.


VOL. 8, NO. 4, APRIL 2013 ISSN 1819-6608




309

Q act = 0.000H3.529

R² = 0.998

Q act = 0.001H3.259

R² = 0.998

Q act = 0.000H3.607

R² = 0.999Q act = 0.000H3.432

R² = 0.999

8

10

12

14

16

18

20

22

24

26

28

15 16 17 18 19 20 21 22 23

MeasureddiscargeQactx10-3m

3/s

Total head H x10-2 m

Height of gate d= 0.02 mAlfa 30

Alfa 45

Alfa 60

Alfa 90

Figure-3. Relation between the discharge and upstream head for d =0.02 m.

Q act = 0.005H2.840

R² = 0.992 Q act = 0.009H2.556

R² = 0.999 Q act = 0.003H2.834

R² = 0.996 Q act = 0.002H2.959

R² = 0.997

8

10

12

14

16

18

20

22

24

26

28

15 16 17 18 19 20 21 22 23 24


3/s



Alfa 45

Alfa 60

Alfa 90

Figure-4. Relation between the discharge and upstream head for d = 0.03m.

Q act = 0.024H2.335

R² = 0.995Q act = 0.024H2.260

R² = 0.998 Q act = 0.011H2.460

R² = 0.995

Q act = 0.003H2.837

R² = 0.999

8

10

12

14

16

18

20

22

24

26

28

30

15 16 17 18 19 20 21 22 23 24


3/s



Alfa 45

Alfa 60

Alfa 90



VOL. 8, NO. 4, APRIL 2013 ISSN 1819-6608




310

Q act = 0.190H1.668

R² = 0.948Q act = 0.046H2.080

R² = 0.998Q act = 0.048H2.007

R² = 0.996

Q act = 0.005H2.686

R² = 0.998

8

10

12

14

16

18

20

22

24

26

28

30

15 16 17 18 19 20 21 22 23 24 25


3/s



Alfa 45

Alfa 60

Alfa 90


The reasonable power relationship shown inFigures 3 to 6 between the measured discharge and theupstream head (H) of the form Q=K H n, the power (n) hasa certain trend of decreasing value with increase of heightopening of the gate (d), the constant (K) has the increasingtrend values with increasing value of (d), to explain thistrend of increasing values is due the increasing dischargecapacity passing through the gate. It can be also mentioned

that all the equations with a high coefficient ofdetermination.

The calculated value of discharge coefficient Cd

in equation (3) was studied with the dimensionlessparameters in equation (4) it is clear that the value of Cd

increases with the increase of h/d and decreases with thedecrease of oblique angle from the direction of flow,Figure-7 shows the relation.

0.40

0.45

0.50

0.55

0.60

0.65

0.0 0.5 1.0 1.5 2.0 2.5 3.0

DischargeCoefficintCd

h/d

d=0.03 m

Alfa 90

Alfa 60

Alfa 45

Alfa 30

0.40

0.45

0.50

0.55

0.60

0.65

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Disc

harg

e Co

effic

int

Cd

h/d

Alfa 90

Alfa 60

Alfa 45

Alfa 30

d = 0.04 m

(a) (b)

Figure-7. Relation between the discharge coefficient and h/d.

The value of Cd increase with increase of H/d Figure-8 shows the tendency for different values of oblique angle tothe direction of flow:

0.40

0.45

0.50

0.55

0.60

0.65

0.0 2.0 4.0 6.0 8.0 10.0 12.0


H/d

Alfa 90

d = 0.02 m

d = 0.03 m

d = 0.04 m

d = 0.05 m

0.40

0.45

0.50

0.55

0.60

0.65

0.0 2.0 4.0 6.0 8.0 10.0 12.0


H/d

Alfa 60

d = 0.02 m

d = 0.03 m

d = 0.04 m

d = 0.05 m

(a) (b)

Figure-8. Relation between discharge coefficient and H/d.

It also found that the value of Cd decreases withincreases of (P/h) and (L/h) as shown in Figures 9 and 10.The decreases of Cd are due to decrease of head acting on

the weir causing less performances of weir relative to thegate flow:


VOL. 8, NO. 4, APRIL 2013 ISSN 1819-6608




311

0.40

0.45

0.50

0.55

0.60

0.65

0 1 2 3 4 5

CoefficientofdischargeCd

P/ h

d = 0.02 m

d = 0.03 m

d = 0.04 m

d = 0.05 m

Alfa90

0.40

0.45

0.50

0.55

0.60

0.65

0 1 2 3 4 5 6 7


P/ h

d = 0.02 m

d = 0.03 m

d = 0.04 m

d = 0.05 m

Alfa45

(a) (b)

Figure-9. Relation between discharge coefficient and P/h.

0.40

0.45

0.50

0.55

0.60

0.65

0 5 10 15 20


L/ h

d = 0.02 m

d = 0.03 m

d = 0.04 m

d = 0.05 m

Alfa60

0.35

0.40

0.45

0.50

0.55

0.60

0 10 20 30 40 50


L/ h

Series1

Series2

Series3

Series4

Alfa30

(a) (b)

Figure-10. Relation between discharge coefficient and L/h.

The coefficient of discharge for weir is heigherthan that for a gate due to the contraction under the gate,that fact effects also the conbined stucture causing betterperformance of the flow over the wier than that under thegate. To find the mathematical relation of the coefficientof discharge Cd with other dimensionless parameters, thevalue of discharge coefficient Cd were in the range from0.623 to 0.403, With Standard Error 0.0047 and StandardDeviation 0.051. The total experimatal measures of fouroblique angles, four heights of gate openings and thecalculated values of the dimensionless parameters of theequation (4) were combinrd to carry stastical analysis forthe data by using the fasilites of the SPSS 17 Package. The

correlation between the depentent variable Cd with thecalculated dimiensionless parameters was studidet, it wasfound that the indepentednt parametres (H/d, h/d, P/d, P/h,L/h, L/d and L/W) have a significant correlation at the0.01 level (2- tailed) and the highest positve PearsonCorrelationis factor 0.828 between the Cd and h/d.

Nonlinear Regression Analysis of 26 differentmodels is carried on by the same package. The modelswere defined in three equation types, the linear, square andpower. The best 9 models obtained from differentrelationships analysis of the dimensionless parameterswith the highest R2 are shown in Table-2.


VOL. 8, NO. 4, APRIL 2013 ISSN 1819-6608




312

Table-2. The regression models analysis.

No. Equation R2

1d

P

d

L

W

L

d

hCd 018.0007.0138.0033.0639.0 0.972

2W

L

h

L

h

P

d

P

d

h

d

HCd 075.0000062.0007.0010.0098.0011.0565.0 0.944

3W

L

d

P

d

hCd 083.0074.0076.0595.0 0.915

4222222

024.0000004.00002.0007.0013.0005.0504.0

W

L

h

L

h

P

d

P

d

h

d

HCd 0.935

52222

001.00001.0039.0007.0562.0

d

P

d

L

W

L

d

hCd 0.946

622

035.0006.0558.0

W

L

d

hCd 0.951

7663.0198.0266.0125.1425.0855.044.0

219.0

W

L

d

L

h

L

h

P

d

P

d

h

d

HCd 0.940

8008.2207.2203.2233.0440.0

536.2

W

L

h

L

h

P

d

P

d

HCd 0.940

9199.0245.0455.0

331.0

W

L

d

P

d

HCd 0.940

The best and simplest equation for predecting thevalue of discharge coefficient Cd is the first one in theTable-2, which has been found by the regression of thedata of Cd assusieted with 7 dimensionsless parametersusing stepwise method of including independent varablesin modele to determing statisticaly signifucnce pridictorsin the equation by starting the modele with the higherindepent correlation varaible in the matrix at confidencelevel of 95% while after including four indepentent

varibles and stopped with Adjusted R square is 0.971 andstadard Error of estimate equle to 0.0087664.

)5(018.0007.0138.0033.0639.0d

P

d

L

W

L

d

hCd

The statistical analysis output details for theproposed equation (5) are shown in Table-3 and Table-4.The plot of the normal P-P regression standardizedresidual is shown on Figure-11.

Table-3. Stepwise regression analysis.


VOL. 8, NO. 4, APRIL 2013 ISSN 1819-6608




313

Table-4. Stepwise regression coefficients.

Figure-11. Normal P-P plot regression standardizedresidual.

The sugested above equation (5) assummed thatthe coefficient of dicharge is the same for the weir and thegate in the combined structure, while each one performs

depending on its phenomena of flow. To find percent offlow over weir and under gate, a linaer regression analysiswas caried for the actual measured discharge as dependentvariable and the thoretical calculated dicharges over theweir and under the gate as independent variables. Themodel of the relation is pesented in equation (6).

)6(.. weirThowgateThogmeasured QCQCQ

Where

Cg= percent of theoretical flow under gateCw= percent of theoretical flow over weir

The output of the model analysis for the range ofexperimatal measrements shown in Table-5 and Table-6.

Table-5 (a). The regression models analysis for equation (6).

Table-5 (b) Coefficients for models in equation (6).


VOL. 8, NO. 4, APRIL 2013 ISSN 1819-6608




314

The analysis lieds to form equation (7) betweenthe flow of weir and flow under the gate.

)7(754.0403.0 .. weirThogateThomeasured QQQ

Comparing the calculated values of the dischargefrom the two segusted equations (5) and (7) it clear thatequation (7) has predicted more scattering values than

equation (5), see Figure-12, Using statistical descriptiveanalysis which shown in Table-6 for percent errorcalculated relative the measured discharge. From Table-6the mean percent error 0.03 with stabdard error of 0.154in equation (5) and 1.459 mean percent error in equation(7) with atanderd error of 0.488 that mean eqution (5) ismore confidence to predicte the dischargein the combinedstructure.

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

Measureddischargex10-3(m

3/s)

Predicted Value of discharge x 10-3 (m3/s)

Discharge calculated from Cd of equation (5)

Discharge calculated from equation (7)

Figure-12. Comparison between measured and calculated discharge.

Table-6. Descriptive analysis or error in the proposed equations.

Error % in Equ.(5) Error % in Equ.(7)Mean -0.030565392 Mean 1.459114Standard Error 0.154663671 Standard Error 0.488033Median -0.036369837 Median 1.682439Standard Deviation 1.687181467 Standard Deviation 5.323809Sample Variance 2.846581302 Sample Variance 28.34294Kurtosis -0.114304391 Kurtosis -0.66915Skewness 0.263401481 Skewness -0.16699Range 8.739196522 Range 22.48266Minimum -3.86426555 Minimum -10.5863Maximum 4.874930972 Maximum 11.89634Sum -3.637281657 Sum 173.6346Count 119 Count 119Confidence Level(95.0%) 0.306276173 Confidence Level(95.0%) 0.966438


VOL. 8, NO. 4, APRIL 2013 ISSN 1819-6608




315

CONCLUSIONSThe flow over weir and under gate in combiened

structure was studied experimantaly in open channel as adevice for measuring flow in chanel system. From studingthe effects of geometrical parameters and hydraulicfeatures by statistical analysing of experimental data thefollowing conclusions may fixed.

a) The major parameters effecting significantly on

discharge ared

P

d

L

d

h,,, .

b) The value of Cd increases with the increase of h/d anddecreases with the decrease of oblique angle but thecapacity of the structure increase.

c) The value of Cd decreases with increases (L/d) and(P/d).

d) The value of Cd range from 0.623 to 0.403, withStandard Error 0.0047

e) Within the limitations of the present experimentalwork a discharge prediction (Equation5) is developedwith mean percent error of 0.030 %.

f) A simple discharge prediction (Equation7) with meanpercent error of 1.459 %.

REFERENCES

Abdel-Azim M. Negm, A.M. Al-Brahim and A.A.Alhamid. 2002. Combined-Free Fow over Weirs andbelow Gates. Journal of Hydraulic Research. 40: 359-365.

Aldabakh A.J. and Jumaa E.A. 2007. DischargeMeasurement in Rectangular Channels Using PortablePrisms. Journal of Engineering and Technology. 3:132-142.

Bahzad M. A. Noori and Tahsseen A. H. Chilmerau. 2005.Characteristics of Flow over Normal and Oblique Weirswith Semicircular Crests. Al-Rafidian EngineeringJournal. 13(1).

Hayawi H. A. M., Hayawi G. A. M and Amal A. G. 2009.Coefficient of Discharge for a Combined HydraulicMeasuring Device. Al-Rafidain Engineering Journal. 17:92-100.

Hayawi H. M., Yahia A. G and Hayawi A.G. 2008. FreeCombined Flow Over a Triangular Weir and UnderRectangular Gate. Damascus Univ. Journal. 24: 9-22.

Jung-Fu Yen, Chih-Han Lin and Chang-Tai Tsai. 2001.Hydraulic Characteristics and Discharge Control of SluiceGates. Journal of the Chinese Institute of Engineers. 24:301-310.

Kassem Salah El-Alfy. 2005. Effect of Vertical Curvatureof Flow at Weir Crest on Discharge Coefficient. 9th

International Water Technology Conference, IWTC9,Sharm El-Sheikh, Egypt. pp. 249-262.

Nguyen Ba Tuyen. 2007. Influences of the ObliqueObstacles to the Flow. Japan-Vietnam Estuary Workshop,August 20th-24th, Hochiminh, Vietnam.

Nguyen Ba Tuyen. 2006. Flow over Oblique Weirs.Master of Science Thesis, Delft University of Technology,Netherlands.

Roger C. Baker. 2000. Flow Measurement Handbook.Cambridge University Press.

Sara Bagheri and Manouchehr Heidarpour. 2010. Flowover rectangular sharp-crested weirs. Spriger, Irrig. Sci.28: 173-179.

Shesha Prakash M.N., Ananthayya M. B. and Gicy M.Kovoor. 2011. Inclined Rectangular Weir-Flow Modeling.Earth Science India, ESi. 4: 57-67.

U. S. Department of the Interior Bureau of Reclamation.1997. Water Measurement Manual, U.S. GovernmentPrinting Office, Washington, DC 20402.


Experimental Study of Combined Oblique Weir and … · combined flow over weir and under gate was...

Documents

Transcript of Experimental Study of Combined Oblique Weir and … · combined flow over weir and under gate was...