# Experimental determination of contraction coefficient and velocity coefficient for radial gates with elliptical lips

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## Abstract

Radial gates are widely used to control the flow in irrigation channels and spillways. Radial gates require lower hoisting force and have better discharge characteristics in partial gate openings. The accurate discharge measurement through a radial gate is a challenging problem especially in submerged flow conditions. The coefficient of contraction \( C_{c} \) is an important parameter for accurate discharge measurement in open channels. In this study, an attempt has been made to determine the coefficient of contraction\( C_{c} \) and velocity coefficient \( C_{v} \) for radial gates both for free flow and submerged flow conditions. The flow emanating from a gate is similar to the wall jet emerging from a nozzle. The \( C_{c} \) and \( C_{v} \) values under free and submerged flow conditions are obtained from the measured jet velocity and the discharge. The coefficient of discharge values under submerged flow conditions show large variations with submergence and hence discharge characteristics needs to be improved for better control of flow. Hence, experiments are conducted so as to improve the discharge characteristics by modifying the exit geometry of the radial gate by attaching a quarter of an elliptical lip. Three different geometries of elliptical lips were attempted and the results show reasonable increase in the contraction coefficient.

## Keywords

Radial gates contraction coefficient wall jet acoustic doppler velocimeter (ADV) laboratory experiments## List of symbols

- a
height of gate opening

- b
length of the semi minor axis of the quadrant lip

- \( C_{c} \)
coefficient of contraction of the gate

- \( C_{v} \)
coefficient of velocity

- \( C_{dw} \)
coefficient of discharge of the weir

- d
length of the semi major axis of the quadrant lip

- \( g \)
acceleration due to gravity

- H
difference in manometer readings in the u-tube

- \( H_{w} \)
head over the crest of the weir

- \( H_{1} \)
upstream energy head

- \( L \)
width of the channel and length of the weir

- P
height of the weir

- p
pinion height of the gate

*Q*_{act}actual discharge in the flume

- R
radius of the radial gate

- \( R_{e} \)
Reynolds number

- \( v \)
velocity downstream of the gate

- \( v_{j} \)
jet velocity

- \( v_{1} \)
average velocity upstream of the gate

- \( y \)
depth of water immediately downstream of the gate

- \( y_{j} \)
depth of water at the vena-contracta

- \( y_{1} \)
depth of water upstream of the gate

- \( y_{2} \)
depth of water downstream at the exit of the gate

- \( y_{3} \)
tail water depth in the flume

- α
velocity distribution coefficient

- β
energy loss coefficient

- \( \nu \)
kinematic viscosity

- θ
gate angle

## References

- 1.Henry H R 1950 Discussion of diffusion of submerged jets
*. Trans. Am. Soc. Civ. Eng.*115(1): 665–693Google Scholar - 2.Rajaratnam N and Subramanya K 1967 Flow equation for the sluice gate.
*J. Irrig. Drain Division.*93(3): 167–186Google Scholar - 3.Swamee P K 1992 Sluice-gate discharge equations.
*J. Irrig. Drain. Eng.*118(1): 56–60CrossRefGoogle Scholar - 4.Montes J S 1997 Irrotational flow and real fluid effects under planar sluice gates.
*J. Hydraul. Eng.*123(3): 219–232CrossRefGoogle Scholar - 5.Ferro V 2000 Simultaneous flow over and under a gate.
*J. Irrig. Drain Eng.*126(3):190–193CrossRefGoogle Scholar - 6.Ferro V 2001 Closure of simultaneous flow over and under a gate.
*J. Irrig. Drain Eng.*127(5): 325–328CrossRefGoogle Scholar - 7.Lin C H, Yen J F and Tsai C T 2002 Influence of sluice gate contraction coefficient on distinguishing condition.
*J. Irrig. Drain Eng.*128(4): 249–252CrossRefGoogle Scholar - 8.Lozano D, Mateos L, Merkley G P and Clemmens A J 2009 Field calibration of submerged sluice gates in irrigation canals.
*J. Irrig. Drain Eng.*135(6): 763–772CrossRefGoogle Scholar - 9.Belaud G, Cassan L and Baume J P 2009 Calculation of contraction coefficient under sluice gates and application to discharge measurement.
*J. Hydraul. Eng.***135**(12): 1086–1091CrossRefGoogle Scholar - 10.Sepúlveda C, Gómez M and Rodellar J 2009 Benchmark of discharge calibration methods for submerged sluice gates.
*J. Irrig. Drain Eng.*135(5): 676–682CrossRefGoogle Scholar - 11.Cassan L and Belaud G 2011 Experimental and numerical investigation of flow under sluice gates
*. J. Hydraul. Eng.*138(4): 367–373CrossRefGoogle Scholar - 12.Castro-Orgaz, O Lozano D and Mateos L 2010 Energy and momentum velocity coefficients for calibrating submerged sluice gates in irrigation canals.
*J. Irrig. Drain Eng.*136(9): 610–616CrossRefGoogle Scholar - 13.Habibzadeh A, Vatankhah A R and Rajaratnam N (2011) Role of energy loss on discharge characteristics of sluice gates.
*J. Hydraul. Eng*. 137(9): 1079–1084CrossRefGoogle Scholar - 14.Buyalski C P 1983 Discharge algorithms for canal radial gates (No. 627.13 B8). Engineering and Research Centre, U.S. Bureau of Reclamation, DenverGoogle Scholar
- 15.Clemmens A J, Strelkoff T S and Replogle J A 2003 Calibration of submerged radial gates.
*J. Hydraul. Eng.*129(9): 680–687CrossRefGoogle Scholar - 16.Wahl T L 2005 Refined energy correction for calibration of submerged radial gates.
*J. Hydraul. Eng.*131(6): 457–466CrossRefGoogle Scholar - 17.Shahrokhnia M A and Javan M 2006 Dimensionless stage–discharge relationship in radial gates.
*J. Irrig. Drain Eng.*132(2): 180–184CrossRefGoogle Scholar - 18.Bijankhan M, Ferro V and Kouchakzadeh S 2012 New stage-discharge relationships for radial gates.
*J. Irrig. Drain Eng.*139(5): 378–387CrossRefGoogle Scholar - 19.Replogle J A, Adler R and Gooch R S 2003 Operational evaluations of new radial gate design. Water for a sustainable world—limited supplies and expanding demand In:
*Proceedings of 2nd International Conference on Irrigation and Drainage*, Phoenix, AZGoogle Scholar - 20.Pani B S 2012
*Turbulent jets*. Foundation Books: 186Google Scholar - 21.Tel J 2000
*Discharge relations for radial gates*. Master of Science Thesis, Delft Technical University, DelftGoogle Scholar - 22.Rusello P J, Lohrmann A, Siegel E and Maddux T 2006 Improvements in acoustic Doppler velocimetery, Food and Agricultural organisation of United Nations, http://www.ifremer.fr/avano/
- 23.Speerli J and Hager W H 1999 Discussion of irrotational flow and real fluid effects under planer gates, by J S montes.
*J. Hydraul. Eng.*125(2): 208–213CrossRefGoogle Scholar