SLUICE-GATE DISCHARGE EQUATIONS By Prabhata K. Swamee' ABSTRACT: Sluice-gate discharge coefficient is an involved function of geometric and hydraulic parameters. For free flow, it is related to upstream depth and gate opening, whereas for submerged flow, in addition to these parameters, it depends on tail-water depth. The present practice of discharge coefficient determination is from curves drawn relating discharge coefficient and upstream-depth gate-opening ratio with tail-water-depth gate-opening ratio being the third parameter for sub- merged flow. This method lends itself to sufficient error of judgment due to in- terpolation between two types of curves. Furthermore, the graphical information cannot be used for any analytical and/or numerical method for flow control and flow profile determination. In this paper high-accuracy discharge coefficient equa- tions for free and submerged flows have been developed along with the criterion for determination of free and submerged flow. Procedures for solution of various gate-opening problems have also been given. INTRODUCTION A sluice gate is an opening in a hydraulic structure used for controlling the discharge. Fig. 1 shows flow through a sluice gate with no side or bottom contraction. Downstream free flow occurs at a (relatively) large ratio of upstream depth to the gate-opening height. However, submerged flow at the downstream would occur for low values of this ratio. For a freely issuing stream from a sluice gate, the water surface is quite smooth whereas for a submerged flow, the corresponding flow profile is extremely rough. The conventional sluice-gate discharge equation is written in the form: Q = C.abVWo (1) in which Q = the sluice-gate discharge; a = the sluice-gate opening; b = the sluice-gate length; h 0 = the upstream water depth; g = gravitational acceleration; and C d = discharge coefficient. Fig. 2 shows the variation of C d under free and submerged flow conditions as obtained by Henry (1950). Henry's experimental investigation is considered most extensive and relia- ble. Henry's investigation was later confirmed by Rajaratnam and Subra- manya (1967). Presented herein are accurate equations of discharge coefficient for free and submerged flow conditions. It is hoped that these equations will find use in flow regulation in canals and flow analysis involving sluice gates. DISCHARGE COEFFICIENT EQUATIONS Free Flow Condition A perusal of Fig. 2 indicates for free flow the discharge coefficient pro- gressively increases to a saturation value of 0.611. Hydraulically the sluice gate ceases to exist when h 0 = a or less. Thus for h a = a the discharge 'Prof, of Civ. Engrg., Univ. of Roorkee, Roorkee—247 667, India. Note. Discussion open until July 1, 1992. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on December 28, 1990. This paper is part of the Journal of Irrigation and Drainage Engineering, Vol. 118, No. 1, January/February, 1992. ©ASCE, ISSN 0733-9437/92/0001-0056/$1.00 + $.15 per page. Paper No. 1113. 56 ownloaded 14 Aug 2009 to 124.124.247.56. Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copy