Technical Note Discharge Characteristics of Weirs of Finite Crest Length with Upstream and Downstream Ramps Amir Hossein Azimi 1 ; Nallamuthu Rajaratnam, F.ASCE 2 ; and David Z. Zhu, M.ASCE 3 Abstract: This paper considers flow measurement in open channels with transverse weirs of finite crest length with sloping crests and upstream or downstream ramps—or both—for free flows. Using the broad-crested weir equation with a discharge coefficient as the basis and following the earlier studies of broad-crested weirs, robust correlations have been developed for the discharge coefficient by using the experimental results available in the literature. Effects of upstream and downstream ramps were studied by introducing the upstream and the downstream length scales, respectively. The proposed correlations of embankment weirs were compared with the head-discharge formu- lations of embankment weirs in the literature. Triangular (hump) weirs with either upstream or downstream ramps (or both) have also been considered. It was found that in triangular (hump) weirs, the discharge coefficient increases when the downstream slope increases, but it decreases when the upstream slope increases. DOI: 10.1061/(ASCE)IR.1943-4774.0000519. © 2013 American Society of Civil Engineers. CE Database subject headings: Weirs; Embankments; Flow measurement; Open channel flow; Water flow; Slopes; Wave crest. Author keywords: Broad-crested weirs; Embankment weirs; Flow measurement; Hump; Open channel flow; Triangular weirs; Water flow. Introduction Weirs are generally divided into two groups, namely, sharp-crested weirs and weirs of finite crest length. The second group has been further subdivided into three groups, namely, long-crested, broad- crested, and narrow-crested weirs, depending on the value of the h=L, where h is the head over the weir, measured some distance upstream of the weir, where the water surface is essentially hori- zontal; and L is the crest length in the longitudinal direction. For the long-crested weir, h=L is approximately in the range of 0–0.1. For the broad-crested weir, h=L is in the range of 0.1–0.4, whereas for the narrow-crested weir, h=L is in the range of 0.4 to approximately 2.0. For h=L greater than approximately 2.0, it behaves like a sharp-crested weir. Furthermore, the upstream end of the weir could be square-edged or rounded. Many experi- mental studies have been carried out to investigate broad-crested weirs with upstream and/or downstream ramps. Despite the fact that some researchers have tried to formulate head-discharge rela- tionships based on their measurements and limited data from the literature (see Table 1), a generally satisfactory correlation has not been found. Recently, Azimi and Rajaratnam (2009), based on the assumption of the occurrence of parallel critical flow on the crest, wrote the discharge equation for the finite crest length weirs as Q ¼ C d B ffiffiffiffiffiffiffiffiffiffi 8=27 p ffiffi g p h 3=2 ð1Þ for all the three groups, where Q = discharge; C d = discharge co- efficient when the upstream head is used; B = width of the channel in which the weir is installed perpendicularly across the full width; and g = acceleration attributable to gravity. Using the experimental observations from the literature, they studied the variation of the discharge coefficient for the long-crested, broad-crested, and narrow-crested weir ranges and developed correlations for the C d for the three types of weirs for both square-edged and rounded entrances. The present work attempts to extend this earlier work of Azimi and Rajaratnam (2009) to finite crest length weirs, which can be referred to simply as broad-crested weirs (see Fig. 1, section a1), with sloping crests and with sloping upstream and downstream ramps. It is also extended to triangular (hump) weirs (in which the crest length is zero) with either upstream ramps, downstream ramps, or both. A summary of experimental studies with classifi- cation according to types of weirs is shown in Table 1. The devel- oped empirical formulations of each type of weir in this study are valid for the range of experimental parameters shown in Table 1. Brief Summary of Experimental Investigations on Weirs of Finite Crest Length Woodburn (1932) conducted a limited set of experiments for long- crested and broad-crested weirs with positive slopes (see Table 1). Experimental results for broad-crested and narrow-crested weirs with negative crest slopes are available from the United States Deep Waterways (USDW) and USGS investigations and from the work of Murphy (results are available in Horton 1907). Numerous exper- imental investigations have been carried out on broad-crested weirs with either upstream ramps, downstream ramps, or both. These include the works of Bazin (available in Horton 1907), Fritz and Hager (1998), Sargison and Percy (2009), and Noori and Juma (2009). The detailed parameters of each experiment are shown in Table 1. Fritz and Hager (1998) investigated broad-crested weirs with the upstream and downstream ramps with slopes of 1V to 2H and combined their results with the observations by Bazin 1 Postdoctoral Fellow, Dept. of Civil and Environmental Engineering, Univ. of Alberta, Edmonton, AB, Canada T6G 2W2. E-mail: azimi@ ualberta.ca 2 Professor Emeritus, Dept. of Civil and Environmental Engineering, Univ. of Alberta, Edmonton, AB, Canada T6G 2W2. E-mail: nrajaratnam@ ualberta.ca 3 Professor, Dept. of Civil and Environmental Engineering, Univ. of Alberta, Edmonton, AB, Canada T6G 2W2 (corresponding author). E-mail: david.zhu@ualberta.ca Note. This manuscript was submitted on December 13, 2011; approved on June 25, 2012; published online on December 16, 2012. Discussion per- iod open until June 1, 2013; separate discussions must be submitted for individual papers. This technical note is part of the Journal of Irrigation and Drainage Engineering, Vol. 139, No. 1, January 1, 2013. © ASCE, ISSN 0733-9437/2013/1-75-83/$25.00. JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING © ASCE / JANUARY 2013 / 75 J. Irrig. Drain Eng. 2013.139:75-83. Downloaded from ascelibrary.org by Lakehead University on 09/10/13. Copyright ASCE. For personal use only; all rights reserved.