INTRODUCTION

A.1. Crump Weir

Weirs are considered as hydraulic structures usually used for indirect flow measurement and/or controlling water elevation in basins and channels [1],[2]. When installing a weir in an open channel, a relationship between flow rate and water flow height above weir may be derived according to weir geometry on the basis of the Bernoulli equation [3]. Water viscosity and surface tension as well as weir surface roughness and geometry are all parameters included in that relationship. However, surface tension effect is very small compared to the other parameters and can be neglected [4]. The relationship “flow rate equation” is, principally, consist of dimensions related to weir geometry and upstream water depth, whereas the other parameters are included in a term called “discharge coefficient, Cd” in the equation. The Cd is assumed to cover effects of vertical curvature of the upstream flow streamlines in the vicinity of weir which cause head differences at both upstream and over weir. It also covers the assumption of considering pressure distribution upstream weir is hydrostatic [5]. According to downstream flow conditions, flow over weir may be modular or non-modular. In modular flow, the weir operates undrowned, and the upstream head is not affected by the downstream head, whereas in nonmodular, the weir operates drowned, and the upstream head is affected by changes in the downstream head. Therefore, it is possible to determine the flow rate depending on only upstream head measurement in modular flow in contrast to non-modular, which has to include downstream head by means of “submergence factor” [6],[7], [8]. Weirs installed in open channels can take a verity of applications, such as in rivers, irrigation channels, water treatment plants, industries…etc. However, the most popular type of weirs adopted in rivers and relatively wide streams are long base weirs for their structural stability and simplicity, and also comparative good accuracy in flow measurement. Crump weir is considered one of the Broad crested weirs (long base weirs) [9],[10]. Its hydraulic behaviour approaches to the stepped weirs that considerably dissipate hydraulic jump energy in downstream side that may endanger stability of the weir [11],[12]. Standard crump weir has a triangular section along flow direction with an upstream slope of 1 (vertical) to 2 (horizontal) and a downstream slope of 1 to 5, and the intersection of upstream and downstream surfaces forms a straight line crest, horizontal and at right angles to the direction of flow in the approach channel [10]. However, some modifications for the geometry of the weir have been investigated for certain purposes. Servais carried out a study through which several physical models of low-cost modifications to the Crump weir investigated in order to improve fish passage in England and Wales. Her study included the hydraulic investigation for installing baffles with different numbers, geometry and arrangement [13]. AL-Naely et. al. studied the effect of longitudinal flow openings (holes) penetrating upstream and downstream faces of crump weir, horizontally, to do as energy dissipaters, and as an improver for the discharge coefficient [14]. Triangular profile flat-V weir is a modification for the crump weir to measure a wider range of discharges by adopting a transverse symmetrical V-shaped crest, having small side-slopes (typically 1:10, 1:20 or 1:40) in the planes normal to the flow direction (upstream and downstream faces)[15],[16],[17],[18],[19]. Its longitudinal section is triangular same as that of crump weir but with possibility of equal (1:2) longitudinal slopes rather than the standard slopes (1:2) and (1:5) of upstream and downstream faces of standard crump weir [20]. Keller studied a standing inclined crest Crump weir. He concluded that at relatively large heads, the weir behaves as one half of a flat-V Crump weir for the same transversal crest slope. At lower heads, the flow cross section becomes strongly asymmetrical with a significant decrease in discharge coefficient value, [21]. Through the present study, a modified crump weir is adopted. The modified weir have triangular section along flow direction with equal longitudinal slopes as (1 vertical: 2 horizontal) for the upstream and downstream plane faces, with a transverse symmetrical V-shaped crest of three slopes (1:8, 1:4, 1:2.5). So, the invert of the V-shaped crest of the adopted modified weir represent horizontal line parallel to flow direction rather than the common triangular profile flat-V weir which has a point invert not as line, Figure 1. According to available literature, such modified weir may be investigated for the first time through present study. Justification for such study is that it investigates a weir that provide solution for wider flow range in open channels. This modified weir if replicated to form a structure consisting of successive attached weir segments, transversally, can provide a solution for the problem of uneven distribution of crest water depth along wide section channels. Test experiments of four weir models for different water flow rates and depths (upstream and downstream) have been evaluated. The results used to conclude a multiple regression equation for the discharge coefficient of the modified weir for variables driven from dimensional analysis.

2. Methodology

2.1. Hypothesis And Constrains

This study assumes constant values as constrains for some variables related to the models tested and conditions of experiments. The variables assumed to have constant values are: weir length, width, crest height of sides and longitudinal slopes (upstream and downstream slopes), whereas middle crest height is variable. Hydraulic variables considered are flow rate and flow depth in upstream and downstream sides. Water temperature was nearly constant throughout experiments (around 25 ±1 ºC). Channel bottom slope is zero (horizontal).

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