## VOL. 3, NO. 2, APRIL 2008

ISSN 1819-6608

# ARPN Journal of Engineering and Applied Sciences

©2006-2008 Asian Research Publishing Network (ARPN). All rights reserved.

www.arpnjournals.com

INVESTIGATION OF THE UPSTREAM AND DOWNSTREAM SLOPE OF THE LONG-THROATED FLUMES ON THE DISCHARGE COEFFICIENT

Samad Emamgholizadeh^{1 }and Kazem Assare^{1 }^{1}Department of Water and Soil, Agriculture College, Shahrood University, Shahrood, Iran E-mail: s_gholizadeh517@yahoo.com

# ABSTRACT

Long-throated flumes provide economical and flexible water measurement capabilities for a wide variety of open- channel flow situations. Primary advantages include minimal head loss, low construction cost, adaptability to a variety of channel types, and ability to measure wide ranges of flows with custom-designed structures. Discharge coefficient of long- throated depends on many parameters such as upstream and downstream slope, step height and throat length. In order to investigate the effects of these parameters on the values of discharge coefficient, in this study a series of laboratory experiments were carried out in a flow measurement flume of rectangular cross section.

The experiments carried out with different upstream and downstream slope, two step height (P = 7.62 and 15.62cm), constant throat width (w = 25cm) and throat length (L = 30.48cm). Eleven different models made of Plexiglas were tested in a horizontal flume for large range of discharges. The results of this study indicated the long-throated flume can be used for flow measurement with average of 1.6% flow measurement error. Also the results reveled that the decreasing of upstream slope and the increasing of downstream slope would caused the discharge coefficient is increased.

Keywords: flumes, water, flow, measurement, slope, upstream, downstream, step height, throat length.

# 1.0 INTRODUCTION

The most common structures used to measure flow in open channels operated by producing critical flow or flow at critical-depth through a control section of known dimensions under this flow condition, the discharge through the critical section is a function of the section shape and the upstream potential energy, as indicated by the water level upstream from the structures. By definition, the presence of critical flow in the control section prevents the downstream water level and flow conditions from affecting the flow through the critical section, and the discharge can be computed as a function of the measured upstream head. Sharp-crested weirs, broad-crested weirs, and a wide variety of flumes are examples of critical-flow devices. To apply a critical-flow device for flow measurement, one must define the particular relation between flow rate and upstream head, and the range over which it is applicable (Clemmens et al., 2001).

These two issues present a significant problem for some critical-flow devices are:

The flow through the critical section of many of these devices is three- dimensional and cannot be easily analyzed with available one dimensional hydraulic theory. Therefore these devices must be calibrated with the aid of physical models, laboratory tests, or complex three- dimensional numerical modeling; laboratory calibration tests that determine empirical discharge coefficients are the most commonly used.

The discharge coefficients of many critical- flow devices vary widely when operating outside of a narrow rang of conditions. For example the discharge coefficients of sharp-crested weirs change significantly if tail water level exceeds the crest elevation of control section (i.e. the crest is submerged).

Studies of flow measuring structures in open channels, such as broad crested weirs and long throated flumes of different cross sections have been reported by various investigators (Bos, 1977; Bos, 1978; Bos and Reinink, 1981; Bos, Replogle and Clemmens, 1984). In all these studies theoretical analyses were followed by experimental investigations to obtain relations between hydraulic and geometric parameters.

# 1.1. Long-throated flume

The term long-throated flume describes a broad family of critical-flow flumes and used to measure open- channel flows. A variety of specific configurations are possible depending on the type of approach channel, the shape of the throat section, the location of the gauging station, and the use or lack of a diverging transition section(Wahl et al., 2000). Figure-1 shows the general longitudinal profile of flow through a long-throated flume. The subscripts 1 and 2 refer to conditions in the approach and tail water channels, respectively, and the subscript c will refer to conditions at the critical section. In this Figure Q is discharge, v is the flow velocity, p is the step height, y is the water depth, and h is the step referenced head; H is the total energy head and ∆H is the energy loss across the flume.

The hydraulic theory for predicting discharge through long-throated flumes has resulted from over a century of development. The first laboratory and theoretical studies on critical-depth flumes were made by Belanger in 1849 and by Bazin in 1896 (ref. Clemmens et al., 2001). Theoretical predictions of flow were investigated by Ackers and Harrison (1963) and further by Replogle (1975) (ref. Clemmens et al., 2001). Bos et al., (1984) described the theory for determining discharge through these flumes. The head-discharge equations for a

flow measurement flume of rectangular cross section were

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