MODIFIED MONTANA FLUME (MMF)

Abstract

Flow measurement has become essential in the field of water engineering. Accuracy is required in various fields, such as industrial, municipal, and agricultural effluents. It allows better knowing and sizing the equipment of water supply, water collection or treatment works, or even to better know the quality of water bodies and to quantify the availability of water resources. In open channels, the measurement of flow rates would enable knowing with great precision the evacuation capacity of the structure. For irrigation needs, part of this water is diverted, and the plot to be irrigated requires a quantity of water that must be assessed with the greatest exactness.

For open channel flow measurement, flumes are the most commonly used structures, the best known of which are the Parshall and the Venturi. The principle of these devices is based on a lateral contraction of the walls, sometimes on a localized elevation of the bottom, or else on both. As a general rule, they are formed of three static parts, namely, a converging part as the first part, followed by a canal of a constant section called the neck or throat as the second part, and finally, a terminal divergent part at the outlet of the device called the discharge section as the third part. All cross-section shapes of the device are mostly rectangular. The throat acts as a control section, where flow is critical, allowing the device to produce a relationship between the upstream water level and the flow rate, also called the stage-discharge relationship. Thus, the flow rate sought is deduced as soon as the depth of the upstream flow is measured.

Montana Flume, which is the subject of investigations during this study, is less well known than the aforementioned two devices, although it has certain advantages. It is a truncated version of the Parshall since it is only formed by a flat-floored converging part; it has no throat or discharge section. As a result, it takes up less space and is less expensive. As with most flumes, the Montana flume is an empirical device on which tests were performed to derive the empirical stage-discharge relationship. Under downstream free-flow conditions, the stage-discharge relationship is expressed as , where Q is the discharge, h is the upstream stage, K is the flume discharge constant depending on the flume size, and n is the discharge exponent depending also on the flume size, as reported in the specialized literature.

It is not the form of the previous stage-discharge relationship that is disputed by the authors of the present study, but it is the fact that the exponent n varies from one device to another according to their size. The variation in the exponent n inevitably leads to a change in the dimensions of the constant K, which does not conform to the proven principles of flow measurement. Additionally, the exponent n takes values varying between 1.522 and 1.566 for devices from 1-inch to 36-inch in size, while it should be equal to 1.5 given the involved rectangular cross-section shape.

The main objective of the present study is to give more rationality to the stage-discharge relationship of Montana flumes, derived from a convincing theoretical development based on simplifying hypotheses with reduced effect. The resulting stage-discharge relationship takes the accepted form of weirs, where the exponent n is equal to 1.5 and does not change with device size. However, the rationality thus expected results in modifying one of the linear dimensions of the original Montana flume, in particular the width of the outlet section; this leads to suggest modified Montana flumes that are more efficient, requiring less space. Based on the very wide range of experimental discharges and measured upstream depths provided by the literature, the modified Montana flume is characterized by an optimal contraction rate deduced from the optimization of the theoretical stage-discharge relationship. Moreover, the theoretical stage-discharge relationship, corrected for the effects of a given constant and the relative upstream depth related to the channel approach width, causes deviations in flow rates computation often lower than those inferred by using the original Montana flumes. In addition, the optimization carried out on the device induces smaller linear dimensions than those of the original Montana flume, thus requiring less material for its design. Finally, the authors recommend a relevant approach for appropriate sizing of the advocated flume.