Analytical Expression for Measurement of Discharge Using Conical Obstruction in Small Rectangular Channels

Abstract

AbstractFlow measurement in rectangular channels can easily be carried out using measuring flumes. The type of flume used in a particular application depends on the need for precision and cost. Traditional flumes such as cutthroat flumes are usually built with the channel itself by channel side convergence. Their construction or removal involves engineering work on the channel. The authors feel this as the limitation of the traditional flumes; as for similar sections of the network of channels, a new and independent construction of flume is required. The present study negates this drawback and proposes a particular kind of flume for flow measurement in rectangular irrigation channels in which the throat section of the flume is obtained with a cone shaped object, placed at the center of the rectangular channel. The limitation of a fixed structure can be overcome by using a mobile structure that works on the same principle and remains effective in similar situations. The present study involves the use of a cone shaped obstruction to restrict the flow in order to achieve critical condition. An analytical model is developed for discharge measurement in rectangular channels using the conical obstruction. The geometry of the channel at the location of the obstruction becomes complex due to the presence of cone shaped object. The study presents various comprehensive equations defining the flume geometry. The cone shaped obstruction is equipped with a gauge at its upstream side to measure the depth of flow upstream of the critical flow section. The reading of the gauge is directly related to the flow rate. The relation between upstream flow depth and rate of flow is obtained analytically using energy concept. An experiment is performed in the laboratory by observing flow depth after placing a cone in the rectangular channel under free flow condition. The experiment results validated the developed analytical model. The maximum error of the flow discharge obtained using the analytical approach was found to be 5.19 percent when compared with the actual flow rate. The proposed flume is appropriate for temporary use and can replace the traditional flumes for flow measurement in small conduits. The flume is a simple and affordable device for flow measurement which is easy to construct, carry, and mount. The cone is physically independent of the channel and can be used in different, similar sections of the network of channels. The unit can be quickly fixed and detached for momentary use in open channels. This flume can be used as a mobile device for momentary flow measurement in open channels under free flow condition.KeywordsFlow measurementMeasuring flumesFroude numberRectangular channelConical obstruction