Geometrically Linear Flumes for Denser Fluid Flow Measurement in Rectangular Open Channel

Abstract Discharge measurement in an open channel within a pre-fixed degree of accuracy with least compromise on the head of flowing liquid is a challenging task. Sharp crested and broad crested weirs have been tried to the maximum extent and have not been popularly used in the field due to its intrusive nature, reducing the fluid head. Further, discharge measuring flumes like Venturi flume, Standing wave flume have been successfully used with least disturbance in flow. However, the accuracy of flow depends on the fabrication. In addition, the change in bed levels may also induce slight changes in streamline flow resulting in loss of head. Even a slight error in the fabrication to the designed profiles may induce large errors. Further, use of monograms or charts or computations with equations is mandatory to obtain the instant discharge in the flume at any instant. Seldom has the discharge-depth connection for denser fluids in regular channels been studied to improve the usefulness of flow metres. For the first time, the authors have proposed a theoretical and experimental inquiry on Denser Fluid Flow Measurement in open rectangular channels. The results show that a nearly linear depth-discharge relationship may be obtained even in rectangular channels. This paper presents a novel generic optimisation approach that determines the flow parameters. The near-linear depth-discharge connection is found to be valid from YA to YB, with an inaccuracy of ± 2 percent. The proposed linear equations for water and grey water of density 1.3 are respectively given for a channel of square cross-section by, \({Q_{l{a\,1.0}}}=0.6319( {Y - 0.103} ),\)\({Q_{l{a\,1.3}}}=0.7204( {Y - 0.103} )\)and \({Q_{l{t\,1.3}}}={0}{.7493}( {Y - 0.1137} ),\)where Qla and Qlt represent the corresponding actual and theoretical depth-discharge relationships and further suffixes indicate the density of the fluid. It can be observed that the flow parameters of the flume are independent of the density and the flow parameters will remain linear. For the first time, the Chezy’s discharge equation has been explored to get a new density coefficient to be used in discharge equations with which we can convert the equation of the flow parameters of water to any other fluid of different density. Further, it has been shown that the linearity range and its validity remain unchanged with respect to that of water but the linear equation can be obtained by just multiplying the linear parameters by the density coefficient, given by square-root of specific gravity of the fluid. The proposed research is significant since it aims to detect grey water output directly with a calibrated piezometer, eliminating the need for manual intervention.