Computation of discharge and discharge coefficient of subcritical flow in trapezoidal flumes with prismatic pier under free flow conditions

One of the simple and cheap ways for flow measurement in canals is to use flumes. In this study, the efficiency of trapezoidal flumes with prismatic piers for flow measurement in trapezoidal canals was investigated. Laboratory investigations on four prismatic piers installed in the trapezoidal canal floor with an adjustable side slope were conducted. Based on the results of conducting several experiments, in the first analysis, a relationship and graph to calculate the discharge for each side slop and a relationship for all of the investigated side slopes were separately presented using dimensional analysis. In the second analysis the relationship and graph to calculate the discharge coefficient for each side slope and a single relationship for all of the investigated side slopes were separately obtained through the simultaneous use of the concept of energy principle and dimensional analysis. To investigate the accuracy of the obtained relationships, the statistical parameter of Mean Absolute Relative Error (MARE) was used. In the first analysis the mean value of the relative error to estimate the discharge in the investigated side slopes (z=0.268, 0.4663, 0.7 and 1) were 8.8, 10, 7.7 and 8.3 percent, respectively. Also in the second analysis, the value of this statistical parameter to estimate the discharge in the investigated slopes were 6.5, 10, 1.8 and 3.4 percent respectively and based on the single relationship for all of the investigated side slopes was 9%. Therefore, to calculate the discharge, the second analysis was recognized to be more appropriate than the first.