Discharge Measurement in Trapezoidal Lined Canals Utilizing Horizontal and Vertical Transitions

Most of previous works for discharge measurement structures were carried out in canals with rectangular cross sections. However, in irrigation systems most common irrigation canals, especially lined canals, have trapezoidal cross sections. From practical view point, it is preferable to construct measuring structures without changing the side slopes of the original canals. Usually, a horizontal contraction is used as a permanent measuring device and a vertical hump as temporarily measuring device. In contrary to rectangular contraction, direct analytic solution of head-discharge relation is not possible as the governing equations are implicit. The solution requires tedious methods of trial and error. Tabular and graphical methods are also available for solution which are subject to errors of double interpolation and errors of judgment in reading the graphs. Reported herein are explicit equations for head-discharge relation for both horizontal contraction and vertical hump in trapezoidal canals without changing the side slope of canal. Both horizontal and vertical transitions in the trapezoidal canals are analyzed by the one dimensional momentum equation. An optimization tool is used to compute the critical depth and critical width simultaneously for horizontal contraction, and the critical height of the hump and critical depth for vertical transition. Where the objective function is to adjust the specific energy at the contraction equal to the specific energy at the approach channel according the constraint of the Froude number at contraction equal to 1.0. An explicit approximate equation was developed for the critical depth and other equation was developed for the critical width in the case of horizontal contraction. Other equations were developed for computing the critical height of hump and the critical depth over it. A general depth-discharge relationship was obtained for both types of transitions. Predicted discharges using this general relationship were compared with experimental data and gave a good agreement.