Head-Discharge Equation for Sharp-Crested Weir with Piecewise-Linear Sides

This research presents a new weir section with $n$-segment linear sides and a horizontal bottom. For large $n$, the section sides of the weir become smooth curves. However, piecewise-linear sides provide a weir shape simple enough for ease of construction. General head-discharge equations are analytically derived for the flow discharge. The proposed weir with $n$-segment linear sides can be applied in an optimization procedure to produce a wide range of head-discharge behaviors. An elegant optimization model that implements the general equations is presented and applied in the design of linear and quadratic weirs. This simple model is solved using the Solver toolbox of Microsoft Excel. The versatility of the proposed weir is demonstrated by optimizing the weir parameters to obtain the maximum ranges of measurement under linear and quadratic characteristics. These weirs have least relative errors because of their linear and quadratic head-discharge relationships and are very useful as a flow recorder in irrigation canals. Optimum design parameters for these weirs are presented in a simple dimensionless form suitable for water structure designers to adjust the weir dimensions to suit field conditions. Application of the proposed weir section is not limited to these two weirs; it can also be used to design other specific weirs.