Mathematical modeling of flow discharge over compound sharp-crested weirs

• The well known Shiono and Knight model has been applied to compound sharp crested weirs.
• Through comparison of numerical with experimental results, good agreement achieved.
• Weir equations with 12.5% mean absolute error have low accuracy in sloping crests compound weir.
• SKM approach with 4.9% mean absolute error has the lowest accuracy for the same compound weirs.
• This study facilitates the computation of flow discharge over complex shapes of compound weirs.

Water measurements play a pivotal role in hydraulic and environmental management of river systems, irrigation and drainage networks, and sewer conduits. Due to effective limitations of simple sharp crested weirs, recently compound sharp crested weirs have attracted great attention of civil engineers. With this type of weir, flow discharge is measured with a reasonable sensitivity over a wide range of flow rates. In this paper, the Shiono and Knight (SKM) quasi 2-D mathematical model has been numerically solved for discharge prediction of compound weirs, based on the assumption of flow similarity between compound sharp crested weirs and compound open channels. The modeled results are compared with the experimental data and the conventional method (linear combination of theoretical equations of simple weirs). The comparisons revealed that the proposed method shows improved discharge calculation within 3.8 percent absolute mean error while the traditional method has more than 12.5 percent error.