Simulation of Flow over V-Notches with Application of Density, Gravity, Head and Notch Angle

Abstract

This study simulates flows through triangular notches and weirs in a controlled water channel using both experimental measurements and dimensional analysis. The governing parameters considered were the head of flow (H), Density of water (?), acceleration due to gravity (g), notch angle (?), and discharge (Q). By applying the Buckingham’s-? theorem, two dimensionless groups were derived, establishing a functional relationship between discharge and the dependent parameters. Experiments were carried out in a laboratory channel to compare observed discharges with those predicted by the mathematical model. The results showed that flows increased non-linearly with head. Variation with angle indicated that discharge peaked at 45°, suggesting the presence of an optimum notch geometry. Model performance was evaluated using statistical indices. The coefficient of determination (r²=0.9992) indicated near-perfect agreement between observed and predicated values, while the Nash-Sutcliffe efficiency (NSE = 0.88) and Relative BAIS (rBAIS = 0.15) confirmed very good predictive ability with minimal systematic error. The study concludes that the triangular notch is a reliable, cost-effective, and accurate device for measuring low discharges in open channels. Its integration of theoretical modeling, dimensional analysis, and experimental validation provides a strong foundation for both academic research and practical water resources and management applications. 

KEYWORDS: Mathematical modelling, Discharge, Head, Acceleration due to gravity, Angle of Notch