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Mathematical Modelling of Flow Over Triangular Notches
Abstract
The hydraulic performance of triangular notches along open flow channels were thoroughly simulated in this research, with an emphasis on experimental analysis, mathematical modelling, and validation using statistical performance measures. To ascertain discharge characteristics under controlled flow conditions, laboratory experiments were carried out utilizing a hydraulic flow channel fitted with triangular notches of different angles (30°, 45°, 60°, 75°, and 90°). The importance of notch geometry in flow measurement accuracy was confirmed by the results, which revealed that wider notch angles (75° and 90°) showed decreased sensitivity to low flows, whereas sharper notch angles (30° and 45°) showed increased sensitivity. The Buckingham-π theorem was used to create a predictive mathematical model that expressed discharge as a function of head, notch angle, and velocity. For practical use, the model was linearized and compared to the outcomes of the experiment. With a Nash–Sutcliffe Efficiency (NSE) of 0.989, Relative Bias (rBIAS) of 1.35%, and Coefficient of Determination (r²) of 0.993, validation using performance matrices demonstrated exceptional predictive ability. These numbers show that, with little departure from measured discharges, the model dependably represents the underlying hydraulic relationships. The results expand the body of knowledge by offering a proven dimensionless framework for predictive modelling and confirm the appropriateness of triangular notches for accurate flow monitoring, particularly in low-flow regimes. This work provides useful insights for hydraulic engineers, water resource managers, and researchers looking for reliable, economical, and sustainable technique to flow measurement, control, monitoring and water management applications by linking experimental data, dimensional analysis, and performance evaluation.
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