Numerical investigation of Semicircular Sharp-Crested Weirs

Sharp-crested weirs (SCWs) are widely used hydraulic structures for measuring discharge in small and confined channels. Their hydraulic performance is primarily governed by the relationship between flow head and discharge (H-Q), along with the associated discharge coefficient (Cd). The derivation of the H-Q relationship typically involves the integration of the velocity profile over the flow cross-section. However, for semicircular sharp-crested weirs (SCCWs), this process becomes analytically complex due to the emergence of elliptic integrals. To address this, the present study employed Simpson’s numerical integration rule to approximate the relevant elliptic integrals with high accuracy, with a specific focus on determining Cd. A simplified analytical expression for the H-Q relationship was developed and thoroughly validated against an extensive dataset obtained from laboratory experiments. The model exhibited strong agreement with observed data, confirming its predictive capability. Furthermore, dimensional analysis using Buckingham’s π-theorem revealed that the discharge coefficient is a function of the dimensionless ratios H/P, H/D, and D/P, where H is the upstream flow head, P is the weir height, and D is the crest diameter. The observed Cd values ranged between ۰.۹۵ and ۰.۹۷ within a ۹۵% confidence interval for flow conditions where H/P varied from ۰.۰۶ to ۱.۱ and D/P from ۰.۳۳ to ۳.۵۴. In addition, a nonlinear empirical model was formulated to estimate Cd, achieving a mean absolute percentage error (MAPE) of approximately ۷.۴%, indicating the robustness and applicability of the proposed methodology for semicircular weir configurations

کلیدواژه ها:

Discharge Coefficient ، Simpson’s rule ، Flow Measurement ، Confidence interval ، sharp crested weirs