Irrigation Sciences and Engineering

Irrigation Sciences and Engineering

Numerical investigation of Semicircular Sharp-Crested Weirs

Document Type : Research Paper

Authors
Abbas Parsaie 1
Mohammad Bahrami Yarahmadi 2
Mahziar Basitnejad 3
1 Assistant Professor, Department of Water Structures, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz,
2 Associate professor, Department of Water Structures, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
3 Ph.D Student, Department of Water Structures, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
10.22055/jise.2025.49460.2161
Abstract
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 0.95 and 0.97 within a 95% confidence interval for flow conditions where H/P varied from 0.06 to 1.1 and D/P from 0.33 to 3.54. In addition, a nonlinear empirical model was formulated to estimate Cd, achieving a mean absolute percentage error (MAPE) of approximately 7.4%, indicating the robustness and applicability of the proposed methodology for semicircular weir configurations
Keywords
Discharge Coefficient
Simpson’s rule
Flow Measurement
Confidence Interval
Sharp Crested Weirs
Subjects

 

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Irrigation Sciences and Engineering
Volume 48, Issue 4
Winter 2026
Pages 37-48

  • Receive Date 22 April 2025
  • Revise Date 06 September 2025
  • Accept Date 27 September 2025
  • Publish Date 04 January 2026