Application of convex streamline theory to circular-crested weir

• Convex streamline theory is used for circular-crested weir.
• Newton's second law and Bernoulli equation used.
• Existing experimental data used to evaluate the obtained equations.
• The obtained equations have good agreement with experimental data.
• Proposed theory predicts the velocity profile with the better precision.

Circular-crested weirs are overflow structures that can be used for flow measurement, water level control in open channels and flood control in reservoirs. Combining Newton's second law for a rectangular fluid particle on a convex streamline with Bernoulli's equation, the differential equation of velocity profile at crest section of circular-crested weir is obtained. This equation was used to derive the discharge coefficient, crest velocity profile and crest pressure profile of the weir. A wide range (0.44 ≤ H/R ≤ 7.56) of existing experimental data of circular-crested weir is used to evaluate the obtained equations. Results of the study indicated that obtained equations have good agreement with experimental data. Also, in comparison with Dressler and potential flow theories, proposed theory predicts the crest velocity profile with the better precision.