New Approach for Design of Broad-Crested Weirs with Exponential Sections

A design framework is presented for broad-crested weirs with exponential (power-law) head–discharge behavior and three practical control-section shapes: Rectangular, parabolic, and triangular. Unlike ideal-flow sizing, the approach explicitly accounts for real-flow effects through a velocity coefficient at the control section. Starting from the energy equation and the critical-depth condition, analytical relations are obtained for the control-section depth, the critical depth, and the velocity and discharge coefficients. These relations are coupled with geometry-specific critical-flow expressions to derive a general, dimensionless design equation that links the required contraction ratio to the approach-velocity coefficient, the control-section velocity coefficient, and the head exponent n. The core innovation of the framework is a general dimensionless design equation that directly yields the required control-section area ratio A*/Ao, i.e., the geometric contraction relative to the approach section, for a specified design head and approach-velocity condition. The method provides direct design parameters for each section family: Rectangular width, parabolic parameter, and triangular head angle. A short quantitative check against representative classical experimental ratios shows very good agreement with measured values. For the applied design example based on a trapezoidal approach section and conservative lower-bound Cv values, neglecting real-flow effects underpredicts the required contraction ratio by about 28–39%, depending on the selected section shape. The developed framework provides a transparent, theoretically grounded, and practical tool for the hydraulic design of broad-crested weirs.