Geometrically Simple Logarithmic Weir

This paper discusses the design and experimental verification of a geometrically simple logarithmic weir. The weir consists of an inward trapezoidal weir of slope 1 horizontal to n vertical, or 1 in n , over two sectors of a circle of radius R and depth d , separated by a distance 2 t . The weir parameters are optimized using a numerical optimization algorithm. The discharge through this weir is proportional to the logarithm of head measured above a fixed reference plane for all heads in the range 0.23 R ≤ h ≤ 3.65 R within a maximum deviation of ±2% from the theoretical discharge. Experiments with two weirs show excellent agreement with the theory by giving a constant average coefficient of discharge of 0.62. The application of this weir to the field of irrigation, environmental, and chemical engineering is highlighted.