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1995•Journal of Irrigation and Drainage EngineeringRequires access

Geometrically Simple Logarithmic Weir

K. Keshava Murthy, H. Ramesh, M. N. Shesha Prakash

Open publisher page 6 citations

Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Weir, Logarithm, RADIUS, Mathematics, Discharge coefficient, Constant (computer programming), Geometry, Hydrology (agriculture)

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