Development of Parabolic Weirs for Simplified Discharge Measurement

Abstract

Discharge equations of all existing sharp crested flow measurement weirs involve some fractions such as exponents of flow depth, which make manual calculations difficult. In the present research work, weirs with a simplified discharge equation were designed by manipulating the weir profile so that the flow depth exponent was a whole number. A parabolic weir profile gave the simplified discharge equation with two as the flow depth exponent. A relationship for obtaining the parabolic weir profile with any weir angle was developed. The theoretical discharge of flow across the parabolic weir was derived using a geometric constant based on the weir profile. Four parabolic weirs with 30°, 45°, 60°, and 90° weir angles were developed and evaluated in laboratory hydraulic flume. The flow regime across weirs was turbulent and the average coefficient of discharge was estimated as 0·55±0·05. Weir angle specific discharge models (coefficient of determination R 2 ⩾ 0 · 986 ) were developed based on two approaches; the first based on the product of geometric constant and the mean coefficient of discharge, and the second on a non-linear regression model constant. Weir constant linear regression prediction equations ( R 2 ⩾ 0 · 993 ), capable of predicting discharge characteristics in combination with discharge models at any intermediate weir angle, were fitted. Parabolic weirs have the merits of both rectangular and triangular weirs, and may find application in field irrigation, industrial flow, and automated control systems measurements.