A View on the Discharge Coefficient for Rectangular Weir of Large Proportions

Abstract

Numerous empirical formulas for the discharge coefficient of flow rate over rectangular weirs have been proposed by many authors. Most of them are expressed with utmost fidelity and simplicity based on precise experimental data. The present author deals with the same problem under somewhat simple but logical considerations. The analysis starts from R. von Mises' theoretical investigation of a two-dimensional flow between two parallel walled channel having a slit at the center of the channel end. We assume that the stream lamina in the channel, whether they are horizontal or vertical, contract independently following the Mises' formula. It is natural to consider that near the corners in the weir plane, two directioned contractions experience mutual interference to each other. The author introduces the "interference factor" whose value is determined from an extreme case in which the channel breadth and depth under weir crest are both infinite. Finally the author establishes a generalized formula (8) for the discharge coefficient of rectangular weirs of any proportions, including all possible cases conceivable.