Discharge coefficient relationship for the sharp-edged width constriction new theory and experiment

Abstract

In the field of flow measurement, what is needed in general rule is to design devices that are inexpensive, fairly accurate, and easy to implement. Some devices are more accurate than others but are very expensive.The present study examines a device for measuring flow in rectangular open channels that combines the three abovementioned advantages. It is made up of two separate vertical thin plates arranged in such a way that they form a central opening of width b less than the rectangular channel width B in which they are inserted. It is the simplest device ever imagined and designed for flow measurement in open channels.It is planned to derive the stage-discharge relationship by borrowing a rigorous theoretical development based on classical hydraulic formulas, accounting for the effect of the approach flow velocity. The intended stage-discharge relationship will allow us to derive the resulting discharge coefficient equation of the device.It is established that the resulting theoretical discharge coefficient is formally identified as being exclusively dependent on the contraction rate β = b/B, and this finding is predicted by dimensional analysis. Both dimensional and experimental analyses show no effect of the upstream water depth on the discharge coefficient for the selected values of β. The derived theoretical discharge coefficient relationship is straightforward, although it contains trigonometric functions that are somewhat cumbersome when the designer needs to perform a rapid field calculation.The theoretical and mean-experimental discharge coefficients of the eight tested devices are carefully compared using the one hundred and fifty-seven experimental values collected. An excellent agreement, even perfect, is observed since the maximum deviation worked out over the tested range of β is only 0.05%. This confirmed the validity of the theoretical relationship governing the discharge coefficient, which does not need any correction.