DISCHARGE MEASUREMENT IN A RECTANGULAR OPEN-CHANNEL USING A SHARP-EDGED WIDTH CONSTRICTION THEORY AND EXPERIMENTAL VALIDATION

Abstract

Flow measurement in open channels can be performed using a variety of devices such as multi-shaped weirs or hydraulic jump flow meters. Most of them have a sill at which solid deposits can accumulate. Self-Cleaning devices are those with a flat bottom which also corresponds to the bottom of the channel in which they are inserted. There is no bottom elevation in these devices. It is one of these devices that the present study sets out to examine from both a theoretical and an experimental point of view. It is a lateral contraction formed by a thin plate with a full central opening of width b placed perpendicular to the flow in a rectangular channel of width B. It is the simplest device that can be used for flow measurement. The theory is based on taking into account two sections, one located upstream of the device and the other taken to the right of the opening where critical flow could take place. The head loss caused between these two sections is not negligible, but current knowledge does not allow it to be evaluated. For this reason, this head loss is neglected in the theoretical development. By writing the equality of the heads between the two previously mentioned sections and introducing the dimensionless parameter , a third degree equation in  is obtained. This equation is written in the following functional form . The dimensionless parameter represents the ratio between the depth h₁ and the critical depth h_c in the initial section. Thus, for a given value of the contraction rate B / b, is a constant. This fact is corroborated by experimental tests.  The only real root to consider from the third degree equation is such that  > 1 because the flow is subcritical in the initial section upstream of the device. In addition, the theoretical development clearly shows that the discharge coefficient C_d of the device is closely related to by an explicit relation. In other words, knowing the value of the ratio B/b, is then given by solving the third degree equation, and consequently the discharge coefficient is then worked out.

The theoretical development is confronted with the results of the tests carried out on eight devices whose contraction rate b / B varies between 0.15 and 0.45. The main conclusion to retain is that the maximum relative deviation between theoretical and experimental discharge coefficients is less than 2%. All the observed relative deviations are taken into account in the fitting of the theoretical discharge coefficient relationship.