TRIANGULAR BROAD CRESTED WEIR THEORY AND EXPERIMENT

Abstract

The article looked at the possibility of making use of a triangular broad crested device, provided with a crest height P and a constant apex angle q, as a flow measurement weir. The device has a triangular gorge which extends over a certain length L. This must be sufficient to allow the creation of a control section in a given section of the gorge, which represents the prerequisite condition for the proper functioning of the device. Inserted in a rectangular channel of width B for which the measurement of the flow rate Q is needed, the device causes a lateral contraction of the cross section located above the crest height P. It is shown that the dimensionless parameter  reflects the effect of this lateral contraction, where , and  is the upstream flow depth counted above the crest. Due to the crest height P, the flow also undergoes vertical contraction. The effect of both lateral and vertical contractions can be grouped together in a single dimensionless parameter noted y such that  where  denotes the relative crest height.

After the detailed description of the device as well as the resulting flow, a dimensional analysis has been proposed in order to identify the parameters on which the discharge coefficient  of the device depends. It has been clearly demonstrated that the flow coefficient can be written as a function of both  and , i.e. .

In order to define the function l, a theoretical approach is proposed based on the momentum theorem and the energy equation. This approach turned out to be judicious since it led to expressing the theoretical relationship that governs the discharge coefficient . This was presented as an explicit function of the dimensionless parameter y, depending therefore on both  and  as predicted by dimensional analysis.

After that, experimental tests were rigorously carried out on six devices with different geometric characteristics. The objective was to verify the validity of the theoretical relationship governing the discharge coefficient. The tests were carried out under suitable hydraulic conditions and the flow rate Q and the upstream depth h₁ were measured using high precision instruments. In total, 122 measurement points were collected and were carefully analyzed. The use of linear least-squares fitting method involving experimental and theoretical data gave the following trend line relationship:

It was thus concluded that the theoretical discharge coefficient relationship did not need any correction and it could be used with great confidence since the maximum deviation observed rarely reached 0.2%. This is also the case for the relationship that governs the flow rate Q.