Volume 19, Numéro 1, Pages 117-154

Rectangular Broad-crested Flow Meter With Lateral Contraction – Theory And Experiment

Authors : Achour Bachir . Amara Lyes .


An in-depth theoretical and experimental study is carried out on a semi-modular device for measuring flow in open channels, in the current instance a rectangular open-channel of width B. The device is provided with both a crest height P and a lateral contraction forming a gorge of opening width b extending over the entire length L of the apparatus. This is chosen so as to ensure in all cases the appearance of a control section inside the gorge. This is the prerequisite condition for the correct functioning of the apparatus as a flow measuring device. The flow undergoes the double effect of a lateral and vertical contraction which is reflected in the following dimensionless parameters and where is the upstream flow depth counted over the crest height. It is shown that these two parameters can be grouped together in a single  variable such that varying in the range . The main objective of the theoretical study is to derive the stage-discharge relationship (Q  ) and therefore that of the discharge coefficient of the device. This ultimate goal is comfortably achieved based on both the momentum theorem and the energy equation, after having made certain fully justified simplifying assumptions. The theoretical stage-discharge relationship thus obtained is consistent with semi-modular devices since the flow rate Q depends both on the geometric characteristics of the device and on the upstream depth . Regarding the derived theoretical relationship governing the discharge coefficient, it explicitly indicates the dependence of with respect to the dimensionless parameter  exclusively, i.e.  and parameters, which is predicted by dimensional analysis. The theoretical discharge coefficient relationship is subjected to an experimental program as intense as it is strict. The objective is either to validate this relationship or to correct it for the effect of a correction coefficient if the theoretical and experimental values present some deviations. No less than 240 measurement points are collected during tests carried out on thirteen devices with different geometric characteristics. The 240 experimental and theoretical values of the discharge coefficient are compared with each other revealing a near perfect agreement since the ratio is extremely close to unity. This high-quality result suggests that the theoretical relationship governing the discharge coefficient can be used with confidence in its current form without undergoing any correction. Therefore, it is quite obvious to conclude that the theoretical relationship of the flow rate Q is also reliable and does not require any adjustment or correction.


Weir ; Discharge ; Rectangular borad-crested weir ; Theory ; Experiment ; Discharge coefficient