Theoretical and experimental investigation of a lateral broad-crested contraction as a flow measurement device

Abstract

The article looked at the possibility of making use of a lateral contraction as a flow measurement device in a rectangular open channel. The contraction under consideration consisted of two removable prismatic elements placed on either side of the walls of the channel. This configuration resulted in the creation of a throat of length L and opening width b less than the channel width B so that the contraction rate has been defined as β = b/B. This ratio actually reflects the degree of the lateral contraction while there is no vertical contraction because the device is devoid of crest height. Its longitudinal axis thus merges with that of the channel, which gives the device a self-cleaning property. Due to the changeover of the subcritical flow upstream of the device to a supercritical flow inside the throat, firmly confirmed by laboratory observations, a control section has been created in a given section at the entrance of the throat. This is the prerequisite for the correct functioning of a flow measuring device in open channels.The essential steps undertaken during the study were firstly the research for the theoretical relationship governing the flow rate Q for forthwith deriving the resulting discharge coefficient Cd equation. This aim has been successfully achieved through the simultaneous application of the momentum and the energy equations taking care to include the effect of the approach flow velocity. The obtained theoretical flow rate QTh was identified in the form of explicit functions depending both on the geometric characteristics of the device and the upstream depthh1 which is fully consistent with semi-modular devices. Likewise, the resulting discharge coefficient Cd,Th was formally identified as being exclusively dependent on the contraction rate β and this finding was predicted by the dimensional analysis.The statistical analysis of the 157 collected experimental values allowed observing an excellent agreement between the theoretical and experimental discharge coefficients. The maximum deviation calculated over the tested range of β was only 1.22%. The use of linear least-squares fitting method involving experimental and theoretical data gave the following trend line relationship Cd,Exp=0.9911Cd,Th obtained with a coefficient of determination R2=0.9906. Thereby, using the previous equation, the accuracy on the discharge coefficient Cd,Th computation has been highly improved since the maximum deviation reduced to only 0.66%.