CONTROL OF THE HYDRAULIC JUMP BY A BROAD-CRESTED SILL IN A RECTANGULAR CHANNEL NEW THEORY AND EXPERIMENT

Abstract

The present research focuses on hydraulic jumps of initial and final depths h₁ and h₂, respectively, controlled by a broad-crested sill of height s in a horizontal rectangular channel. The main objective is to know which parameters influence the height of the sill in such a way as to create a full hydraulic jump on the stilling basin. First, the study reviews the essential works of Forster and Skrinde published in 1950, which are still in force today. An in-depth study of these works shows that the theoretical development carried out by the aforementioned authors is based on two simplifying assumptions that risk compromising the reliability of the derived equations, in particular, that govern the relative sill height S = s/h₁, as a function of the incident Froude number F₁. A detailed and appropriate calculation shows that this relationship is not recommendable and therefore requires an adjustment.

For this, a much more rigorous theoretical development is proposed, which leads to establishing a surrogate relationship safely allowing the explicit calculation of the relative sill height value required for the formation of the hydraulic jump on the stilling basin. Contrary to what has been proposed by previous studies, the current theoretical development takes into account the effect of the approach flow velocity immediately upstream of the sill.

This effect is represented by the dimensionless parameter s defined as a kinetic factor. The calculation showed that for a wide range of incident Froude numbers, the kinetic factor cannot be neglected. A table comparing the values of the relative sill height S calculated according to Forster and Skrinde and the current approach shows that the maximum deviation observed for s ¹ 0 is significant, reaching 26.15% for F₁ = 3 and 8.41% for F₁ = 11. If the effect of the approach flow velocity was to be neglected, which corresponds to s = 0, the maximum deviation could reach 5%, which is not insignificant.

The second part of the study is devoted to the experimental investigation. It has the main objective of corroborating or correcting the theoretical relationships developed during the first part. For this, a specially designed easy and efficient hydraulic installation is put into operation, highlighting an original device generating an incident flow of high velocity. It consists of a pressurized box-convergent assembly directly fed by a pump via a flexible pipe.

The analysis of the experimental measurements shows that the theoretical sequent depth ratio Y of the hydraulic jump, according to Belanger’s equation, is not affected by the setup of the broad-crested sill. Everything happens as if the sill does not exist. Thus, it seems that the sill is only useful in controlling the position of the hydraulic jump such that it forms completely on the horizontal apron.

Moreover, the accuracy of the new rigorous derived theoretical relationship S(F₁) is experimentally confirmed.