Calcul hydraulique des conduits d'aération des vidanges de fond et dispositifs déversants

Hydraulique design of aeration ducts for weirs and bottom outlets

Chef du Département Recherches de la Société B.V.S., chargé de cours à l'Ecole N.S. des Mines de Saint-Etienne.

Résumé

Hydraulically speaking, two extreme cases can be distinguished, depending on the degree of envelopment of the flow by solid walls, i.e. a) the flow is completely surrounded by the walls, e.g. as in a bottom outlet (Fig. 1) ; b) the liquid is in free fall through the air (Figs. 4 and 6). The aeration coefficient α (ratio of air flow rate to liquid flow rate) is given by equation (3) for case (a) and by graphs 5 a and 5 b for case (b) * *. Symbols H and he are explained in Figures 1 and 2 and the coefficient K is given by table No. 1, in terms of the geometric and hydraulic characteristics of the bottom outlet. The symbols used in graphs 5 a and 5 b are explained in Figures 4 and 6. The vent cross-sectional area for a bottom outlet (case a) is found from equation (11), in which the number 28 is found from √(Ywater/Yair), ma is given by (7), Bc and hc are the width and depth respectively of the contracted section of the jet of water immediately downstream of the gate and Ha the permissible depression in metres of water. Equation (13) gives the area of the aeration ducting for case (b). α. is taken as 0.5 α to allow for the fact that aeration need only affect the lower part of the sheet of water. mdev. = the weir discharge coefficient. The other symbols are indicated on Figures 4 and 6. The critical negative pressures and corresponding air velocities for cases (a) and (b) are shown in tables Nos. 2 and 3 respectively, the former with ma = 0.7 and the latter with ma= 0.95. Paragraph V consists of two complete numerical examples, i.e. Case (a) : a 3.5 m diameter bottom outlet with a flat 3 by 2.8 m gate. The critical opening is about 80 %. Case (b) : rectangular weir of width B = 4 m, head of water hdev = 0.85 m. Vertical distance between weir crest and downstream channel Z = 1.80 m. The dimensions of the shafts on each size of the weir can be calculated from Figure 6. A very short bibliography is appended.