Débit d'un orifice percé dans la paroi d'un tube circulaire

Discharge through an orifice in the side of circular section tube

Résumé

This investigation was associated with the author's dry dock filling system design work. It considers the operation of an orifice in the side of a blind-ended horizontal tube (see Fig. 1), with the centre of the orifice lying in the horizontal diametral plane of the tube. The jet discharges from this orifice at a certain angle α towards downstream. Theoretical investigation. Taking h1 and h3 for the pressures (as heights of water) at cross-sections S1 and S3 respectively (both being equal to S), Q for the discharge, and mw for the jet contraction, Euler's theorem applied to projections of forces and momentum derivatives on the Ox axis produces expressions (4), (5), (5'), (5") and (6). Effects due to velocity distribution in cross-sections S1 and S2 are neglected, and the pressure drop between them is also assumed to be negligible. Experimental layout. The main system dimensions are shown in Figure 2 (in millimetres). h3 was measured at pressure tappings 3' and 3", both of which gave identical results throughout. The same applied to tappings 1' and 1" measurïng h1; h4 was measured by tappings 4' and 4" positioned 125 mm upstream from cross-section S1. These values were consistently slightly higher than h1 because of the linear pressure drop between the two stations ; h'A was measured at a tapping A' opposite the centre of the orifice A. Purpose of the experiment. Experimental values were obtained for h1 and h3 Q, h4 and h'A, from which the mean velocity V1 was obtained, and V2 then by formula (4). Formula (6) supplied cos α., and formula (1) mw The purpose of the experiment was to compare α.calculated as above with the angle found by direct observation. The jet flares out in a complex shape, due to the flow spreading out over a large area after passing through the contraction. An interesting fact is that most of the flow is in the part of the jet nearest the downstream end of the tube. The mean angle resulting from this tendency was denoted α'.Measurement was by direct observation, but a certain number of flow photographs were also taken. Results. The discharge Q ranged from 1.01 litres/sec. to 3.11 litres/sec. Table I gives the values obtained for h1, h3, h4, and h'A, which are seen to have been remarkably consistent. Table II lists results for α and mw. This and the curves in Figures (3) and (4) show that the values obtained for α., α' and mw were all of the order of the following average figures : α = 79° α' = 75° mw = 5.57 cm2 Jet contraction remained practically constant, and the small difference between α and α' satisfactorily confirms the theoretical reasoning. Figures (5) (6) and (7) show flow photographs taken at Q 1.01 litres/sec., Q = 2.53' litres/sec. and Q = 3.11 litres/sec. respectively.