Efflux through a Circular Orifice

Stefan G. Bauer


The purpose of this research was the establishment of the law of efflux from a vessel under pressure through a suddenly opened orifice of comparatively large dimensions. In order to simplify the approach to the problem, it was decided to investigate the efflux of an incompressible fluid, e.g. water. The methods of approach were based on analogies with electric circuit theory, and accordingly an apparatus was built in which the equivalent of a.c. experiments with resonant circuits could be performed. An orifice in the apparatus represented the inertia in the resonant system. Acoustic theory gives the inertance of such an orifice for infinitesimal amplitudes. In the experiments described, this inertance was measured at a wide range of finite amplitudes, by observations of phase shift between power input and displacement at the orifice. By this means it was possible to determine the exact resonance frequencies of the hydraulic system in spite of its high damping. By this means, the effective mass or inertance of the fluid flowing through the orifice was deduced. In the course of these experiments some interesting flow phenomena, to the author's knowledge not previously recorded, were observed and photographed. There appear to be three distinct modes of flow, as compared with the two commonly observed in the steady state. The contraction coefficient of the flow through the orifice was found to be unity for small amplitudes and to approach the steady state value for large amplitudes. The differential equation of the efflux through a suddenly opened orifice is stated and its solution given. A numerical example is worked out with the constants derived from measurements and the results are shown by graphs. They were checked by visual observation though a recording of the efflux experiment was not found possible. It can be seen that a suction effect must follow a discharge. Further that this suction and the following oscillations are practically independent of the pressure in the vessel before the discharge, provided this pressure is above a certain value. These findings are of interest in connexion with the exhaust phenomena in internal combustion engines, in particular those working on the two-stroke cycle.