Research on Wave Phenomena in Hydraulic Lines : (7th Report, theoretical Investigation on End Correction Problem - Part 1, Mathematical Analysis of Flow)

抄録

This paper mathematically analyzes the flow structure and convective nonlinearity in the 'end correction' problem. The Laplace equation of the velocity potential is rigorously solved for a boundary geometry formed by a plane wall and a circular aperture in it. Applying three different kinds of flow conditions over the aperture to the solution, we obtain three different values of end correction and functional expressions for the potential and velocities. One of those end corrections proves to be larger than (8/3π)α(α ; radius of aperture) which Rayleigh has regarded as the upper limit. The distribution patterns of the potential and velocities in the flow are shown in diagrams. Moreover the Bernoulli equation gives the pressure and makes it possible to theoretically estimate the convective nonlinearity caused by the kinetic energy. The effects of hamonic wave-distortion on the end correction impedance due to this nonlinearity are also discussed.