Numerical and analytical calculations of the free surface flow between two semi-infinite straights

Abstract

The problem of two-dimensional flow with the free surface of the jet in a region between two semi-infinite straights intersections at point O is calculated analytically for each angle Beta and numerically for each of the various values of the Weber number and angle Beta. By assuming that the flow is potential, irrotational and that the fluid is incompressible and inviscid, and by taking account only the surface tension for a numerical method using the series truncation, and without the effect of gravity and surface tension for the analytic method utilize the hodograph transformation. The obtained results confirmed a good agreement between them when the Weber number tends to infinity, and the comparison of these surface shapes is illustrated. MSC 2010: 30C30, 65E05, 76B07, 76D05, 76D45