Two-Dimensional Free Surface Flow Through Solid Walls With Surface Tension Effects

We examine the two-dimensional, steady, and irrotational flow of an inviscid and incompressible fluid emerging from certain cases of flow through solid walls. Surface tension (T) is considered, while gravitational effects are neglected. This problem is complicated by the nonlinear boundary condition imposed by the Bernoulli equation on the free surface, which presents challenges when adapting numerical methods used by many researchers. We employ a series truncation method for numerical solution. We computed solutions for various values of the angle (β) between the walls AB and the horizontal, the length of the vertical wall BC, and different Weber numbers. For determining the shape of the free surface, most of the calculations were performed for N = 50. We were able to find approximate solutions for $\alpha \ge 1$ To validate our results, they were compared with studies using other numerical methods and in special cases of the angle β, compared with the exact solution in the limit of $\alpha \to \infty$.