Abstract
A numerical method is presented for computing the shape of a vertical slender jet of fluid falling steadily under the force of gravity. The problem to be solved is fomulated as a nonlinear free boundary value problem for the cross-sectional shape of the jet. The numerical method of solution treats the boundary conditions of the problem as a pair of nonlinear hyperbolic pseudo-differential equations to be integrated in the stream-wise direction. The original differential equation appears as an auxiliary condition. This formulation is shown to be well-posed. The numerical method is found to be stable and second-order accurate. Computations are presented for jets issuing from several different orifice shapes. The numerical method of solution appears to be new and may be applicable to other nonlinear free boundary value problems.
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