The surface evolver (SE) algorithm is a valued numerical tool for computations of complex equilibrium interfacial phenomena. In this work, an iterative procedure is implemented such that SE can be employed to predict steady-state flows along capillary channels of arbitrary cross-section. As a demonstration, a one-dimensional stream filament flow model is solved that approximates the pressure changes inside the channel. Despite its simplicity, the precision, stability, and speed of the method affirm it as an efficient and unique design tool for a variety of capillary flow problems. The procedure is ideally suited for slender column flows such as open wedge channel flows, several of which are validated herein via parabolic flight and drop tower experiments.