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Botimer and Taborek (2016) measured the mass flux of superfluid $^4$Hethrough a capillary into an evacuated chamber for various temperatures andpressures of the reservoir chamber. They found a sharp transition from low fluxat low pressures to high flux at large pressures. Here it is shown that thesuperfluid condition of chemical potential equality predicts the inducedtemperature and also the transition pressure, which is attributed to thetransition from a semispherical cap to a pool of $^4$He at the exit of thecapillary. The results show that the two-fluid equations of superfluid flow,Landau's phonon-roton theory, and Feynman's critical vortex theory areunnecessary for a quantitative account of the measured transition pressure.

Comment on pressure driven flow of superfluid $^4$He through a nanopipe (Botimer and Taborek 2016)