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

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