Flow of Helium II in Narrow Slits

The isothermal flow properties of helium II have been studied at pressure heads between 1 and 16 cm of helium and in slits with an average width between 2 and 5 microns. The results can be partially described in terms of the mutual friction theory of Gorter and Mellink. The prediction of the theory that the flow rate should be proportional to the one-third power of the pressure head was verified for the entire pressure range investigated. The agreement is not complete, since our work is consistent only with a mutual friction constant, $A$, which is a function of temperature and of the slit dimensions. There was no evidence of critical velocity effects in the velocity range investigated (10-30 cm/sec). Interpretation of the experimental work of Allen and Reekie and of Hollis-Hallet indicates that there is a small superfluid friction proportional to the square of the superfluid velocity in addition to the mutual friction. This friction was not observed in the velocity range of our experiments.