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The most naive way of thinking would suggest that because there is no viscosity it drains as fast as if you turned the container upside down and let it fall out. However, assuming the hole is smaller in diameter than the container that cannot happen because the fluid would have to accelerate faster than the force of gravity allows. Except... it is under pressure from the liquid above it so maybe it could do that. Except... energy arguments mean we are limited to gravitational potential only so perhaps it doesn't drain any faster than a normal liquid?

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  • $\begingroup$ Correct me if I am wrong, but can't we treat superfluids like any other ordinary incompressible non-viscous fluid? (For this case? ) $\endgroup$ Sep 8 '15 at 16:32
  • $\begingroup$ The superfluid state breaks down above a critical velocity, which for 4He is on the order of 0.2m/s for thin films, I believe. Baring any other limiting effects, that's probably about as fast as superliquid-He can flow without friction. $\endgroup$
    – CuriousOne
    Sep 8 '15 at 20:06
  • $\begingroup$ Is that intrinsic to the nature of a superfluid, or only Helium? $\endgroup$
    – user56903
    Sep 9 '15 at 7:20
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Don't forget that with fluid flow you need to consider both inertial and viscous forces. A superfluid will have zero viscous forces but there will still be inertial forces.

In the limit where viscosity is negligable and inertial forces dominate the flow is described by the Darcy-Weisbach equation. However superfluid flow may be a bit odd due to the long range correlations in it. I don't know enough about the subject to know what corrections if any this would cause to the DW equation.

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