  In one of the most celebrated examples of the theory of universal critical
phenomena, the phase transition to the superfluid state of $^{4}$He belongs to
the same three dimensional $\mathrm{O}(2)$ universality class as the onset of
ferromagnetism in a lattice of classical spins with $XY$ symmetry. Below the
transition, the superfluid density $\rho_s$ and superfluid velocity $v_s$
increase as power laws of temperature described by a universal critical
exponent constrained to be equal by scale invariance. As the dimensionality is
reduced towards one dimension (1D), it is expected that enhanced thermal and
quantum fluctuations preclude long-range order, thereby inhibiting
superfluidity. We have measured the flow rate of liquid helium and deduced its
superfluid velocity in a capillary flow experiment occurring in single $30~$nm
long nanopores with radii ranging down from 20~nm to 3~nm. As the pore size is
reduced towards the 1D limit, we observe: {\it i)} a suppression of the
pressure dependence of the superfluid velocity; {\it ii)} a temperature
dependence of $v_{s}$ that surprisingly can be well-fitted by a powerlaw with a
single exponent over a broad range of temperatures; and {\it iii)} decreasing
critical velocities as a function of radius for channel sizes below $R \simeq
20$~nm, in stark contrast with what is observed in micron sized channels. We
interpret these deviations from bulk behaviour as signaling the crossover to a
quasi-1D state whereby the size of a critical topological defect is cut off by
the channel radius.
