  The relationship between the apparently unrelated physical quantities --
kinematic viscosity of liquid He-4, $\nu$, and quantum of circulation,
$\kappa=2\pi \hbar/m_4$, where $\hbar$ is the Planck constant and $m_4$ denotes
the mass of the $^4$He atom -- is examined in the vicinity of the superfluid
transition occurring due to Bose-Einstein condensation. A model is developed,
leading to the surprisingly simple relation $\nu \approx \kappa/6$. We
critically examine the available experimental data for $^4$He relevant to this
simple relation and predict the kinematic viscosity for the stretched liquid
$^4$He along the $\lambda$-line at negative pressures.
