= Helium slit-flow experiment
<Pyotr Leonidovich Kapitza>'s 1938 test compared <helium> flow through optically flat glass disks. Suspension set the tube-to-bath level difference; a cathetometer read levels. The gap was estimated as $0.5\,\mathrm{\mu m}$. Levels barely moved over minutes above the transition, but equalized in seconds below. A <laminar flow> <viscosity> calculation gave only an upper bound.<Viscosity of Liquid Helium below the λ-Point by Pyotr Leonidovich Kapitza>[Kapitza, 1938 viscosity paper, reprint chapter 34, pp.506–507]{ref}
The essential control is to compare the same restriction and level readout at different <temperatures>. A changed <pressure> head is not itself evidence for a changed material response: the driving head must be included when interpreting the flow. For an idealized comparison at equal vapor <pressure>, negligible <surface tension> corrections and nearly constant <mass density> $\rho$, <hydrostatic equilibrium> gives
$$
\Delta P\simeq\rho g\Delta h.
$$
Here $\Delta h$ is the difference in free-surface heights and $g$ is <gravitational acceleration>. This explains why following a liquid level provides both a driving <pressure> and a transported <volume (thermodynamics)>; it does not turn a finite-resolution observation into proof of zero <viscosity>.
\Image[/superfluid-helium-flow-and-thermomechanical-apparatus.png]
{title=Driving and reading <superfluid> flow}
{description=Original functional schematics, not historical reconstructions. Left: level-head flow measurement with an enlarged slit. Right: ideal <thermomechanical effect> with imposed <heat> input, suppressed <normal component of a superfluid> flow, and <temperature> and <pressure> readouts. The heated chamber is closed; its final <pressure> rise is distinct from a flowing fountain.}
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