  Reynolds similitude, a key concept in hydrodynamics, states that two
phenomena of different length scales with a similar geometry are physically
identical. Flow properties are universally determined in a unified way in terms
of the Reynolds number ${\cal R}$ (dimensionless, ratio of inertial to viscous
forces in incompressible fluids). For example, the drag coefficient $c_D$ of
objects with similar shapes moving in fluids is expressed by a universal
function of ${\cal R}$. Certain studies introduced similar dimensionless
numbers, that is, the superfluid Reynolds number ${\cal R}_s$, to characterize
turbulent flows in superfluids. However, the applicablity of the similitude to
inviscid quantum fluids is nontrivial as the original theory is applicable to
viscous fluids. This study proposed a method to verify the similitude using
current experimental techniques in quantum liquid He-II. A highly precise
relation between $c_D$ and ${\cal R}_s$ was obtained in terms of the terminal
speed of a macroscopic body falling in He-II at finite temperatures across the
Knudsen (ballistic) and hydrodynamic regimes of thermal excitations. Reynolds
similitude in superfluids can facilitate unified mutual development of
classical and quantum hydrodynamics.
