  It has recently been revealed that spinning black holes of the photon-fluid
model can support acoustic `clouds', stationary density fluctuations whose
spatially regular radial eigenfunctions are determined by the
$(2+1)$-dimensional Klein-Gordon equation of an effective massive scalar field.
Motivated by this intriguing observation, we use {\it analytical} techniques in
order to prove a no-short hair theorem for the composed
acoustic-black-hole-scalar-clouds configurations. In particular, it is proved
that the effective lengths of the stationary bound-state co-rotating acoustic
scalar clouds are bounded from below by the series of inequalities
$r_{\text{hair}}>{{1+\sqrt{5}}\over{2}}\cdot r_{\text{H}}>r_{\text{null}}$,
where $r_{\text{H}}$ and $r_{\text{null}}$ are respectively the horizon radius
of the supporting black hole and the radius of the co-rotating null circular
geodesic that characterizes the acoustic spinning black-hole spacetime.
