On the possibility of laboratory simulation of quasi-spherical accretion
  onto black holes with a shallow-water experimental setup
  We describe the concept of a shallow-water setup for simulation of gas
accretion onto a black hole in the mode of a quasi-spherical accretion. The
bottom for the shallow-water container must have the funnel-shaped curvilinear
concavo-convex shape. We calculate the configuration surface of the properly
shaped bottom that simulates precisely the Newtonian or pseudo-Newtonian
gravitational potentials. Like the spatial part of the Schwarzchild metric, the
funnel's surface metric has a (removable) singularity at the finite distance
from the funnel's center and places the certain funnel's depth which we call
`gravitational length'. The gravitational length is analogous to the
gravitational radius and defines the equivalent of the black hole's mass in the
laboratory model. The mass equivalent corresponds to $\sim 0.367\cdot 10^{12}$
g for the funnel as deep as 5 cm. We define more precisely the inviscid shallow
water equations for the arbitrary bottom curvature. We show that in general
case the shallow water pressure obeys the non-barotropic equation of state. We
suggest the schematic course for experiments for simulation of accretion in a
thick accretion disk mode as well as the Bondi-Hoyle accretion.
