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We describe the concept of a shallow-water setup for simulation of gasaccretion onto a black hole in the mode of a quasi-spherical accretion. Thebottom for the shallow-water container must have the funnel-shaped curvilinearconcavo-convex shape. We calculate the configuration surface of the properlyshaped bottom that simulates precisely the Newtonian or pseudo-Newtoniangravitational potentials. Like the spatial part of the Schwarzchild metric, thefunnel's surface metric has a (removable) singularity at the finite distancefrom the funnel's center and places the certain funnel's depth which we call`gravitational length'. The gravitational length is analogous to thegravitational radius and defines the equivalent of the black hole's mass in thelaboratory 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 shallowwater equations for the arbitrary bottom curvature. We show that in generalcase the shallow water pressure obeys the non-barotropic equation of state. Wesuggest the schematic course for experiments for simulation of accretion in athick accretion disk mode as well as the Bondi-Hoyle accretion.

On the possibility of laboratory simulation of quasi-spherical accretion onto black holes with a shallow-water experimental setup