  We theoretically study hydrodynamic phenomena originating from
electron-electron collisions in a two-dimensional Fermi system. We demonstrate
that an electron beam sweeping past an aperture creates a pumping effect,
attracting carriers from this aperture. This pumping effect originates from the
specific electric potential distribution induced by the injected electrons. In
the regions nearby the main stream of injected electrons, a positive potential
is induced by the injected electrons. Thus, the normally repulsive Coulomb
interaction leads to an attractive force in the Fermi system. This quantum
pumping mechanism in a Fermi system differs qualitatively from the Bernoulli
pumping effect in classical liquids. We also discuss possible experimental
realizations.
