  A two-dimensional steady problem of a potential free-surface flow of an ideal
incompressible fluid caused by a singular sink is considered. The sink is
placed at the horizontal bottom of the fluid layer. With the help of the
Levi-Civita technique, the problem is rewritten as an operator equation in a
Hilbert space. It is proven that there exists a unique solution of the problem
provided that the Froude number is greater than some particular value. The free
boundary corresponding to this solution is investigated. It has a cusp over the
sink and decreases monotonically when going from infinity to the sink point.
The free boundary is an analytic curve everywhere except at the cusp point. It
is established that the inclination angle of the free boundary is less than
$\pi/2$ everywhere except at the cusp point, where this angle is equal to
$\pi/2$. The asymptotics of the free boundary near the cusp point is
investigated.
