  We develop a hydrodynamic description of the classical Calogero-Sutherland
liquid: a Calogero-Sutherland model with an infinite number of particles and a
non-vanishing density of particles. The hydrodynamic equations, being written
for the density and velocity fields of the liquid, are shown to be a
bidirectional analogue of Benjamin-Ono equation. The latter is known to
describe internal waves of deep stratified fluids. We show that the
bidirectional Benjamin-Ono equation appears as a real reduction of the modified
KP hierarchy. We derive the Chiral Non-linear Equation which appears as a
chiral reduction of the bidirectional equation. The conventional Benjamin-Ono
equation is a degeneration of the Chiral Non-Linear Equation at large density.
We construct multi-phase solutions of the bidirectional Benjamin-Ono equations
and of the Chiral Non-Linear equations.
