  We study a stochastic Hamiltonian system of $N$ particles with many particles
interacting through a potential whose range is large in comparison with the
typical distance between neighbouring particles. It is shown that the empirical
measures associated to the position and velocity of the system converge to the
solutions of stochastic compressible Euler equations in the limit as the
particle number tends to infinity. Moreover, we quantify the distance between
particles and the limit in suitable Sobolev norm.
