  A system of inelastic hard disks in a thin pipe capped by hot walls is
studied with the aim of investigating velocity correlations between particles.
Two effects lead to such correlations: inelastic collisions help to build
localized correlations, while momentum conservation and diffusion produce long
ranged correlations. In the quasi-elastic limit, the velocity correlation is
weak, but it is still important since it is of the same order as the deviation
from uniformity. For system with stronger inelasticity, the pipe contains a
clump of particles in highly correlated motion. A theory with empirical
parameters is developed. This theory is composed of equations similar to the
usual hydrodynamic laws of conservation of particles, energy, and momentum.
Numerical results show that the theory describes the dynamics satisfactorily in
the quasi-elastic limit, however only qualitatively for stronger inelasticity.
