  We study long wavelength perturbations of neutral black p-branes in
asymptotically flat space and show that, as anticipated in the blackfold
approach, solutions of the relativistic hydrodynamic equations for an effective
p+1-dimensional fluid yield solutions to the vacuum Einstein equations in a
derivative expansion. Going beyond the perfect fluid approximation, we compute
the effective shear and bulk viscosities of the black brane. The values we
obtain saturate generic bounds. Sound waves in the effective fluid are
unstable, and have been previously related to the Gregory-Laflamme instability
of black p-branes. By including the damping effect of the viscosity in the
unstable sound waves, we obtain a remarkably good and simple approximation to
the dispersion relation of the Gregory-Laflamme modes, whose accuracy increases
with the number of transverse dimensions. We propose an exact limiting form as
the number of dimensions tends to infinity.
