  We present a differential equation for the flow rate of granular materials
during the discharge of a silo. This is based in the energy balance of the
variable mass system in contrast with the traditional derivations based on
heuristic postulates such as the free fall arch. We show that this new equation
is consistent with the well known Beverloo rule, providing an independent
estimate for the universal Beverloo prefactor. We also find an analytic
expression for the pressure under discharging conditions.
