Since the early work of Hagen [G. H. L. Hagen, Ber. Verhandl. K. Preuss. Akad. Wiss. Berlin 17, 35 (1852)] and Beverloo <i>et al.</i> [W. Beverloo <i>et al.</i>, Chem. Eng. Sci. 15, 260 (1961)CESCAC0009-250910.1016/0009-2509(61)85030-6], the flow rate of granular material discharging through a circular orifice from a silo has been described by means of dimensional analysis and experimental fits and explained through the free-fall arch model. Here, in contrast to the traditional approach, we derive a differential equation based on the energy balance of the system. This equation is consistent with the well-known Beverloo rule due to a compensation of energy terms. Moreover, this equation can be used to explore different conditions for silo discharges. In particular, we show how the effect of friction on the flow rate can be predicted. The theory is validated using discrete element method simulations.Facultad de Ciencias ExactasInstituto de Física de Líquidos y Sistemas Biológicos