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Only a small amount of literature has been published on the gravity flow of particulate solids down pipes. Earlier work showed that in such conditions considerable volumes of air could be entrained with the solids, often resulting in considerable air-pressure difference across the ends of the pipe. A model is developed which makes possible prediction of the pressure differences for known flow rates from system parameters. Considering the rather large number of basic assumptions required and the paucity of experimental data, the agreement between theory and practice is fairly good. The model, however, throws little light on the problem of predicting solids flow rates, emphasizing that further work, both theoretical and experimental, is needed.