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The variation of pressure along a single cylindrical capsule resting on the bottom of a pipe is predicted by using the one-dimensional energy equation, the momentum equation, and the continuity equation with proper consideration for the head losses including entrance and exit effects, as well as by using experimental values of the energy correction factor Alpha and the momentum correction factor Beta of the eccentric annular flow around the capsule. The theory is compared with previously published experimental data and they agree reasonably well. The theory is extended to predict the drag on a single stationary capsule resting on pipe floor, the pressure coefficient of the capsule end, and the incipient velocity. Comparison with experimental data from several sources shows the superiority of the new theory to the existing theory, which ignores entrance and exit effects and assumes concentric capsules. The new theory can also be used to predict the behavior of a capsule train provided that the roughness created by the ends of individual capsules is properly estimated.