The use of capillary systems in space and biotechnology applications requires the regulation of the capillary flow velocity. It has been observed that constricted sections act as flow resistors. In this work, we also show that enlarged sections temporarily reduce the velocity of the flow. In this work, the theory of the dynamics of capillary flows passing through a constricted or an enlarged channel section is presented. It is demonstrated that the physics of a capillary flow in a channel with a constriction or an enlargement is different and that a constriction acts as a global flow resistor and an enlargement as a local flow resistor. The theoretical results are checked against experimental approaches.