Here we present a simple method of fluid delivery via control of capillary size differences present between the inlet and outlet reservoirs of a microchannel. The driving capillary fills the corner region present in the outlet reservoir of a microchannel, retaining the benefits of a small internal capillary while taking up an area of only several square millimeters. Precise fluid delivery is accomplished through control of multiple parameters describing the system, such as the geometries of the reservoirs and microchannel, volume of the inlet drop, and the surface characteristics of the channel itself. We show that controlled, constant flow rates can be delivered through a microchannel for periods of up to several hours, with required sample volumes of less than a microliter.