Poly(dimethylsiloxane) is currently the material of choice for rapidly fabricating microfluidic devices. As the size of these devices decreases, a significant hydrodynamic flow is generated due to permeation of fluid through the channel walls. We develop a theoretical model verified by single bead tracking experiments, which demonstrates that large flow rates (> 10 mu m/s) can be passively generated in a straight microchannel filled with water. Realizing that this flow may be unwanted in some applications, we present a method to eliminate it by inhibiting mass transfer of water into the poly(dimethylsiloxane) walls. Furthermore, we explore applications to harness this passively generated flow inside a microfluidic device such as bead stacking, chemical concentration, and passive pumping.