We directly evaluate the fluid-flow and electrical conductivity of model three dimensional random porous medium at a microscopic level. This allows a direct test of the popular assumption that fluid-flow and electrical current follow equivalent flow paths in porous solids. Visualization of the fluid-flow and electric-current streamlines within identical porous samples show this assumption is incorrect. The tortuosity factors, characterizing the geometry of the flow paths associated with fluid-flow and electrical current transport, are directly evaluated. Fluid-flow tortuosity is systematically larger than the electrical tortuosity, and can differ by as much as an order of magnitude at lower porosities. ¿ American Geophysical Union 1995