Textured surfaces, comprised of grooves filled with air, e.g., air-filled surfaces (AFS), or with liquid, e.g., liquid-filled surfaces (LFS), significantly influence fluid flows and the related electrokinetic streaming potential (V-s). Here, electroosmotic mobility related tensorial effects on the V-s were experimentally investigated. A significant modulation of the V-s, as high as 100%, due to transverse pressure gradients, was demonstrated. The study yields insights into understanding geometrical effects in electrolyte flows with implications to the establishment of local electric fields, energy generation, and biological separations.