A measuring element for a flow rate sensor is described, in which the number of terminals is minimized to reduce the dimensions of the measuring element. In accordance with some embodiments, the apparatus has a rotatable abrasive surface, and a tool support structure which contactingly supports a body portion of a tool while a cutting surface of the tool is presented against the abrasive surface during a sharpening operation. The fluid source includes a non-collapsible walled container for dispensing or introducing fluid. The channel region of the thin film transistors are disposed in the intersection regions.