This paper describes the design of a device for measuring fluid flow in a pipe. It deals with a particular type of flowmeter, one that measures the differential pressure developed across an orifice or other primary element and puts out an air pressure directly proportional to flow rate. Square root must be extracted in such an instrument. The square-root-extracting part of the device is of the shaped displacer and mercury type, in which the displacer does not move. Formulas are derived for calculating the shape.