The flowmeter described here consists of a bistable fluid amplifier which is made to oscillate by interconnecting the two control ports. For suitably designed flowmeters and at Mach numbers less than 0.2, the oscillation is independent of compressibility and the frequency is uniquely related to volume flowrate. A simple transducer can be used to transmit a frequency modulated indication of the flow rate so the accuracy of metering depends only on the fluid mechanics of the flowmeter. The operation of the flowmeter is explained with particular emphasis on the dimensionless characterization of periodic flows as derived from the Navier-Stokes equations. Dimensionless constraints on the operating range and the design of such flowmeters are derived from the known properties of fluid amplifiers and fluid transmission lines. Within certain limits, frequency is proportional to flow rate and this greatly simplifies signal processing. It is primarily intended that the flowmeter would form the basis of an on-line control system transmitting signals to a central computer; in this context linearity is not essential.