A flowmeter has a vane which is caused to vibrate at one of its resonant frequencies and a flexure standing wave set up along it. Two piezoelectric sensors are used to monitor characteristics of the standing wave and hence the mass flow rate of a fluid flowing past the vane along a pipe.The vane comprises a ceramic planar member on which a conductive ceramic ink is laid down to form tracks. The ink also bonds a ceramic piezoelectric transducer to the member to drive and maintain it in vibration. A non-conductive layer is laid down on the surface of the member covering the conductive tracks surrounding the transducer. A metal layer forms the external surface of the vane and acts as a ground plane for the transducer.