The velocity of fluids containing particles that scatter ultrasound can be measured by determining the Doppler shift of the ultrasound scattered by the particles in the fluid. Measuring fluid flow in cylindrical vessels such as blood vessels is an important use of Doppler ultrasound. This invention teaches using various configurations of cylindrical diffraction-grating transducers and cylindrical non-diffraction-grating transducers that suppress the Doppler shift from non-axial components of fluid velocity while being sensitive to the Doppler shift produced by axial velocity components. These configurations thus provide accurate measurement of the net flow down the vessel, even when the fluid flow is curved or not parallel to the vessel wall.