A higher-order quadrature driven diffraction grating ultrasonic transducer and mode of operation, useful for determining the velocity of a fluid under investigation. The diffraction grating of the transducer is easier to fabricate compared to prior art first order quadrature driven diffraction grating ultrasonic transducers because the higher order design allows the grating to be expanded. The higher order design also eliminates the need to vary the frequency or phase of pulse generator used to drive the transducer in order to produce multiple beams needed for fluid velocity measurements.