Ultrasonic flowmeters are widely used for flow measurement. We proposed a theoretical model to quantify the measurement error caused by the deviation of ultrasonic propagation trajectory in complex flow regimes. The three-dimensional ultrasonic propagation model is based on the assumption of ray acoustics. The results show that the trajectory offset of ultrasonic waves and velocity measurement errors in a three-dimensional non-uniform flow field is of the first order of the Mach number. Unlike gas flow, the Mach number of open channel flow is small, and the velocity measurement error of open channel ultrasonic flowmeter can be safely ignored.
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