Mathematical model of multipath ultrasonic flowmeter for its automated designing

In the paper, numerical integration methods are analyzed to apply them for designing multipath ultrasonic flowmeters. The mathematical model of a multipath ultrasonic flowmeter based on the Gauss-Jacobi integration method is developed. Applying the Gauss-Jacobi method, the authors also proposed the analytical dependences to determine the location coordinates and weighting factors of acoustic paths, which allows it to be used while designing the structures of 2, 3, and 4-path ultrasonic flowmeters. These dependencies supplement the developed mathematical model.