Abstract: A flow meter (10) employs phased arrays (14a, 14b, 16a, 16b, 18a, 18b, 20a, and 20b) of ultrasonic transducers mounted on the exterior of a pipe (12) to transmit and receive sound directed through paths that pass through the pipe interior. The flow meter (10) determines the rate of fluid flow through the pipe (12) by comparing the sound-propagation times for sound traveling the same paths in opposite directions. By driving the transducers as phased arrays, the flow meter (10) can employ sound-propagation paths that form angles to the normal to the interior pipe wall that exceed those dictated by Snell's law as applied to the relative propagation speeds in the pipe wall and the fluid.